Self-Healing and Self-Recovering Hydrogels [1st ed.] 9783030545550, 9783030545567

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Advances in Polymer Science  285

Costantino Creton Oguz Okay   Editors

Self-Healing and Self-Recovering Hydrogels

285

Advances in Polymer Science Editorial Board Members: A. Abe, Yokohama, Kanagawa, Japan A.-C. Albertsson, Stockholm, Sweden G.W. Coates, Ithaca, NY, USA J. Genzer, Raleigh, NC, USA S. Kobayashi, Kyoto, Japan K.-S. Lee, Daejeon, South Korea L. Leibler, Paris, France T.E. Long, Blacksburg, VA, USA M. M€ oller, Aachen, Germany O. Okay, Istanbul, Turkey V. Percec, Philadelphia, PA, USA B.Z. Tang, Hong Kong, China E.M. Terentjev, Cambridge, UK P. Theato, Karlsruhe, Germany M.J. Vicent, Valencia, Spain B. Voit, Dresden, Germany U. Wiesner, Ithaca, NY, USA X. Zhang, Beijing, China

Aims and Scope The series Advances in Polymer Science presents critical reviews of the present and future trends in polymer and biopolymer science. It covers all areas of research in polymer and biopolymer science including chemistry, physical chemistry, physics, and material science. The thematic volumes are addressed to scientists, whether at universities or in industry, who wish to keep abreast of the important advances in the covered topics. Advances in Polymer Science enjoys a longstanding tradition and good reputation in its community. Each volume is dedicated to a current topic, and each review critically surveys one aspect of that topic, to place it within the context of the volume. The volumes typically summarize the significant developments of the last 5 to 10 years and discuss them critically, presenting selected examples, explaining and illustrating the important principles, and bringing together many important references of primary literature. On that basis, future research directions in the area can be discussed. Advances in Polymer Science volumes thus are important references for every polymer scientist, as well as for other scientists interested in polymer science - as an introduction to a neighboring field, or as a compilation of detailed information for the specialist. Review articles for the individual volumes are invited by the volume editors. Single contributions can be specially commissioned. Readership: Polymer scientists, or scientists in related fields interested in polymer and biopolymer science, at universities or in industry, graduate students.

More information about this series at http://www.springer.com/series/12

Costantino Creton • Oguz Okay Editors

Self-Healing and Self-Recovering Hydrogels

With contributions by A. Bose
S. Ciarella
C. Creton
K. Cui
T. Davris
R. de la Cruz
D. D. Dı´az
W. G. Ellenbroek
J. Fu
Q. Guo
R. Kilic
R. Long
A. V. Lyulin
T. Narita
O. Okay
C. Raffaelli
A. Sanyal
C. Shao
C. Storm
T. L. Sun
N. B. Tito
B. D. Vogt
C. H. M. P. Vrusch
R. A. Weiss
J. Yang
J. Zhao

Editors Costantino Creton Laboratory of Soft Matter Science and Engineering ESPCI Paris - PSL Paris, France

Oguz Okay Department of Chemistry Istanbul Technical University Istanbul, Turkey

ISSN 0065-3195 ISSN 1436-5030 (electronic) Advances in Polymer Science ISBN 978-3-030-54555-0 ISBN 978-3-030-54556-7 (eBook) https://doi.org/10.1007/978-3-030-54556-7 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

As hydrogels are increasingly used as biomaterials, scaffolds in tissue engineering, drug delivery systems, or superabsorbents, one of the scientific challenges in the past decade has been to introduce a self-healing ability in order to extend their service time. The present volume entitled Self-Healing and Self-Recovering Hydrogels is intended to review recent experimental and theoretical advances in self-healing/self-recovering hydrogels based on both synthetic and natural polymers. Self-recovery behavior in a chemically cross-linked hydrogel can be generated through the introduction of additional reversible cross-links. The small and large strain behavior of a representative dual cross-linked hydrogel is systematically investigated in the first chapter and the role played by the reversible cross-links in the mechanism of crack propagation is discussed. Because self-healing efficiency decreases with increasing lifetime of cross-links, it is generally a challenge to generate self-healing ability in high-strength hydrogels with modulus and tensile strength in the range of MPa. Chapter “How to Design Both Mechanically Strong and Self-Healable Hydrogels?” tries to answer the question of how to design both mechanically strong and self-healable hydrogels. Chapter “Simulations of Reversibly Bonded Hydrogels” reviews some modern computational techniques based on statistical physics to simulate dynamic polymer networks of flexible chains and presents some recent results demonstrating the potential of such approaches. Incorporation of dynamic, reversible bonds into the polymer network of soft gels has been exploited as a strategy to enhance fracture toughness and to enable selfhealing. Chapter “Mechanics of Polymer Networks with Dynamic Bonds” discusses the recent efforts in introducing physical meaning into macroscopic constitutive solid mechanics models in order to connect the molecular-level bond kinetics to the continuum-level viscoelasticity. Hydrophobically associating hydrogels based on copolymers of a water-soluble monomer with a fluoro(meth)acrylate possess microphase-separated morphologies that provide unique properties. Chapter “Hydrophobically Associating Hydrogels with Microphase-Separated Morphologies” reviews the characteristics of these v

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Preface

microphase-separated, hydrophobically associating hydrogels and discusses their potential applications. The preparation, structures, properties, and applications of tough and responsive hydrogels cross-linked by triblock copolymer micelles are reviewed in the chapter “Triblock Copolymer Micelle-Crosslinked Hydrogels.” The micellar hydrogels show outstanding strength and toughness due to the micelles serving as energy dissipation centers and exhibit good responsivity to changes in pH, salt concentration, electric field, and temperature. Chapter “SelfHealing Hydrogels Based on Reversible Covalent Linkages: A Survey of Dynamic Chemical Bonds in Network Formation” highlights, through examples, the synthesis and self-healing properties of hydrogels based on various types of reversible dynamical cross-linking chemistries. The main focus of this chapter is on the chemistry of cross-linking and the conditions under which self-healing can be achieved. Polyampholyte (OA) hydrogels have attracted great attention as innovative materials due to their toughness and self-healing and viscoelatic behaviors. In the chapter “Tough and Self-Healing Hydrogels from Polyampholytes,” the role of dynamic ionic bonds on the mechanical, viscoelastic, and self-healing behavior of PA hydrogels and their recent applications are discussed. Cellulose-based hydrogels have emerged as promising materials for a wide range of applications due to their inherently renewable, biocompatible, and biodegradable characteristics. Chapter “Dynamics in Cellulose-Based Hydrogels with Reversible CrossLinks” addresses the advances in the synthesis methods of such hydrogels from native cellulose, cellulose derivatives, or composites and focuses on the design and preparation of reversibly cross-linked cellulose-based hydrogels featuring a selfhealing or dynamic response to stimuli. Hydrogels derived from biopolymers such as those made from collagen type I are very promising candidates for the repair of nervous tissues due to their biocompatibility, noncytotoxic properties, injectability, and self-healing ability. Chapter “Self-Healing Collagen-Based Hydrogel for Brain Injury Therapy” reviews the most relevant results obtained from both in vitro and in vivo studies using self-healing biohydrogels based on collagen type I as a key component in the field of neuroregeneration. The editors believe that the present volume will contribute a better understanding of the design and properties of self-healing/self-recovering hydrogels and their potential application areas. We would like to thank all the authors who have contributed to this exciting volume on self-healing/self-recovering hydrogels. Paris, France Istanbul, Turkey

Costantino Creton Oguz Okay

Contents

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics and Mechanics Under Large Deformation . . . . . . . . Jingwen Zhao, Tetsuharu Narita, and Costantino Creton

1

How to Design Both Mechanically Strong and Self-Healable Hydrogels? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oguz Okay

21

Rheology, Rupture, Reinforcement and Reversibility: Computational Approaches for Dynamic Network Materials . . . . . . . . . . . . . . . . . . . . . Chiara Raffaelli, Anwesha Bose, Cyril H. M. P. Vrusch, Simone Ciarella, Theodoros Davris, Nicholas B. Tito, Alexey V. Lyulin, Wouter G. Ellenbroek, and Cornelis Storm

63

Mechanics of Polymer Networks with Dynamic Bonds . . . . . . . . . . . . . . 127 Qiang Guo and Rong Long Hydrophobically Associating Hydrogels with Microphase-Separated Morphologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Bryan D. Vogt and R. A. Weiss Triblock Copolymer Micelle-Crosslinked Hydrogels . . . . . . . . . . . . . . . 211 Jun Fu Self-Healing Hydrogels Based on Reversible Covalent Linkages: A Survey of Dynamic Chemical Bonds in Network Formation . . . . . . . . 243 Ruveyda Kilic and Amitav Sanyal Tough and Self-Healing Hydrogels from Polyampholytes . . . . . . . . . . . 295 Tao Lin Sun and Kunpeng Cui Dynamics in Cellulose-Based Hydrogels with Reversible Cross-Links . . . 319 Changyou Shao and Jun Yang

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Contents

Self-Healing Collagen-Based Hydrogel for Brain Injury Therapy . . . . . 355 Raquel de la Cruz and David Dı´az Dı´az Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Adv Polym Sci (2020) 285: 1–20 https://doi.org/10.1007/12_2020_62 © Springer Nature Switzerland AG 2020 Published online: 15 June 2020

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics and Mechanics Under Large Deformation Jingwen Zhao, Tetsuharu Narita, and Costantino Creton

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Linear Viscoelastic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Uniaxial Tensile Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Strength of P(AAm-co-VIm)-Ni2+ Dual Crosslink Gel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Tunable Dynamics: Linear Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Stress Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Intermediate Strain Tensile Cyclic Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Uniaxial Tensile Tests to Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Step-Cycle Uniaxial Tensile Tests and Energy Dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

J. Zhao Laboratoire Sciences et Ingénierie de la Matière Molle, ESPCI Paris, PSL University, Sorbonne Université, CNRS, Paris, France T. Narita (*) and C. Creton (*) Laboratoire Sciences et Ingénierie de la Matière Molle, ESPCI Paris, PSL University, Sorbonne Université, CNRS, Paris, France Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Japan e-mail: [email protected]; [email protected]

2 4 4 6 6 6 7 7 8 10 11 12 16 18 19

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Abstract Introducing additional physical and reversible crosslinks to a chemically crosslinked hydrogel is an interesting and viable alternative to increase the toughness of a hydrogel. Yet while in general the physical crosslink points provide dissipative mechanisms, there are still many details that are unknown in particular on the role that physical crosslinks play on the large strain behavior. We explore the mechanical properties in small and large strain of two dual crosslink gels made from a random copolymer of poly(acrylamide-co-vinylimidazole) with a range of elastic moduli in the tens of kPa. The interaction between vinylimidazole groups and metal ions (Zn2+ and Ni2+) results in physical crosslink points and in a markedly stretch-rate-dependent mechanical behavior. While a main relaxation process is clearly visible in linear rheology and controls the small and intermediate strain properties, we find that the strain hardening behavior at stretches of λ > 4 and the stretch at break λb are controlled by an additional longer-lived physical crosslinking mechanism that could be due to a clustering of physical crosslinks. Keywords Mechanical properties · Metal-ligand coordination bonds · Tough hydrogel · Transient crosslink

1 Introduction Hydrogels are promising candidates for biomedical applications such as artificial organs or tissue engineering thanks to their liquid-like and solid-like properties [1]. However, contrary to biological hydrogels such as cartilage, conventional synthetic hydrogels made by free radical polymerization suffer from mechanical fragility, due to the heterogeneous network structures and the lack of dissipative mechanisms [2]. Mechanical reinforcement has become one of the hottest topics of gel science in the last decades [3–9]. Among the different reinforcement strategies, the introduction of sacrificial bonds inside the gel in order to dissipate energy near the crack tip has proved promising. The pioneering work of Gong [9] in 2003 provided a good solution by creating two interpenetrated networks having different properties: a low volume fraction of highly crosslinked and stretched network and a high volume fraction of loosely crosslinked second network. This hydrogel has a much better fracture toughness than either network on its own. However, this network design strategy based on irreversible bond breaking results in permanent damage in the network [10]; thus the same mechanical behaviors of the virgin gels cannot be recovered after loading cycles. A successful alternative can be the incorporation of reversible crosslinks into the network. Because the reversible crosslinks serve as sacrificial bonds they can break and reform under strain and hence make the propagation of a crack more energetically costly [11]. Although the detailed mechanism by which these dynamic bonds delay crack propagation may be complex, it has been proposed that the presence of

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .

3

these additional bonds may reduce local stress concentration, delaying the rupture of the chemical networks [12]. As reversible bonds, various non-covalent and dynamic covalent bonds can be employed, and there have been many examples reported in the literature [3, 5, 13, 14]. It should be noted that hydrogels with only physical crosslinks (and possibly entanglements) may irreversibly plastically flow at long time scales if the longest characteristic relaxation time is comparable to or shorter than the inverse of the strain rate. Adding a small amount of chemical crosslinks to prevent the terminal flow and keep the reference state of deformation is a practical solution as employed in the certain number of the systems reported in the literature, especially for the networks with short-lived reversible bonds [15–17]. Creton, Narita, and their coworkers have reported an intriguing example of such “dual crosslink” hydrogels, having a small amount of permanent crosslinks and a large amount of transient crosslinks [18–21]. Based on polyvinyl alcohol, PVA, permanently crosslinked by glutaraldehyde and transiently crosslinked by borate ions (by dynamic covalent bond), their PVA dual crosslink gels exhibit timedependent elasticity. Prepared by a simple procedure, consisting of incorporating physical crosslinks by diffusion of borate ions into a previously prepared chemical gel, some unique rheological features of the PVA dual crosslink gel have been experimentally and theoretically characterized with the corresponding chemical gel as reference [18, 20–26]. The chemical and physical crosslinks contribute to the viscoelasticity independently, and the moduli of the dual crosslink gels can be decomposed into the contribution of the chemical bonds (the same as that of the reference chemical gel) and that of the physical bonds (not identical to a corresponding physical gel due to the suppression of the terminal flow by the chemical crosslinks) (additivity) [22, 25]. The stretch-rate-dependent stress can be then separated into the product of a time-dependent term (equivalent to a relaxation modulus) and a strain-dependent term (expressed as a neo-Hookean model) [22]. This behavior can be quantitatively described by a constitutive model combining large strain elasticity and time-dependent sticker dynamics [19, 23, 24], and using only four physically based parameters is sufficient to fit both tensile and torsion tests results. The systematic studies of the mechanical properties of the PVA dual crosslink gels over a wide range of time scales and strain rates indicate the importance to study the properties at different characteristic bond breaking rates as well as at very high extension [22, 25]. Does the dual crosslink gel behave similarly to the chemical gel at time scales much longer than its transient bond breaking time? Or can the strain rate be normalized by a characteristic time measurable in linear rheology to obtain a universal law for the time-dependent properties? In order to answer these questions, it is important to investigate the mechanical properties of dual crosslink gels having a short characteristic time and/or at very slow stretch rate. The relaxation time of the PVA dual crosslink gel is relatively long (of the order of 1 s), and it is difficult to tune it in a physicochemical manner. It is also experimentally difficult to perform timeconsuming mechanical tests at very slow stretch rates, due to problems of drying or poroelastic relaxation. Metal-ligand coordination bonds can be a promising option as tunable transient crosslinks: by changing metal ion, species dynamics can be tuned. Various physical

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gels crosslinked by metal-ligand coordination bonds have been reported [27– 30]. Holten-Andersen et al. developed physical gels crosslinked by catechol-Fe3+ complexes exhibiting pH-sensitive mechanical properties [27]. Histidine-modified star PEG polymers were synthesized to mimic the histidine-rich regions of the mussel byssal thread collagen [28]. 4-arm-PEG-histidine (4PEG-His) crosslinked with metal ions was synthesized to produce hydrogels with tunable relaxation times, which follow the order Ni2+ > Cu2+ > Zn2+. More recently various tough dual crosslink hydrogels with metal-ligand coordination bonds have been reported [31–33]. While macroscopic tests of their toughness and self-recovery properties were studied, the nonlinear mechanical properties as a function of the transient bond relaxation time and the strain rate have not been systematically studied. Kean et al. synthesized a series of dual crosslink organogels with metal-ligand coordination bonds, and showed that the short-lived transient crosslinks do not increase the modulus (thus they are invisible), while they can improve the extensibility of the network better than the long-lived transient crosslinks [34]. This intriguing observation is one of the motivations of the work we report. We investigate here a new dual crosslink hydrogel based on polyacrylamide, another simple neutral hydrosoluble polymer, copolymerized with N-vinylimidazole. This gel possesses a fast and tunable dynamics due to imidazole – metal ion coordination bonds and ingredients are commercially available and readily soluble in water. Poly(acrylamide-co-vinylimidazole) was synthesized by free radical copolymerization in the presence of physical crosslinkers (transient metal ions, Ni2+ or Zn2+) and a chemical crosslinker (methylene bisacrylamide) (Fig. 1). With this relatively easy and quick “one-pot” synthesis (simultaneous chemical and physical crosslinking and polymerization), we successfully synthesized hydrogels having both chemical and physical crosslinks. This simple fabrication process from inexpensive readily available components sacrifices precise network and structural control but makes it possible to produce the necessary amount of material samples to perform systematic mechanical tests in large strain. In this work we attempt to understand the relation between the macroscopic mechanical properties in large strain and the dynamics of the coordination bonds over a wide dynamic range.

2 Experimental Section 2.1

Materials

Acrylamide (AAm), 1-vinylimidazole (VIm), methylenebisacrylamide (MBA), potassium persulfate (KPS), N,N,N0 ,N0 -tetramethylethylenediamine (TEMED), nickel chloride, and zinc chloride were purchased from Sigma Aldrich and used as received. Milli-Q water is used for the sample preparation.

Acrylamide

NH2

C=O

CH2 = CH

Acrylamide

NH2

C=O

CH2 = CH

N

N N

1-Vinylimidazole

+

CH2 = CH

1-Vinylimidazole

+ N

CH2 = CH

M2+

MBA

MBA

M2+ M2+

M2+

Poly(acrylamide -co- 1-vinylimidazole)

M2+

Poly(acrylamide -co- 1-vinylimidazole)

Fig. 1 Schematic presentation of the formation of the chemical gel and the dual crosslink gel

Dual crosslink gel

Chemical crosslink gel

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . . 5

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Sample Preparation

Dual crosslink gels and the corresponding chemical gels were prepared by radical polymerization. For the chemical gel, an aqueous solution containing AAm (1.8 M), VIm (0.2 M), MBA (2–10 mM, corresponding to 0.1–0.5 mol% of the total monomer concentration, 2 M), and KPS (6 mM) was prepared under nitrogen flow at low temperature (in an ice bath). The solution was then transferred in a glovebox, and TEMED (20 mM) was added to initiate radical polymerization. After the overnight reaction, the obtained P(AAm-co-VIm) chemical gels were used for measurements as prepared. P(AAm-co-VIm)-M2+ dual crosslink gels were prepared in the same procedure, by adding further NiCl2 or ZnCl2 in the solution; the concentration of MBA was fixed at 3 mM (0.15 mol%). After the overnight crosslinking reaction, the obtained P(AAm-co-VIm)-M2+ dual crosslink gels were used for measurements as prepared.

2.3

Linear Viscoelastic Properties

The linear viscoelastic properties of the dual crosslink gels in small strain oscillatory shear were characterized in a parallel plate geometry with roughened surfaces (20 mm in diameter) with the ARES LS1 rheometer (TA instruments). The sample thickness was 1.5 mm. Frequency sweep tests with a dynamic range varying from 0.1 to 100 rad/s were carried out at 25 C within the linear viscoelasticity regime (0.2–0.8% strain).

2.4

Uniaxial Tensile Tests

The large deformation behavior of the gels was investigated by uniaxial tensile test to fracture and step-cycle loading – unloading tests on an Instron 5565 tensile tester with a 10 N load cell. Samples were rectangular in shape with 5 mm in width, 1.5 mm in thickness, and 15 mm in length L0 (length between clamps). We kept the samples in paraffin oil during all the tests to prevent them from drying following a previously published procedure [18].

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .

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3 Results and Discussion 3.1

Strength of P(AAm-co-VIm)-Ni2+ Dual Crosslink Gel

In order to confirm that the introduction of the metal-ligand coordination bonds can improve the strength of the polyacrylamide gel, we performed uniaxial stretching experiments and characterized the nonlinear (large strain) behavior of the P (AAm-co-VIm)-Ni2+ dual crosslink gels, at different Ni2+ concentrations (5–100 mM). The tensile stress σ was plotted as a function of the stretch ratio λ (defined as λ ¼ L/L0) at the same stretch rate λ_ ¼ 0.06 s1. The results for the dual crosslink gels with different values of [Ni2+] and for the corresponding chemical gel are shown in Fig. 2. For all values of [Ni2+], the dual crosslink gels have higher extensibilities than the chemical gel, and the strain at break dramatically increases with the introduction of physical crosslinks: with a value of λ at break λb varying from less than 4 for the chemical gel to over 6 for the dual crosslink gels. λb can reach to about 8.5 when the concentration of the transient crosslinker [Ni2+] is increased to 100 mM. For the values of the stress, a complex [Ni2+] dependence is seen. For [Ni2+] > 20 mM, the increase of [Ni2+] leads to a significant increase of the stress over the whole range. The stress vs. stretch curves resemble more those of a straincrystallizing rubber such as natural rubber [35] or a pressure-sensitive adhesive [36]: softening at intermediate strains, indicating the breakup of a network structure, and strain hardening at large strain indicating finite extensibility of the polymer chains. This strain hardening behavior becomes significant at λ > 5, a stretch level which is not easily accessible for conventional chemical gels or even with the PVA dual Fig. 2 Stress-strain curves of the dual crosslink gels with different Ni2+ concentrations compared with the corresponding chemical gels at a stretch rate of 0.06 s1 at room temperature

80

s (kPa)

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Dual crosslink gel C(Ni2+) 5 mM 10 mM 20 mM 50 mM 100 mM Chemical gel

40

20

0

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l

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crosslink gels [18]. For gels with low Ni2+ concentration (5 and 10 mM), the stressstrain curve is similar to that of the chemical gel, but with much higher extensibility, with λb > 6. It should be pointed out however that the modulus of the dual crosslink gel with [Ni2+] ¼ 5 mM is lower than that of the chemical gel. We assume that this comes from the modification of radical polymerization due to the presence of nickel ions which reduces the chemical crosslinking density in the dual crosslink gel. For the rest of this paper, we investigated the dual crosslink gel with [Ni2+] ¼ 100 mM, corresponding to the stoichiometric amount needed to complex the ion with two imidazole ligands ([VIm] ¼ 200 mM).

3.2

Tunable Dynamics: Linear Rheology

By changing the nature of the metal ions, the dynamics of the transient crosslinks and the relaxation time of the dual crosslink gel can be tuned. Here, we chose Ni2+ and Zn2+ as two relatively fast-exchanging transient metal ions to study the tunable mechanics of dual crosslink hydrogels with metal-ligand coordination. Figure 3 shows the dynamic moduli as a function of angular frequency for P (AAm-co-VIm)-Ni2+ and P(AAm-co-VIm)-Zn2+ dual crosslink gels at 5 C and G0 (ω) for the corresponding chemical gel (the value of G00 was very low (0.05–0.4 kPa) and is not shown). For the Ni2+-based dual crosslink gel, G0 increased with frequency up to an elastic plateau at ω > 20 rad/s, while G00 showed a broad peak correlated with the rate of decrease in G0 . This result indicates that the dissociation of the physical crosslinks by imidazole-Ni2+ ion interactions induce a large dissipation Fig. 3 Angular frequency dependence of G0 (ω) and G00 (ω) for the P(AAm-coVIm)-M2+ dual crosslink gels compared with the corresponding chemical gel. [M2+] ¼ 100 mM, at 5 C

100 2+

5 C°

G' Ni

G', G'' (kPa)

G'' Ni

2+

10 2+

G' Zn

G'' Zn

2+

1 G' Chemical gel 0.1

1

10

ω (rad/s)

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Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . . 1

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1

(b)

tan δ

tan δ

(a)

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0.1

2+ 2+

Zn

Chemical gel

0.1

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10

w (rad/s)

100

0.0001

0.01

1

100

w (rad/s) (shifted)

Fig. 4 (a) The loss tangent tan δ of Ni2+ and Zn2+ dual crosslink gels and the chemical gel, as a function of ω. (b) tan δ as a function of shifted ω

around ω ¼ 4–5 rad/s. The P(AAm-co-VIm)-Zn2+ gel has a lower G0 over the whole frequency range, and no clear elastic plateau is observed within the tested frequency window. Similarly G00 does not show a peak indicating that the dissociation kinetics of Zn2+ – imidazole is much faster than that of Ni2+ – imidazole and the peak of G00 are not experimentally accessible with this rheometer. A simple physical picture of the dual crosslink gels suggests an additive contribution of permanent and transient crosslinks to the dynamic moduli, and the dynamics of the transient bonds can be characterized by a main relaxation time. Note that in principle the value of G0 (ω) for these gels should approach the value of G0 of the chemical gel at low frequency. However, as shown in Fig. 3, the measured values of G0 are still significantly higher than that of the chemical gel even at the lowest frequency studied. This result indicates that there can be a second slower transient component in the dual crosslink gel systems. In order to estimate the characteristic relaxation time of the P(AAm-co-VIm)-Zn2+ dual crosslink gel which does not show a peak of G00 in an accessible frequency range, we constructed a master curve of the loss tangent tan δ. Figure 4 shows tan δ(ω) of the two P(AAm-co-VIm)-M2+ dual crosslink gels. The values of tan δ(ω) of the P(AAm-co-VIm)-Ni2+ gel show a peak at about ω ¼ 1 rad/s, while for the P (AAm-co-VIm)-Zn2+ tan δ increases monotonously with ω. The P(AAm-co-VIm)Zn2+ curve was horizontally shifted to successfully obtain a master curve (Fig. 4b) so that the characteristic relaxation time of P(AAm-co-VIm)-Zn2+ can be estimated to be 0.56 ms.

10

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J. Zhao et al.

Stress Relaxation

In order to investigate the dynamics of the dual crosslink gels over a larger time window, shear stress relaxation tests were performed. Figure 5a shows the relaxation modulus of P(AAm-co-VIm)-Ni2+ (red) and P(AAm-co-VIm)-Zn2+ (blue) dual crosslink gels at a fixed strain of 1%. The relaxation modulus of the P(AAm-coVIm)-Ni2+ gel shows two relaxation processes at t < 1 s and after about 10 s. After several thousand seconds, G(t) of this dual crosslink gel appears to approach the value of the chemical gel. On the other hand, the relaxation modulus of the P (AAm-co-VIm)-Zn2+ gel starts from lower values than that of P(AAm-co-VIm)Ni2+ gels, and the following relaxation is less pronounced. Interestingly, the values of the modulus of these two gels intersect with each other after about 3 s, confirming the different behavior at long times. Our physical picture of the dual crosslink gels assumes that the modulus of the dual crosslink gel at low frequency should be equivalent to that of the corresponding chemical gel. However, even at 1,000 s, the dual crosslink gels do not fully relax suggesting the existence of a slower relaxation mode in the dual crosslink gels. The results in the frequency domain and time domain can be compared by using the Cox-Merz rule. For the gel with Ni2+, the relaxation modulus and the dynamic modulus do not match: in fact during the stress relaxation, breaking and healing of the physical crosslinks occurs, but the healed bonds do not carry stress, while during the dynamic measurement the oscillatory deformation is continuous and the elastically active chains between healed bonds carry stress. Thus the dynamic modulus is slightly higher than the relaxation modulus. For the P(AAm-co-VIm)-Zn2+ gel, the

10

100

(b)

(a) 25 °C 2+

G* Ni 2+

2+

G* Zn

Zn

1

G(t) (kPa)

G(t) (kPa)

2+

Ni

10

Strain 2+

Zn

2+

Zn

G* chem

0.1 0.01 0.1

2+

1

t

10 (s)

100 1000 10000

1 0.01

1% 10 %

Zn

20 %

0.1

1

10

100

1000

t (s)

Fig. 5 (a) Stress relaxation G(t) as a function of time of the dual crosslink gels with Ni2+ (red) and Zn2+ (blue) at 25 C and the dynamic modulus obtained with the Cox-Merz rule for the chemical gel (yellow line) and the dual crosslink gels with Ni2+ (black dotted line) and Zn2+ (black solid line). (b) Shear stress relaxation modulus G(t) for different imposed strains (1, 10, and 20%) for the P (AAm-co-VIm)-Zn2+ gel

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .

11

difference between the relaxation modulus and the dynamic modulus is small, due to the fast dynamics of the transient crosslinks with Zn2+. In order to make a connection with the large strain behaviors discussed in the next section, let us check the strain dependence of the stress relaxation in shear. A shear stress relaxation was carried out for different imposed strains (1, 10, and 20%), and results are shown in Fig. 5b for the P(AAm-co-VIm)-Zn2+ gel. The relaxation modulus of the P(AAm-co-VIm)-Zn2+ gel decreases with increasing strain, suggesting that the slower relaxation did not satisfy the separability between the strain- and time-dependent terms of the stress. This point is further discussed in the next section.

3.4

Intermediate Strain Tensile Cyclic Tests

At intermediate deformations, we carried out a series of loading and unloading cycles up to λ ¼ 2 at seven different stretch rates (0.0003, 0.01, 0.003, 0.01, 0.03, 0.1, and 0.3 s1) on both types of dual crosslink gels to investigate the strain dependence of the modulus as well as the hysteresis (Fig. 6a, c). These gel samples were not stretched to rupture, and the same sample was stretched repeatedly at different stretch rates after a sufficiently large recovery time of 30 min between each cycle. Both initial modulus and hysteresis show a strong stretch rate dependence for the P(AAm-co-VIm)-Ni2+ gel, while for the P(AAm-co-VIm)-Zn2+ gel the dependence is weaker. At the end of the unloading cycle, we observed a small residual deformation increasing with stretch rate due to the bending of the sample. This residual deformation disappears during the recovery period. This large strain behavior is now analyzed in terms of separability between the strain-dependent and time-dependent component of the tensile stress. In a previous publication [18], we showed that for a similar system, the reduced stress f ¼ σ/(λ  λ2) measured at different stretch rates, plotted as a function of time, formed a master curve. For these gels, for λ < 2, the stress could be separated into a strain-dependent term (neo-Hookean contribution) and a time-dependent term f (dynamics of the physical crosslinks). By using the loading part of the data of Fig. 6a, c, we plotted the reduced stress f as a function of time in Fig. 6b, d, and a reasonable master curve was obtained for both dual crosslink gels with Ni2+ and Zn2+, demonstrating the approximate separability into a strain-dependent neo-Hookean term, and a timedependent term f in that range of intermediate strain where only softening is observed (see Fig. 2).

12

J. Zhao et al. 100 2+

20

(a) Ni

15

2+

-1

stretch rate (s ) 0.3 0.1 0.03 0.01 0.003 0.001 0.0003

0.1 0.03

10

0.01 0.003 0.001 0.0003

f* (kPa)

σ (kPa)

(b) Ni

0.3

10

5 -1

stretch rate (s )

0 1

1

2

0.1

1

10

λ

100

1000

t (s) 100

20

2+

2+

(d) Zn

(c) Zn

-1

Stretch rate (s ) 0.3 0.1 0.03 0.01 0.003 0.001 0.0003

-1

σ (kPa)

0.3 0.1 0.03 0.01 0.003 0.001 0.0003

10

f* (kPa)

Stretch rate (s )

15

10

5

0

1

2

1

0.1

λ

1

10

100

1000

t (s)

Fig. 6 (a) and (c) Stress-strain curves of loading and unloading cycles with different stretch rate of dual crosslink gels with [Ni2+] ¼ 100 mM (a), [Zn2+] ¼ 100 mM (b) and (d) corresponding reduced stress from loading curves as a function of time

3.5

Uniaxial Tensile Tests to Fracture

Tensile stress-strain curves of the dual crosslink gels with Ni2+ and Zn2+ at various stretch rates λ_ (from 0.9 to 0.0003 s1) are shown in Fig. 7a, c together with the data for the corresponding chemical gel at the stretch rate λ_ ¼ 0.03 s1. Note that the chemical gel does not exhibit any particular stretch rate dependence (data not shown). It is immediately evident that the addition of the transient crosslinks significantly increases the extensibility at rupture λb compared to that of the chemical gel and that λb does not show a clear stretch rate dependence for both gels. For the P(AAm-co-VIm)-Ni2+ gel, the values of λb were found around 6.5–8.5, and for the P(AAm-co-VIm)-Zn2+ gel, they were slightly higher than that of P

-1

200

stretch rate (s )

150

0.9 0.6 0.3 0.1 0.03 0.003 0.0003 chemical gel (0.03)

100

(a)

40

30

10

0 2

4

6

8

10

0.2

0.4

−1

0.6

0.8

λ 14

(c)

-1

stretch rate (s )

Zn

12

f* (kPa)

2+

0.9 0.6 0.3 0.1 0.03 0.003 chemical gel (0.03)

10

100

(d)

-1

stretch rate (s )

2+

0.9 0.6 0.3 0.1 0.03 0.003 chemical gel (0.03)

150

σ (kPa)

2+

Ni

20

λ 200

13

(b)

0.9 0.6 0.3 0.1 0.03 0.003 0.0003 chemical gel (0.03)

Ni

50

0

-1

stretch rate (s )

2+

f* (kPa)

σ (kPa)

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .

Zn

8 6 4

50

2 0

2

4

6

λ

8

10

0

0.2

0.4

0.6

0.8

-1

λ

Fig. 7 Stress-strain curves of dual crosslink gels with [Ni2+] ¼ 100 mM (a), [Zn2+] ¼ 100 mM (c), and the corresponding Mooney plots (b, d)

(AAm-co-VIm)-Ni2+ gel, around 8.5–10. These results indicate that transient crosslinks, even with very fast dynamics relative to the applied stretch rate, can increase the extensibility of the dual crosslink gels without increasing the modulus (thus rheologically invisible) as observed previously for organogels [34]. Both gels display a marked stretch-rate-dependent softening at intermediate strains and a rate-dependent strain hardening at large strain. To further analyze the details of the stress-strain relationship and the contribution of the transient crosslinks, the Mooney representation of the stress, classically used in rubber elasticity, was applied [37, 38]. In this representation of the data, the relationship between f and λ reveals the difference in stiffness between the sample and a hypothetic material with the same initial modulus and following classical rubber elasticity. A decreasing f indicates softening relative to rubber elasticity, and an increasing f reveals hardening.

14

J. Zhao et al. 20

7

(a)

Ni

2+

(b)

2+

Zn

Ni

2+ 2+

Zn

6 5 min

f*min (kPa)

15

10

4 3

5 2

0 0.0001

0.001

0.01 -1

(s )

0.1

1

1 0.0001

0.001

0.01

0.1

1

-1

(s )

Fig. 8 The minimum value of reduced stress fmin (a) and the corresponding value of stretch λmin (b) as a function of stretch rate of Ni2+ (red) and Zn2+ (blue) dual crosslink gels. Error bars were calculated by increasing the value of fmin by 0.05 kPa

The reduced stress can be plotted as a function of λ1 (Fig. 7b, d). As expected, the reduced stress of the chemical gel at a stretch rate of 0.03 s1 is almost independent of λ1, which indicates that, in the absence of physical bonds and polymer entanglements, the uniaxial deformation of the chemical gel is well described by the rubber elasticity model, and the constant value of the reduced stress is equivalent to its shear modulus. For dual crosslink gels, the values of reduced stress are higher than that of the chemical gel over the whole range of λ, even at very low stretch rates, which can be explained by the existence of the slow components. At almost all stretch rates, a nonlinear viscoelastic softening occurs in the small λ region (λ1 > 0.3): with increasing λ the reduced stress decreases. In the large λ region (λ1 < 0.2), the reduced stress increases again, or a strain hardening appears relative to the neo-Hookean behavior. We characterized the stretch rate dependence of the strain hardening behavior, with the values of the minimum in f ( fmin) and those of the corresponding stretch λ1min in Fig. 8. For both gels, fmin increases with stretch rate (Fig. 8a). Since this increase is due to the dynamics of the physical crosslinks, at slower stretching rate, the physical bonds can exchange more effectively and relax the stress leading to a lower value of fmin. The values of λmin are plotted as a function of λ_ in Fig. 8b. We observed a slight stretch rate dependence of λmin suggesting the existence of a second longer relaxation time. In principle if the observed strain hardening is due the limiting extensibility of the chains between physical crosslinks, the value of λmin should be related to the chain length between the effective crosslinks and decrease with increasing fmin. We do not see any clear correlation between the two values. If the strain hardening is due to the non-Gaussian stretch of the chains between chemical crosslinks (containing many transient physical crosslinks), then λmin is expected to be independent of the stretch rate. One can argue that this is roughly the

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . . Fig. 9 Modulus E and minimum value of reduced stress fmin of Ni2+ (red) and Zn2+ (blue) dual crosslink _ R gels as a function of λτ

15

100 Ni

f* min ,

Zn

G initial , G initial ,

f*min (kPa)

2+

f* min ,

2+ 2+

Ni

2+

Zn G initial , chemical gel

10

1 -5 10

-4

10

-3

-2

10

10

-1

10

0

10

· λ⋅τR case (from Fig. 8b), but the value of is too small to be consistent with the crosslink density of the chemical gel. This again suggests the existence of a second (slow) physical crosslinking mechanism that would always be active at the investigated stretch rates. With the relaxation time of both gels known from linear rheology, it is possible to compare these two gels by shifting horizontally the data by τR. To study the large strain (nonlinear) properties, the minimum value of the reduced stress fmin was plotted as a function of stretch rate λ_ (Fig. 8a). We can now replot fmin as a function _ R _ R (Fig. 9). The relatively high value of fmin at high λτ of a Weissenberg number λτ represents the non-relaxed physical bonds, which result in more elastic gels. At low _ R, the physical bonds relax completely, leading to the plateau of fmin values of λτ around 4 kPa. Theoretically, without a second relaxation mechanism, this plateau should be reaching the value of the chemical gel, which is not true for this system: the plateau value is still higher than that of the chemical gel (about 3 kPa). In Fig. 9 we also replotted the values of fmin to compare them to those of the initial modulus Ginitial as a function of stretch rate. Both small strain and large strain moduli show a _ R; however, the two curves are not qualitatively similar stretch rate dependence on λτ  _ R parallel. The fact that the difference between f min and Ginitial is larger at high λτ indicates that fmin relaxes more slowly than Ginitial; thus, it is mostly controlled by the slower relaxation mode.

16

3.6

J. Zhao et al.

Step-Cycle Uniaxial Tensile Tests and Energy Dissipation

Loading-unloading step-cycle extension tests at incremental values of strain were performed, at a constant stretch rate of λ_ ¼ 0.3 s1. Thirty min of rest time was applied before each cycle, and the maximum stretch was increased by λ ¼ 0.5 for each cycle up to the sample rupture. As shown in Fig. 10, the hysteresis (Hys) of each loop can be calculated by integrating the area between the loading and unloading curves, while the normalized hysteresis (Hys/W) is the ratio of the hysteresis to the total work input which can be determined by the area under the loading curve of each loop. The initial modulus of each loop Einitial can be determined by fitting the loading curves at low deformation. Figure 11 shows the step-cycle curves of dual crosslink gels with Ni2+ and Zn2+. These two gels show similar dissipative behaviors: the P(AAm-co-VIm)-Ni2+ gel has a higher modulus and lower extensibility, consistent with the tensile uniaxial stretching result and a remaining residual extension after the rest time was observed for both gels in large strain, due to the permanent change in the structure. A few interesting features which can be learned from plotting the initial modulus E and normalized hysteresis as a function of the maximum stretch λmax of each loop are shown in Fig. 12. Einitial of both gels stays almost constant at small strain, and then starts to decrease slightly for λmax > 4. The extensibility of the corresponding chemical gel is about 4, suggesting that the chemical network starts to be irreversibly and locally damaged at large strain and that the transient crosslinks can prevent propagation of the local damages allowing further deformation of the dual crosslink

Fig. 10 The calculation of the hysteresis (Hys), normalized hysteresis (Hys/W), and the initial modulus (Einitial)

Zn 30

2+

λ max = 10.5

σ (kPa)

Hysteresis 20 E initial 10

W

0 2

4

6

λ

8

10

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .

λ

(a) Ni

2+

1.5 3 4.5 6 7.5 9 10.5

60

σ (kPa)

σ (kPa)

60

40

20

40

2 3.5 5 6.5 8 9.5

(b)

2.5 4 5.5 7 8.5 10

2+

Zn

20 -1

stretch rate: 0.3 s

-1

stretch rate: 0.3 s

0

17

2

4

6

8

10

0

12

2

4

6

λ

8

10

12

λ

Fig. 11 Step-cycle extension tests of dual crosslink gels with [Ni2+] ¼ 100 mM (a) and [Zn2 + ] ¼ 100 mM (b) 0.7

(a)

60

Ni

0.6

2+

(b)

2+

Zn

50

0.5

40 Ni

2+ 2+

30

Zn

Hys/W

Initial modulus (kPa)

70

0.4 0.3

20

0.2

10

0.1

0

2

4

6

λmax

8

10

0.0

2

4

6

8

10

λmax

Fig. 12 Initial modulus (a) and energy dissipation (b) and as a function of the maximum stretch λmax of each loop of dual crosslink gels with [Ni2+] ¼ 100 mM (red) and [Zn2+] ¼ 100 mM (blue)

gels. The values of Hys/W of both gels decrease with λmax, which indicates that the gels become more elastic with increasing maximum strain. Additionally a higher hysteresis represents a larger energy dissipation, and it is important to assess the consistency between the large strain (nonlinear) and small strain (linear) energy dissipation. Compared to the P(AAm-co-VIm)-Zn2+ gel, the P (AAm-co-VIm)-Ni2+ gel has a significantly higher W (area under the loading curve) and also a higher normalized hysteresis Hys/W consistent with the small strain results of Fig. 3.

18

J. Zhao et al.

4 Conclusion In order to investigate systematically the effect of the dynamic bond exchange rate on the macroscopic properties of hydrogels containing physical and chemical crosslinks, we designed and synthesized P(AAm-co-VIm)-M2+ dual crosslink gels having a tunable characteristic relaxation time in order to characterize their timedependent mechanical properties in small and large strains. These dual crosslink gels were permanently crosslinked by methylene bisacrylamide and transiently crosslinked by a metal ion – imidazole ligand coordination, with two different ions, Ni2+ and Zn2+, having different characteristic breaking/reforming times. Linear rheological measurements showed that the P(AAm-co-VIm)-M2+ dual crosslink gels exhibit time-dependent elasticity, i.e., the G0 (ω) increases with frequency, and G00 (ω) shows a peak, due to the dissociation of the transient crosslinks followed by chain relaxation. The dynamics of the dual crosslink gels can be tuned by changing the metal ions: the P(AAm-co-VIm)-Zn2+ dual crosslink gel exhibited a much faster relaxation process than the P(AAm-co-VIm)-Ni2+ dual crosslink gel, hence more suitable to characterize the mechanical properties at very slow stretch rate (relative to the characteristic time). In addition we observed signs of the existence of a slower relaxation component due to a more long-lived physical crosslinking mechanism, since the elastic modulus of the dual crosslink gels did not reach to the value of the corresponding chemical gel even at times of the order of 1,000 s. At intermediate strains (λ < 2), the P(AAm-co-VIm)-Zn2+ dual crosslink gel, having much faster association/dissociation dynamics than that of the P(AAm-coVIm)-Ni2+ dual crosslink gel, exhibits a lower hysteresis in the tensile loops. Based on the strain-rate-dependent tensile behavior at small strain, a master curve of the reduced stress as a function of time was obtained for both gels; thus in that strain range, a separability of the stress into strain-dependent and time-dependent terms holds. The key result at larger strain is the difference in extensibility between the dual crosslink gels and the chemical gel even at stretch rates significantly slower than the inverse of the main relaxation time of the gel, a situation where the stress-strain curves are nearly identical except for the fracture point. The stress at large strain proved to be also strongly strain-rate dependent, with in particular a strongly rate-dependent strain hardening at large strain. Mooney plots of the reduced stress were used to characterize this strain hardening behavior and showed that the reduced stress at the onset of strain hardening kept increasing with stretch rate, suggesting the existence of a second relaxation time due to a longerlived physical crosslinking mechanism. Finally we found that the initial elastic modulus of the gel during step-cyclic tests started to decrease at values of λ~4 close to the stretch a break of the chemical gel. This suggests that in dual crosslink gels, molecular damage occurs at that stage, but no macroscopic crack forms and propagates. This strongly supports a mechanism where the physical crosslinks are actively protecting (or shielding) neighboring

Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .

19

covalent bonds from the stress transfer occurring when a chemical bond breaks, in qualitative agreement with the model recently proposed by Tito et al. [12]. Acknowledgments Jingwen Zhao has benefitted from a scholarship from the Chinese Scholarship Council. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under grant agreement AdG No 695351.

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Adv Polym Sci (2020) 285: 21–62 https://doi.org/10.1007/12_2019_53 © Springer Nature Switzerland AG 2020 Published online: 10 April 2020

How to Design Both Mechanically Strong and Self-Healable Hydrogels? Oguz Okay

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 H-Bonding Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Hydrophobic Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Hydrophobically Modified Associative Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Mechanically Strong Hydrophobically Modified Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 26 36 36 44 53 55

Abstract Several strategies have been developed in the past decade for the fabrication of self-healing or self-recovery hydrogels. Because self-healing and mechanical strength are two antagonistic features, this chapter tries to answer the question “How to design both mechanically strong and self-healable hydrogels?”. Here, I show that although autonomic self-healing could not be achieved in high-strength hydrogels, a significant reversible hard-to-soft or first-order transition in cross-link domains induced by an external trigger creates self-healing function in such hydrogels. I mainly focus on the physical hydrogels prepared via hydrogen-bonding and hydrophobic interactions. High-strength H-bonded hydrogels prepared via selfcomplementary dual or multiple H-binding interactions between hydrophilic polymer chains having hydrophobic moieties exhibit self-healing capability at elevated temperatures. Hydrophobic interactions between hydrophobically modified hydrophilic polymers lead to physical hydrogels containing hydrophobic associations and crystalline domains acting as weak and strong cross-links, respectively. Semicrystalline self-healing hydrogels exhibit the highest mechanical strength reported so far and a high self-healing efficiency induced by heating above the melting temperature of the alkyl crystals. Research in the field of self-healing hydrogels provided several O. Okay (*) Department of Chemistry, Istanbul Technical University, Istanbul, Turkey e-mail: [email protected]

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important findings not only in the field of self-healing but also in other applications, such as injectable gels and smart inks for 3D or 4D printing. Keywords Hydrogels · Hydrogen-bonding interactions · Hydrophobic associations · Mechanical properties · Self-healing · Semicrystalline hydrogels

Abbreviations βo ηo ε εf ε_ λ λbiax,max λmax νedry ξH σf σ nom ω AAc AAm AMPS BAAm C12M C17.3M C18A C22A CNFs Co CTAB DAT DMAA DMSO DNA E EtBr fν G0 G00 GO MAAc NAGA

CTAB/AAc molar ratio in the gelation solution Zero-shear viscosity Strain Fracture strain Strain rate Deformation ratio Maximum biaxial extension ratio Maximum deformation ratio Cross-link density Hydrodynamic correlation length Fracture stress Nominal stress Frequency Acrylic acid Acrylamide 2-Acrylamido-2-methyl-1-propanesulfonic acid N,N0 -Methylenebis(acrylamide) Dodecyl methacrylate Stearyl methacrylate N-Octadecyl acrylate Docosyl acrylate Cellulose nanofibrils Initial monomer concentration Cetyltrimethylammonium bromide Diaminotriazine N,N-Dimethylacrylamide Dimethyl sulfoxide Deoxyribonucleic acid Young’s modulus Ethidium bromide Fraction of associations broken during the loading Storage modulus Loss modulus Graphene oxide Methacrylic acid N-Acryloyl glycinamide

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

NIPAM PAAc PAAm PAMPS PDMAA PEG PVP SDS SFS tan δ Tm Uhys UPy WLMs

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N-Isopropylacrylamide Poly(AAc) Poly(AAm) Poly(AMPS) Poly(DMAA) Poly(ethylene glycol) Poly(N-vinylpyrrolidone) Sodium dodecyl sulfate Scanning force microscopy Loss factor (¼G00 /G0 ) Melting temperature Hysteresis energy Ureidopyrimidinone Worm-like micelles

1 Introduction Hydrogels are 3D networks of chemically and/or physically cross-linked polymer chains swollen in water. They are soft and smart materials with a variety of applications including superabsorbents, tissue engineering, drug delivery, soft contact lenses, and so on [1–4]. Because the first-generation classical hydrogels prepared using a chemical cross-linker were too weak or brittle in nature, extensive studies conducted in the past decade explored a new design principle for the fabrication of mechanically strong hydrogels of high toughness [5–12]. This principle bases on creating an effective energy dissipation in the hydrogel network using sacrificial or reversible bonds that prevent propagation of crack and hence a catastrophic damage even under large strain. Otherwise, that is, if the crack energy localizes around the crack tip and cannot be dissipated as in the classical hydrogels, rapid crack propagation leads to the fracture of the whole hydrogel. By manipulating the gel structure to induce dissipative mechanisms at the molecular level, the secondgeneration hydrogels developed so far exhibit Young’s moduli and tensile strengths in the range of MPa and hence are a good candidate for the replacement of loadbearing tissues such as cartilage, tendons, and ligaments [2]. For example, doublenetworking strategy developed by Gong and co-workers bases on creating two interpenetrated and interconnected networks in a single hydrogel material, namely, highly and loosely chemically cross-linked polymer networks acting as brittle and ductile components, respectively [6, 13]. The sacrificial bonds of the brittle network break under a low strain to produce many microcracks by dissipating energy, while the ductile network keeps the macroscopic sample together. Another important challenge emerging in the field of mechanically robust hydrogels is to generate self-healing or self-recovery ability in these materials. Self-healing, which is an inherent property of many biological systems, is defined

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Fig. 1 (a, b) Cut-and-heal test (a) and on-off strain cycles (b) to monitor the self-healing and selfrecovery capability of hydrogels, respectively. In (a), the images of two hydrophobically modified hydrogel specimens are shown; one of them was colored for clarity. After cutting the specimens into two parts followed by bringing the cut surfaces together, they merge to form their original shapes. From [14] with permission from the American Chemical Society. In (b), the storage modulus G0 and the loss factor tan δ (¼G00 /G0 , G00 is the loss modulus) of a nanocomposite DNA/clay hydrogel are shown as a function of the test time. The test consists of strain cycles composed of a stepwise increased high strain (from 2 to 300%) separated with a low strain (1%), as shown by the dashed red lines. Temperature ¼ 25 C. From [15] with permission from the American Chemical Society. (c) The number of publications and citations with keywords “self-healing” or “self-recovery” and “hydrogels” according to the ISI Web of Knowledge portal on November 2, 2019. The total numbers of papers and citations are 1,478 and 39,613, respectively

as the capability of a material to heal macroscopic cracks such as cuts or scratches autonomously or under the effect of a stimulus such as the temperature. Thus, selfhealing requires reformation of all bonds broken in a material to recover its original shape and mechanical properties. Although self-healing and self-recovery have sometimes been used synonymously, self-recovery more refers to cases of repairing internal microcracks in a material remaining externally intact after damage. Thus, cut-and-heal tests and rheological measurements have generally been conducted to monitor the efficiency of self-healing and self-recovery, respectively (Fig. 1a, b) [14, 15]. Self-healing is a highly desirable property for commercial polymers because it extends their lifespan and also reduces the burden of waste polymers

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

25

such as microplastics causing serious pollution in the seas [16]. It is also important for hydrogels as they are used as biomaterials, scaffolds in tissue engineering and drug delivery systems, and superabsorbents where their extended service time is of prime importance. The number of the works published on self-healing/self-recovery hydrogels has grown almost exponentially during the past 10 years (Fig. 1c). Several reviews have been published covering exhaustive collection of all results reported so far [17– 24]. A critical survey over the published works reveals that many studies deal with the preparation of self-healing physical hydrogels exhibiting a frequency-dependent low storage modulus and a Young’s modulus and fracture stress in the Pa to kPa range. Because self-healing and mechanical strength are inversely related, it is not surprising to detect self-healing in such weak hydrogels having short-lived crosslinks. However, hydrogels with a good mechanical performance such as cartilage require existence of cross-links with long lifetimes together with an efficient energy dissipation mechanism to prevent crack propagation. Because self-healing efficiency decreases with increasing lifetime of cross-links, it seems a challenge to generate self-healing in high-strength hydrogels with modulus and tensile strength in the range of MPa. This review tries to answer the question “How to design both mechanically strong and self-healable hydrogels?”. The capability to self-heal in hydrogels is generated by forming a reversible 3D network of polymer chains via dynamic covalent bonds or non-covalent interactions. Thus, instead of chemical cross-links, intermolecular bonds with finite lifetimes are used to build a hydrogel network. The type of the physical bonds and their lifetimes are key elements determining many of the properties of self-healing physical hydrogels. Dynamic covalent bonds such as phenylboronic ester, acylhydrazone, disulfide, dynamic imine bonds, as well as reversible radical and Diels-Alder reactions have been used to create self-healing in hydrogels. One may expect that such bonds will combine the strength and reversibility of covalent and non-covalent bonds, respectively. However, hydrogels formed via dynamic covalent bonds generally exhibit insufficient mechanical properties for load-bearing applications, and their preparation often requires sophisticated synthetic procedures [17]. Therefore, this review covers publications on creating mechanically strong self-healing/selfrecovery hydrogels via non-covalent interactions. We focus here on hydrophobic and hydrogen-bonding interactions as well as on their combinations with ionic interactions. Self-healable polyampholyte hydrogels formed via ionic bonds [25], and physical double-network hydrogels have been reviewed by Sun and Cui in this volume [26]. Because of the inverse proportionality between self-healing efficiency and lifetime of intermolecular cross-links, one may argue that an effective self-healing could not be achieved in a mechanically strong hydrogel with long-lived cross-links. However, it could be achieved in a short period of time if an external trigger induces a significant, reversible hard-to-soft, or first-order transition from order to disorder in the cross-link domains of the hydrogels leading to a dramatic change in the crosslink lifetime. For example, if a semicrystalline physical hydrogel with a modulus and tensile strength in the MPa range is damaged, heating the damaged region above the

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melting temperature Tm of crystal cross-links induces almost three orders of magnitude decrease in the modulus in that region so that, after cooling below Tm, the released crystallizable groups reform in that area to recover the original mechanical properties [27]. Thus, independent on the mechanical properties of hydrogels, self-healing requires a significant reversible softening in the damaged area induced by an external stimulus providing an enhanced mobility to the network chains. A prerequisite for the preparation of tough and self-healing hydrogels is to reduce their water content to a moderate level, generally between 50 and 70 wt%. This is mainly due to the decrease in the polymer concentration of the hydrogels as the water content is increased leading to a reduced viscoelastic energy dissipation between the polymer chains inducing a tough-to-brittle transition. In addition, at high water contents, the polymer chains are already stretched due to the swelling pressure of water so that their further stretchability under an external force and hence tensile strength reduce significantly. For example, superabsorbent hydrogen (H)-bonded hydrogels in their as-prepared state with 65% water exhibit 1,000% stretchability and complete self-healing efficiency, whereas, in equilibrium swollen state with 99.9% water, they become brittle in tension and lack of self-healing [28]. The water content also affects the strength of the non-covalent bonds between the polymer chains in the hydrogel network. The strength of H-bonds between proteins, nucleic acids, or hydrophilic polymers in an aqueous environment is known to be much weaker than the H-bonds between water molecules. This weakening effect arises due to the fact that the formation of a H-bond between two polymers requires disruption of their H-bonds with water. To hinder the weakening of intermolecular interactions between polymers, mechanically robust and self-healable hydrogels reported so far generally have a water content between 50 and 70 wt%, which is, in fact, similar to that in living cartilage, skin, tendons, and ligaments [2].

2 H-Bonding Interactions Because H-bonds between polymer chains are easily disrupted by water molecules and hence not stable in an aqueous environment, several strategies have been developed to create mechanically strong H-bonded hydrogels. These strategies mainly base on creation of self-complementary dual or multiple H-bonding interactions between polymer chains as well as incorporation of hydrophobic segments into the hydrophilic polymers to amplify the H-bonding interactions. The use of H-bond acceptor and donor comonomers in the hydrogel preparation, dual amide groups, ureidopyrimidinone units, and diaminotriazine-diaminotriazine interactions has been reported to create high-strength H-bonded hydrogels. Inspired by nature such as the double and triple H-bonds in double-stranded deoxyribonucleic acid (DNA), stronger H-bonding interactions in hydrogels can be generated by using polymer chains having arrays of H-bonding sites. Because dual amide H-bonds are quite stable as compared to a simple amide H-bond, Liu and co-workers prepared hydrogels based on N-acryloyl glycinamide (NAGA), a

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

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glycinamide-conjugated polymerizable monomer with dual amide in one side group (Fig. 2a) [29]. Photopolymerization of aqueous NAGA above 10 wt% concentration without a chemical cross-linker leads to physical hydrogels exhibiting good mechanical properties (mechanical strength, MPa level; stretch at break, ~1,400%) together with an excellent fatigue resistance (Fig. 2b–d) [29, 30]. This improved mechanical performance as compared to hydrogels derived from the monomers like acrylamide with a simple amide H-bond was attributed to the effect of stable multiple H-bonding domains serving as physical cross-links. NAGA hydrogels also exhibit thermoplasticity, remoldability, recyclability, reusability, and a high self-healing efficiency. The healing of a damaged NAGA hydrogel at 90 C for 3 h provides a healing efficiency of around 80%, i.e., the healed hydrogel sustains tensile stresses up to 1 MPa. During heating, the H-bonds at the cut region are disrupted so that the released H-bond donor and acceptor groups reform new H-bonds at the cut interface leading to healing of the NAGA hydrogels [29]. Incorporation of diaminotriazine (DAT) groups as the side chains into a hydrophilic polymer backbone also produces high-strength hydrogels due to the DAT-DAT interactions forming H-bonded dimers or higher-order aggregates [31– 34] (Fig. 3a). It was shown that the DAT groups provide a hydrophobic microenvironment in hydrogels leading to strengthened DAT-DAT interactions in water. The ureidopyrimidinone (UPy) units developed by Meijer et al. are popular building blocks able to form self-complimentary dimers with quadruple H-bonds [35]. Although the dimer activity of UPy decreases in hydrophilic environment,

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Fig. 3 (a) Structure of DAT groups and their H-bonding sites shown by the dashed lines. From [33] with permission from the Royal Society of Chemistry. (b) UPy unit in a segmented amphiphilic polymer chain (upper panel) and quadruple H-bonds between UPys forming semicrystalline polymer morphology in dry state and reversible transition to hydrogel after swelling in water (bottom panel). From [36] with permission from the American Chemical Society

introduction of hydrophobic segments into the hydrophilic chains protects the quadruple H-bonding between UPy units. Physical hydrogels with 80 wt% water and containing UPy units in the backbone of segmented amphiphilic polymers having hydrophilic poly(ethylene glycol) (PEG) sustain up to ~1 MPa stresses (Fig. 3b) [36]. Bulk images of the hydrogels show existence of UPy-UPy dimers serving as physical cross-links which are surrounded by segregated hydrophobic regions dispersed within the PEG matrix. H-bonded hydrogels via UPy units were

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

29

also fabricated by the micellar copolymerization of acrylamide and an amphiphilic cross-linker consisting of an acrylic head, alkyl spacer, and UPy group providing both hydrophobic associations and H-bonds [37]. To increase the solubility of the cross-linker in the micellar solution, salt was included into the reaction solution to induce the micellar growth [38]. However, weak hydrogels with a modulus of around 2 kPa could be obtained likely because of the weakening effect of surfactant molecules on the hydrophobic interactions [38, 39]. Physical hydrogels via both H-bonding and hydrophobic interactions were recently fabricated by free-radical copolymerization of UPy methacrylate, n-octadecyl acrylate (C18A), and acrylic acid [40]. The hydrophobic interactions between crystallizable alkyl side chains of C18A and the quadruple hydrogen bonds between UPy segments act as dual crosslinks of the hydrogels. The hydrogels with a water content between 40 and 80 wt% exhibit a high tensile strength (up to 4.6 MPa) and elongation at break (680%). It was shown that the UPy units promote formation of alkyl crystals, while alkyl side chains stabilize UPy-UPy dimers [40]. Incorporation of hydrophobic groups into the hydrogel network has a significant effect on the strength of H-bonds and hence the mechanical performance of hydrogels consisting of H-bond acceptor and donor comonomer units. For instance, introduction of methyl motif to acrylic acid (AAc), that is, the use of methacrylic acid (MAAc) instead of AAc, significantly improves the mechanical performance of H-bonded hydrogels [41]. The hydrogel based on MAAc and 1-vinylimidazole containing 50–60 wt% water exhibits a Young’s modulus up to 170 MPa, whereas it two orders of magnitude decreases when MAAc is replaced with AAc in the gel preparation [42, 43]. High-strength self-recovery hydrogels with a high Young’s modulus (28 MPa), tensile strength (2 MPa), stretch at break (800%), and a good fatigue resistance were prepared by free-radical copolymerization of N,N-dimethylacrylamide (DMAA) and MAAc in aqueous solutions without a chemical cross-linker [41]. It was shown that the strong H-bond acceptor carbonyl group of DMAA and H-bond donor carboxylic group of MAAc form multiple H-bonds, leading to the formation of polymer-rich aggregates stabilized by the hydrophobic interactions of the α-methyl groups of MAAc units (Fig. 4). These aggregates serving as sacrificial cross-links ensure a high energy dissipation within the gel network. If MAAc segments in the hydrogel are replaced with AAc ones at the same concentration and water content, soft hydrogels with a fracture strength of less than 100 kPa could be obtained [41]. However, insolubility of DMAA/MAAc hydrogels in aqueous urea solutions reveals the existence of chemical cross-links in these self-recovery hydrogels likely due to the chain transfer reactions during copolymerization. High-strength self-recovery H-bonded hydrogels were also prepared by simply heating aqueous solutions of acrylamide (AAm) and poly(N-vinylpyrrolidone) (PVP) at 56 C for 36 h without any chemical initiator or cross-linker (Fig. 5) [44]. The hydrogels with 60% water exhibit a high Young’s modulus (84 MPa), tensile strength (1.2 MPa), and elongation at break (~3,000%). It was shown that AAm polymerization occurs by self-initiation at elevated temperature, whereas the presence of PVP provides formation of high-strength hydrogels. Insolubility of

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Fig. 4 Scheme illustrating formation of MAAc/DMAA hydrogels. Formation of oligomeric radicals (i), their phase separation due to multiple H-bonds to form polymer-rich clusters with trapped radicals (ii), and formation of a hydrogel containing clusters embedded into a polymer poor phase (iii). Stretching the hydrogel leads to fragmentation of weak (iv) and strong clusters (v) followed by complete recovery after unloading (vi). From [41] with permission from Wiley

Polymerization N2, Heating PVP Chains AAm Monomer Hydrogen Bonding PAAm Chains

Fig. 5 Cartoon showing formation of PVP in situ PAAm hydrogels. From [44] with permission from the American Chemical Society

the hydrogels in water but their solubility in aqueous solutions of urea, a powerful Hbond-breaking reagent, reveal that they are purely formed via H-bonding interactions between the amide group of AAm and the pyrrolidone ring of PVP segments [44]. Interestingly, the copolymerization of AAm with the monomer of PVP, i.e., N-vinyl-2-pyrrolidone, instead of its homopolymerization in the presence of preexisting PVP under the same reaction condition leads to physical hydrogels with an order of magnitude lower tensile strength. This indicates that, as compared

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

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Fig. 6 (a) Images of a PAMPS hydrogel specimen formed at 60 wt% AMPS just after preparation and after equilibrium swelling in water. From [28] with permission from the American Chemical Society. (b) GPC curves of PAMPS primary chains obtained by solubilization of the hydrogels in an aqueous urea solution. The hydrogels were prepared by thermal and UV polymerizations at 50 wt% AMPS. (c) Cartoon presenting formation of multiple H-bonds (red lines) due to the proximity effect

to the preexisting PVP, in situ formed PVP produces much weaker H-bonds with the in situ formed PAAm chains. This finding was explained with the higher molecular weight of preexisting PVP than the in situ formed one, creating stronger cooperativity in H-bonding interactions due to the so-called proximity effect [45, 46]. Thus, once H-bonds are formed between two polymer molecules, their conformational freedom is restricted, facilitating formation of subsequent H-bonds, the extent of which increases with increasing number of segments in a polymer molecule. In addition, trapping effect of H-bonds may also increase the lifetime of chain entanglements leading to entanglement cross-links. Increasing H-bond cooperativity with increasing molecular weight of primary chains was also observed for 2-acrylamido-2-methyl-1-propanesulfonic acid (AMPS) hydrogels, which are attracting increasing interest for the fabrication of superabsorbent materials [47]. Physical poly(AMPS) (PAMPS) hydrogels without any added chemical cross-linker and initiator were first prepared by Xing et al. using thermal polymerization of aqueous solutions of AMPS at 80 C [48]. Although PAMPS hydrogels exhibit a high stretchability (~2,500%) and self-healing efficiency, they are easily soluble in water indicating that the H-bond strength between the amino and carbonyl groups of AMPS segments is insufficient to withstand the osmotic pressure of AMPS counterions [48, 49]. Interestingly, AMPS polymerization under the same experimental condition except under UV light using a photoinitiator at room temperature produces water-insoluble PAMPS hydrogels exhibiting a degree of swelling of around 1,000 g g1 (Fig. 6a) [28]. The hydrogels exhibit a Young’s modulus of 30 kPa which is around threefold higher than those formed by thermal polymerization. PAMPS hydrogels formed by thermal and UV

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polymerizations are easily soluble in aqueous solutions of urea indicating that they both form by H-bonding interactions. The main difference between two hydrogels was the molecular weight of the primary chains, i.e., 8.3  103 vs 7.5  105 g mol1 for those formed via thermal and UV polymerization, respectively (Fig. 6b) [28]. This finding also highlights the importance of the proximity effect in the H-bond connectivity [45, 46]. As schematically illustrated in Fig. 6c, formation of a H-bond between two polymer chains facilitates formation of additional H-bonds in the vicinity because of the restricted conformation of chain segments in this volume element. As a consequence, increasing chain length also increases the number of H-bonds between polymers in H-bonded hydrogels. Poly(DMAA) (PDMAA) is a versatile hydrophilic biocompatible polymer exhibiting associativity due to its dimethyl groups [50–54]. Although the segments of PDMAA with their dimethyl amino groups cannot form H-bonds between each other, they have an enhanced H-bond acceptor capability through their carbonyl groups via σ-donation effect of the methyl groups. Therefore, DMAA increases the H-bonding cooperativity in hydrogels when it is copolymerized with H-donor monomers. For example, UV polymerization of aqueous solutions of AMPS and DMAA in the absence of a chemical cross-linker leads to high-strength physical hydrogels with water contents between 30 and 40% [28]. Quantum mechanical calculations indeed reveal that the H-bond strength between AMPS/DMAA copolymers is much stronger than that between AMPS polymers [28]. AMPS/DMAA hydrogels in as-prepared state have a high Young’s modulus (up to 0.41 MPa), tensile strength (~0.57 MPa), stretch at break (~1,000%), and self-healing efficiency (100%) and absorb a large amount of water at swelling equilibrium (up to ~1,700 g g1) (Fig. 7). The effective cross-link density νedry of the hydrogels significantly increases as the DMAA content of the network chains increases indicating formation of increased number of strong H-bonds serving as crosslinks [28].

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

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DNA existing in all living cells acts as the carrier of genetic information in their base sequences. Previous work shows that the entrapment of double-stranded (ds)DNA within a clay hydrogel network enhances its bioresponsivity and degradation stability [55, 56]. For example, ds-DNA is easily digested by the DNase, whereas it is efficiently protected from DNase digestion and conserves its biological function in a clay environment [56]. The protection of ds-DNA provided by clay hydrogel is possibly important in the life’s origin and sustainability on the earth. Haraguchi showed that Laponite clay nanoparticles in water serve as a multifunctional crosslinker during the polymerization of hydrophilic monomers such as N-isopropylacrylamide (NIPAM) or DMAA leading to the formation of highly stretchable and tough hydrogels [57–63]. Recently, self-healable DNA/clay nanocomposite hydrogels were fabricated by free-radical polymerization of DMAA in aqueous solutions of ds-DNA (~2,000 bp, molecular weight ¼ 1.3  106 g mol1) and Laponite [15]. From the cyclic mechanical tests, the intermolecular bond strength in the hydrogels was estimated as 2.7  0.2 kJ mol1 which is close to that of H-bonds. It was shown that Laponite nanoparticles contribute to the elastic behavior of DNA/clay hydrogels, whereas their DNA component promotes the energy dissipation under stress [15]. This is due to the repulsive interactions between equally charged DNA and surfaces of disk-like Laponite nanoparticles in water [57, 64, 65], preventing H-bonding between each other so that DNA can move freely between the nanoparticles contributing to the energy dissipation. Although DNA/clay hydrogels have a low modulus and tensile strength in the kPa range, they are highly stretchable (up to 1,500%) and display the characteristics of ds-DNA such as its thermally induced denaturation and renaturation behavior [15]. To highlight this feature, the hydrogels were prepared in the presence of ethidium bromide (EtBr), which is known to intercalate between ds-DNA base pairs leading to a higher fluorescence intensity as compared to the single-stranded (ss)-DNA [66, 67]. Figure 8a shows fluorescence spectra of EtBr in a DNA/clay hydrogel during a thermal cycle between 25 and 90 C, while the inset shows temperature dependence of EtBr emission intensity at 600 nm [15]. With increasing temperature, labeled by 1 to 5 in the figure, the peak intensity decreases, whereas it again increases after cooling back to 25 C, labeled by 6, revealing denaturationrenaturation of ds-DNA within the gel network. The optical images of a gel sample under UV light also visualize this conformational transition between ds- and ss-DNA (Fig. 8b); the yellow-orange color of the gel becomes lighter with increasing temperature up to 90 C but cooling back to 25 C recovers its initial color. Thus, ds-DNA in the hydrogels dissociate into single strands when heated above its melting temperature Tm, whereas the double-stranded conformation is recovered after cooling back below Tm. DNA/clay hydrogels also display an interesting healing mechanism based on the denaturation and renaturation behavior of ds-DNA encapsulated within the hydrogel [15]. When the cut regions of a hydrogel specimen are heated above Tm of ds-DNA and then pushed together following by cooling below Tm, the hydrogel exhibits a high healing efficiency. For instance, heating a damaged hydrogel specimen

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Cooling below Tm

Fig. 8 (a) Effect of temperature on the fluorescence spectra of EtBr in a DNA/clay hydrogel. For the spectra labeled by 1–6, the temperatures are 25, 40, 55, 75, 90 C, and after cooling back to 25 C, respectively. The inset shows temperature dependence of EtBr emission intensity at 600 nm. Laponite ¼ 5 w/v %. DNA ¼ 4 w/v %. (b) Optical images of a EtBr-containing DNA/clay hydrogel sample under UV light at 25 and 90 C and after cooling back to 25 C. (c) Schematic presentation of the cut area of a DNA/clay hydrogel (a), after bringing the cut surfaces together at T > Tm (b), and after cooling below Tm of ds-DNA (c). From [15] with permission from the American Chemical Society

containing 5 w/v % Laponite and 4 w/v % DNA at 90 C for 30 min results in an almost complete healing with respect to the stretch ratio. Because denaturation of the semiflexible ds-DNA at 90 C produces flexible ss-DNA strands with much higher mobility [66, 68, 69], the single strands at the cut region can easily move between the

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

35

surfaces so that, after cooling below Tm, ds-DNA bridges formed between the surfaces provide healing of the hydrogels (Fig. 8c) [15]. Self-recovery hydrogels via both dipole-dipole and H-bonding interactions were fabricated by copolymerization of the dipole acrylonitrile, H-bonding acrylamide (AAm), anionic AMPS, and a hydrophilic cross-linker in DMSO as the solvent, which was replaced with water after the reaction [70]. It was shown that the amount of ionic AMPS segments in the gel network regulates the water content between 32 and 98%, whereas the collaborative effect of H-bonding and dipole-dipole interactions leads to mechanically robust hydrogels with a tensile strength and elongation at break up to ~8 MPa and 700%, respectively. Self-recovery doublenetwork hydrogels based on poly(acrylic acid) and poly(N-isopropyl acrylamide) were prepared by both chemical cross-links and H-bonds [71]. Young’s modulus of the hydrogels is around 226 MPa at room temperature, but it significantly decreases at elevated temperature indicating that the cooperative H-bonds mainly determine the cross-link density of the hydrogels. Hydrogels via both electrostatic and H-bonding interactions were prepared by mixing of a solution of the cationic polyelectrolytes poly(diallyldimethylammonium chloride) and branched poly(ethylenimine) (PEI) with another solution of anionic polyelectrolytes poly(sodium 4-styrenesulfonate) and poly(acrylic acid), followed by molding, drying, and rehydration [72]. The hydrogels with 42% water content having oppositely charged ionic groups and H-bond forming sites exhibit a modulus, tensile strength, and elongation at break of 0.4 MPa, 1 MPa, and 2,400%, respectively, and a complete healing efficiency after immersing in water at room temperature for 14 h. Mixing of aqueous solutions or hydrogels of ionic polymers with oppositely charged ions was also utilized to create hydrogels via reversible ionic bonds enabling an efficient energy dissipation [73, 74]. Immersion of a loosely cross-linked poly(acrylamide-co-acrylic acid) hydrogel in aqueous FeCl3 solution to form the physical cross-links followed by washing with water to remove the excess ions leads to self-recoverable hydrogels with a high modulus (3 MPa), tensile strength (6 MPa), and 500% elongation at break [75]. Ionic nanocomposite selfhealing hydrogels were prepared from acrylic acid (AAc), vinyl hybrid silica nanoparticles (VSNPs), and Fe3+ ions by free-radical polymerization [76]. Physical cross-links between PAAc chains and Fe3+ ions lead to nanocomposite physical hydrogels with a tensile strength and elongation at break of 0.9 MPa and 2,300%, respectively, exhibiting self-healing ability at elevated temperature recovering 1,800% elongation at break and 0.56 MPa tensile strength [76]. Self-healing hydrogels were also prepared using Fe3+ ions and carboxylated cellulose nanofibrils (CNFs) as physical cross-linkers [77]. Carboxylated CNFs form H-bonds with poly (acrylic acid) (PAAc) chains, whereas Fe3+ forms ionic bonds with the carboxylic groups of both PAAc and carboxylated CNFs. The hydrogels exhibit a relatively high tensile strength, elongation at break, and healing efficiency of 4 MPa, 180%, and 87%, respectively [77]. Hydrogels based on cationic polyacrylamides reinforced with graphene oxide (GO) exhibit an efficient energy dissipation under stress due to the H-bonding and ionic interactions between AAm-GO and GO-cationic segments, respectively [78]. Both the amount of GO and the copolymer composition are the

36

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main factors determining the mechanical performance and self-healing efficiency of the hydrogels. The hydrogels with a tensile strength of 0.5 MPa exhibit a selfhealing efficiency of around 90% with respect to the tensile strength, elongation at break, and toughness. Elastin-like polypeptides consisting of a long hydrophobic block with hydrophilic ends also form self-healing hydrogels via hydrophobic and ionic interactions [79]. Heating polypeptide solution triggers the self-assembly of polypeptides to form micelles which were then cross-linked using zinc ions via metal coordination. At 10% polypeptide concentration, the hydrogels exhibit a storage modulus of ~1 MPa and an effective self-healing behavior within minutes [79].

3 Hydrophobic Interactions Segregation tendency of water-fearing (hydrophobic) molecules and water, which is called hydrophobic interactions, is important in many self-assembly processes such as formation of micelles, protein folding, and molecular recognition [80]. The driving force for the hydrophobic interactions arises to reduce the hydrophobic moieties of their exposure to water leading to hydrophobic associations and crystalline regions. Fu et al. used the amphiphilic triblock copolymer F127 for preparing hydrophobically cross-linked micellar hydrogels [81], which are reviewed in this volume [82]. Weiss et al. used fluoroacrylate monomers in the preparation of hydrophobically modified fluorocarbon-based hydrogels [83]. The strong hydrophobic interactions between fluoroacrylate segments lead to core-shell nanodomains within the hydrogels providing a MPa level modulus, as also detailed in this volume [84]. In the following, we first discuss the studies conducted on self-healing hydrocarbon-based hydrogels formed by hydrophobic associations exhibiting a modulus in the kPa range and a high stretchability. In the second section, the order-to-disorder transition from association to alkyl crystals and formation of high-strength selfhealing semicrystalline hydrogels with a modulus and tensile strength in the range of MPa are discussed.

3.1

Hydrophobically Modified Associative Hydrogels

Creton and co-workers were the first to report that hydrophobic modification of chemically cross-linked polyelectrolyte hydrogels creates variable dissipative properties at almost identical cross-link densities [85]. They showed that the incorporation of hydrophobic side groups into polyelectrolyte hydrogels significantly increases their loss moduli and hence generates energy dissipation because of the formation of hydrophobic associations serving as reversible cross-links. However, a complicated three-step synthetic approach was used for the synthesis of such hybrid cross-linked hydrogels due to the solubility mismatches between hydrophilic and hydrophobic monomers [85]. The micellar polymerization technique is a simple and

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

(A)

tan δ

G' / kPa + BAAm

100

(B)

+ C12M

(C)

x=

G', G'' / kPa

6/6 8 6 0

n-hexylacrylamide mol % = 5

100

10-1

37

10

100

0

-1 + C12M 10

6/6 8 6

10

10-2 + BAAm

10-2

5

10-1

10-3

0

0 0

60 Time / min

120

10-3

10-1

100 ω / Hz

101

10-1

100

101

ω / Hz

Fig. 9 (a) Storage modulus G0 (symbols) and the loss factor tan δ (lines) during the micellar polymerization of AAm in the presence of dodecyl methacrylate C12M or BAAm, each 1 mol%, in aqueous 7 w/v % SDS solution. ω ¼ 6.28 rad/s. γ o ¼ 0.01. From [96] with permission from Elsevier. (b, c) Frequency dependences of G0 (filled symbols) and loss modulus G00 (open symbols) of chemically cross-linked PAAm hydrogels containing N-alkylacrylamide segments. γ o ¼ 0.01. BAAm ¼ 1.25 mol%. (b) N-Hexylacrylamide concentration ¼ 0 (, ◯), 5 (, Δ), and 10 mol% (, ∇). (c) Hydrophobic monomer ¼ 5 mol%. The alkyl chain length x of the hydrophobes is indicated. From [95] with permission from Elsevier

versatile alternative for copolymerizing water-soluble and water-insoluble monomers in aqueous solutions [86–90]. By this technique, hydrophobic monomers solubilized in a micellar solution are copolymerized with hydrophilic monomers by free-radical mechanism. Because of the locally high concentration of hydrophobic monomers within the surfactant micelles, copolymer chains containing blocks of hydrophobes are obtained providing stronger hydrophobic interactions as compared to the random copolymers formed by solution or bulk polymerizations [91]. The length of hydrophobic blocks and the number of blocks per copolymer chains can easily be adjusted by the concentrations of surfactant and hydrophobic monomer. Candau et al. showed significant effects of the number and length of hydrophobic blocks on the zero-shear viscosity of semi-dilute solutions of hydrophobically modified polyacrylamides [86–90, 92–94]. However, physically or hybrid, i.e., chemically and physically, cross-linked analogs of these polymers in their as-prepared or swollen states in water as well as their mechanical and viscoelastic properties draw attention only in the past years [95–100]. Figure 9a illustrates a typical example comparing the effect of a hydrophobic monomer, dodecyl methacrylate (C12M), as a physical cross-linker with the classical chemical cross-linker N,N0 -methylenebis(acrylamide) (BAAm) on the hydrogel formation [96]. Here, the storage modulus G0 (symbols) and the loss factor tan δ (lines) of the reaction systems are shown as a function of the reaction time during the micellar polymerization of acrylamide (AAm) with C12M or BAAm, each 1 mol% (with respect to AAm) in an aqueous sodium dodecyl sulfate (SDS) solution. Incorporation of C12M segments into the PAAm chains produces a hydrogel with one order of magnitude higher tan δ than that obtained using BAAm cross-linker

38

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during which the storage modulus G0 only slightly decreases. This indicates the dynamic nature of the cross-link regions in C12M-containing hydrogels as compared to the chemically cross-linked ones because of the reversible dissociation and reassociation of the dodecyl side chains. Figure 9b shows frequency dependences of G0 (filled symbols) and G00 (open symbols) of hybrid cross-linked PAAm hydrogels containing 0–10% n-hexylacrylamide and 1.25 mol% BAAm [95]. At low frequencies, i.e., at long experimental time scales, they all exhibit similar mechanical spectra, i.e., G0 is frequency independent and G00 is more than an order of magnitude smaller than G0 , as typical for strong gels. However, at the high frequency range, G00 significantly increases both with the frequency and the hydrophobe content reflecting energy dissipation due to the reversible nature of hydrophobic associations that are captured at short experimental time scales. The length x of the alkyl side chain of n-alkylacrylamides has a similar effect on the properties of PAAm hydrogels (Fig. 9c) [95]. Increasing the side chain length x at a fixed hydrophobe content shortens the width of G0 plateau, i.e., G00 and G0 start to increase at lower frequencies. This reveals increasing lifetime of hydrophobic associations with increasing alkyl side chain length of the hydrophobic monomers. Thus, long-lived hydrophobic associations and hence mechanically strong hydrogels could be generated using long alkyl side chains. However, (meth)acrylates larger than 12 carbon atoms at their side chains such as n-octadecyl acrylate (C18A) or docosyl acrylate (C22A) could not be solubilized in monomeric, spherical surfactant micelles due to their larger sizes as compared to the micelles, hindering their micellar copolymerization with hydrophilic monomers. Worm-like micelles (WLMs) formed by self-assembly of surfactant micelles exhibit interesting rheological properties and a significant solubilization power for hydrophobes, and thus, they are able to form nano-sized oil depots dispersed in water [14, 38, 91, 101–103]. A simple way to produce WLMs is the addition of salts such as NaCl to the aqueous solutions of ionic surfactants which weakens the electrostatic repulsion between the monomeric micelles and hence promotes their growth to form “polymer-like” micelles. As shown in Fig. 10a, addition of 1 M NaCl in an aqueous solution of 7.6 w/v % SDS increases the zero-shear viscosity ηo by more than two orders of magnitude, and simultaneously, the hydrodynamic correlation length ξH increases from below 1 to 20 nm due to the micellar growth [102]. Formation of WLMs provides solubilization of large hydrophobes in SDS-NaCl solutions. For instance, C18A monomer, which is insoluble in aqueous SDS solutions, could be solubilized up to 15 w/v % in WLMs formed by the addition of 1.5 M NaCl into 22 w/v % aqueous SDS at 55 C (Fig. 10b) [91]. Interestingly, after solubilization of the hydrophobes in WLMs, both the zero-shear viscosity and hydrodynamic correlation length ξH reduce to a low level (Fig. 10c). SANS and cryo-EM measurements revealed that WLMs undergo a conformational transition from cylindrical to spherical shape after addition of hydrophobes, which is responsible for the decrease in the zero-shear viscosities [14, 102]. The accumulation of the hydrophobic monomers inside the core of the micelles creating a curvature on the micelle surface seems to be responsible for the conformational change in SDS micelles. Moreover, micellar copolymerization of hydrophilic monomers with a large amount of hydrophobic

How to Design Both Mechanically Strong and Self-Healable Hydrogels? ηo / Pa.s

(A)

ξH / nm

10-1

101

100

10-3 0.0

0.5 NaCl / M

1.0

ηo / Pa.s

Solubility (w/v %) (B)

ξH / nm

(C)

n-hexadecane C17.3M

10-1

15 (55 °C)

10

10-2

39

C18A

10-2 (35 °C)

5 0 0.0

101

C18A C17.3M C22A

0.5

1.0 NaCl / M

1.5

10-3 100 0

50

100

150

Hydrophobe / mM

Fig. 10 (a) NaCl concentration dependences of the zero-shear viscosity ηo (circles) and hydrodynamic correlation length ξH (triangles) of 7.6 w/v % SDS solution at 35 C. From [102] with permission from the American Chemical Society. (b) NaCl concentration dependence of the solubility of C17.3M, C18A, and C22A in aqueous SDS solutions. The data are for 7 and 22 w/v % SDS at 35 and 55 C, respectively. (c) Variations of ηo and ξH of 7.6 w/v % SDS – 1 M NaCl solution at 35 C with the addition of n-hexadecane and C17.3 M monomer. From [102] with permission from the American Chemical Society

monomer such as C18A or stearyl methacrylate C17.3M (a mixture of n-octadecyland n-hexadecyl methacrylates with an average alkyl side chain length of 17.3 carbons) solubilized in WLMs results in hydrogels with strong hydrophobic interactions providing transformation of hydrophobic associations into alkyl crystals as will be discussed in the next section. Depending on the presence of surfactant micelles, hydrophobically modified hydrogels undergo drastic changes in their viscoelastic and self-healing properties [38]. Those with surfactant are mechanically weak with a few kPa modulus and exhibit autonomic self-healing behavior, whereas without surfactant, the modulus increases to tens of kPa, but they have no more self-healing ability even at elevated temperatures. A typical example is the hydrogels synthesized by micellar polymerization of 10 w/v % AAm in the presence of 2 mol% C17.3M (with respect to AAm) in aqueous solutions of worm-like SDS micelles [104]. The corresponding SDS-free hydrogels were fabricated by extracting SDS from as-prepared hydrogels in an excess of water. It was shown that Young’s modulus and compressive strength around five- and ninefold increase, respectively, while the stretch at break twofold decreases after extraction of SDS from the hydrogels [104]. This reveals a significant increase in the strength of hydrophobic interactions in the absence of surfactant molecules. Theoretical studies indeed indicate that surfactant molecules considerably affect the hydrophobic associations in the hydrogels [105]. It was shown that the sorption of surfactant molecules by hydrophobically modified hydrogels is noncooperative and they continuously incorporate within the existing hydrophobic aggregates to form mixed micelles, thereby decreasing the effective cross-link density of the hydrogel. Recent works show stiffening effect of SDS on hydrophobically modified physical hydrogels at a low SDS concentration which is due to the increased chain mobility facilitating formation of additional

40 Fig. 11 Multistep tensile cyclic tests conducted on SDS-free and SDS-containing PAAm hydrogels with 2 mol% C17.3M. The inset is zoomin to the data of hydrogel with SDS. From [104] with permission from Springer

O. Okay

σnom / kPa SDS-free 9

100

6 3 0

50

1

3

5

7

9

11

with SDS

0

1

3

5

7

9

11

λ

supramolecular bonds [106, 107]. However, increasing SDS concentration in the hydrogel results in a gel-to-sol transition due to the dissolution of the mixed micelles. Mechanical cyclic tests are a mean to compare the strength of hydrophobic interactions in the hydrogels. Figure 11 shows typical multistep tensile cycles conducted on PAAm hydrogels containing 2 mol% C17.3M with and without SDS where the inset is zoom-in to the data of the SDS-containing hydrogel [104]. The data are shown as the nominal stress (σ nom)-strain (λ) curves where λ is the stretch ratio. The tests were carried out by stepwise increasing the maximum strain with a wait time of 7 min between each cycle. For a given maximum strain λ, the mechanical hysteresis in SDS-free hydrogel is much larger than that of the corresponding SDS-containing one, indicating higher strength of hydrophobic associations in the former hydrogel. Moreover, as seen in the inset to Fig. 11, the hydrogel containing SDS undergoes reversible tensile cycles, i.e., each loading curve follows the path of the previous loading indicating healing of the damage during the wait time between cycles. In contrast, SDS-free hydrogel exhibits irreversible cycles each of which creates additional damage that cannot be healed during the wait time. Indeed, SDS-containing hydrogel has a complete self-healing efficiency, whereas SDS-free hydrogel has lack the ability to self-heal even after prolonged healed times at elevated temperature or by treating the cut regions with 7 w/v % SDS solution up to 12 days [104]. Healing in SDS-free hydrogels could only be induced by the treatment of the cut region with an aqueous solution of wormlike SDS micelles. This reveals that WLMs are able to solubilize the hydrophobic domains at the cut surfaces so that they merge together by reformation of the physical cross-links. To highlight the effect of the hydrophilic monomer type on the mechanical properties of hydrophobically modified hydrogels, micellar copolymerizations of

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

41

hydrophilic AAm, NIPAM, and DMAA monomers were conducted with 2 mol% C17.3M hydrophobe in aqueous solutions of WLMs [38, 108, 109]. The surfactantcontaining hydrogels prepared using DMAA exhibit the highest stretchability, 4,200  400%, as compared to those formed using AAm and NIPAM that can sustain stretches up to 2,000%, which was attributed to the associative behavior of DMAA segments (Fig. 12a). Hydrophobically modified PDMAA hydrogels σnom / kPa

Uhys / kJ.m-3

(A)

25

102

20

101

15

100 10

5

10-2 10-3

100

10

20

30

λ

40

fv

50

100

λ max, λ biax,max

101

σnom / kPa

(C) 10

Uniaxial Biaxial

-1

10

0

(B)

25

-1

virgin sample

(D)

20min

20

10-2

15min 15

10-3

Uniaxial Biaxial

10 min 10

10-4

5 min 5

2min

10-5 100

101

λ max , λ biax,max

0

10

20

30

40

λ

Fig. 12 Large strain and self-healing behaviors of a PDMAA hydrogel with 2 mol% C17.3M. The hydrogel was prepared at 10 w/v % DMAA concentration in an aqueous 0.5 M NaCl solution containing 7 w/v % SDS. (a) Typical tensile stress-strain curve of a hydrogel specimen at a strain rate of 1.56  102 s1. (b, c) Hysteresis energy Uhys (b) and the fraction of reversibly broken intermolecular bonds, fv, (c) of the hydrogel calculated from successive tensile (filled circles) and compression cycles (open symbols) plotted against the maximum stretch ratio (λmax and λbiax,max). The waiting time between cycles is 7 min. (d) Tensile stress-strain curves of virgin and healed hydrogels at various healing times at 24 C as indicated. From [108] with permission from Elsevier

42

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subjected to mechanical cycles exhibit hysteresis whose extent continuously increases with the maximum strain indicating breakage of intermolecular bonds of varying strength [108]. However, if the cyclic tests are repeated several times with a wait time of 7 min between cycles, all the cycles overlap well for a given maximum strain, which is an indication of reformation of the broken bonds during the wait time. Figure 12b shows maximum strain dependence of the hysteresis energy Uhys, calculated as the area surrounded by the loading and unloading curves, of successive tensile (filled circles) and compressive cycles (open circles). Because uniaxial compression ratio equals to the reciprocal of the square root of the biaxial extension ratio, Uhys data could be plotted against a common abscissa, namely, the uniaxial (λmax) and biaxial maximum stretch ratios (λbiax,max). Over the whole range of maximum strain, the hysteresis energies Uhys fall into a single curve revealing that Uhys is independent on the type of strain, and it only depends on the value of the maximum strain. Calculation of the fraction fv of reversibly broken bonds during the mechanical cycles reveals that more than half of the intermolecular bonds, i.e., up to at least fv ¼ 0.56, can be broken reversibly at a stretch ratio of around 20 (Fig. 12c) [108]. This is a sign of a high self-healing efficiency of PDMAA hydrogels without any external stimuli. Indeed, a complete healing in these hydrogels was achieved by holding their cut surfaces together at 24 C for 20 min (Fig. 12d) [108]. The mechanism of autonomic self-healing in surfactant-containing hydrogels was recently investigated by scanning force microscopy (SFM) measurements [102]. For this purpose, the surface of a hydrophobically modified PAAm hydrogel containing 2 mol% C17.3M was first cut with the SFM tip to create trenches of 20–40 nm in depth and protrusions of around 10 mm in height. Figure 13A shows topographic images (left panel) and cross sections of the gel surface (right panel) just after cutting (a), a few seconds after cutting (b), and after a wait time of 75 min (c). Interestingly, a terraced topography was observed for both protrusions and trenches with a step height between 3.8 and 5.0 nm, or multiples thereof, as indicated by the horizontal dotted lines in Fig. 13A. XRD measurements revealed that the smallest step height is close to the d spacing of the hydrogel (3.9 nm) [102]. This indicates the existence of layered hydrophobic nanodomains in the hydrophobically modified hydrogels as observed in comb-like polymers with alkyl side chains [110] and fluorocarbon-based hydrogels [83, 84]. Moreover, immediately after damaging, both the trenches and protrusions on the gel surface transform into rounded shapes without affecting their depth and height, respectively (a to b in Fig. 13A). In contrast to the fast reshaping process in the damaged area, the healing process, that is, the size reduction of the holes and islands on the hydrogel surface, and their disappearance require a relatively long time (b to c in Fig. 13A). Thus, healing of the gel surface occurs in two steps, namely, a fast reshaping of the damaged area into circular forms without healing followed by slow size reduction of this area and finally complete healing to recover the virgin surface [102]. The first step was attributed to the strong attractive interactions between the alkyl side chains of hydrophobic units locating in close

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

(A)

43

Height (nm)

(B)

Cut region

Height (nm)

Height (nm)

Mixed micelles

KEY: SDS C17.3M segment AAm segment …. Polymer chain

Cross secon length (nm) Fig. 13 (A) Topographic SFM images (left panel) and cross sections of the surface (right panel) of a PAAm hydrogel specimen with 2 mol% C17.3M. The images were taken just after cutting (a), right after the first image (b), and after a wait time of 75 min at 35 C and 87% relative humidity (c). The red and blue dotted lines across the trenches and protrusions on the images, respectively, show their cross sections at the right panel in respective colors. The dotted lines on the surface cross sections indicate steps of 3.8 nm or multiples thereof. Color scale ¼ 50 nm (from black to white). (B) Schematic illustration of fast reshaping process of the trenches and protrusions on the gel surface into circular shapes due to the attractive interactions between hydrophobic C17.3M segments locating at the edge of a damaged micelle. From [102] with permission from the American Chemical Society

vicinity to each other, i.e., at the edge of the trenches, leading to the formation of round holes, as seen schematically in Fig. 13B. Because the consumption of the islands by the round holes and their disappearance require interlayer mobility of mixed micelles which is slow as compared to their mobility along the layers, the second step needs much longer times than the first one [102].

44

3.2

O. Okay

Mechanically Strong Hydrophobically Modified Hydrogels

Hydrogels formed in the presence of a small amount of a hydrophobic monomer via micellar polymerization discussed in the previous section have a high self-healing efficiency, but they exhibit an insufficient mechanical performance for load-bearing applications. Although their mechanical strength could be improved by incorporation of hydrophobic acrylates instead of the corresponding methacrylates into the hydrophilic polymer backbone, or by increasing the length of alkyl side chain of the hydrophobic monomers from 12 to 22 carbon atoms, the tensile strength only slightly increases from 20 to 65 kPa after these modifications [101]. Chen et al. conducted the micellar copolymerization of AAm and C18A by the addition of 1-pentanol as a cosurfactant of SDS solubilizing the hydrophobe in the micellar solution [111]. After γ-radiation induced polymerization without any initiator, they produced a hydrogel sustaining kPa level compressive stresses. However, swelling of this hydrogel in a second aqueous AAm-BAAm solution followed by polymerization leads to a self-recovery double-network PAAm hydrogel exhibiting a compressive strength of 2.8 MPa under 90% compression [111]. Micellar polymerization reactions conducted using a polymerizable (acrylated) cationic surfactant in the absence of free surfactants or reducing surfactant content using amphiphilic hydrophobic monomers lead to hydrogels with tensile strength up to ~300 kPa but with a low self-healing efficiency [112, 113]. Micellar polymerization of AAm and 2 mol% C17.3M in aqueous mixtures of cationic and anionic surfactants produces PAAm hydrogels with a high stretchability (1,800–5,000%) and complete self-healing efficiency but a low mechanical strength [114]. Thomas et al. prepared hydrophilic-hydrophobic hydrogels based on polyvinyl alcohol and poly(ethyleneco-vinyl alcohol) with 15–25% water content that exhibit good compressive properties with a modulus of around 20 MPa [115]. Moreover, creating hybrid crosslinked hydrophobically modified hydrogels by incorporation of chemical cross-links also provides some improvement in the compressive mechanical properties without affecting much their self-healing behavior, but they are brittle in tension [116]. Considering the load-bearing tissues such as cartilages, tendons, and ligaments containing 60–75% water and exhibiting a modulus and tensile strength in the range of MPa, one needs to improve the tensile mechanical performances of hydrophobically modified self-healing hydrogels to the MPa level. In the following subsections, two attempts will be discussed for fabrication of high-strength hydrophobically modified hydrogels with a high self-healing efficiency.

3.2.1

Hydrophobically Modified Polyelectrolyte Hydrogels with Oppositely Charged Surfactants

One attempt in this direction was to use oppositely charged surfactants in the preparation of hydrophobically modified polyelectrolyte hydrogels by micellar

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

45

Fig. 14 (A) Images of two PAAc hydrogel specimens in as-prepared (a) and equilibrium swollen states in water (b). (B) Images of a spherical swollen PAAc hydrogel during loading (upper row) and 2, 10, and 60 s after unloading (bottom row). Co ¼ 20 w/v%. βo ¼ 1/8. From [117] with permission from the American Chemical Society

polymerization [117]. The interactions between polyelectrolytes and oppositely charged surfactants in an aqueous solution such as poly(acrylic acid) (PAAc) and cetyltrimethylammonium bromide (CTAB) have been investigated in detail during the past two decades [118–125]. It was shown that, at a high ionization degree of PAAc, electrostatic interactions determine the complex formation between PAAc and CTAB, whereas hydrophobic interactions start to dominate when the ionization is suppressed by decreasing the pH of the solution [118, 121]. Moreover, PAAcCTAB interactions become stronger when a small amount of a hydrophobic segment carrying alkyl side chain is incorporated into the PAAc backbone because of the formation of mixed micelles composed of CTAB and alkyl side chains of hydrophobically modified PAAc [126, 127]. High-strength self-healing PAAc hydrogels were recently fabricated by micellar copolymerization of AAc and 2 mol% C17.3M in aqueous solutions of worm-like CTAB micelles [117]. It was found that PAAc-CTAB complexes in the hydrogel start to form after immersion in water, as visualized by its appearance changes from transparent to opaque (Fig. 14A). The late complexation between PAAc and CTAB within the hydrogel network is due to the low pH (1.5) of as-prepared hydrogels, while the pH increases to 6.7 after immersing in water, providing ionization of AAc segments and hence their complex formation with the cetyltrimethylammonium (CT) ions. Simultaneously, both G0 and G00 increase by one order of magnitude, while the loss factor tan δ remains above 0.1 revealing that the viscous character of the hydrogels is preserved in their swollen state [117]. This behavior is in contrast to the hydrophobically modified nonionic hydrogels prepared via micellar polymerization as discussed in the previous section. The viscoelastic nature of water-swollen PAAc hydrogels is presented in the images of Fig. 14B showing compression of a spherical PAAc hydrogel under load and complete recovery of the original shape within 1 min after unloading. It was shown that the as-prepared hydrogels have weak physical cross-links consisting of mixed C17.3M and CTAB micelles [117], which are similar to those existing in SDS-containing nonionic hydrogels. However, after swelling equilibrium, i.e., after ionization of PAAc chains, a second type of much stronger

46

O. Okay (A)

σnom / MPa

2.0

(B)

σnom / kPa

swollen state

2.0

swollen state

Healing me / min =

1/6

1.5

30

400

1/8

60

10

1.0

0

200

0.0

1.5

20

1/10

1.0 2

4

6

as-prepared state

0.5

20

λ

30

8

30

10

15

0.5

1/10 1/8 1/6

10

(C)

σnom / MPa

as-prepared state

0

40

2

4

6

λ

5

8

10

0.0

2

4

6

λ

8

10

Fig. 15 (a) Tensile stress-strain curves of as-prepared (dashed curves) and water-swollen PAAc hydrogels (solid curves) formed at various CTAB/AAc mole ratios (βo) as indicated. Co ¼ 30 w/v%. (b) Five-step tensile cycles with increasing maximum strain conducted on a PAAc hydrogel specimen in its as-prepared and swollen states. The inset is a zoom-in to the data of the as-prepared hydrogel. Co ¼ 20 w/v%. βo ¼ 1/8. (c) Tensile stress-strain curves of virgin (solid curve) and healed PAAc hydrogels (dashed curves) in their swollen states in water at various healing times as indicated. Co ¼ 30 w/v%. βo ¼ 1/6. From [117] with permission from the American Chemical Society

cross-links appear due to the formation of aggregates composed of oppositely charged AAc and CTA ions and alkyl side chains of C17.3 segments. These second cross-links lead to a dramatic increase in the mechanical properties of water-swollen PAAc hydrogels during which their viscous, energy-dissipating properties do not change [117]. Figure 15a shows tensile stress-strain curves of as-prepared (dashed curves) and water-swollen PAAc hydrogels (solid curves) formed at a constant AAc concentration (Co) of 30 w/v % but at various CTAB/AAc mole ratios (βo) as indicated. Young’s modulus and tensile strength increase up to 23- and 14-fold, respectively, while stretch at break decreases by two- to threefold after swelling of the hydrogels in water. PAAc hydrogels formed at Co ¼ 30 w/v% and βo ¼ 1/6 in their equilibrium swollen state with 55% water exhibit the highest Young’s modulus (0.61 MPa), tensile strength (1.7 MPa), and a pretty good stretchability (900%). Figure 15b shows the results of five-step tensile cyclic tests with increasing maximum strain conducted on a PAAc hydrogel specimen in its as-prepared and swollen states. In contrast to the SDS-containing nonionic hydrogels [38], PAAc hydrogels formed in the presence of the oppositely charged surfactant CTAB exhibit reversible mechanical cycles in both their as-prepared and swollen states revealing that their physical cross-links break reversibly under loading. Cut-and-heal tests indeed show self-healing ability of PAAc hydrogels. All hydrogels in their as-prepared states exhibit autonomic self-healing at 24 C within a few minutes. Hydrogels in their swollen states could also be healed after treatment of the cut region with an aqueous solution of worm-like CTAB micelles at 35 C which provides dissociation of PAAc-CTAB complexes, followed by washing the cut region with water to remove free surfactants. After a healing time of 60 min, the hydrogels formed at Co ¼ 30 w/v%, and βo ¼ 1/6 sustains 1.5 MPa stresses at 600% elongation (Fig. 15c).

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

3.2.2

47

Hydrogels Containing Crystalline Domains

Another attempt to fabricate mechanically strong hydrophobically modified hydrogels with self-healing ability was to create alkyl crystal cross-links in the gel network providing temperature-induced hard-to-soft transitions and thereby selfhealing [27, 128]. Thus, when the local temperature of the damaged area of a semicrystalline physical hydrogel is increased above the crystalline melting temperature, the crystalline order is lost along with the strength of the crystal cross-links providing a rapid healing due to the increased chain mobility in that area. Preparation of semicrystalline chemically cross-linked hydrogels and the observation of an order-to-disorder transition in the gel network were first reported 25 years ago by Osada et al. [129–132]. They fabricated hybrid hydrogels containing both chemical and alkyl crystal cross-links by free-radical copolymerization of AAc and C18A in the presence of the chemical cross-linker BAAm in ethanol, a common solvent for both monomers. The amorphous hydrophilic region of the hydrogels provides water absorption, while the crystalline region is responsible for their high modulus. The alkyl crystals have a short range ordering with a d1 spacing of around 0.42 nm corresponding to side-by-side packing of n-octadecyl (C18) side chains (Fig. 16A). In addition, a long-range ordering was also observed with a d2 spacing of 6.3 nm, which is around twice the fully stretched length of C18, revealing non-interdigitated, tail-to-tail alignment of alkyl side chains (Fig. 16a). This type of alignment in semicrystalline hydrogels is in contrast to comb-like polymers with alkyl side chains (B)

(A)

d1

d2

T > Tm

T < Tm

KEY: Amorphous domain C18A side chains

Fig. 16 (a) Scheme showing alkyl crystals and amorphous regions in semicrystalline hydrogels based on hydrophilic monomers and N-alkyl (meth)acrylates. From [127] with permission from the American Chemical Society. (b) Scheme showing melting of alkyl crystals to form hydrophobic associations and their recrystallization below Tm

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Tcry

Tm

(A)

(B) G' / MPa

100 10-1

100

10-1

100 10-1

10-2 100

10-2

0.4

tan δ

50 %

35 %

101

G'' / MPa

G'' / MPa

G' / MPa

101

0.2

10-1

10-2

0.0

80

60

40

20

20

60

80

5 °C

15

30

45

15

30

45

60

Temperature / °C

Temperature / °C

Temperature / °C

80 °C

40

80 °C

Fig. 17 (a) Temperature-dependent variations of the dynamic moduli G0 and G00 and tan δ of semicrystalline hybrid PAAc hydrogels with varying amount of C18A during a thermal cycle between 80 and 5 C. C18A ¼ 20 (), 35 (), and 50 mol% (). BAAm ¼ 1 mol%. (b) G0 and G00 of PAAc hydrogels with 35 (left panel) and 50 mol% C18A (right panel) during the thermal cycle. Down and up arrows indicate increasing and decreasing temperatures, respectively. ω ¼ 6.28 rad s1. γ o ¼ 0.1%. From [91] with permission from the American Chemical Society

forming an interdigitated side chain structure [110, 133, 134]. Hybrid semicrystalline hydrogels undergo up to 120-fold reversible change in their modulus by changing the temperature between below and above the crystalline melting temperature [129]. Later on, semicrystalline hybrid hydrogels of Osada et al. were synthesized via micellar polymerization in aqueous solutions of WLMs instead of the solution polymerization in ethanol [91]. The block-like structure of poly(AAc-co-C18A) copolymer chains formed in a micellar solution enhances the hydrophobic interactions leading to two to three orders of magnitude change in the storage modulus in response to a change in the temperature. Figure 17a shows temperature-dependent variations of G0 , G00 , and tan δ during a thermal cycle between 80 and 5 C for PAAc hydrogels formed via micellar polymerization with 1 mol% BAAm and varying amounts of C18A between 20 and 50 mol%. The dotted vertical lines in the upper panel indicate the melting Tm and recrystallization temperatures Tcry. The hydrogels at 5 C exhibit a storage modulus G0 in the MPa level, i.e., 3.6, 8, and 17.6 MPa for 20, 35, and 50 mol% C18A, respectively. During heating, G0 drastically decreases at around Tm, 48  2 C, and attains a value between 16 and 27 kPa at 80 C, which is 130- to 700-fold smaller than the initial modulus at 5 C [91]. The temperatureinduced modulus change is totally reversible as such upon cooling, G0 rapidly increases at around Tcry, 43  2 C, to attain the initial MPa level modulus (Fig. 17b) [91].

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

49

To generate self-healing in semicrystalline hydrogels, they were recently prepared in the absence of a chemical cross-linker by micellar, bulk, and solution polymerizations using several hydrophobic and hydrophilic comonomer pairs [27, 128, 135, 136]. Because of the cooperative H-bonding and hydrophobic interactions, AAc/C18A comonomer pair leads to the formation of hydrogels with the highest melting temperature (48–56 C), degree of crystallinity (10–33%), Young’s modulus (up to 308  16 MPa), and tensile strength (up to 5.1  0.1 MPa) [135]. Compressive mechanical tests conducted on virgin and cut-repaired hydrogels reveal extraordinary self-healing capability of the hydrogels. The healing of the hydrogels was induced by heating locally the cut region above Tm followed by pressing the cut surfaces together and finally cooling below Tm to reform alkyl crystals bridging the cut surfaces (Fig. 16b). Healed DMAA/C18A hydrogels with 50 mol% C18A exhibit a compressive strength of 138  10 MPa, which is around 87% of the virgin ones [135]. Moreover, the healing can also be induced by internal heating using laser light if the hydrogel contains gold nanoparticles that generate heat due to the surface plasmon resonance [137]. On/off switching of the laser light provides melting and recrystallization of alkyl crystals in the damaged area resulting in healing of the hydrogel. Instead of the temperature-induced healing, treatment of the cut surfaces with ethanol was also reported which provides solubilization of the cut surfaces to allow merging the surfaces together [136]. One disadvantage of highly crystalline hydrogels prepared from hydrophilic and hydrophobic monomers is their low stretchability due to the existence of stiff and strong alkyl crystals. One may apparently overcome this drawback by changing the tensile testing parameters, i.e., by reducing the strain rate to provide enough time for the relaxation processes in the physical network. For instance, the toughness and stretch at break of DMAA/C18A hydrogels increase by five- and sevenfold, respectively, when the strain rate is reduced from 7.8  103 to 4  103 s1 (Fig. 18a) [135]. However, a versatile alternative strategy to induce such a brittle-to-tough transition without changing the testing parameters is to incorporate hydrophobic monomers with relatively short alkyl side chains creating mobility in the gel network [128]. Figure 18b shows the effect of the non-crystallizable, weak hydrophobe C12M on the stress-strain curves of DMAA/C18A hydrogels at a fixed strain rate. The hydrogels were prepared at a fixed content of the hydrophobes (30 mol%) but at various fractions of C12M between 0.1 and 20 mol%. In the absence of C12M, the hydrogel ruptures in a brittle fashion, as seen by the blue thick curve labeled by “0” in the inset to the figure. However, incorporation of a small amount of C12M induces significant yielding accompanied with a brittle-to-ductile transition. For instance, without and with 0.2 mol% C12M, the hydrogels exhibit almost identical Young’s moduli E, i.e., 71  3 and 70  5 MPa, respectively, indicating that the cross-link density is not effected from the added amount of C12M. However, this tiny amount of C12M affects considerably the ultimate mechanical properties of the hydrogels. The hydrogel without C12M ruptures at 20% stretch, while that with 0.2 mol% C12M sustains eightfold larger stretches (167%) and exhibits tenfold larger toughness (9.6  0.3 vs 1.0  0.2 MJ m3) [128]. Moreover, the highest yield stress σ y of 7.3 MPa was observed after incorporation of the smallest amount of C12M

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σnom / MPa

σnom / MPa

(A)

(B)

.

8

7

102 ε / s-1 = 6

7.8

6

C12M % = 0 0.1

6

0.2

3.8

0.4 0.8 1.2 1.6 2.0

2.5 4

0.4 2

2

6

1.0

8 10

0

1.0

1.5

λ

2.0

5

C12M % = 4

1.0

4

2.5

5

1.5

15 10

2.0

2.5

20 15

λ

Fig. 18 Stress-strain curves of DMAA/C18A hydrogels at various strain rates ε_ (a) and at various C12M contents (b). (a) C18A ¼ 30 mol%. From [135] with permission from Elsevier. (b) ε_ ¼ 8.3  102 s1. C18A + C12M ¼ 30 mol%. C12M contents are indicated. The inset is a zoom-in to the curves of the hydrogels with C12M contents below 4 mol%. From [128] with permission from the American Chemical Society

(0.1 mol%) into the polymer backbone, which is close to the tensile strength of C12M-free hydrogel. σ y linearly decreases with increasing C12M content by the equation, σ y ¼ 7.1  0.1 – C12M mol%, indicating that the weak hydrophobe C12M increases the number of mobile segments in the hydrogels and hence enhances the molecular mobility between crystalline regions. We have to mention the modulus and the fracture stress rapidly decrease above 2 mol% C12M due to a significant decrease in the degree of crystallinity leading to highly stretchable but mechanically weak hydrogels (Fig. 18b). The significant effect of a weak hydrophobe on the ultimate mechanical properties of semicrystalline hydrogels was explained with the formation of more ordered and thinner alkyl crystals, as demonstrated by SAXS measurements [128]. During stretching of the hydrogels containing strong and weak hydrophobic segments, lamellar clusters formed from layered alkyl crystals appear that are interconnected by tie molecules. The tie molecules in amorphous domains create an energy dissipation mechanism by transmission of the external load between the lamellar clusters leading to their bending and finally breaking at the yield point [138–140]. Because lamellar clusters are physical in nature, they could be repaired by heating above Tm followed by cooling. The solid and dotted curves in Fig. 19a present two successive loading curves up to a 100% stretch ratio for a DMAA/C18A hydrogel specimen prepared in the presence of 0.4 mol% C12M [128]. According to the first loading curve, Young’s modulus E and yield stress σ f are 68 and 6.5 MPa, respectively (Fig. 19b). The modulus significantly decreases, and yielding disappears during the second loading indicating the occurrence of an irreversible damage in the lamellar clusters. However, repairing the clusters by the heating-cooling treatment as

How to Design Both Mechanically Strong and Self-Healable Hydrogels? σnom / MPa

E / MPa

(A)

1st loading

(B)

51 σy / MPa

E

6

6

σy

60 2th loading (after heating-cooling)

4

4

40

2

0 1.0

2nd loading

0 1.4

λ

1.8

2

20

1st loading

2nd loading

0 2nd loading (after heating-cooling)

Fig. 19 (a) Two successive stress-strain curves up to an elongation ratio λ ¼ 2 for a DMAA/C18A hydrogel specimen containing 0.4 mol% C12M. The second loading was conducted immediately after the first one (dotted curve) and after the heating-cooling treatment (dashed curve). ε_ ¼ 8.3  102 s1. (b) Young’s modulus E and yield stress σ y of the hydrogel calculated from the first and second loading steps. From [128] with permission from the American Chemical Society

mentioned above and then conducting the second loading almost completely recovers the mechanical properties of the virgin hydrogel (Figs. 19a, b). The selfhealing efficiency is 93% with respect to the modulus (63  5 MPa) and yield stress (6.0  0.4) [128]. Semicrystalline physical hydrogels were also fabricated with a macroscopically anisotropic structure consisting of hard and soft regions joined together through a strong interface [141]. Such segmented hydrogel structures mimic many biological systems such as the intervertebral disk (IVD) which provides flexibility, load transfer, and energy dissipation to the spine. IVD consists of a soft inner core, called nucleus pulposus, surrounded by mechanically strong annulus fibrosus [142, 143]. This structural design provides IVD an extraordinary mechanical performance, as such it can withstand millions of loading cycles over the human lifespan. Another example is the enthesis, the connective tissue between the tendon/ligament and bone, which not only acts as a connector of soft-to-hard tissue but also reduces the risk of damage under stress [144]. The synthetic strategy of semicrystalline segmented hydrogels bases on the stratification of aqueous solutions even at very low density differences, as observed in many seas and lakes [141]. For example, Fig. 20a shows two monomer mixtures composed of DMAA together with 30 mol% C18A (red) and 50 mol% C12M (blue). The slightly lower density of the blue mixture by 0.6% provides formation of two liquid layers if blue mixture is dropwise added on top of the red one, as seen in the upper panel of Fig. 20a. Otherwise, if red mixture is dropped on top of the blue one, they mix completely in a short period of time (bottom panel). In this way, layered monomer mixtures

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(B)

50% C12M 30% C18A

30% C18A

50% C12M

Fig. 20 (a) Stratification of the monomer mixtures composed of DMAA together with 30 mol% C18A (red) and 50 mol% C12M (blue). Two liquid layers only form when red solution is on the bottom due to its slightly higher density. (b) Synthetic procedure for the fabrication of segmented hydrogels. From [145] with permission from Wiley

containing photoinitiators were prepared and then subjected to UV polymerization to obtain two or more segmented semicrystalline hydrogels (Fig. 20b) [141, 145]. Figure 21a presents the photograph of a dumbbell-shaped segmented hydrogel specimen consisting of C1 and C3 components. C1 and C3 have a common PDMAA backbone, but they contain 30 mol% C18A and 50 mol% C12M hydrophobic units, respectively. Thus, C1 is a semicrystalline hydrogel with Tm ¼ 48 C and exhibits a high modulus E (54 MPa), a tensile strength σ f (5 MPa), and a low stretchability εf (79%), whereas C3 is an amorphous hydrogel due to the relatively short alkyl side chain of C12M. C3 has a low modulus and tensile strength of around 0.1 MPa but a high stretchability (1,140%). DSC scans conducted at the interface region reveal that the melting peak of C1 at 48 C gradually disappears by moving from C1 to C3 part through the interface indicating perfect fusion of the two hydrogel segments (Fig. 21b) [141]. Figure 20c, d shows stress-strain curves and mechanical parameters of C1 and C3 segments and the interface region of C1/C3 hybrid. The interface region exhibits the average properties of both segments and hence has a higher modulus and tensile strength as compared to the C3 segment. As a consequence, when C1/C3 hydrogel is subjected to tensile testing, the interface remains intact, while it ruptures at C3 segment (Fig. 21e) [141]. Thus, despite large mismatches in the mechanical properties of C1 and C3 segments, stratification technique provides a smooth interface that remains stable under loading. Two- and three-segmented hydrogels with various chemical compositions and mechanical properties have been reported recently [141, 145]. Because of the physical nature of segmented hydrogels, they all exhibit self-healing behavior after heating-cooling treatment of the damaged areas.

How to Design Both Mechanically Strong and Self-Healable Hydrogels? (E)

(A) Interface

C1

53

C3

C3

C3

1 23456

E = 54 Mpa, σ f = 5 MPa

E, σ f = ~ 0.1 MPa

C3

C1

C1

(B)

Heat flow / a.u.

4 3 2

C1

Interface

100

C3

10-1

E / MPa

σnom / MPa

5

(D)

σf / MPa

Endo

101

C3

6

(C)

εf %

1

C1 20

30

40

50

60

10-2

0

Temperature / oC

300 600 900 1200

ε%

101 100 10-1 100 10-1 103 102 C1

Interface C3

Fig. 21 (a) Photograph a dumbbell-shaped hybrid hydrogel composed of C1 and C3 segments whose mechanical parameters are indicated. (b) DSC scans performed at the interface region of segmented C1/C3 hydrogel. The numbers correspond to the location numbers in (a). (c, d) Tensile stress-strain curves of C1 and C3 components and the interface of segmented C1/C3 hydrogel together with their Young’s modulus E, tensile strength σ f, and stretch at break εf. The horizontal dashed lines in the right panel show the respective values for the segmented hydrogel. (e) Photograph during the mechanical tests of C1/C3 hydrogel. The interface regions are indicated by the white arrows. From [141] with permission from the American Chemical Society

4 Conclusions and Outlook Recent developments in the field of hydrogels enable to enhance their mechanical strength to MPa level at a water content between 60 and 75 wt%, which is similar to the load-bearing tissues. Another challenge immersing in the last years is to generate self-healing function in such hydrogels without affecting their good mechanical properties. Because self-healing and mechanical strength are inversely related, autonomic self-healing in high-strength hydrogels formed by long-lived crosslinks could not been created. However, a significant hard-to-soft or first-order transition induced by an external trigger creates self-healing in such high-strength hydrogels and hence combines the two antagonistic features in a single hydrogel material. In this review, I mainly focused on hydrogels formed via H-bonding and hydrophobic interactions, which are generally highly stretchable and exhibit Young’s modulus and tensile strength in the range of MPa. The strategies developed so far for the fabrication of H-bonded hydrogels are based on forming self-complementary dual or multiple H-bonding interactions between polymer chains. In addition, hydrophobic segments have been incorporated into the hydrophilic chains to amplify these interactions. Polymer chains consisting

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of H-bond acceptor and donor segments, dual amide groups, UPy moieties, and DAT-DAT interactions create high-strength H-bonded hydrogels with self-healing or self-recovery functions. Such hydrogels with 40–80 wt% water exhibit a Young’s modulus up to 84 MPa and sustain 1–5 MPa tensile stresses at 800–1,400% elongations. H-bonded hydrogels prepared by polymerization of NAGA monomer with dual amide groups in aqueous solutions exhibit the highest stretchability, while those formed by combination of hydrophobic and H-bonding interactions via UPy and C18A units, respectively, have the highest tensile strength. DMAA and MAAc are attractive H-bond acceptor and donor monomers, respectively, for the preparation of H-bonded hydrogels. As compared to AAm, DMAA has an enhanced H-bond acceptor capability through their carbonyl groups via σ-donation effect of the methyl groups contributing to the H-bonding cooperativity in hydrogels when it is copolymerized with H-donor monomers. Moreover, the use of MAAc instead of AAc as a H-bond donor monomer significantly improves the mechanical performance of H-bonded hydrogels due to the hydrophobic interactions of the α-methyl groups of MAAc units. The primary chain length of H-bonded hydrogels is also effective in determining their mechanical strength due to the proximity effect. Increasing the chain length of the primary chains facilitates formation of H-bonds in the vicinity of preexisting H-bonds contributing H-bond cooperativity leading to high-strength hydrogels. Recently developed H-bonded hydrogels capable of absorbing a large amount of water (~1,700 g g1) and those containing ds-DNA in a clay environment are attractive self-healing soft materials for various applications such as superabsorbent polymers and in gene delivery systems, respectively. Hydrophobic interactions between hydrophobically modified polymers in an aqueous environment lead to the formation of hydrogels containing crystalline domains and/or hydrophobic associations acting as strong and weak physical cross-links, respectively. Such hydrogels have recently been prepared using bulk, solution, and micellar copolymerization of a variety of hydrophilic and hydrophobic monomers via free-radical mechanism. The feed molar ratio of the monomers, alkyl side chain length of the hydrophobes, type of the hydrophilic monomer, water content, and the presence of surfactant micelles are the main experimental parameters providing precise control of the mechanical, viscoelastic, and self-healing properties of the hydrogels. When the hydrophobe content is limited to 2 mol%, SDS-containing self-healing hydrogels obtained from DMAA and C17.3M exhibit the highest stretchability (4,200  400%) due to the associative behavior of DMAA segments. They also exhibit a complete self-healing without any external stimuli at 24 C within 20 min. Replacing nonionic DMAA with the anionic AAc monomer and SDS with the cationic CTAB surfactant produces physical hydrogels of high tensile strength (1.7 MPa) due to the dual hydrophobic and ionic interactions. Moreover, a significant mechanical property improvement in the hydrogels could be achieved when the hydrophobe content is increased above 10 mol% providing formation of crystalline domains in addition to the hydrophobic associations. AAc/C18A comonomer produces semicrystalline hydrogels with the highest melting temperature (48–56 C), degree of crystallinity (10–33%), Young’s modulus (up to 308  16 MPa), and tensile strength (up to 5.1  0.1 MPa). Damaged hydrogels with

How to Design Both Mechanically Strong and Self-Healable Hydrogels?

55

50 mol% C18A after heating-induced healing exhibit a compressive strength of 138  10 MPa, which is around 87% of the virgin ones. Semicrystalline hydrogels can also be made highly stretchability when a small amount of non-crystallizable units are incorporated in the gel network to create mobility. Research directed toward synthesis of self-healing hydrogels provided several important findings not only in the field of self-healing but also in other hydrogel applications. For instance, the presence of surfactants in hydrophobically modified hydrogels significantly changes their viscoelastic and mechanical properties. Surfactant micelles solubilize hydrophobic associations and alkyl crystals and hence facilitate the diffusion of polymer chains, thereby inducing self-healing. They are also able to solubilize semicrystalline hydrogels of high mechanical strength opening up their applications as injectable gels and as smart inks for 3D or 4D printing. Similarly, H-bonded self-healing hydrogels dissolve in aqueous urea solutions, while the injectable solution thus formed turns into a gel when the urea is forced to diffuse out of the solution. The viscoelastic and mechanical properties of H-bonded and hydrophobically modified hydrogels can be tailored by aqueous urea solutions or surfactant micelles, respectively, to fit a variety of needs. Thus, urea- or surfactant-induced processability may provide several future applications of high-strength H-bonded and hydrophobically modified physical hydrogels. Acknowledgment Work was partially supported by the Turkish Academy of Sciences (TUBA). The author would like to thank all collaborators and graduate students for their contributions in the development of hydrophobically modified and H-bonded physical hydrogels.

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Adv Polym Sci (2020) 285: 63–126 https://doi.org/10.1007/12_2020_61 © Springer Nature Switzerland AG 2020 Published online: 14 June 2020

Rheology, Rupture, Reinforcement and Reversibility: Computational Approaches for Dynamic Network Materials Chiara Raffaelli, Anwesha Bose, Cyril H. M. P. Vrusch, Simone Ciarella, Theodoros Davris, Nicholas B. Tito, Alexey V. Lyulin, Wouter G. Ellenbroek, and Cornelis Storm

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2 Background: Topology and Dynamics in Network Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.1 Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.2 Reversible and Exchange Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3 Computational Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.1 Coarse-Grained Strategies for Polymer Networks in Molecular Dynamics . . . . . . . . . 73 3.2 Modelling Reversible Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.3 Modelling Exchange Reactions: Three-Body Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.4 Generation of Multiple Network Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.5 Computational Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4 Structure and Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.1 Spatial Distributions of Reversibly Linked Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.2 Dynamic Bulk Rheology of Reversibly Linked Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.3 Effect of Reversible Cross-Links Near Percolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.4 Stress Relaxation in Vitrimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

C. Raffaelli, A. Bose, C. H. M. P. Vrusch, S. Ciarella, T. Davris, and A. V. Lyulin Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands N. B. Tito, W. G. Ellenbroek, and C. Storm (*) Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands Institute for Complex Molecular Systems, Eindhoven University of Technology, Eindhoven, The Netherlands e-mail: [email protected]

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4.5 Mechanical Reinforcement and the Payne Effect in Nanocomposites . . . . . . . . . . . . . . . 4.6 Fracture of Double Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract The development of high-performance polymeric materials typically involves a trade-off between desirable properties such as processability, recyclability, durability, and strength. Two common strategies in this regard are composites and reversibly cross-linked materials. Making optimal choices in the vast design spaces of these polymeric materials requires a solid understanding of the molecularscale mechanisms that determine the relation between their structure and their mechanical properties. Over the past few years, a wide range of computational techniques has been developed and employed to model these mechanisms and build this understanding. Focusing on approaches rooted in molecular dynamics, we present and discuss these techniques, and demonstrate their use in several physical models of novel polymer-based materials, including nanocomposites, toughened gels, double network elastomers, vitrimers, and reversibly cross-linked semiflexible biopolymers. Keywords Dynamic networks · Mechanical properties · Mechanical reinforcement · Modelling · Nanocomposites · Polymer materials · Simulation

1 Introduction Pretty much every talk on the mechanics of polymer materials will feature, at one point or another, an image of a plate of spaghetti and/or a snake. Two iconic metaphors, representing the two quintessential determinants of the mechanical quality of classical polymer materials: structure and dynamics. Classical polymer texts will emphasize the fact that the long polymer strands become entangled, impeding each other’s ability to explore space much more than ordinary non-extended particles do. As a result, polymer solutions and melts – in addition to the viscous characteristics expected for these ultimately liquid systems – exhibit mechanical properties usually found in solids even in the absence of chemical crosslinking and do so over broad ranges of timescales. These liquidlike traits, possibly enhanced by elevated temperatures, facilitate the structural relaxations that provide malleability and ensure the easy processing of entangled polymer materials: desirable properties in their own right but also beneficial to the recyclability of polymeric materials. For these and many other reasons, regimes of deformability and plasticity are highly sought-after in application. Those same applications, however, generally also require that – once formed into a product – the materials are strong, are tough

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and provide good long-term integrity. To remedy the long-time liquidlike behaviour, and to impart additional resilience, the chains may be permanently linked together with chemical cross-links to form so-called network materials. In the end, the dynamical mechanical response of the fully formed material is determined by a combination of chain length, chain density, cross-linking functionality and density, solvent properties, the mechanical properties and the topology of the individual polymer strands in a complex interplay that continues to surprise and confuse. But, a general challenge remains. The product-scale demands on resilience and stability are, in general, at odds with the requirements on malleability, processibility and recyclability. Improvements in one aspect occur at the detriment of the other; because they rely on the same architectural and dynamic processes, optimization must be accomplished respecting these trade-offs. In recent years, the field of polymer materials has embraced two exciting new avenues towards a reconciliation between these incompatible properties: composites and reversibly linked materials. In composites, multiple materials that may, or may not, be chemically connected to each other occupy the same space. The resulting material properties are far richer than the simple sum of the constituents, and as a result of the cross-talk between the components, the elastic and viscous responses of the composite material become much more independent, to the point of being individually addressable in design. In reversibly linked materials, the cross-linkers themselves become dynamic either through non-covalent links or by reconfigurable covalent connectivity. While the dynamical response of permanently linked materials is determined by the relaxational processes of the polymer chains, reversibly linked materials there possess at least one fully separate relaxation time set by the binding/unbinding/rebinding kinetics of the reversible cross-links. Clearly, neither of these two mechanisms is new. Natural polymer materials, for instance, make abundant use of both a heterogeneous composition and cross-linker properties to tune elastic response. All proteinaceous linkers forge supramolecular bonds, the dynamics of which are dictated by a cohesive energy scale that quantifies the effective potential well responsible for the connection. In biology, such bonds range from rapidly unbinding to effectively permanent, and the various cross-links and their timescales play an important role in the dynamical remodelling of networks and tissues. A prime example is the cytoskeleton, a dynamic composite structure composed of actin filaments, microtubuli and intermediate filaments, which is the internal framework of cells and determines cell shape and mechanical properties. The cytoskeleton remodels continually and adapts its structure, and thereby the shape of the cell, to changes in the environment. This adaptive mechanical character, where relaxations are actively tuned and are largely decoupled from elastic rigidity, where structure is constantly evolving in response to external and intrinsic cues, all the while preserving extraordinary mechanical performance, serves as inspiration for the design of novel polymeric materials. Indeed, in the realm of synthetic polymer materials, it is becoming increasingly clear that there, too, clever uses of composition and reversible linkage unlock exceptional mechanical qualities. In this vastly enhanced design space, optimization will be an even greater challenge than it has been. This is where

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computational modelling comes in: Predictive mechanical models cast light on the mechanisms underpinning the enhanced performance and may give direction or identify promising formulations in the search for further improvements. In this paper, we delve deeper into some exciting recent advances based on the use of reversible linkers and composition in hydrogels and elastomers and review some of essential computational techniques required to model these materials. In the concluding sections, we share some recent and new results that demonstrate the potential of such approaches: at various length scales, from molecular to bulk, simulations allow us to ask and answer some basic questions that relate structure, dynamics and properties in modern polymeric materials. While this overview is obviously non-exhaustive, we nonetheless hope to convince the reader that spaghetti and snakes no longer suffice to capture the exquisite, rich and surprising mechanical performance of the next generation of polymer materials.

2 Background: Topology and Dynamics in Network Materials 2.1 2.1.1

Composite Materials Polymer-Polymer Composites: Homocomposites and Multiple Networks

Composites are ubiquitous, found in nature or synthetically engineered to solve complex functional problems. They are a combination of two or more constituents, working together as a cohesive unit to showcase high-calibre mechanical performance, typically unattainable by a material composed of single constituent. Polymer-based composites including fibreglass, carbon fibre and shape-memory polymer have wide applications in automotive, aerospace, construction and sporting industry for their low cost, strength, flexibility and renewability. The human body contains multiple composites of proteins that are essential for optimal function. Cells, whether plant or animal, are made up of cytoskeleton – a complex network of filaments and tubes. Homocomposites are a subset of composites built from the same chemical unit. Polymer-polymer homocomposites consist of identical polymer networks, covalently bonded or purely entangled to each other. Each network has its unique structural identity, even though they can be chemically identical. Homocomposites are a shining example of camaraderie between chemistry and design ingenuity – leading to hybrid materials showcasing high performance and sustainability. Traditionally elastomers have been toughened by combining a well-chosen glass transition temperature, which sets the temperature range of viscous dissipative mechanisms, and the use of nanofillers (like carbon black and silica). The nanofillers introduce strain-dependent damage mechanisms and increase the stiffness of the material at the same time [1] – more on this in Sects. 2.1.2 and 4.5. However,

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elastomer homocomposites by [2] are remarkable rubbers exhibiting exceptional fracture toughness. Composed of linear and flexible acrylate chains, they combine reversible elasticity and strain-dependent damage with nearly no viscoelastic dissipation. The multinetwork systems have a complex structure owing to the distinct prestretch in every generation of network, a specific feature of the synthesis protocol. Typically in a double-network system, the first network is highly prestretched with tensile (pre)stress. In systems with two or more embedded networks, the (pre)stress is different in each network generation. This unique interplay of local network structure, cross-link density and inbuilt (pre)stress are known to influence the overall mechanical performance of the elastomers [3]. The toughening mechanism is attributed to the sacrificial bonds from the prestretched networks – confirmed by mechanoluminescence experiments [3]. The composites also show noticeable Mullins effect [4, 5], strong localized softening due to scission of covalent bonds followed by a stable necking process, a phenomenon never observed before in elastomers. One of the critical research themes is to uncover the influence of the microscopic architecture on the mechanics of the material. The parameters that define the design of the multinetwork structures is huge, and the exact influence of these parameters on the mechanical response is still poorly understood. Since prestress is tightly linked to network architecture, the use of molecular dynamics simulations to shed light on these relations requires careful construction of the network architectures. In Sect. 3.4, we present a method based on lattice random walks to do this. Then, we focus our efforts on understanding how the presence of covalent cross-links between the two generations of a double-network structure affects the mechanics. We find that such intergenerational cross-links have crucial influence on the stress transfer and fracture of double-network systems. We describe the methods to model the topology of the networks and explore fracture dynamics at the microscopic bond level in Sect. 4.6.

2.1.2

Polymer-Particle Composites: Nanocomposites and Filled Rubbers

A further way to enhance the properties of polymer materials such as elastomers is to blend them with particulate filler material. Even at relatively small filler fractions, the synergy between a polymer matrix and small inclusions may be curiously strong – a fact that has been exploited extensively in the tire industry where carbon black, a material produced by the incomplete combustion of many heavy petroleum derivatives, is incorporated into an elastomer matrix. Such nanocomposites – carbon blackenriched rubbers, with matrices typically composed of synthetic styrene-butadiene copolymers – present drastically improved properties most notably, among which are a greatly improved toughness, wear resistance and stiffness. Specific types of silica fillers (and filler-matrix attachments) can lead also to improved rolling resistance. This rolling resistance is a key determinant factor for the energy efficiency of

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automotive propulsion, and even modest improvements can entail significant impact on global emissions. An important drawback of the use of carbon black in tires is that as the tire wears, these compounds enter the atmosphere and the environment as micro- and nanopollutants. Considering that over the course of its useful lifetime, a typical car tire will shed about 1.5 kg of material and that carbon black may be linked to human health and environmental issues, it is no surprise that the industry is looking for cleaner alternatives; tires may be made less of an environmental burden either by reducing the rolling resistance, leading to less shedding, or by replacing the harmful and pollutant carbon black with less noxious alternatives. In order to effectively screen for sustainable alternatives for carbon black, it is imperative that the basic physics underlying the enhanced performance of nanocomposite rubbers be understood. The essence of this enhanced performance may be summarized by two, potentially related, effects: mechanical reinforcement (or stiffening) and the Payne effect [6, 7]. The mechanical reinforcement due to the addition of nanofiller particles is defined as
 G φf
  1, R¼ G φf ¼ 0

ð1Þ

where φf is the nanofiller volume fraction. The reinforcement R may nominally split up into two contributions: an intrinsic increase in G due to the addition of some amount of generally stiffer filler material and the excess reinforcement – the synergistic stiffening beyond the intrinsic component. Rheological experiments [8] have demonstrated that excess reinforcement is due to interactions, both direct and mediated by the polymer matrix, between the filler nanoparticles. Crucial to the effectiveness of these interactions, even at moderate filler fractions, is the fillerinduced organization of the polymer matrix: filler particles effectively act as nodes in a spatial ‘supranetwork’ in which glassy bridges – regions of polymer matrix vitrified due to filler-induced confinement – link the nanofiller particles together to produce a material with large excess reinforcement [9], a structure whose mechanical rigidity is markedly higher than what could be expected on the basis of the added nanofillers alone. Importantly, the network of glassy bridges is reconfigurable; under the effects of applied loads it may break and reconstitute, differently organized. The second effect, which we will address in more detail in Sect. 4.5, is the so-called Payne effect (see Fig. 1). While nanofilled rubbers typically display hyperelastic (strain-hardening) behaviour (i.e. a mechanical modulus that rises with the applied strain) over the course of a single strain cycle, the effect of repeated cyclic loading is quite the opposite. LAOS (large amplitude oscillatory strain) experiments show a significant loss of rigidity at higher setting in at amplitudes of around 10%. After each cycle, the material response is irreversibly altered with the material exhibiting a lower modulus for all the strains it has experienced before, only rejoining the original (extrapolated) stress-strain curve when the previously experienced maximal strain is exceeded.

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Fig. 1 The Payne effect in MD simulations: As the amplitude of oscillatory shear strain is increased, the shear modulus G0 of a polymer nanocomposite drops steeply around strain amplitudes γ max of around 0.1 (corresponding to a deformation of 10%). Different curves show results for different values of the nanofiller size, expressed in units of σ, the monomer diameter

Reinforcement and the Payne effect are challenging issues in computational soft matter science: Complex interactions between constituent phases at the atomic level ultimately manifest themselves in macroscopic properties, and for this reason a large range of length and timescales must be, in principle, addressed in such simulations. Typically, a combination of modelling techniques is required to meaningfully simulate the bulk-level behaviour of nanocomposites. Raos et al. [10] were among the first who studied the effect of the interactions between stiff colloidal filler particles and polymer networks using large-scale, coarse-grained dissipative particle dynamics (DPD) models. The nonlinear viscoelastic results of these simulations, however, were rather different from the experimentally observed Payne effect. The authors conclude that the origin of the Payne effect is not solely related to the particle-particle interactions. The reasons of the observed discrepancies could also be in the specificity of the soft DPD potentials used in these simulations. At the same time, recent DPD simulations of [11] reproduced nicely the experimental reinforcement in elastomer nanocomposites. Evidence that in elastomer-based nanocomposites the filler nanoparticles play the role of temporal cross-links in a supranetwork was presented by [12, 13]. They investigate the formation of temporal networks and the role of polymer-nanoparticle interactions in coarse-grained molecular dynamics (MD) simulations, with filler particles represented as Lennard-Jones spheres. The authors find that the observed reinforcement is correlated with the minimization of the relative mobility of the filler

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particles with respect to the polymer segments. On even smaller scales, numerous molecular mechanisms of the Payne effect and reinforcement for polymer nanocomposites filled with model (mainly ideal, spherical) nanofillers are studied by [14] and in a series of publications from Liu and Lyulin groups [15–20]. The role of the direct particle-particle interactions and segmental orientation at the particlematrix interface were both investigated. Still, questions remain about the dominant molecular mechanism and about the potential effects of a more realistic shape of the filler particles. Overall, there are now two distinct proposals regarding the molecular origins of the excess reinforcement (the reinforcement in addition to what is induced by the mere presence of rigid nanoparticles): one attributes it exclusively to the aggregation of the nanoparticles, whereas the other ascribes it mainly to the formation of filler-polymer interphases. The aggregation scenario, understandably, features more prominently at high filler fractions, whereas the formation of a mesoscopic network of filler-matrix-filler bridges appears to be more prevalent at lower filler fractions. Currently, despite strenuous effort from both the experimental and the computational scientific community [9, 21–42], there is no consensus on the molecular origin of the Payne effect. What is clear, however, is that filler-filler and filler-matrix interactions at the scale of the fillers are of crucial importance both in the reinforcement and in the Payne effect and that tuning these interactions is a prime candidate for a mechanism by which to rationally design superior nanocomposites. In Sect. 4.2, we present some of our recent findings for the role and effect of fillermatrix interactions in and out of equilibrium.

2.2 2.2.1

Reversible and Exchange Materials Reversible Networks

As remarked in the introduction, most natural materials including the cytoskeleton and the extracellular matrix are held together by non-permanent links. This results in dynamic, transient connectivity that is used to reshape networks and tissues, connecting, releasing and rebinding actin and collagen filaments as they remodel. But also outside of living systems, transient links change mechanical properties in important ways: In [43–45] it is shown that the association and dissociation of crosslinks strongly affect the mechanical behaviour of in vitro actin networks, causing them to be able to shift, purposely, from rubberlike, purely elastic behaviour to viscous flow in transiently bonded networks. Such switchable properties are of clear interest outside of biology, and because of their structural similarities to natural materials in animals and plants, synthetic hydrogels have been the materials of choice to attempt to copy some of the natural behaviours. One particularly important aspect of the mechanical properties of hydrogels that requires improvement in general is their toughness; classical hydrogels are generally brittle materials that fracture abruptly and absorb little mechanical energy before doing so. As with natural materials, physical –

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nonpermanent, reversible – links between the polymer strands in (supramolecular) hydrogels are a promising avenue towards materials that are easier to process and recycle and that are less brittle than permanently connected or purely entangled systems. The mechanism that underpins the improved mechanical performance has been suggested [2] to be related to the fact that physical cross-links are generally weaker than chemical cross-links and permit the materials to dissipate more mechanical energy before ultimately failing due to delocalized dissipation (spreading the typically concentrated mechanical loads at the tip of a propagating crack over larger volumes) and the potential to reform previously dissociated bonds – the same mechanism that gives rise to some of the self-healing qualities of reversible hydrogels. The binding and rebinding of cross-linking agents can change more than just the connectivity of a polymer network; the orientational distribution, too, can adapt as the material remodels. Synthetically mimicking the self-healing mechanism observed in biological tissues is a long-term goal of materials science in general [46–49], holding great promise to improve, enhance or altogether change the mechanical quality of man-made materials. Thus, in systems with dynamical, physical bonds, the mechanical and rheological properties can be controlled to yield materials that are dynamical, anisotropic and responsive to external stimuli, in a manner similar to tissues and cells, the properties of which respond to changes in the environment and to active, internal cues. The classic review [50] on supramolecular polymers describes a number of examples of physical interactions that may be used to synthesize physically linked polymer gels. Arrays of hydrogen bonds (also important in organizing the interactions between proteins) are a powerful way to create very stable and mechanically strong physical gels [50] – the ureidopyrimidinone-based supramolecular polymers are particularly interesting in this respect and show mechanical properties that are extremely temperature dependent: response ranges from viscoelastic at room temperatures to fluid-like at more elevated temperatures [51]. This behaviour is strongly reminiscent of the fluid-solid transitions achievable in reconstituted biopolymer networks. In addition to hydrogen bonding, other interactions may be used to create transient bonds over a broad range of strengths: π  π interactions, hydrophobic interactions and metal-ligand coordination bonds among them [50]. However, a merely transiently cross-linked elastomer has relatively poor mechanical properties, e.g. it flows at long timescales and the toughness is usually low. Recent, more advanced hydrogel and elastomer chemistries demonstrated that a combination of permanent and transient cross-links can dramatically improve the toughness of a material while retaining the capacity to self-heal. This has led to greatly increased interest in ‘dual cross-linked’ materials – both hydrogels and elastomers – over the recent years [47, 52–55]. In those systems, the transient cross-links are hypothesized to act as sacrificial bonds, whose dissociation provides the material with a parallel channel for energy dissipation [56]. As a result, the material can absorb more energy before physically rupturing, leading to enhanced toughness of the material. Permanent bonds imprint the original network structure and permit the network to remain elastic even at large and slow deformations. Interestingly, this behaviour is strongly rate-dependent: materials may display very

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different mechanics depending on the speed or strength of applied deformation. These properties can be controlled by using reversible cross-links whose dynamic properties themselves depend on externally addressable parameters such as pH or temperature; the resulting hybrid networks can be used as tunable stimuli-responsive materials. A beautiful example of this is found in [53], where a hybrid organogel is synthesized that, owing to the addition of transient, supramolecular cross-links to a covalent polymer gel, displays a dramatically increased extensibility. This occurs with remarkably little change to the linear modulus of the material. The effect disappears when the material is deformed at a rate comparable to, or faster than, the typical bond lifetime: At these high deformation rates, the reversible links have no time to adapt to the changing state of strain which causes them to act, effectively, as permanent, irreversible connections. In Sect. 4.2, we will revisit these observations and provide evidence from models to support the scenario. In summary, reversible and hybrid (reversible/permanent) networks have opened the doors to new combinations of mechanical properties that are difficult to achieve in permanently cross-linked or entangled polymer materials. In what follows, we describe some of the computational approaches that permit computational investigations into the origins of these properties and the extent to which their beneficial contributions may be optimized.

2.2.2

Vitrimers

Vitrimers are a revolutionary class of polymer, combining the malleability and recyclability of thermoplastics with the insolubility and creep resistance of thermosets [57, 58]. Their unique connectivity-preserving bond exchange mechanism [59, 60] with well-controlled exchange rate makes their cross-links dynamic. At low exchange rates, they operate like thermosets, while at high rates, they are malleable like thermoplastics. These activable bond swaps allow vitrimers to release internal stresses without losing shape, unlike cross-linked elastomers or gels. This unique bond swapping provides also a welding strategy [61] or grants them responsiveness to light, pH, voltage, metal ions, redox chemicals and mechanical stimuli [62–64]. Interestingly, vitrimer topology plays a crucial role in determining their dynamics, granting them additional tunability while designing smart materials. The reason is that loops affect equilibrium elastic properties of any cross-linked network [65], but since topology in vitrimers is dynamic, dramatic differences appear in stress relaxation from different (although mechanically similar) molecular topologies. In a past work, we showed that novel vitrimers can be designed explicitly considering defects as a means to control separately mechanical and dynamical properties [66]. Strongly connected to both topology and dynamics is also their self-healing ability. The ideal self-healing material needs a fully controllable long-time solid-like mechanical behaviour, the ability to heal without any form of external intervention, and lastly the healing process has to be effective to the point that the location of the damage can no longer be identified, possibly even do so repeatedly for multiple

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localized damages. In vitrimers, covalent bond swapping across the cut elegantly takes care of healing any damage that the material sustains, so effectively that swaps can also act as a welding strategy to naturally merge two equilibrated surfaces into a single piece of material. If the vitrimer is engineered such that the stress is relaxed much later than the swap time [67], the material can effectively heal autonomously while still being a solid. Lastly, vitrimers behave as super-strong glass formers [57] exhibiting a very slow growth of the viscosity approaching their glass transition. This grants them vast (re)processing power because they keep flowing as slow viscous liquids in a wide temperature range. Interestingly we have been able to model their fragility [68] and unravel that the topology becomes important also close to the glass transition.

3 Computational Approaches 3.1

Coarse-Grained Strategies for Polymer Networks in Molecular Dynamics

Molecular simulation presents the opportunity to systematically study the static and dynamic properties of a polymer network. Detailed molecular properties may be harvested from the simulation trajectories, and parameters systematically varied. There are two general approaches to polymer simulations: ‘atomistic’ and ‘coarse-grained’ [69]. In an atomistic approach, atoms or small groups of atoms are represented explicitly, and interactions between the entities are defined by empirical force fields. The advantage of this approach is that specific polymeric chemistries can be studied. However, given the level of detail present in the model, it becomes computationally challenging to study large systems or long timescales. For polymer networks where overall structural relaxation times grow large, this limitation of the atomistic approach can become prohibitive. In a coarse-grained approach [69, 70], simplified models of the polymers are used in order to reduce computational complexity while still retaining essential physical interactions between the monomers. The approach is useful for exploring more general features of polymer behaviour in a network, without specificity towards particular chemistries or monomer functional groups. For example, the bead-spring model of polymers represents monomers as spheres and bonds as harmonic potentials between the monomers. The monomers interact via a Lennard-Jones intermolecular potential. Three-body angle potentials and four-body dihedral potentials can be added in order to study semiflexible polymers. The coarse-grained approach allows one to study larger systems, and longer timescales, compared to the atomistic approach. In practice, a molecular dynamics (MD) simulation amounts to solving Newton’s ! equation of motion for the trajectories r ðt Þ of N (generally, a large number) of

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(possibly coarse-grained) particles evolving under the influence of forces acting on them ! ! € mi r i ðt Þ ¼ F tot,i ðt Þ:

ð2Þ

! F tot,i

is the total force acting on particle i. In general, the total force comprises a conservative part, a dissipative/frictional part and a random part accounting for the interactions with non-resolved molecular environment ! F tot,i ðt Þ

!

!

!

¼ F c,i ðt Þ þ Ff ,i ðt Þ þ F r,i ðt Þ:

ð3Þ

In Langevin dynamics, the frictional force is computed from the velocities !

F

f ,i ðt Þ

!_ ¼ ζ i r i ðt Þ,

ð4Þ

with ζ i the friction coefficient of particle i. In the widely assumed case of Stokesian hydrodynamic friction and spherical particles, ζ i ¼ 6πηRi with η the solvent viscosity and R the radius of the particle. The random force consists ofwhite noise with zero mean  Di! E  !  ! pffiffiffiffiffiffiffiffiffiffiffiffiffi F r,i ðt Þ ¼ 0 and δ-correlations F r,i ðt Þ F r,j ðt 0 Þ ¼ 2kB Tζ δðt  t 0 Þδμν δij . μ

ν

The conservative force may be derived from a compound potential Vtot ! F c,i

¼

∂ ! U tot ∂ri

n

!

r

oN

j

j¼1

:

ð5Þ

The potential Utot, generally called the force field, encodes for all the interparticle interactions and external fields that act upon the particles in the simulation and is composed of single-body terms (representing the external forces), two-body terms known as pair potentials and many-body terms involving the positions of more than two particles including the particle on which the forces are acting. n U tot

!

r

oN

j

j¼1

¼

N X

N   X   ! ! ! U ð1Þ r i þ U ð2Þ r i , r j

i¼1

þ

i, j¼1 N X



! ! ! U ð3Þ r i , r j , r k



ð6Þ þ 

i, j, k¼1

In the MD simulation of polymers, it is important to distinguish between conservative forces that arise as a result (quasi-)permanent bonds between particles and those that arise as a result of physical phenomena that do not require a bond to be present. For the first class of interactions – the so-called bonded interactions – care must be taken to only consider them for assemblies of particles (pairs or higher

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multiples) that are actually bonded; the MD configuration should therefore contain also a table of the particles between which such bonds exist. General physical interactions like electrostatic (Coulomb) forces, excluded volume effects or hydrodynamic interactions feature regardless of the existence of an explicit bond between particles and therefore are present between all pairs of particles in the simulation box; the potentials that represent them in MD are termed non-bonded. While the random and frictional parts of the total force Ftot, i(t) are fairly generic, the conservative part is where the specifics of a simulation are important. In this manuscript, we encounter several widely used examples of both bonded and non-bonded interactions. All of the MD simulations in this paper will concern so-called bead-spring models, which represent the polymer by a chain of spherical beads connected (bonded) by springs. These beads each experience the generic frictional and random forces detailed above. In one often used approach, the springs between the beads are modelled as finitely extensible nonlinear elastic (for short, FENE) units whose (two-body) potential is given by 

! ! ð2Þ U FENE r i , r j !






r ij  r 0 1 2 ¼  K sp Δr max log 1  , Δr max 2

ð7Þ

!

where r ij ¼ j r i  r j j. The FENE model describes the elastic response of a single polymer segment whose rest length is r0 and which is capable of stretching at most a length Δrmax away from this rest length. For small extensions rij  Δrmax, the FENE model reduces to a simple harmonic spring. For extensionally stiff polymer segments, this approximation is frequently used to reduce computing time.  
2 1 ! ! ð2Þ U HARM r i , r j ¼ K sp r ij  r 0 2

ð8Þ

The non-bonded interactions in polymer-MD models must account for the generic and specific physical interactions that feature between all monomers. In uncharged polymers, the two principal components of such interactions are strong short-range (Pauli) repulsion (a steric interaction prohibiting physical overlap) and weak, long-ranged van der Waals attractions. The two are widely captured in the Lennard-Jones pair potential 

ð2Þ ! ! U LJ r i , r j



"

6 # 12 σ σ  : ¼ 4ε r ij r ij

ð9Þ

The LJ potential has a global minimum at rij ¼ rmin ¼ 21/6σ, where the potential ð2Þ attains its minimal energy U LJ ¼ ε which is why ε is sometimes referred to as the bond energy parameter. Steric repulsion is encoded in the steep rise of the potential for distances shorter than rmin, and van der Waals attraction is reflected in the slow rise of the potential for distances greater than rmin. Typically, the Lennard-Jones potential is cut off at some radius rcut > rmin to save on computational time. In many

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cases, the van der Waals attraction may be neglected altogether, and a smooth potential capable of effecting short-range steric repulsion is required. For such cases, the LJ potential is frequently truncated at rij ¼ rmin and shifted upwards by an amount ε; this results in a potential with strong short-range repulsion that smoothly connects to a non-interacting long-range regime known as the WeeksChandler-Andersen (WCA) potential 0

" # 6   B 4ε σ  σ þε ! ! ð2Þ r ij r ij U WCA r i , r j ¼ B @ 0

r ij  21=6 σ

:

ð10Þ

r ij > 21=6 σ

The simulational setup of using FENE bonds combined with WCA non-bonded interactions is the seminal Kremer-Grest model [71], (variants of) which we use throughout this paper. To capture also the effects of the backbone rigidity of chains, we will also employ angle bending terms in the bonded part of the potential. Such terms are three-body interactions, which constrain the angle θijk between subsequent ! ! segments, i.e. between the segment connecting r i and r i , and the next polymer ! ! segment along the chain connecting r j and r k , to remain close to some equilibrium value θ0. 

ð3Þ ! ! ! r i, r j, r k



UB


2 ¼ K b θijk  θ0 :

ð11Þ

Finite values for the bending modulus Kb yield polymers with a persistence length given by ℓp ¼

4K b R , kB T

ð12Þ

with R the radius of the beads.

3.2 3.2.1

Modelling Reversible Links Statistical Thermodynamics and Chemical Equilibria of Reversible Cross-Links

Reversible cross-links in a polymer network, whether they are freely diffusing additives in a solvent or ‘dangling ends’ embedded within the polymer topology itself, have a well-defined though complicated free energy of binding with their partners. If the reversible cross-links and their partners are placed as monomers in free solution, then their binding free energy is related to the equilibrium constant, defined as

Rheology, Rupture, Reinforcement and Reversibility: Computational Approaches. . .

K ∘eq ¼

½CP : ½P½C 

77

ð13Þ

Here, [CP] is the molar concentration (e.g. mol/L) of cross-links bound to partners, while [C] and [P] are the molar concentrations of unbound cross-links and partners, respectively. If we suppose that the number (though not necessarily the concentration) of reversible cross-links in solution far exceeds the number of partner monomers, then we can calculate the Gibbs free energy of binding between a crosslink and a partner by ΔG1 ¼  ln K ∘eq ½C ∘ : RT

ð14Þ

The quantity [C]∘ is now the fixed molar concentration of reversible cross-links in the solution. The standard Gibbs free energy of binding for the reversible crosslinker is obtained by setting [C] ¼ 1 mol/L. When the reversible cross-links and/or partners are embedded into a polymer network, the Gibbs free energy of binding (or, equivalently, the equilibrium constant) is complicated by additional factors. These include, for example, changes in rotational freedom of the species upon forming a bond and the configurational entropy of the polymer strands themselves. We now outline a simple theory for accounting for these two crucial factors in the equilibrium constant for reversible cross-link binding. To construct this theory, we consider the situation of a permanently cross-linked polymer gel with freely diffusing reversible cross-linking monomers in the solvent phase. The polymer network is composed of polymer strands permanently crosslinked into a given topology. The network is immersed in a solvent, and the reversible cross-links may thereby ‘swim’ through the network as a freely diffusing species. We allow a reversible cross-link to form up to two bonds, with any two segments within the network. The partition function for the network when no reversible cross-links are bound is Q∘. This contains the sum over all possible conformations of the polymer strands, as well – in principle – sums over all the internal degrees of freedom of each monomer (i.e. vibrational and rotational states). Let us fix our attention on a single segment i in the network. The segment has a rotational partition function qirot, representing the possible directional orientations for the reversible cross-link ‘binding site’ on the segment. We refer to this binding site as a sticker. The rotational degree of freedom for the sticker can be factored out of the partition function for the whole network, so that we have Q∘ ! Q∘ qirot

ð15Þ

where Q∘ is now re-defined as the partition function for the whole network with the rotational contribution from segment i factored out.

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Suppose now that an unbound reversible cross-link forms one of its two bonds with the sticker on segment i. First, the system thermodynamically gains the energy associated with the bond formation. Let this be defined as ΔHbond. Second, the reversible cross-link must pay the price of the chemical potential μ for localizing next to segment i in order to form the bond. The chemical potential for the reversible cross-link in the solvent phase has three contributions: μ μ μ μ ¼ id þ rot þ ex : RT RT RT RT

ð16Þ

These are, respectively, the ‘ideal’, ‘rotational’ and ‘excess’ contributions. The ideal contribution is related to the concentration [C]∘ of the reversible cross-links in the gel by μid ¼ ln ð½C ∘ N A vÞ RT

ð17Þ

where NA is Avogadro’s number and v is the ‘localization volume’ – the volume of space around the segment i within which the reversible cross-link must be in order to form a bond. The rotational chemical potential is the rotational entropy of the linker in solution. Lastly, the excess chemical potential represents all other factors not explicitly captured in the former two terms; this is typically small when the reversible cross-link concentration in the solvent is low. With this, the partition function for the polymer network with segment i bound to a reversible cross-link is Qb,1 ¼ Q∘ qirot eμ=RT eΔH bond =RT

ð18Þ

¼ Q∘ ½C ∘ N A vqirot eΔH bond =RT eμrot =RT eμex =RT

ð19Þ

Next, we consider how the partition function changes when the reversible crosslink forms a bond with a second segment j in the network. Here we restrict our attention to the case where this new segment is on a different polymer strand in the network. As before, we can factor out the rotational degree of freedom for segment j from Q∘ for the whole network. In addition, we also now factor out the configurational partition functions Q∘poly,A and Q∘poly,B for the two polymer strands that segments i and j are a part of. This factorization step represents an approximation in which the configurational partition function of each polymer in the network is assumed to be independent from all the others. Turning back to Eq. (19) and implementing these factorizations yield

Rheology, Rupture, Reinforcement and Reversibility: Computational Approaches. . . j Qb,1 ¼ Q∘ ½C∘ N A vqirot qrot Q∘poly,A Q∘poly,B

eΔH bond =RT eμrot =RT eμex =RT

79

ð20Þ

where Q∘ has again been re-defined to be the partition function of the rest of the network. When the reversible cross-link forms its second bond with segment j, three changes occur. • The reversible cross-link connects polymers A and B to form a ‘loop’, wherein Q∘poly,A Q∘poly,B ! Qloop,AB :

ð21Þ

This entails a significant entropy penalty, even when polymer strands A and B are already bound by one or more permanent cross-links. This is introduced at length in [72] and discussed in the context of simulation results in Sects. 3.2.2 and 4.1. • The two segments i and j lose their independence of rotation, so that j qirot qrot ! qijrot

ð22Þ

is now the restricted rotational partition function for segments i and j given they are both attached to the reversible cross-link. • The system gains an additional bond energy contribution ΔHbond. Note that the reversible cross-link does not need to pay any additional chemical potential cost to form this second bond. The entropy penalty for the network to localize segment j adjacent to the reversible cross-link is captured in the ‘loop’ contribution Qloop, AB. With these changes, the partition function for the polymer network with the reversible cross-link now bound to segments i and j is Qb,2 ¼ Q∘ ½C∘ N A vqijrot Qloop,AB  e2ΔH bond =RT eμrot =RT eμex =RT

ð23Þ

Relative to the original partition function for the network when the reversible cross-link is unbound j Qub ¼ Q∘ qirot qrot Q∘poly,A Q∘poly,B ,

this reads

ð24Þ

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ij

Qloop,AB Qb,2 qrot ∘ ¼ ½C  N A v i j Qub Q∘poly,A Q∘poly,B qrot qrot

ð25Þ

e2ΔH bond =RT eμrot =RT eμex =RT : The term

qijrot j qirot qrot



eΔGrot =RT

ð26Þ

represents the overall loss in rotational free energy of the reversible cross-link and segments i/j when the link forms. Similarly, the term

Qloop,AB Q∘poly,A Q∘poly,B



eΔGpoly =RT

ð27Þ

captures the loss in configurational entropy of the network due to link formation. These definitions allow us to write the overall free energy change for the reversible link formation as

Qb,2 ΔGlink ¼  ln RT Qub 2ΔH bond ΔGpoly ΔGrot þ þ RT RT RT   ∘  ln ½C  N A veμex =RT eμrot =RT

¼

ð28Þ

The free energy of link formation is readily expressed in terms of equilibrium constants. In free solution, the experimental equilibrium constant K ∘eq for a reversible cross-link forming one bond with a partner is K ∘eq N A veμrot =RT eΔH bond =RT

ð29Þ

Next, using the same form as Eq. (14), the effective equilibrium constant for formation of a reversible link in the polymer network is K eq,eff

eΔGlink =RT : ½C ∘

ð30Þ

Substituting the definition for K ∘eq into the equation for ΔGlink found above yields

Rheology, Rupture, Reinforcement and Reversibility: Computational Approaches. . .

K eq,eff ¼

 2 K ∘eq NAv

eΔGpoly =RT eðΔGrot þμrot Þ=RT eμex =RT

81

ð31Þ

The effective equilibrium constant for forming a reversible link in the network therefore depends on the square of the free-solution equilibrium constant, along with additional factors representing the more complicated changes happening to the polymer network and the segments involved in the link. In general, the terms ΔGpoly and ΔGrot are positive and therefore unfavourable, i.e. forming a reversible link in the network entails loss of configurational entropy to the two polymer chains involved in the bond, as well as loss in the rotational entropy of the participating segments. These terms can be on the order of several units of RT [72], leading the free energy of link formation ΔGlink to often be significantly less favourable than the intrinsic bond formation enthalpy ΔHbond in free solution. If the loss in rotational entropy of the reversible cross-link is approximately the same as the loss in rotational entropy of the centre of mass of segments i and j together, then ΔGrot + μrot 0. In a dilute regime where μex 0, then  K eq,eff

K ∘eq

2

NAv

eΔGpoly =RT :

ð32Þ

This states that the effective equilibrium constant for forming a reversible link is heavily dependent on the entropy cost ΔGpoly for constraining segments i and j in the network to be connected. The polymer configurational free energy term ΔGpoly reflects the cost for forming a loop in the network, wherein a freely diffusing reversible cross-link connects two polymer chains together at two given points along their contour lengths. If the connection is formed near a permanent cross-link, or existing reversible links, then the entropy cost for forming the loop is small. On the other hand, forming a connection between two chains far from existing cross-links is entropically costly [72]. The net effect is that reversible cross-links are entropically biased to bind near existing permanent or reversible cross-links in the network. If the reversible bond enthalpy is small and few reversible cross-links are bound at equilibrium, then these links will tend to be localized near the permanent cross-links. On the other hand, if the binding enthalpy is large, then clusters of bound reversible cross-links can nucleate at other points throughout the network.

3.2.2

Stickers and Valence-Limited Bonding in Molecular Simulation

In the previous section, reversible cross-links formed attachments to polymer segments in a network by interactions between stickers. Stickers are a convenient theoretical concept for representing the instantaneous orientation of the binding

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Fig. 2 Snapshot of a molecular dynamics simulation of two polymers (blue beads, red beads) each of 100 segments, permanently cross-linked at their midsection (brown bead). Reversible cross-link stickers are shown in orange, and reversible cross-linking monomers are shown in purple, with green stickers. (Images generated with OVITO [73]), reproduced from [72])

site(s) on a reversible cross-link or a polymer segment. They are also practical for implementing directional interactions in coarse-grained molecular simulation. Stickers are readily implemented in molecular dynamics as beads attached to their host reversible cross-link or polymer segment. An example of an implementation is shown in Fig. 2. The molecular dynamics model consists of two polymer chains, each of 100 segments, connected together at their midsection (segment 50) by a permanent cross-link bead. The polymer segments are connected together by harmonic bonds. Non-bonded monomers interact via a repulsive inverse power law potential U(2)(r) / r12 (with r the intermonomer distance). Each monomer has attached to it a sticker, shown in yellow. The simulation box also contains reversible cross-linkers. These each consist of a single bead, with two stickers attached and held at an angle of π relative to each other by a strong three-body angle potential. Stickers on a reversible cross-link interact with stickers on the polymers via an attractive Gaussian potential, via a tunable binding strength Ebind, eff. Bonds between reversible cross-links and the polymer segments are reversible and dynamic during the course of the simulation, while the geometry of the bonding sites and their host beads ensures that the interactions are valence-limited (i.e. only one reversible cross-link may bind to one polymer segment at a given time). Even in this simple model, the ΔGpoly contribution to the reversible cross-link formation free energy can be observed. Let us consider the probability that a reversible link forms at position j along the two polymers in Fig. 2. In order to restrict our attention only to intermolecular reversible cross-link binding, i.e. to prevent binding between segments on the same chain, the model is defined to further distinguish between stickers on the red and blue polymer. The two stickers on a given reversible linker may also be distinct types, so that one can bind only to stickers on the red polymer, while the other only to those on the blue polymer. In Fig. 3, we record the simulation-average probability that segment j (from 1 to 100) is bound to a doubly bound reversible cross-link, for six different choices of reversible cross-link sticker binding strength Ebind, eff. The simulation results reflect the entropy-governed binding discussed at the end of Sect. 3.2.1. At low and intermediate binding strength, there is very clear preference for binding near the permanent cross-link, at j ¼ 50. The reversible cross-links form a

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Fig. 3 Simulation-averaged probability that a doubly bound reversible cross-link is attached to monomer n. Values for βEbind, eff for each dataset are given in figure legends. Reversible cross-link density in the simulation box is 1.25  104 particles=D 3 . Distributions are normalized so that a value of unity at a given monomer index n means that a doubly bound reversible cross-link is always bound to that monomer throughout the duration of the simulation, while a value of 0 means that there is never a reversible cross-link bound to that monomer. Average number of doubly bound reversible cross-links and their standard deviation in panel (a) are 0.16  0.41 (blue), 0.43  0.69 (green) and 1.8  1.6 (red). In panel (b), these are 7.8  3.6 (purple), 25  5.0 (grey) and 43  3.9 (orange). Reproduced from [72]

‘zipper’ domain around the permanent cross-link, resembling what is observed in more detailed molecular simulation studies [74]. The permanent cross-link is acting like a nucleation site for the zipper domain. At larger binding strength, the reversible linkers nucleate bound domains more pervasively between the two polymers, and the overall number of bound linkers is larger.

3.2.3

Using Monte Carlo Moves for Forming and Breaking Reversible Bonds

In the case of a single polymer that is intermittently and transiently cross-linked to others, an efficient way to encode the transient dynamics is to use stochastic traps that are switched on and off on the fly during an MD run. Later on, in Sect. 4.2, we

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will demonstrate this technique for an effective medium computational rheology simulation. Single semiflexible chains are simulated in the LAMMPS Molecular Dynamics package [75], using the Kremer-Grest bead-spring model [71] with linearized bond elasticity. This models a polymer as a sequence of N spherical beads, with diameter d, connected by harmonic springs. The bonded potential energy associated with stretching one such spring away from its rest length r0 is given by Eq. (8), and chain stiffness is introduced by a three-point angle potential ð3Þ

U B ðθ Þ ¼ K b θ 2 ,

ð33Þ

where π  θ is the angle formed by the two bond vectors between three consecutive beads and Kb is the bending stiffness, which is related to the persistence length through ‘p ¼ (2Kbd )/kBT. In LAMMPS, the viscosity (in the NVT ensemble) is effectively set by fixing the single-bead friction coefficient γ ¼ 3πηd. Eliminating the viscosity η from this equation, we find that the transverse friction per unit length is given, in LAMMPS parameters, by ζ¼

4 γ: 3d ln ð0:6N Þ

ð34Þ

In their simplest form, reversible bonds may be represented by transient potential wells, which we turn on stochastically and from which the temporarily trapped bead dissociates through its fluctuations. Let us first discuss the binding kinetics. Upon starting the simulation (or directly after the last dissociation), a rebinding timer is reset. We then draw a rebinding time τR from an exponential rebinding time distribution with mean hτRi: PðτR Þ ¼

1 eτR =hτR i : hτ R i

ð35Þ

After this time has elapsed (at a total time we shall call t1), a new reversible bond is formed. We implement this bond by switching on a harmonic potential UREV, centred on the instantaneous position r(t1) of the bead concerned: 8   2 rc,

ð36Þ

where r(t) ¼ j r(t)  r(t1)j. Even though it does not act on all particles, this pinning potential may still be thought of as an external field hence the classification as a U(1)type potential. The energy u0 sets the overall strength of the bond. The length scale rc is the dissociation length of the reversible bond: the first time the transiently trapped bead fluctuates to a position r(t) > rc, the link dissociates and the potential UREV is switched off. Figure 11b sketches the situation: the flat potential landscape beyond rc

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represents the fact that the putative other polymer in the network, to which the chain was temporarily linked, will likely move away after dissociation. Different physical or chemical reversible bonds may be represented by different values of u0 and rc. Once dissociation has occurred, the rebinding timer is reset to zero and – as described above – the bead fluctuates freely as the clock counts down to the next transient binding event. In molecular dynamics simulations where the entire network is simulated, rather than only a single chain embedded in the effective medium, it is more efficient to employ a different, explicit Monte Carlo strategy for the reversible links. A valuable approach for this purpose has been developed for reversibly binding telechelic polymers in [76]. We now present their original formulation while also modifying it so that it obeys detailed balance (i.e. the binding and unbinding rates are chosen such that the populations of bound and unbound linkers match the free energy difference between bound and unbound states). Monte Carlo moves that bind and unbind reversible cross-links are carried out every NMC time steps in the MD simulation, which is at those points temporarily paused to rearrange the transient connections. This time interval is set to be N MC ¼

τLJ : δt

ð37Þ

The quantity τLJ is the characteristic Lennard-Jones timescale given by τLJ

rffiffiffiffi m , ¼σ ε

ð38Þ

where m is the mass of the binder (in units of M) and ε is the LJ bond energy parameter (in units of E). On an MC step, bind/unbind moves are attempted on a fraction ξ of the total number of reversible cross-link stickers in the system. Tuning ξ allows for control over the rate of reversible cross-link bond exchange, without affecting their equilibrium binding free energy. Choosing a smaller value of ξ leads to a slower rate of bond swapping. If a sticker chosen on the MC sweep is currently unbound, then a ‘bind’ move is attempted. This consists of the following steps: • Determine the number J of available binding partners within a radius of r < r0, where r0 is the bond length parameter in VFENE(r) in Eq. (7). • Choose one of the available binding partners, j, at random. • Attempt to form a bond with success probability Pbind(r( j), J), where r( j) is the distance to partner j. On the other hand, if the chosen sticker is currently bound, then an ‘unbind’ move is attempted. This consists of attempting to break the bond with a success probability of Punbind(r( j), J ).

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In order for the success probabilities Punbind(r( j), J) and Pbind(r( j), J ) to obey detailed balance, they must satisfy the standard equality: pðubÞπ ðub ! jÞPbind ðr ð jÞ, J Þ

ð39Þ

¼ pðb, jÞπ ð j ! ubÞPunbind ðr ð jÞ, J Þ

Here, π(ub ! j) is the probability for attempting to bind to partner j (out of the total J available binding sites for the sticker), and π( j ! ub) is the probability for attempting the unbind move. The quantities p(ub) and p(b, j) are the canonical ensemble probabilities for the system being in the microstate where, respectively, the sticker is unbound and the sticker is bound to partner j – both assuming that all particle positions including the sticker and partner j are at their current fixed positions in the simulation. These canonical probabilities, expressed as a ratio, are related to the difference in total energy ΔE(r( j)) between the two microstates by pðb, jÞ ¼ eβðEb ðrð pðubÞ

jÞÞE ub Þ

eβΔEðrð

jÞÞ

,

ð40Þ

where Eb(r( j)) is the total energy of the system when the sticker is bound to partner j and Eub is that for when the sticker is unbound. When there are J possible binding sites for the sticker, then π(ub ! j) ¼ 1/J. On the other hand, the unbinding attempt probability is always π( j ! ub) ¼ 1. This leads the detailed balance equation to read Pbind ðr ð jÞ, J Þ ¼ JeβΔEðrð Punbind ðr ð jÞ, J Þ

jÞÞ

,

ð41Þ

resulting in h i Pbind ðr ð jÞ, J Þ ¼ min 1, JeβΔEðrð jÞÞ  eβΔEðrð jÞÞ : Punbind ðr ð jÞ, J Þ ¼ min 1, J

ð42Þ

In the unbinding expression, J represents all of the possible binding sites for the sticker including the one it is currently bound to.

3.3

Modelling Exchange Reactions: Three-Body Potentials

We have seen in the previous sections that stickers or pairwise potentials are optimal for simulating monomers interacting within polymeric structures. However, exchange reactions are intrinsically more complex involving a local topological

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rearrangement; thus, they cannot be captured by any standard pairwise interaction. A simple solution for modelling bond swaps is to embed Monte Carlo hops into hybrid molecular dynamics or Monte Carlo (MD,MC) simulations [77–80], but this breaks the continuous time of MD, and it requires fine tweaking in order to follow the real dynamics of the system. We propose instead a fully MD method based on the implementation of a three-body potential [81] that already has been shown to provide meaningful results in the context of vitrimers [66, 67, 82] as well as a trick to speed up the equilibration of strong network formers [83]. This additional three-body potential is built upon the specific pairwise interaction of the system and enriches it with a mechanism to rearrange bonds formed by this pairwise attraction. At the same time, it also provides single bond per site condition, preventing the clusterization of the whole system around a highly connected region. To show how the three-body mechanism works, we will start picking an optimal pairwise interaction in the form of a generalized Lennard-Jones: ð2Þ
 U GLJ r ij

!

"

n # 2n σ σ ¼ 4ε  r ij r ij

r < r cut ,

ð43Þ

!

where as usual r ij ¼ j r i  r j j and rcut is some cut-off distance. Its parameters have to mimic the physics of the system, so if the bonds are covalent, we will pick the bond energy ε kBT and n 6 in order the make short-range bonds with an equilibrium distance of rmin ¼ 21/nσ. The choice of a large n is particularly relevant in order to achieve computational efficiency: since the main cost associated with the evaluation of the three-body potential comes from the number of interacting triplets to account, it is desirable to reduce it by selecting the smallest cut-off rc, consistent with the speed at which the interaction vanishes. After the pairwise interaction is set up, the three-body term quantifies how much the force between monomer i and j is affected by the presence of an additional monomer k within range of interaction. The effect of this interacting triplet is captured by the following three-body exchange (E3) potential   2Þ
 2Þ ð3Þ ! ! ! b ðE2 b ðE2 U E3 r i , r j , r k ; λ ¼ λε U r ij  U ðr ik Þ,

ð44Þ

which is the product of two two-body exchange potentials related to the generalized Lennard-Jones potential as 2Þ
 b ðE2 U r ij ¼

1

ð2Þ
 ð1=εÞU GLJ r ij

r  r min r > r min :

ð45Þ

In Eq. (44) we introduced the three-body energy parameter λ that directly controls the swap rate by tuning the energy required for a swap event to happen, thus mimicking the process that controls swap, e.g. catalyst concentration. Its role is made clear in the following example where Eq. (44) is rewritten for a monomer a at

88 ! ra

C. Raffaelli et al. !

!

bonded to monomer b at r b , while monomer c at r c approaches the interaction range: ð3Þ b ðE22Þ ðr ac Þ U abc ¼ λε U ð2Þ

¼ λU GLJ ðr ac Þ

ð46Þ ð47Þ

Notice that in the above, we apply Eq. (45) and assume that rab < rmin and that rmin < rac < rcut. From this we conclude that (1) if λ ¼ 1, then the three-body term in Eq. (47) exactly shields the attraction between a and c, without influencing the ab bond. This allows monomer c to follow its path and eventually to become the bonding partner of a, if thermal fluctuations push it closer to a than b, and that (2) if instead λ > 1, the repulsive contribution from Eq. (47) would trump the ac attraction, making it harder for c to get closer to a and ‘steal’ the bond from b. This situation (λ > 1) effectively defines a swap energy barrier ΔEswap ¼ ε(λ  1) that grows linearly with λ. Lastly (3), if λ < 1, then Eq. (47) would not be enough to compensate the ac attraction, and the system will form both ab and ac promoting aggregation of all monomers, instead of swapping out one binary bond for another. Equation (47) is applicable even if the c monomer comes within the range of both a and b if λ 1; the more partners participate in the multiple-bond intermediate, the lower the activation barrier. So, we showed in this section that there is a smooth way to introduce swaps in MD simulations and that it is possible to tune the swap rate through the energy barrier ΔEswap. These swaps closely mimic the exchange chemistry of vitrimers, since the lowest-barrier pathway for the exchange occurs via a triply connected intermediate. By tuning the various energetic parameters in the potentials, this becomes effectively the only way for exchange to happen. In the results section, we demonstrate how the material properties, and the stress relaxation in particular, depend on this swap rate.

3.4

Generation of Multiple Network Structures

A crucial obstacle in any computational study of polymeric materials is generating initial input structures which faithfully represent the structural complexities of the polymer architecture. This is already the case in melts, where the challenge is to speed up equilibration so that chain conformations are representative of the intended ensemble. In covalently cross-linked networks, one additionally needs to start from a network topology that is representative of the materials that result from the experimental synthesis procedure. Since the topology is fixed during the simulation, except for possible bond breaking events, no amount of equilibration time can fix nonrepresentative topologies. We tackle this issue using a method based on random walkers on a lattice that mimic the actual free radical polymerization reaction process of acrylate polymers

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89

cross-linked using diacrylates [2]. The method is straightforward for a single network, gives precise control over the cross-link density and can be adapted for multigeneration networks using an iterative procedure that we detail below. The result of the network generation procedure is a coarse-grained bead-spring network model for elastomers, with a controllable number of generations, and a well-defined density of cross-links within each generation, as well as between generations. The coarsegraining scale is set by the rest length b of the springs, which typically will be chosen to be the Kuhn length of the polymer. By using random walkers as the basis, the method aims to provide physically sound statistical network properties, such as bridge lengths and entanglements.

3.4.1

Modified Random Walk Networks

Within each generation, the network preparation method can be visualized as a cubic lattice with lattice constant b. A fraction p of the sites is marked as cross-linking sites. The method to generate polymer networks amounts to modified self-avoiding random walk on this lattice that can be interpreted as a free radical polymerization path. Normal sites can be visited exactly once by a random walker, as in a standard self-avoiding walk. Cross-linking sites can be visited twice, mimicking the fact that they contain two polymerizable moieties. In essence, we have made a lattice version of the chain generation method of [84] and have expanded it to include the possibility of generating cross-links. We will refer to this procedure as our modified selfavoiding random walk (m-SARW). Note that p ¼ 0 represents the case in which there are no cross-links and the process is reduced to a standard SARW [85]. The m-SARW algorithm is illustrated in Fig. 4a and is composed of the following steps, largely following [84].

(a)

(b)

Fig. 4 (a) Two generations of polymer networks are initialized on lattice using the modified selfavoiding random walks algorithm. The segments of the second network (in orange) are coiled around the stretched chains of the first network (in green), with cross-link sites (in red) in and between networks. (b) Equilibrated samples double-network samples, prepared for a uniaxial fracture test

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Initiation Multiple walkers are randomly initialized within the periodic box. They may be given a designated maximum length or be deemed free to grow as long as they can. Propagation Each walker takes a step to a randomly chosen neighbouring site that is still available to be visited, extending the polymer with one bead, by placing a spring of rest length b on the lattice link. We will refine this step in the next subsection when we discuss how to use the method to generate swollen networks. Site Marking If the newly visited site is a cross-linking site that has not been visited before, it will be marked to be available 1 further time. If it is a normal site, or a cross-linking site that was visited once before already, it will be marked unavailable. Termination The previous two steps are repeated until the polymers have reached their designated maximum length or until the propagation step fails because none of the neighbouring sites are available to visit. Note that we start all random walkers at the same time, and they propagate in parallel, so that all chains are statistically equivalent. If, instead, we were to generate the walks one at a time, the statistics would change during the process because screening of excluded volume effects would become more and more important as the process progressed. Note that the networks thus created are generally not spacefilling because the walkers terminate when they get stuck. We will get back to this at the end of this section. The final result is a cross-linked network, within which all polymer bridges obey random walk statistics.

3.4.2

Lattice Swelling and Intergenerational Cross-Linking

To make double networks, we follow the experimental procedure in the sense that we create the generations of the networks one after another in the model. To do this, we need to extend our method in two ways. Firstly, we need to generate polymer bridges with statistically larger end-to-end distances, to represent the swollen state of the first network. Secondly, we need to implement a parameter that governs how many sites of the first network are available for the walkers that make the second network to visit, so that we have control over the amount of intergenerational crosslinking. To start with the latter, we consider again the link with experiment, in which a source of intergenerational cross-linking is the possibility of chain transfer reactions where partially unreacted sites from the first network are available for the second moiety to react in the polymerization of the second network. In our model, this means considering the cross-linker sites of the first network that were only visited once during the first polymerization. At the beginning of the second polymerization, we mark a fraction ξ of these half-reacted sites as available, while the rest is marked unavailable. Setting ξ ¼ 0 thus prevents all intergenerational cross-linking (IGC) and corresponds to the experimental situation of when there is no covalent connection between the two networks. They are entangled via interpenetrating polymer bridges, but not covalently linked.

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The swelling is introduced in a statistical fashion, by having the walkers in the first generation take steps of size bα, where α is an integer larger than 1. The steps themselves are not stretched, as we map each step onto a sequence of α consecutive bonds of length b, but the resulting conformations are statistically stretched because a random walk of N/α steps of length bα gives a mean square end-to-end length of    2 N R ¼ ðbαÞ2 ¼ αNb2 ð48Þ α   which is a factor α larger than the equilibrium value R20 . Thus, the first generation pffiffiffi is constructed to represent a sample that was swollen by a linear factor α after polymerization. At the same time, it still lives on the lattice of lattice constant b, allowing to generate the second network on the same lattice, with the option of having intergenerational cross-links. The swelling procedure can in principle be iterated, introducing another swelling factor αi for each generation i, allowing to make multinetworks with more than two generations. Naturally, at the end of the procedure, the geometric constraint of having all the particles sit on the sites of a cubic lattice can be relaxed by performing off-lattice equilibration within a Monte Carlo or molecular dynamics simulation.

3.4.3

Double-Network Parameters

Having introduced the double-network generation procedure in general terms, we will now specify how we employ the procedure to make the starting configurations for the simulations we present in this chapter. For generating the network samples, the parameters are summarized in Table 1. 15 %  20% of the chains belong to the filler, while the majority is from the matrix. We create an ensemble of over 50 network configurations, for the range of ξ values, to draw statistics about their mechanical response. The cross-link connects the chains inside the periodic box, and as the ξ parameter increases, their density also increases. Even though the IGCs are varied, the average number of beads and bonds are similar in the networks. Since the networks are generated stochastically, there is always a slight variation (5%) in the number of beads and bonds that make up the entire system. The average hNBeadsi ¼ 17500, hNBondsi ¼ 16700. Table 1 Input parameters for generating networks

Parameter Walkers Chain length Step size Revisit prob. p ξ a

Network one 12 (32a) 350 (550a) 5 (1a) 0.40–0.55 0–1

Corresponds to single-network samples

Network two 30 550 1 0.14–0.18 –

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Since the eventual purpose is to fracture the double networks, individual networks are checked for independent percolation in all the three directions X-Y-Z using an algorithm based on connected components and breadth-first-search algorithm, partially adapted from [86]. If the chains don’t show isotropic percolation, they don’t represent the material. While the m-SAWR method is fast and flexible, the method is unable to generate highly dense space-filling networks. The walkers with chain length greater than (N > 500) get stuck during propagation, not finding available sites to visit. From an experimental point of view, elastomers are dry polymers, highly dense space-filling networks. To address this, we have developed a novel algorithm [87] that statistically ensures the creation of polymer networks that fill the periodic box. This is inspired from vertex-based ice models [88].

3.5

Computational Rheology

One of the central objectives of most computational soft matter studies is to relate structure to mechanical properties. To quantify these in the linear regime, one generally considers the mechanical response of a viscoelastic material to small amplitude cyclic shear loading (to be specific, we will consider such loading in the bxbz-direction), where the dimensionless shear strain is given by (the real part of) γ ðω, t Þ ¼ γ 0 eiωt ;

γ 0  1:

ð49Þ

The shear stresses that develop in the material in response define the dynamical 00 shear modulus G⋆(ω) ¼ G0(ω) + iG (ω) in the sense that σ xz ðω, t Þ ReðG⋆ ðωÞγ ðω, tÞÞ:

ð50Þ

For viscoelastic materials, both the real part of the dynamic modulus (G0(ω), also 00 called the storage modulus) and its imaginary part (G (ω), the loss modulus) are generally non-zero. A viscoelastic solid is defined as a material, the storage modulus of which remains finite and independent of frequency at long timescales: lim G0 ðωÞ Geq 6¼ 0 , a viscoelastic liquid conversely as a material where this ω!0

limit does approach zero. The dynamic modulus G⋆(ω) is related to the so-called stress relaxation modulus G(t) (a real quantity) which measures the rate at which the stress incurred by a step strain γ 0 is relaxed: σ xz ðt Þ ¼ Gðt Þγ 0 :

ð51Þ

The stress relaxation modulus (whose long-time limit is also given by lim Gðt Þ ¼ Geq ) and the dynamic modulus are related by a Fourier transform:

t!1

Rheology, Rupture, Reinforcement and Reversibility: Computational Approaches. . . ⋆

Z

1

G ðωÞ ¼ iω


 dt Gðt Þ  Geq eiωt :

93

ð52Þ

0

The linear viscosity η of a viscoelastic liquid may be extracted from either G⋆(ω) or G(t) using G00 ðωÞ ¼ η ¼ lim ω ω!0

Z

1

dtGðt Þ:

ð53Þ

0

Thus, the full linear rheology of a viscoelastic material is encoded in either G⋆(ω) or G(t). Clearly, then, to determine these quantities is of central interest to computational soft matter science. In the previous, we have detailed how the various interactions and structural features may be encoded in a molecular dynamics simulation, possibly combined with other approaches such as Monte Carlo to efficiently capture stochastic processes. The result of a properly setup simulation framework will be a dynamic representation of the material under study, allowing access to a time series of the positions and connections of each coarse-grained (or atomistic) particle in the system. To extract linear rheological properties from such data sets, various options exist. A particularly straightforward option, and one that most closely mimics a typical experiment, would be to deform the entire simulation box and record the mechanical response. For systems with a well-defined steady state, this is typically done in periodic fashion. This approach has the great advantage that it allows one to interrogate the nonlinear response, but is generally very timeconsuming and limited in the range of accessible timescales. Fortunately, the response may be extracted without actually performing a bulk deformation: by virtue of the fluctuation-dissipation theorem, it is also contained within the equilibrium fluctuations of the particles that make up the material. This correspondence may be exploited either by studying the dynamics of single chains embedded in an effective medium or by considering stress fluctuations in an ensemble.

3.5.1

Effective Medium Approach/Single Chain Response Function

For affinely deforming, spatially uniform materials, the full dynamical behaviour may be extracted from the contour length fluctuations of a single chain. Without losing generality, we may summarize the linear response (in Fourier space) by the following relation between force f and extension δ‘ e δℓðωÞ ¼ α⋆ ðωÞef ðωÞ,

ð54Þ

with α⋆(ω) ¼ α0(ω) + iα00(ω) the dynamic compliance (i.e. the reciprocal of the dynamic modulus for the single chain). The autocorrelation function of the end-toend length fluctuations, defined as

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ϕðt Þ ¼ hδℓðt Þδℓð0Þi

ð55Þ

is directly related – by the fluctuation-dissipation theorem – to the imaginary part of the dynamic compliance in the sense that 0

α0 ðωÞ ¼

ω e ϕðωÞ: 2kB T

ð56Þ

e ðωÞ the temporal Fourier transform of ϕ(t). Once the imaginary part is known, with ϕ the real part may be computed using the Kramers-Kronig relation: 2 α ð ωÞ ¼ π 0

Z

1

Z dt cos ðωt Þ

0

1

0

dν α0 ðνÞ sin ðνt Þ:

ð57Þ

0

Finally, in a relation that holds only for affinely deforming isotropic systems (such as Gaussian networks; see [89]), the complex modulus G⋆ ðωÞ may now be computed using G ⋆ ð ωÞ ¼

1 2 ρℓ αðωÞ1 : 15 c

ð58Þ

In this final relation, ‘c is the average contour length of the constituent polymers. Thus, by tabulating the fluctuating end-to-end length of a single polymer embedded in an environment of similar polymers, a simulator may gain efficient access to dynamical rheology without the need for whole-box deformations. In many real systems, however, the conditions of isotropy and/or affinity may be violated and a different approach needed. In that case, a simulation involving many chains might be in order, but even then it may not be necessary to perform a full deformation on the entire system.

3.5.2

Relaxation via Stress Correlations

Stress relaxation is intrinsically an out of equilibrium phenomenon, thus not easily manageable with tools optimized for system at (or closer to) equilibrium, like MD. As with the single-chain results however, the manner in which a system reverts to equilibrium after small deformations may be computed using the fluctuationdissipation. In particular, the full stress relaxation modulus G(t), rather than doing out of equilibrium MD calculating the stress tensor σ(t) after a step strain, can also be computed directly using the autocorrelation method, based on the following relation: Gðt Þ C ðt Þ

D E V σ αβ ðt Þσ αβ ð0Þ kB T

ð59Þ

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where the off-diagonal components of the stress tensor σ αβ are evaluated in the NVT ensemble at constant number of molecules N, volume V and temperature T. This relation is obviously similar in spirit to Eq. (55), but importantly now focuses on stress fluctuations rather than strain fluctuations. Clearly, as these are related through the linear response relation, similar information is contained in, and may therefore be extracted from, both. The bar and brackets denote averaging over time and ensemble, respectively. Strictly speaking, the equivalence between stress autocorrelation function C(t) and stress relaxation modulus G(t) assumed in Eq. (59) holds only in liquids [90, 91]. The correct way to define the stress relaxation modulus is then

Gðt Þ ¼

C ðt Þ,

liquids

C ðt Þ þ Geq  C 1 ,

solids

ð60Þ

where Geq is the shear modulus and C1 is the long-time limit of C(t) defined by C 1 lim Cðt Þ / hσ i2 t!1

ð61Þ

As anticipated, the stress autocorrelation function C(t) and the stress relaxation modulus G(t) coincide in the liquid phase, but when a material is solid (and thus Geq 6¼ 0), C(t) deviates from G(t) by a constant corresponding to the difference between shear modulus and long-time stress autocorrelation [91]. In self-assembled networks or in the thermodynamic limit, they become identical [80], so under that circumstances, G(t) ¼ C(t). However, Eq. (59) can be always used to distinguish a solid from a liquid, even in a finite ensemble. The reason is that the only way to have C1 ¼ 0 is when σ αβ ¼ 0 for every configuration, which happens only for liquids, so Eq. (59) will relax to 0 only if the system is a liquid. This is why this method is extremely simple to use and well suited to characterize a material by only measuring σ αβ(t) from equilibrium simulations. Notice that it is also possible to include contributes from a three-body potential like the one introduced in Sect. 3.2 by carefully including them in the stress tensor. In the Supplemental Material of Ref. [66], we show how to derive them from the standard virial approach [92].

4 Structure and Mechanics 4.1

Spatial Distributions of Reversibly Linked Materials

Freely diffusing reversible cross-links are entropically biased to form connections near existing permanent or reversible cross-links in a polymer network. Sections 3.2.1 and 3.2.2 highlighted that this is due to the entropy cost associated with forming a new loop between two polymer chains. Forming a new cross-link near

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an existing cross-link minimizes the length of the resulting loop, and therefore the entropy cost to the two polymer chains involved. In this section, we take a detailed look at the binding statistics and spatial distribution of freely diffusing reversible cross-links in full three-dimensional polymer gel simulations. Spatial structure is examined in the swollen gel at equilibrium, during isotropic strain, and at equilibrium in the strained sample. To bring our gel simulations a bit closer to experiment, we choose some of the design parameters based on the reversibly cross-linked networks studied experimentally in Kean et al. [53]. These choices are discussed at length where relevant. A hybrid molecular dynamics/Monte Carlo approach is used to simulate the gels with reversible cross-links, following the strategies outlined in Sects. 3.1, 3.2.2 and 3.2.3. Simulation units are expressed as D for the length unit, M for the mass unit and E for the unit. Equations of motion are integrated with a time step size of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qenergy qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

δt ¼ 0:001 MD 2 =E , where MD 2 =E et is the simulation time unit. Simulations are carried out in the HOOMD-Blue molecular dynamics package [93, 94].

4.1.1

Model Ingredients, Interactions and Permanent Network Formation

All networks are constructed in a three-dimensional cubic box of volume of

320, 000D 3 , periodic in all three dimensions. To construct a network, linear polymer strands and permanent cross-links are placed into the box. To connect explicitly to experiments, we focus on the gel described in [53]: a material composed of poly(4-vinylpyridine) polymers and hexyl chain permanent cross-links. The polymers have on average 314 chemical monomers per chain, and permanent cross-links are formed at a ratio of 1 per 50 chemical monomers, or approximately 6.3 per polymer chain. In simulation, these polymers are represented as coarse-grained bead-spring freely jointed chains. A polymer segment in the simulation is formally a ‘statistical segment’ representing a given number n of chemical monomers, set by the persistence length (in monomers) of the polymer. The chemical structure of poly (4-vinylpyridine) is nearly identical to that of poly(styrene), with the exception of the para nitrogen in the aryl ring. The persistence length of poly(styrene) is approximately 6 chemical monomers. Therefore, an average poly(4-vinylpyridine) polymer from the experiment is represented in the simulation by a bead-spring polymer of 314/6 52 statistical segments. For every coarse-grained polymer, we add 6.3 permanent cross-link monomers. In the present simulations, we utilize 705 polymer strands of 52 segments each, along with Nperm ¼ 4, 440 permanent cross-link monomers (initially unbound) following the experimental ratio noted above. Particles interact via the pairwise intermolecular Weeks-Chandler-Andersen (WCA) non-bonded potential (Eq. (10)), where rij is the distance between any two particles, ε is the strength of the potential and σ is the range. This potential is just the

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Lennard-Jones potential shifted such that it is equal to zero at its minimum and then truncated beyond that point. For polymer segments and permanent-reversible crosslinks, the Lennard-Jones parameters are set to ε ¼ 1E and σ ¼ 1D , so that the effective diameter of these particles is d seg ¼ 1D. The polymer segments and permanent cross-links are bound together by FENE bonds, whose (bonded) potential is given by Eq. (7), where r0 ¼ 1.5σ is the bond length parameter and Ksp ¼ 30E/σ 2 is the bond stiffness; σ and ε are the LennardJones length and energy parameters for the particle pair in question. Note that particles bound by the FENE potential also interact via the repulsive WCA potential (Eq. (10)). A permanently cross-linked polymer network is formed in situ from the polymer strands and permanent cross-link monomers in the simulation box. Each polymer segment has one ‘sticker’ (see Sect. 3.2.2), and the permanent cross-link monomers each have two. Strong short-ranged attractive Gaussian potentials between the stickers are switched on, and the system is integrated through time so that the permanent cross-links may form up to two connections with two different polymer segments. Each connection that forms is transformed into a permanent bond with the FENE potential Eq. (7). This network formation phase is carried out until every permanent cross-link has connected its two stickers to polymer segments.

4.1.2

Swelling and Reversible Cross-Links

Once the network is formed, it is swollen to a new box volume of Vswollen. The polymer volume fraction in the resulting new box size is ϕpoly

"

# N segs 4 d seg 3 π ¼ , V swollen 3 2

ð62Þ

where Nsegs is the number of permanent cross-link monomers and polymer segments. In this study we choose V box 625, 000D 3 , leading to a gel-like polymer volume fraction of ϕpoly ¼ 0.03 equal to that in experiment in [53]. Next, Nrev reversible cross-links with a diameter drev are added into the gel at a volume fraction of " ϕrev ¼

N rev V swollen

3 # 4 d rev π 3 2

ð63Þ

In [53], the reversible cross-link species are on the order of the size of the permanent cross-links and are added at a ratio of five times the number of permanent cross-links in the network (given that all reversible cross-links are bound). We therefore define the reversible cross-links in simulation to have drev ¼ dseg – the polymer segment/permanent cross-link diameter – and Nrev ¼ 5Nperm ¼ 22,

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200 units are added into the swollen box. This leads to a reversible cross-link volume fraction of ϕrev 0.02. Reversible cross-links in the simulation comprise the host bead of diameter drev ¼ dseg along with two connected sticker binding sites. The latter have a diameter of d sticker ¼ 0:5D , held at a fixed angle of 180∘ to each other to resemble the van Koten complexes used in [53]. A reversible cross-link binds to a polymer segment via one such
sticker. The  stickers have Lennard-Jones parameters of E ¼ 1E and σ sticker ¼ d sticker þ d seg =2 ¼ 0:75D with polymer segments, permanent cross-links and the host beads of other reversible linkers. (The stickers themselves do not interact with each other.) Reversible cross-link stickers form and unform bonds with polymer segments via the Monte Carlo move defined in Sect. 3.2.3, Eq. (42). To choose the attempt interval NMC for MC moves, the timescale τLJ must be defined as given by Eq. (38). In that equation we take E ¼ 1E, σ ¼ σ sticker ¼ 0:75D, from the Lennard-Jones parameters for the stickers. All particle masses in the simulation are taken to be unity, i.e. m ¼ 1M. Thus, MC moves are attempted every NMC ¼ 750 integration steps. On a given MC move, a bind/unbind move is attempted for every reversible crosslink sticker (i.e. ξ ¼ 1). Reversible cross-link stickers bound to polymer segments have a bond potential of ð2Þ
 ð2Þ
 ð2Þ U REV r ij ¼ U FENE r ij  U FENE ðr min Þ  Erev ,

ð64Þ

where Erev is a parameter to control the strength of reversible cross-link binding and ð2Þ
 ð2Þ
 rmin 0.96σ eye is the minimum of the total potential U WCA r ij þ U FENE r ij for a ð2Þ sticker bound to a polymer segment. The potential U REV is therefore just the standard ð2Þ FENE potential shifted by a constant (E rev  U FENE ðr min Þ). A polymer segment may only be bound to one partner at any given time, and this is enforced in the MC moves. In order to evaluate the Monte Carlo success probabilities given in Eq. (42), the energy change ΔE(r( j)) must be calculated upon addition or deletion of the reversible bond. Since the only difference between the bound and unbound state of a sticker is the presence of the FENE bond connecting the sticker to polymer segment j, then ð2Þ

ΔE ðr ð jÞÞ ¼ U REV ðr ð jÞÞ:

4.1.3

ð65Þ

Simulation Protocol, Strain and Sampling

Once reversible cross-links are added, the network is equilibrated in the NVT ensemble with a Langevin thermostat for the implicit solvent, for 1  107 time

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steps. Equilibration includes the MC reversible cross-link bind/unbind moves. The following protocol is then used to examine the equilibrium and strain response of the network: 1. Record equilibrium statistics over 2  107 time steps. 2. Do an isotropic strain experiment over 3  107 time steps, in which the simulation box is expanded at a constant rate to double its initial length, width and height. 3. Stop straining, and record new equilibrium statistics over 2.5  107 time steps in the strained configuration. In all cases the simulation proceeds via the NVT ensemble with a Langevin thermostat. Simulation results as a function of time are output every 50,000 integration steps. Recall that the Monte Carlo sweep interval is NMC ¼ 750 steps and every reversible cross-link sticker is tested for a bind or unbind move (depending on its current state) on each MC sweep. Therefore, 67 MC sweep are attempted per reversible crosslink sticker during each of these output simulation frames. During the strain time of 3  107 integration steps, the simulation box dimensions are doubled in length, corresponding to an engineering strain of 1.0 in x, y and z. The strain rate is therefore 3:3  105 1=et (recalling the simulation time step size of dt ¼ 0:001et ). For 1 unit of engineering strain in the simulation, there are 40,000 attempted MC moves per reversible cross-link sticker. The strain rate is therefore 2.5  105 units per MC sweep.

4.1.4

Reversible Cross-Link Binding Statistics

Figure 6 presents the bulk statistics of reversible cross-link binding as a function of time, expressed in units of 50,000 integration steps. From t ¼ 1 to 400, the simulation is at the initial swollen volume of Vswollen. A snapshot of the entire network with reversible cross-links is shown in Fig. 5a. Isotropic strain begins at t ¼ 400 and continues at a constant rate until t ¼ 1,000. After that time the simulation is continued at the new strained box size until t ¼ 1,500; a snapshot of the simulation in this state is given in Fig. 5b. Panel (a) in Fig. 6 presents the number of bound stickers (relative to the total number of stickers) through the simulation, for four choices of sticker bond strength Erev. Panel (c) shows the fraction of reversible cross-links that have formed bridges – i.e. that have both of their stickers bound to polymer segments. Panel (d) shows the number of reversible bridges relative to the number of permanent cross-links in the system, with close-ups for the behaviour of the Erev ¼ 10kBT and 15kBT systems in panels (e) and (f). Increasing the binding strength results in a larger fraction of stickers bound to polymer segments at equilibrium, during and after strain. The reversible cross-links are, however, more susceptible to strain when their binding strength grows smaller. For example, when Erev ¼ 15kBT, the fraction of bound stickers and fraction of reversible link bridges remain relatively constant with strain. On the other hand, for

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Fig. 5 Snapshots of the polymer gel simulation before (a, c) and after (b, d) isotropic strain. In (a) and (b), blue beads are polymer segments, red beads are reversible cross-links, orange beads are permanent cross-links, and green beads are stickers. Panels (c) and (d) show only permanent crosslinks from the snapshots in (a) and (b). (Images generated with OVITO [73])

weaker bond strengths, straining the network leads to a rather substantial reduction in binding and loss of reversible bridges. Strong-binding stickers are less kinetically active than weak-binding ones. This result is presented in panel (b) of Fig. 6. For the weakest bond strength examined, Erev ¼ 6kBT, a bit less than 3% of all reversible cross-link stickers change binding partners within one Monte Carlo sweep. For the largest binding strength of Erev ¼ 15kBT, this reduces to less than 0.01%.

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Fig. 6 Reversible cross-link binding statistics as a function of simulation time (in intervals of 50,000 integration steps) for four choices of reversible cross-link binding strength Erev. Begin and end times for isotropic strain are indicated by vertical dashed lines. (a) Fraction of reversible crosslink stickers bound to polymer segments. (b) Percentage of reversible cross-links stickers that change bonding partners in one MC sweep. (c) Fraction of reversible cross-links bound to two polymer segments as a bridge. (d) Number of bridges divided by number of permanent cross-links. (e) Close-up of Erev ¼ 10kBT from (d). (f) Close-up of Erev ¼ 15kBT from (d)

4.1.5

Strain Response

Bound reversible cross-links have an influence on the pressure of the system at equilibrium and during/after strain. Pressure is a direct proxy to the stress, i.e. the force per unit area along a given surface of the sample. Since strain is being done isotropically on the simulated sample, then the xx, yy and zz stress tensor elements are thermodynamically on average identical and equal to the average total pressure, having units of E=D 3 in the simulation.

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Fig. 7 Total system pressure vs. simulation time for three choices of reversible cross-link binding strength Erev

Figure 7 shows the total pressure of the simulation as a function of time for three choices of Erev. The black dataset is the case where the reversible cross-links are present in the gel, but have a bonding energy of 0kBT with polymer segments. Essentially no reversible bonds are formed in this regime. Beginning from an average equilibrium pressure, strain causes the pressure to decrease, arriving a lower value (in this case, negative) once strain finishes. The initial pressure is due to the particular equilibrium configuration of the polymer network, plus the presence of the reversible cross-links. (Adding more reversible cross-links would serve to increase the initial pressure due to their kinetic energy.) The decrease in the pressure during strain is due to stretching of the permanent polymer network, wherein the polymers each exert a restoring force, as well as a reduction in the effective density of reversible cross-links (as the same total number of reversible cross-links is present in the system during the strain experiment). The red curve in Fig. 7 shows the behaviour of the system pressure for a reversible binding strength of Erev ¼ 10kBT. These reversible cross-links form bonds between the polymer chains in the network, reducing the magnitude of their configurational fluctuations and therefore reducing the initial equilibrium pressure from the Erev ¼ 0kBT reference case. Upon strain, a large percentage of the bridging reversible cross-links unbind from the network (as shown by the red curve in Fig. 6c), and the pressure trend increasingly resembles the Erev ¼ 0kBT reference case at large strain. In the yellow dataset in Fig. 7, the bond strength is further increased to 15kBT, leading to a further reduction in the initial pressure due to a larger number of bridging reversible links at equilibrium. During strain these bridging reversible links remain relatively fixed in place: The unbinding rate becomes so low that the reversible bonds do not get a chance to equilibrate on the timescale of the deformation, as shown in the yellow dataset in Fig. 6c. As a result, the pressure follows a different scaling with strain and even exhibits an over-shoot once strain finishes. Following that point, the pressure ‘rebounds’ as thermodynamically unfavourable

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bridges slowly unbind, allowing the permanent network to relax and the negative stress to release to some extent.

4.1.6

Entropy-Driven Clustering of Reversible Cross-Links

Insight into the spatial distribution of bound and bridging reversible cross-links is obtained by examining their radial distribution functions. Figure 8a, b compares the radial distribution functions of permanent cross-links and bridging (doubly bound) reversible cross-links around permanent cross-links, for Erev ¼ 10kBT. Results are shown for the sample at equilibrium before strain (a) and at equilibrium after strain is complete (b). These distributions are obtained directly from the radial distribution function, renormalized so that the sum of the plotted values adds up to 1.0 in the radial domain considered in the plot. The resulting values are proportional to the probability distribution for a single permanent or reversible cross-link, given that it

Fig. 8 (a, b) Average radial probability distributions for permanent cross-links and bridging reversible cross-links, as a function of distance r (in units of D) from a permanent cross-link, for Erev ¼ 10kBT. Results in (a) are obtained as an equilibrium average before strain, between simulation frames 50 and 400. Results in (b) are averaged after strain, from frames 1, 150 to 1, 500. Black dashed lines are radial probability distribution for both bound and unbound reversible cross-links in the reference simulation with Erev ¼ 0kBT. (c, d) Local bridging reversible link number density as a function of distance r from a permanent cross-link for two choices of reversible sticker binding strength Erev before (c) and after (d) strain. Solid coloured horizontal lines are the bulk average bridge number densities in the simulation before and after strain, and black dashed lines are the bulk average reversible cross-link number density (both bound and unbound)

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resides within the spherical volume of radius r ¼ 10D around a given permanent cross-link. For comparison, the black dashed lines are the radial distribution of reversible cross-links (either bound or unbound) in the Erev ¼ 0kBT reference system. Before strain, we see that both the permanent and reversible bridge distributions have distinct maxima near r ¼ 2D. This suggests two structural properties. First, it means that the permanent cross-links tended to cluster during the in situ network formation phase of the simulation described above. This suggests that the polymer network is heterogeneous, with ‘bundled’ regions rich in permanent cross-links and inter-connected polymer chains, separated by less dense regions with sparse connecting polymers. This can be seen in the network snapshots in Fig. 5a, c. Second, these distributions indicate that bound reversible cross-links are localized near permanent cross-links. This is consistent with the theoretical arguments and simple simulation results presented in Sects. 3.2.1 and 3.2.2; that is, by localizing near permanent cross-links, bound reversible cross-links minimize the entropy penalty to the polymer network. The same trend is observed in the strained network at equilibrium, albeit both distributions are actually sharper, indicating two features. First, the bundled parts of the network rich in permanent cross-links remain largely intact, while the ‘unbundled’ parts of the network in between have done most of the sacrificial stretching in order to satisfy the simulation box strain. This can be seen in the snapshot of the strained network in Fig. 5b, d. And second, it suggests that the bridging reversible cross-links are strongly localized to these bundled regions around the permanent cross-links. In fact, the bridging reversible cross-links are more sharply peaked than the permanent cross-links. In contrast, the radial distribution of reversible cross-links around permanent cross-links at zero binding energy (black dashed line) exhibits a local depletion until approximately r ¼ 3D, after which the uniform background density is reached. This depletion effect is due to crowding near the permanent cross-links, where polymer segments and additional permanent cross-links are more likely to be found at equilibrium. Thus, the reversible cross-links with a non-zero bonding energy must overcome this steric effect in order to form bonds near permanent cross-links; apparently, this steric penalty is less significant than the entropy cost that would be entailed in forming the reversible bond further away from permanent crosslinks, where the polymer chains have more a priori configurational freedom.

4.1.7

Enhanced Clustering of Reversible Cross-Links Around Permanent Cross-Links in the Strained Network

The density of bridging reversible cross-links in the gel scales with the reversible cross-link binding strength Erev. Figure 8c, d plots the local number density of bridging reversible cross-links as a function of radial distance around a permanent cross-link. These distributions are obtained by multiplying the radial distribution function by the bulk average density of bridging reversible cross-links before and after strain (given as coloured horizontal lines in the two panels).

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Prior to strain in Fig. 8c, we see as in Fig. 8a that the local density of bridging reversible links is maximized very near permanent cross-links. For both Erev ¼ 10kBT and 15kBT, the local density at the maximum is enhanced by a factor of 4 compared to the bulk average. This enhancement factor grows remarkably larger at equilibrium after strain, in Fig. 8d. For example, in the Erev ¼ 10kBT system, the local density of bridging reversible links at the maximum is just over 29 times larger than the bulk average number of bridges, and for Erev ¼ 15kBT, it is around 27 times larger. This enormous degree of clustering of bridging reversible cross-links around the permanent cross-links in the strained system is due to an extremely strong ΔGpoly contribution to their binding free energy, when attempting to bind far from a permanent link. In strained networks, polymer chains are often stretched to large end-to-end lengths (see the strained simulation snapshot in Fig. 5b for an example). The configurational entropy penalty to link such chains together by a reversible bond can grow very sharply when attempting to form the bond far from an existing crosslink. For example, Fig. 9 presents analytical calculations for the entropic free energy cost of forming a bond between two Gaussian polymers. The polymers are fixed at one end to a common origin, while their other ends are fixed to two points on a circle of radius r and oriented at an angle θ ¼ π/2 relative to each other. Even for moderately stretched polymers, this entropy penalty grows very large – on the

Fig. 9 (a) Cartoon of two polymer chains with two of their endpoints fixed at the origin via a permanent cross-link, and their other endpoints fixed at a distance r from the origin, and at an angle of θ to each other. Light-coloured chains represent other polymers in the network, attached to the three permanent cross-links shown. (b) Entropic binding free energy, βΔGpoly(n; N, r, θ), for forming a reversible cross-link at position n1 + n2 ¼ n along two Gaussian polymers of N ¼ 200 segments each, for different choices of chain stretch r at constant angle θ ¼ π/2. In both panels, the black dashed curve is for when the two polymers have their ends untethered, i.e. free Gaussian polymer chains. Reproduced from [72]

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order of tens of kBT – with contour distance from the existing cross-link. This entropic bias, due to the entropy of the polymer strands themselves, leads to the strongly peaked distribution of reversible binding around permanent cross-links in the simulation.

4.1.8

Spatial Reordering and Kinetics of Clustered Reversible Cross-Links During Strain

As the polymer gel in the simulation is strained isotropically, the length scale between permanent cross-links and bound reversible cross-links grows larger. In an ideal Gaussian network, these distances grow affinely [89], while in a real network such as here in the simulation, this is not necessarily the case. The scaling of the average distance between cross-links is a useful measure for how the spatial arrangement of cross-links changes under strain. Figure 10 presents plots of the average nearest-neighbour distance between permanent cross-links and bridging reversible cross-links as a function of time in the simulation. These results are obtained by calculating the average distance from a given cross-linker type ‘i’, being reversible (‘Rev’) or permanent (‘Perm’), to the nearest cross-linker of type ‘j’. The calculation is performed for all pairs of cross-links of the chosen type on a given

Fig. 10 Average nearest-neighbour distances (in units of D) between pairs of cross-links of given types ‘i’ and ‘j’ (Perm or Rev), as a function of simulation time (in units of 50,000 time steps). Simulation results are shown for Erev ¼ 10kBT (a) and 15kBT (c). Panels (b) and (d) show results from (a) and (c), scaled relative to the initial average equilibrium values before strain

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simulation frame. Figure 10a, c presents the calculations for Erev ¼ 10kBT and 15kBT, and Fig. 10b, d shows the results relative to the average nearest-neighbour distances at equilibrium before strain. All sets of data in Fig. 10a, c hover around an average value before strain commences. For the weaker-binding Erev case in (a), the smallest average nearestneighbour distances are between reversible and permanent cross-links, while the largest values are between pairs of reversible cross-links. For the strong-binding case in (b), the larger extent of reversible cross-link binding leads their nearest-neighbour distances to be the smallest, while the permanent-permanent distances are the largest. Consider first the weaker-binding reversible cross-link simulation in Fig. 10a, b. During isotropic strain, the average nearest-neighbour distances between permanent cross-links grow linearly with time. This is a reflection of the isotropic expansion of the sample. The nearest-neighbour distances between bound reversible cross-links grow much more sharply than the former. This is largely due to the loss in bridging reversible links during strain, as seen in the red curve in Fig. 6c, e. More interestingly, the nearest-neighbour distance between pairs of reversible and permanent cross-links changes very little. Therefore, bridging reversible cross-links remain tightly clustered besides permanent cross-links during and after strain. This is a direct reflection of the entropy-driven clustering discussed in the previous section. Rather different behaviour is observed for the stronger-binding reversible crosslinks in Fig. 10c, d. In particular, the larger bond strength leads the reversible crosslinks to have much slower bond swap kinetics. Recall from Sect. 4.1.4 that on average only 0.01% of the reversible cross-link stickers successfully change binding partners per MC sweep. During the strain interval, 40,000 MC sweeps are carried out as noted in Sect. 4.1.3. Therefore, on average each reversible cross-link sticker only changes binding partners 4 times on average during the entire strain period. In contrast, for the weaker-binding linkers with Erev ¼ 10kBT, where 3% of the reversible cross-link stickers change binding partners per MC sweep, then each sticker changes binding partners approximately 1,200 times during the strain period – a factor of 300 larger than the stronger-binding linkers. The high kinetic mobility of the weaker-binding linkers is what gives them the ability to equilibrate and re-equilibrate around permanent cross-links during strain in Fig. 10a, b, leading to the negligible change in nearest-neighbour distance between permanent-reversible cross-link pairs. Furthermore, their weak-binding strength ensures that they are only able to ‘pay the cost’ (entropically) for binding near permanent cross-links, but not further away. This ensures they always remain in a clustered configuration around permanent cross-links. In contrast, the kinetically sluggish strong-binding linkers in Fig. 10c, d exhibit a notable growth in the nearest-neighbour distance between permanent-reversible cross-link pairs during strain, which only marginally recovers after strain terminates. The nearest-neighbour distance between pairs of reversible cross-links scales similarly with the permanent-reversible scaling (seen in Fig. 10d) while remaining globally smaller than the other two pair types due to the large density of bound reversible linkers overall. Note that the growth in permanent-permanent nearestneighbour distance is largely the same in both the weak- and strong-binding

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reversible cross-link simulation. This suggests that neither the strong- nor weakbinding reversible cross-links influence the spatial structure between the permanent cross-links themselves.

4.2

Dynamic Bulk Rheology of Reversibly Linked Materials

In this section, we apply the simulational concepts laid out in Sect. 3.5.1 to predict the frequency-dependent rheology of a polymer material (elastomeric or hydrogel) containing both permanent and reversible links. In the simulations presented here, we focus on the effects of changing the binding strength depth on the dynamic rheology. To compare apples and apples, we fix a number of other parameters. Throughout the simulations, we fixed kBT ¼ 1 and m ¼ 1. Parameters defining the geometry of the polymers were N ¼ 42, and d ¼ 1 (in MD length units). Only one in six beads is capable of forming a reversible bond. The elastic energy of the chain was fixed by choosing x0 ¼ 1 and Ksp ¼ 2, 500 (this extremely high value suppresses bond length fluctuations, rendering the chain effectively inextensible) and Kb ¼ 15, corresponding to a persistence length ‘p ¼ 30. The single-bead friction coefficient was fixed at γ ¼ 0.1. The rebinding kinetics are independent of the transient potential, as these are determined by the encounter rate between transient binding partners in the network. As such, these depend most strongly on the density ρ. By fixing hτRi ¼ 200, we ensure that we work, approximately, at fixed network density. In our simulations, one end of the polymer is fixed at the origin – this represents the permanent connection. The other end is free. In Fig. 11a, multiple overlaid snapshots of the simulation are shown; those beads coloured blue and green are able to form cross-links. Blue beads are free (unbound); the green ones are transiently bound at the time of the snapshot. A typical simulation runs for 109 time steps, each taking a time of 0.01. To specify the reversible potential, we fix rc ¼ 1 and set ε0 to a given value. Over the course of the run, we record the end-to-end

Fig. 11 (a) Multiple overlaid snapshots of the bead-spring model of a semiflexible fibre with transient cross-linkers, where the green and blue beads are transient cross-links beads in bound and unbound state, respectively. (b) Illustration of a transient bond, a bead is trapped in a confining potential well (green) and can escape due to thermal fluctuations (blue)

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length ‘(t). These data are converted, using the average length h‘(t)i to extensions δ‘(t), which form the raw input to the correlator ϕ(t) in Eq. (55), and the subsequent analysis. To permit the Kramers-Kronig integration across the entire frequency domain, the high-frequency part of h|δ‘ω|2i is analytically extended.

4.2.1

Simulation Results

First, we investigate the relation between the reversible potential strength ε0 and the unbinding kinetics of the transient link. We fix ε0, and we record the unbinding time (the time elapsed between initial formation of the bond and dissociation) and tabulate its average hτUi over many events. Results are collected in Fig. 12 and show a clear, exponential relation; hτUi  exp (ε0/kBT). This is the expected result, from Kramers rate theory [95]. This establishes that indeed ε0 controls the dynamics of unbinding and introduces into the material a relaxation timescale independent of the polymer Rouse modes. Next, we may ask how this timescale is manifested in rheology. The correlation function ϕ(t) of the end-to-end extension fluctuations is shown for different values of the transient bond strength in Fig. 13a, b. The black line graphs the theoretical prediction for a fibre without reversible cross-links (Eq. (55)). From this figure, it is clear that the correlation time increases significantly as ε0 is increased and the unbinding rate decreases. This is a result of the suppression of the end-to-end length fluctuations in a cross-linked configuration. Using Eqs. (55)–(58) then permits these correlation functions to be converted into the network shear modulus: The normalized storage modulus G0(ω) is shown in Fig. 13c and the normalized loss modulus G00(ω) in Fig. 13d. To validate our protocol, we verify that a simulation without reversible crosslinks follows the theoretically predicted dashed curve; it has a plateau modulus in the low-frequency regime and a ω3/4 scaling in the high-frequency limit, where the

Fig. 12 Mean unbinding time hτi of a transient bond as a function of ε0. Solid line is a fit to hτi  exp (ε0/kBT ) – see main text

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Fig. 13 Correlation function of the end-to-end length fluctuations, short time response in (a) and longer correlation in (b), the storage modulus (c) and the loss modulus (d) for a network with transient cross-linkers, as a function of cross-linker binding strength ε0: curves low to high correspond to ε0 ¼ 0,6,7,8,9 respectively. The dashed line shows the theoretical value from [96] for a network without transient cross-links

typical timescale is shorter than the slowest relaxation time of the fibre; ω ω1 ¼ 0.013. As we increase the binding energy of the reversible bonds, Fig. 13c, d shows significant changes in the rheology. The new features may be directly understood. First of all, adding reversible cross-links has no effect on the storage modulus at the lowest frequencies. In this regime, where timescales are much longer than any timescale related to the re- and unbinding of the reversible crosslinks, the polymers can relax completely, unhampered by the reversible constraints; their elastic response is always completely determined by the permanent connections. At the highest frequency, the typical timescale is much shorter than the re- and unbinding time, and therefore, at these timescales, the bound fraction of the reversible cross-links act as additionally fixed cross-links. As a consequence of this, the storage modulus scales as ω3/4 as before (indeed, since this reflects relaxations at the single chain level, this regime should be independent of the reversible links). Because the bound reversible links stiffen the network by suppressing otherwise easier relaxations, the absolute values of both moduli are increased. The intermediate-frequency regime of the storage modulus is most markedly sensitive to the reversible linkers. Compared to a situation where no reversible links are present, the addition of reversible cross-linkers shortens the original plateau domain. At some intermediate frequency, well before the ω3/4 scaling regime is attained, the storage modulus rises. For values of ε0 corresponding to reversible unbinding times hτi(ε0) < (2π/ω1) 480, the gradual rise transitions smoothly into

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Fig. 14 (a) Change in shear modulus due to the reversible linkers as a function of average number of bound linkers per filament. The solid line is a fit ΔG  hNci1.2. (b) Scaled modulus G0/G0 as a function of the normalized frequency. Bottom to top, curves correspond to ε0 ¼ 0,6,7,8,9, respectively. Crosses indicate the frequencies corresponding to the unbinding times hτi(ε0) for each, clearly demonstrating that the additional plateau is controlled by the cohesive energy which, in turn, may be used to program the rheology curve

the ω3/4 regime. For higher values of ε0 however, the unbinding time is inside the original plateau regime (hτi(ε0) > (2π/ω1)); the inability of these linkers to unbind gives rise to a second plateau before the usual high-frequency regime is accessed. Increasing the binding energy ε0 is a direct way to change the unbinding time hτi, and as Fig. 14b shows, the onset of the second plateau coincides exactly with the cross-linked unbinding frequency. Not only the location of the second plateau is controlled by the energy ε0; so is its height. Figure 14a shows that the average number of bound reversible links per polymer, hNci (itself a direct function of ε0), determines the additional stiffness ΔG ¼ G2nd plat  G1st plat. It does so with a weak power law; ΔG  hNci1.2, i.e. with an exponent below the value of 2.2 expected [96] for permanently linked networks. We hypothesize that having a certain number of linkers bound on average supplies less additional rigidity than having that same number of linkers bound permanently, as in the first case dynamic exchange provides additional modes of relaxation. As mentioned in the introduction of this chapter, Wu et al. [55] found a weak power law increase of the G0(ω) with frequency from the plateau modulus at frequencies around the frequencies related to unbinding events. In our data, Fig. 13c, there is no power law relation between G0 and ω, yet the effect much of the transient cross-links on the storage modulus is much stronger than Wu et al. found in their simulations. We speculate that a larger ratio of the average unbinding frequency and ω1 in our simulations gave rise to this stronger effect of the transient cross-links on the modulus. In this section, we have presented single-fibre MD simulations of the effect of transient cross-linking on the linear shear modulus of an otherwise permanently cross-linked network material. In our approach, the simulated fibre is surrounded by an effective network with which it forms transient attachments. We find that the effect of the transient cross-links on the shear modulus is timescale dependent; at timescales much longer than the average unbinding time, there is no influence of the

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transient cross-links on the shear modulus. At short timescales, a fraction of the bound transient cross-links act as effectively permanent bonds. These lead to an increase in modulus around their unbinding frequency 2π/ω. For moderate values of the binding energy, the second plateau is preempted by the Rouselike ω3/4 regime. Combining permanent and transient cross-links in materials can result in various highly functional properties. In addition to the greatly enhanced toughness reported in literature [97], we show that the reversible links may separately serve to implement a graded dynamic response, leading effectively to two distinct rubberlike phases in dynamical rheology. By virtue of the time-temperature superposition principle, moreover, we predict a transition between two differentially elastic solid phases to occur at a critical temperature determined by the reversible linker energetics.

4.3

Effect of Reversible Cross-Links Near Percolation

In this section, we apply the concepts explained in Sects. 2.2.1 and 3.2.2 to study the mechanics of hybrid hydrogels. These gels are employed for their improved toughness and their ability to serve as responsive gels. Their mechanics is crucially determined by the ratio of physical (reversible) to chemical (permanent) crosslinks. Here, we use MD simulations to systematically assess the rigidity and stress relaxation of these hybrid hydrogels. We focus our efforts on the mechanically nontrivial regime where the gel is very soft or even fluid-like if only the chemical cross-links are considered, but where the presence of physical cross-links can make for a significantly stiffer material. In the simulations shown here, we focus on the effect of the relative concentration of reversible cross-links, defined as the ratio of the number of reversible cross-links to the total number of cross-links. The concentration of polymer as well as the total amount of cross-links and the strength of the reversible interactions remain fixed. The model we employ is a coarse-grained description of the tetraPEG hydrogels of Sakai et al. [98]. Starting from a solution of four-arm star polymers with functionalized ends, we first model the formation of a fully covalent gel via a click reaction. Hybrid gels are then obtained from these click gels by replacing a fraction of the click bonds by reversible bonds. More specifically, we mix equal amounts of functionalized four-arm star polymers, denoted as A4 and B4. The polymers are coarse-grained to strings of N ¼ 10 beads connected by springs of unit length, with reactive A and B beads at the ends of the arms. The click reaction is implemented by adding a spring between an A-bead and a B-bead when they are within a cut-off distance during the simulation. After reacting this way, the A-bead and B-bead are changed to an inert bead type, so that each reactive group forms at most one bond. All beads have a purely repulsive WCA potential (see Eq. 10), with σ ¼ 1.3 and ε ¼ 1, the latter defining our units of energy and (with kB ¼ 1) temperature. Both the gelation process and the mechanical testing are performed using coarse-grained

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molecular dynamics in LAMMPS [75], with a Langevin thermostat set to T ¼ 0.6. The reversible interactions introduced by replacing covalent bonds are implemented using stickers with a well depth of 50 (see Sect. 3.2.2 for details). Once we have a percolating covalent gel (and at least 98% of the bonds have reacted), we randomly change a fraction (1  η) of the AB covalently connected beads to A0 and B0 active sticker beads (see Sect. 3.2.2). The parameters of the stickers are such that they only bind 1-to-1. This effectively changes a portion of the covalent bonds into physical bonds. We do this over a range of ratios of reversible/ total bonds (from η ¼ 1, fully reversible, to η ¼ 0, fully covalent). We then perform a long equilibrium simulation for each sample, to obtain statistics on the percolation properties (which are now fluctuating by virtue of the reversible bonds) and the stress relaxation modulus. The latter is determined using the correlated fluctuation method discussed in Sect. 3.5.2. For all values of η, Fig. 15a, b, respectively, shows the probability (time averaged over the whole simulation for a range of seeds) to find a percolating network (i.e. gelation) and the stress relaxation modulus G(t). As a check, the gel’s behaviour is compared to equivalent gels where the sticker interactions are deactivated (i.e. fully covalent gels with some of the bonds removed; see Fig. 15c) and to the initial fully covalent network. Figure 15a shows the probability to observe a percolating network as a function of the fraction of covalent bonds (η), both when considering only the covalent bonds and when considering reversible bonds as well. For intermediate values of η, we see that the networks reach a state in which their behaviour should be heavily influenced by the reversible bonds, as they are non-percolating without them but almost always percolating with them. Indeed, in Fig. 15b, c, we see that we can interpolate smoothly between the fully covalent solid-like gel and the viscoelastic fluid obtained when replacing all bonds with reversible ones. Furthermore, comparing the stress relaxation moduli in (b) to the control experiment (c) in which the reversible links have been made inactive shows that the reversible cross-links influence the longtime mechanics, particularly in the intermediate η regime. This is in accordance with the percolation plot; here we see that for these two ratios of reversible bonds, the system only percolates when the stickers are included.

4.4

Stress Relaxation in Vitrimers

We apply the techniques introduced in Sects. 3.3 and 3.5.2 to characterize a mixture of stars. We show that a hydrogel can be easily made into a vitrimeric network, thus achieving the numerous advantages that vitrimers bring. To emphasize the effect of enriching stars with vitrimeric bonds, we first measure the stress relaxation modulus via the autocorrelation route (Sect. 3.5.2). Results in Fig. 16 show that when swaps do not require any external energy (βΔEswap ¼ 0), G (t) behaves as in a viscous liquid and thus the material flows. In this swapping phase, the material is self-healing and can be reshaped at will. Then, the swap energy barrier

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a

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Fig. 15 (a) The probability to find a percolating gel; in orange, the probability is averaged over a range of seeds, after a fraction (1  η) of covalent bonds is removed; in blue, the removed bonds have been changed to active sticker beads A0 B0 , and the probability is averaged over seeds and time; (b) the stress relaxation modulus for a range of η, when the reversible bonds are included; (c) the stress relaxation modulus for a range of η, in the control experiment where the sticker interaction has been turned off

can be increased continuously, slowing down this relaxation due to topological rearrangements. Above a certain limit (that depends on the experimental timescale; in our example, it is around βΔEswap 10), the material ceases to be a liquid and retains some of its original shape, as proven by the non-zero plateau of G(t). For our second numerical experiment in which we aim to expose the self-healing capabilities of vitrimers, we focus on the βΔEswap ¼ 0 phase. We damage this material by cutting it perpendicular to the z direction as sketched in Fig. 17a. We then let the two halves equilibrate separately for a very long time, in order to mimic the worst-case scenario for self-healing. Lastly, we put them back in contact, allowing stars to diffuse around and swaps to reconnect the two halves as depicted in Fig. 17b. After a self-healing time tsh in which the bonds can effortlessly swap, we prevent any

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t [ps] Fig. 16 Stress relaxation for vitrimeric star network, for a range of swap barrier values βΔEswap. After a regime of quick relaxation due to chain rearrangement, a solid plateau is approached. For energy barriers lower than βΔEswap ¼ 10, swap rearrangements trigger a second relaxation. Data are redrawn from [66]

Fig. 17 Sketch of the self-healing numerical experiment with βΔEswap ¼ 0 vitrimers. (a) The material is cut in half, perpendicular to z. After a very long waiting time, in which the two freshly cut sides can fully equilibrate, we put them back in contact. Since βΔEswap ¼ 0 rearrangement through swaps can rapidly connect the two sides (b), and the material can recover its elastic properties, even before any matter flows to the other side

further event by setting βΔEswap ¼ 1, and then we measure the elasticity of the healed system. In Fig. 18 we measure the elastic plateau along the three orthogonal directions, as a function of the self-healing time tsh after which we stop any swapping. While the xy component is not affected by the cut and thus does not significantly change with tsh, both xz and yz components manifest a rapid recovery of

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Fig. 18 Elastic plateau along the orthogonal directions after a cut along perpendicular to z. The xaxis represents the time tsw until which we allow the vitrimer to heal with βΔEswap ¼ 0. After tsh we set βΔEswap ¼ 1 and measure Gij. At tsh ¼ 0 only the xy component is non-zero because we made the cut perpendicular to z. Already around tsw ¼ 104, the three components become simular, suggesting that most of the healing already happened. After tsh ¼ 3  104 the three components become indistinguishable: the material is fully healed. Data are redrawn from [67]

mechanical stiffness. Already around tsh ¼ 104, the three components are comparable, testifying that the material has recovered its equilibrium bulk properties. If we contrast this result with Fig. 16, the following picture emerges: while the liquid properties of the vitrimer emerge at t > 106, most of the self-healing already happened at t 104. The reason is that while stress relaxation requires a longrange reorganization of the network, self-healing can be achieved with few localized swap events across the cut. In [67] we additionally measure the diffusion timescale which unambiguously lies between the self-healing recovery time that is connected to single bond dynamics and the stress relaxation time which instead requires non-local cooperation and diffusion of the stars. We then conclude that vitrimers have a window tsh < t < trelax in which they behave as solids, but any damage will be autonomously self-healed.

4.5

Mechanical Reinforcement and the Payne Effect in Nanocomposites

As introduced in Sect. 2.1.2, the beneficial effects of transient topologies are not limited to reversible or exchange networks. In nanocomposites, nanoscale fillers may act effectively as dynamic cross-links in a supranetwork of glassy regions of the

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elastomer. To better understand, and perhaps someday to be able to design for desired properties, we have focused [15–17] on the study of the filler-polymer interfaces, under both equilibrium and non-equilibrium conditions. For this to succeed, it is essential to study also the glass transition temperature of the polymer matrix, since it is well known that the mechanical properties of a polymeric material are contingent on its glass transition temperature Tg, as well as on the underlining local segmental mobility of the polymer chains. Those properties are, at least locally, altered by the interfaces which are developed after the addition of the filler particles to the polymer matrix. An approach to understand the reinforcement mechanisms in silica-filled model systems, based on the concept of the glass transition temperature, was taken in [9, 23, 24, 32, 33]. In those papers, the authors propose the existence of a gradient in the polymer glass transition temperature near the silica interface, which was successfully related to the temperature- and frequency-dependent mechanical behaviour of the composite. Then, the strain-induced softening of the percolating glassy bridges connecting the filler particles was held responsible for the observed nonlinear mechanical behaviour (Fig. 19). However, the effect of adsorbing and non-adsorbing interfaces and of the confinement on the glass transition temperature of the polymer matrix is still heavily debated, and no consensus exists about their relevance to the reinforcement [37, 38]. Since the focus in industry has been redirected towards the development of ‘green tires’ in which the CB particles are replaced by silica particles, an important issue is related to the compatibility between the silica nanofiller particles and the polymer matrix. The use of coupling agents [25, 26, 28], which leads to the well-controlled interaction between the non-polar polymer chains and the polar silica surface, may alleviate the problem. The importance of the filler surface energy has been examined

Fig. 19 (Left) Schematic representation of three neighbouring filler particles which are surrounded by a glassy layer (red). The particles are connected by a glassy bridge of diameter D. (Right) Ddependence of the segmental relaxation times from the coarse-grained simulations of capped polymer films, tremendous slowing down, by five-six orders of magnitude, is clearly visible close to the film substrate. (See [15, 16] for a detailed description of the model)

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by [25] on silica-filled SBR rubbers, by modifying the silica surface using different silanes. Their results showed that the presence of chemical links at the silica surface reduces the amplitude of the effect. Based on that result, the authors attempted to provide a theoretical explanation of the Payne effect: the polymer chains are initially bound to the filler surface, but under the applied stress, they de-bond, thus causing the nonlinear mechanical behaviour. The de-bonding effect has also been used in a recently proposed model for the explanation of the nonlinear, large-strain mechanical behaviour of nanofilled elastomers [41]. The majority of the above-mentioned studies have attempted to explain the Payne effect by focusing on the importance of the polymer-filler interactions and the development of glassy bridges between the nanoparticles. Indeed, the behaviour of a polymer under conditions of strong confinement is different than that in the bulk of the material. However, the assumed increase of rigidity due to overlapping glassy layers at high filler volume fractions, and its consequent drop under deformation, has not been verified experimentally. The difficulty arises due to the minuscule length scales that are involved: the approaching surfaces of neighbouring filler particles may result in a geometric confinement with a size on the scale of only a few nanometres, which is difficult to probe experimentally. Therefore, in order to provide insight on the nanoscopic mechanisms which might affect the mechanical properties of polymer nanocomposites, it is important to understand the dynamical and mechanical behaviour of polymer films – strongly confined systems [36]. Various attempts to study the influence of the degree of confinement on the mechanical properties of polymer nanocomposites have deployed a model polymer film, aiming to establish a quantitative equivalence between the thermomechanical properties of the two systems [99]. Indeed, the properties of both systems are strongly influenced by adhesive interactions and by confinement effects, and, depending on the volume fraction of fillers in the nanocomposite, similarities have been identified. In highly filled polymer nanocomposites (40 wt%), it has been shown [36] that the changes in the glass transition temperature with decreasing interparticle spacing are quantitatively equivalent to the corresponding thin-film data. On the other hand, in materials with low filler concentration (less than 1.0 wt %), only a qualitative equivalence has been established [36, 100]. The glass transition of thin polymer films has been also widely examined experimentally [101– 114]. The general conclusion thus far is that the glass transition of a polymer film (and by extension its dynamic response to external perturbations) depends mainly on the degree of confinement, the presence of free interfaces and the polymer-wall interactions. However, due to the fact that the measured properties seem to be influenced by the employed experimental technique as well as by the preparation procedure of the samples, the reported results have shown disagreement among different laboratories and among different experimental methods [115– 122]. Dynamic fragility (a measure of the glass transition abruptness of glassforming materials) has also been employed in order to explain why different

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polymers, under the same conditions, are subjected to diversified confinement effects. Seemingly, under conditions of varying film thickness, correlations do exist among fragility and the amplitude of the Tg change [123]. Alongside the experimental studies, simulations of polymers under confinement have shown that a free interface, or the usage of repulsive interactions among the polymer and the solid walls, induces acceleration in the dynamical response of the polymer [124– 126], whereas the use of attractive polymer-wall interactions has the opposite effect [16, 127]; see Fig. 19 where a tremendous slowing down of the segmental relaxation in polymer matrix is shown upon approaching the nanofiller surface. Essentially, it has been confirmed that the glass transition temperature in films is significantly different than that of the bulk and mostly depends on interfacial phenomena [99, 128]. On the other hand, despite having closely attended to the effect of the degree of confinement and the adhesion interactions on the glass transition temperature and the segmental dynamics in thin polymer films, the effect of cross-links on the properties of confined polymers is much less investigated — especially with molecular dynamics simulations [129]. Concerning the particulate model, the nanofiller particles have been simulated explicitly. Each nanoparticle consisted of a specified number of beads which were randomly packed inside a sphere of a given diameter σ. Due to the random packing of the filler beads, though, each nanoparticle was only approximately spherical. The polymer matrix was composed of homopolymer chains with the same length as those in the film model. The varying parameters in the simulations of the particulate model were the filler volume fraction and the radius of the nanoparticles. Our simulation results of many-filler nanocomposites showed a linear dependence of the reinforcement on the inverse radius of the NPs, in agreement with recent experimental studies [17]. Further, the simulated systems with attractive NP-NP interactions displayed a sharply increasing reinforcement once the average distance between the surfaces of the NPs became smaller than the NP interaction radius. This observation may serve as an indication that, for a high enough volume fraction of fillers, the development of a filler network could indeed be an important source of reinforcement. Further, comparing the film- and many-particles simulation models, we saw that their structural properties (e.g. density profiles), as well as the values of the reinforcement (Fig. 20), are quite similar. This allows us to conclude that the confinement effects, present in the film model, are replaced by another reinforcing factor in the particulate model. This additional factor seems to be the direct, attractive interactions among the nanofillers, which was absent in the film model. Further simulations with a larger number of filler particles are needed so as to study the sensitivity of the reinforcement on the nanofiller interactions.

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Fig. 20 (a) Reinforcement of the capped films versus film thickness, for films with crystalline and amorphous substrates. (b) Reinforcement of the particulate system as a function of the average distance between the surfaces of the NPs for attractive and repulsive NP-NP interactions. No significant reinforcement was observed in the particulate systems with repulsive NP-NP interactions

4.6

Fracture of Double Networks

As previously described we generate double-network samples with varying degree of intergeneration cross-links (IGCs). The network generation protocol produces two distinct categories of double-network samples: cross-link-dominated (0 < ξ < 1) and entanglement-dominated (ξ ¼ 0). Double-network systems are underconstrained solids as per Maxwell’s rigidity rule [130], which states that a network in ddimensions with N sites is rigid if zCN ¼ 2d  2 Nd 6 . Double networks are coarse-grained such that each polymer bridge is an effective spring, which brings z close to 4. Thus, the networks are submarginal and entropic elasticity dominates the mechanics. The initial network configuration is relaxed off-lattice using molecular dynamics on LAMMPS [75]. Once the pressure and temperature have reached equilibrium values of 0.0 and 1.0 with the Nosé-Hoover thermostat and barostat, the network is uniaxially pulled along the Z-axis at a constant strain rate λ_
¼ 0:0001. Thus the box length (L ) changes as a function of time step (t): Lðt Þ ¼ L0 1 þ λ_  dt and L0 is the edge length of the box after equilibration. The network is deformed in steps between which the network is allowed to relax the temperature and lateral pressure. Bonds are allowed to rupture when the forces exceed a critical stress. The very first observation is that the density of IGCs controls the nonlinear fracture behaviour of double-network elastomers, as shown in Fig. 21a. They do that by facilitating stress transfer between the networks. The presence of more IGCs acts as additional cross-links, which makes the network stiff. Figure 21b shows that in cross-link-dominated samples (ξ > 0), bonds break simultaneously in the filler and matrix, even though there is an initial preference in bond breaks in the prestressed filler. The networks fail almost one after the other, triggering an avalanche-like failure.

Rheology, Rupture, Reinforcement and Reversibility: Computational Approaches. . .

σzz

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0.3

ξ ξ ξ ξ

0.2

= = = =

1 0.5 0.2 0

0.1 0.0

0.0

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5.0 γ

7.5

10.0

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Fig. 21 (a) The stressstrain behaviour of the double-network samples for uniaxial pull is shown in this figure. Samples with varying connectivity show different mechanical response. The cross-linkdominated samples with ξ ¼ 1(Δ),0.5(∘),0.2(∇) carry higher stresses but fail relatively faster than entanglement-dominated samples (⌂). (b, c) Mapping the bond break events to individual networks in cross-link-dominated and entanglement-dominated DNs, respectively. In the first category, more bonds are broken and they break simultaneously in both the networks. In the second kind, fewer bonds break and the fracture is a distinct two-step procedure

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101 filler

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matrix

2

4 γ

6

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101 Nb

filler

100

2

matrix

4

γ

6

8

On the contrary, entangled-dominated networks (ξ ¼ 0) show a different response. By mapping the bonds broken in the network to the host network and strain at which they broke, Fig. 21c shows that at small strains, the prestressed filler fractures first. This delays fracture in the matrix; thus, DNs with no IGCs are able to sustain larger strains without breaking the material completely. There are no signatures of stress concentration in fracture of DN types with or without IGCs. Snapshots from simulation, shown in Fig. 22, show progressive damage of networks as network is strained. There is continuous emergence of force chains causing bonds to break, finally culminating in complete failure of the networks.

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Fig. 22 An unperturbed 2D snapshot of the double-network elastomer is shown with first network in green and second network in orange and red cross-links. As the sample is stretched, the first network aligns with the direction of the applied strain and starts to rupture first. Subsequently, at higher strains, the coiled second network unfurls and starts to break

5 Conclusions and Outlook Composite and reversibly linked soft materials provide exciting new opportunities for mechanical functionality. Recent experiments in hydrogels and elastomers have demonstrated enhanced toughness, resilience and self-healing qualities that appear to require little fine-tuning, but rather are intrinsic to these material designs. How precisely these enhanced properties come about is far less clear. Composites are more than the sum of their parts, and polymer networks with reversible or exchanging bonds are more than entangled or cross-linked materials with an additional relaxation time. As more and more systems are developed that take advantage of these newly available properties, the questions surrounding the molecular origins also become increasingly pressing. Polymer science has a long tradition of theory, simulation and experiment advancing hand in hand. Experimental discoveries inspire fundamental insights that, in turn, allow for rational design – microscopic and molecular understanding allow targeted design and optimization. To achieve this level of understanding for reversibly linked materials and various composites, novel computational approaches are required. In this paper, we have attempted to introduce a few such approaches which have been instrumental in our efforts to cast light on the multiscale mechanics of modern polymer matter. These techniques have allowed us to better understand the distribution and redistribution of

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reversible linkers, the effect of these dynamical connections on bulk mechanical response, the role of nanofiller particles in the mechanical enhancement of rubbers, the microscopic pathways by which exchange of connectivity allows for the relaxation of stresses, [49] how realistic multiple network topologies may be generated and how multiple networks break on a strand-resolved level. While the overall picture is far from clear yet, we hope that this broad introduction will inspire further modelling efforts in this exciting new chapter of polymer materials. Acknowledgements Parts of this work were executed under the research programmes ‘Understanding the viscoelasticity of elastomer-based nanocomposites’ (VEC), the Stichting Nationale Computerfaciliteiten (National Computer Facilities Foundation, NCF), the research programme on Marginal Soft Matter (FOM12CSM01) and the ‘Projectruimte’ project 15PR3223 financed by the Netherlands Organization for Scientific Research (NWO) and also under the research programme on Computational Sciences for Energy Research (14CSER005), which is financed by the Netherlands Organization for Scientific Research (NWO) and Royal Dutch Shell.

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Adv Polym Sci (2020) 285: 127–164 https://doi.org/10.1007/12_2020_60 © Springer Nature Switzerland AG 2020 Published online: 12 May 2020

Mechanics of Polymer Networks with Dynamic Bonds Qiang Guo and Rong Long

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Continuum Mechanics and Thermodynamics of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Macroscopic Deformation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Continuum Model to Capture Chain Detachment and Reattachment . . . . . . . . . . . . . . . 3.2 Kinetics of Chain Detachment and Reattachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Constitutive Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Steady-State Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Transient Network Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Statistical Description of Polymer Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Evolution of the Chain Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Macroscopic Constitutive Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Summary and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Incorporation of dynamic, reversible bonds into the polymer network of soft gels has been exploited as a strategy to enhance fracture toughness and to enable self-healing. Gels with dynamic bonds often exhibit macroscopic viscoelasticity which can be traced back to the kinetics of bond dissociation and reformation. This chapter discusses recent efforts in developing constitutive models to connect the molecular-level bond kinetics to the continuum-level viscoelasticity. Two different modeling approaches are described using a model system, i.e., hydrogel with dynamic physical crosslinks and static chemical crosslinks. Both approaches are based on the theoretical framework of continuum mechanics and thermodynamics Q. Guo and R. Long (*) Department of Mechanical Engineering, University of Colorado Boulder, Boulder, CO, USA e-mail: [email protected]

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and aim to quantify how the total network free energy is governed by macroscopic deformation and molecular kinetics. In the first approach, the network is treated as a collection of polymer chains formed at different instants along the loading history. These chains experience different extent of deformation and thus carry different free energy. The total free energy is the sum of contributions from all chains. The second approach considers a statistical distribution of the chain end-to-end vectors, which evolves upon macroscopic deformation and reaction of dynamic bonds. The total free energy is calculated by integrating the single-chain free energy over the chain distribution space. These two approaches, capable of capturing the time-dependent mechanical behaviors of hydrogels with reversible crosslinks, can be extended to model the macroscopic mechanics induced by other molecular mechanisms such as bond exchange and chain scission. Keywords Dynamic bonds · Continuum mechanics · Molecular kinetics · Polymer network · Viscoelasticity

1 Introduction The molecular structure of soft polymeric materials, e.g., hydrogels or unfilled elastomers, can be represented by an amorphous network of crosslinked flexible polymer chains. How the network responds to mechanical loading depends on the force-extension behavior of individual chains [1] as well as on the spatial localization of the crosslinks connecting these chains to the network. For example, when a rubbery network crosslinked by covalent bonds is subjected to external loading, the stretch of single chains leads to reduced configurational entropy and hence increased free energy [1, 2], while the covalent crosslinks preserve the network topology. As a result, the network can fully recover its original size and shape upon unloading and thus behaves as an elastic solid. A large volume of literature has been devoted to modeling the nonlinear elasticity of rubbery networks [3, 4]. These models specify the network’s Helmholtz free energy as a function of the macroscopic deformation, from which the stress-strain relation can be derived based on the theoretical framework of continuum mechanics [5]. Depending on how the free energy function is derived, the nonlinear elasticity models can be divided into two categories. In the first category, the free energy function is motivated by experimental data, e.g., stressstrain curves from uniaxial tensile tests, and thus is phenomenological in nature. Examples include the Mooney-Rivlin model [6, 7], the Ogden model [8], and the Gent model [9]. In the second category, one starts from a molecular model of single chains, e.g., freely jointed chain with Gaussian or Langevin statistics [1], and links it to the network free energy through some kinematic assumptions, e.g., the three-chain [10], four-chain [11], eight-chain [12], or full network [13] model. Examples for this category include the neo-Hookean model [5] and the Arruda-Boyce model [12].

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The physical picture of network deformation under a fixed topology has been revised by the recent development of polymers with dynamic and reversible bonds [14]. When incorporated into a network, these bonds are able to continuously alter the network topology by reshuffling the connectivity of chains through bond dissociation and reformation. The molecular events of chain detachment and reattachment relax the free energy stored in a deformed network, and thus can lead to macroscopic stress relaxation or creep. Many different mechanisms have been developed to implement dynamic bonds in polymer networks, either via physical interactions (e.g., hydrogen bonds [14] or ionic bonds [15]) or chemical reactions (e.g., DielsAlder reaction [16] or transesterification reaction [17]). The practical benefits of using dynamic bonds are myriad. For example, one can leverage dynamic bonds that are sensitive to external stimuli such as light, heat, mechanical stress, and pH-value to obtain stimuli-responsive polymers [14]. Another application is to use dynamic bonds to engineer self-healing hydrogels [18]. As demonstrated in the pioneering work of the double network gel [19], it is possible to use a sacrificial network to substantially enhance the fracture toughness of hydrogels which would be otherwise brittle. The physical mechanism underlying the toughness enhancement is the energy dissipation associated with the damage in the sacrificial network [20]. However, such damage is irreversible if the sacrificial network is crosslinked using covalent bonds. This limitation has motivated the development of hydrogel networks with physical bonds [18, 21, 22]. Breaking of the physical bonds can still induce energy dissipation, but unlike covalent bonds, physical bonds can spontaneously reform and thus allow self-healing of the hydrogel upon unloading [23, 24]. Polymer networks with dynamic bonds exhibit a time-dependent mechanical behavior much like a viscoelastic solid, e.g., stress relaxation, creep, and history dependent stress-strain relation [21, 25]. The macroscopic viscoelastic behavior can be traced back to the molecular kinetics of bond dissociation and reformation [25, 26]. Indeed, it has been demonstrated that the viscoelasticity of hydrogels can be engineered by controlling the type and fraction of dynamic metal-ligand bonds that serve as crosslinks for the transient hydrogel network [27–29]. This chapter discusses how to model the time-dependent mechanics due to dynamic bonds. Unlike conventional phenomenological models that describe viscoelasticity using springs and dashpots, the focus here is to connect the continuum-level viscoelasticity to the molecular-level bond kinetics. Such models are valuable in two aspects. First, they can facilitate the design of applications utilizing polymers with dynamic bonds by enabling predictive simulations. Second, the model can also help reveal molecular kinetics of the dynamic bonds from macroscopic mechanical tests (e.g., relaxation tests). Similar to the modeling methodology for rubbery networks with fixed topology, we will describe two different approaches. The first approach [25, 30], referred to as the macroscopic deformation theory, treats the network as a collection of polymer

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(a)

(b)

Static crosslinks Dynamic crosslinks Polymer chains

(c)

Chain detachment

Chain reattachment

Fig. 1 Illustrations of the model material system. (a) A polymer network with static crosslinks (e.g., covalent bonds) and dynamic crosslinks (e.g., ionic bonds). (b) Chain detachment caused by the dissociation of a dynamic bond. (c) Chain reattachment caused by the reformation of a dynamic bond

chains formed at different instants along the loading history. These chains experience different extents of deformation and thus carry different free energies. The total free energy is the sum of contributions from all chains. The second approach [31, 32], referred to as the transient network theory, considers a statistical distribution of the chain end-to-end vectors, which evolves upon macroscopic deformation and reaction of dynamic bonds. The total free energy is calculated by integrating the single-chain free energy over the chain distribution space. Either approach can specify how the network free energy evolves under macroscopic deformation as well as bond dissociation and reformation. To lay the theoretical foundation, we first review necessary concepts and equations of continuum mechanics in Sect. 2, followed by the descriptions of the two approaches in Sects. 3 and 4, respectively. Although both approaches can be applied to a broad class of dynamic bonds, in this chapter we focus on a model system where the network is crosslinked by two types of bonds: static chemical bonds and dynamic physical bonds, as schematically shown in Fig. 1. An example of such system is the covalently crosslinked poly (vinyl alcohol) (PVA) hydrogel network [15] with additional ionic crosslinks formed between PVA chains and borate ions. In addition, the recently developed transient hydrogel network with metal-ligand crosslinks [27] can be considered as a special case of the model system where the static crosslinks are absent. In Sect. 5, we summarize the two approaches and discuss possible extensions of the two modeling approaches.

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2 Continuum Mechanics and Thermodynamics of Solids 2.1

Kinematics

Let us first consider the polymer medium as a homogeneous continuum identified by the region of space it occupies in a fixed reference configuration1 Ω0, as shown in Fig. 2. The reference configuration Ω0 is assumed to be stress free and with a uniform absolute temperature T0. Any arbitrary material point can be denoted by its initial position vector X in the reference configuration. After deformation, the reference configuration Ω0 is transformed into the current configuration Ω. Correspondingly, the motion of material points is described by a smooth one-to-one mapping function: x ¼ φðX, t Þ,

ð1Þ

where x is the actual position vector in the current configuration Ω. This mapping implies that the displacement of each material point is x  X. The deformation gradient tensor F and the spatial velocity vector ν are defined, in terms of the partial derivative of the mapping function, respectively as [5] F¼

∂φðX, t Þ ¼ ∇X φðX, t Þ, ∂X

ð2Þ

∂φðX, t Þ : ∂t

ð3Þ

v¼

The gradient tensor of the spatial velocity v, normally referred to as the spatial velocity gradient, is given by l¼

∂vðx, t Þ ¼ ∇x vðx, t Þ: ∂x

ð4Þ

The spatial velocity gradient tensor l can be decomposed into its symmetric and skew parts [5]: l ¼ d þ w,

ð5Þ

where the symmetric part d represents the rate of deformation tensor and the skew part w represents the rate of rotation tensor

The term “configuration” is used in continuum mechanics to refer to the macroscopic deformation state of a solid and should be distinguished from its meaning in polymer science involving monomer arrangement on a polymer chain (e.g., tacticity).

1

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Fig. 2 Schematic diagram illustrating the kinematics of deformation. The white regions represent the same cross-sectional surface in the reference and current configurations to expose the traction vectors discussed in Sect. 2.2

 1
l þ lT , 2  1
w ¼ l  lT : 2 d¼

ð6Þ ð7Þ

There is an important relationship between the spatial velocity gradient l and the _ time derivative of the deformation gradient tensor F: _ 1 : l ¼ FF

ð8Þ

In order to further characterize the deformation, the strain tensors related to either the reference or the current configuration are introduced here. With respect to the reference configuration Ω0, two material strain tensors are defined [5]: C ¼ FT F,

ð9Þ

1 E ¼ ðC  IÞ, 2

ð10Þ

where C is the right Cauchy-Green deformation tensor and E is the Green-Lagrange strain tensor. For the current configuration Ω, one can define two spatial strain sensors [5]: b ¼ FFT , e¼

 1
I  b1 , 2

ð11Þ ð12Þ

where b is the left Cauchy-Green deformation tensor and e is the Euler-Almansi strain tensor. For completeness, the deformation rates defined by the time derivatives of the strain tensors in Eqs. (9)–(12) are given as follows [5]:

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2.2

133

C_ ¼ 2E_ ¼ 2FT dF,

ð13Þ

b_ ¼ lb þ blT ,

ð14Þ

e_ ¼ d  lT e  el:

ð15Þ

Stress

The deformation of a continuum body results in the interactions between adjacent material points in the interior part of the body. In order to describe such interactions, one introduces the notion of stress, which can be interpreted as the internal force per unit area. Since two configurations (i.e., Ω0 and Ω in Fig. 2) are introduced to define the deformation, either configuration can be used to define the stress tensor. In the current configuration Ω, the actual interaction between material points in the deformed body can be expressed in terms of an infinitesimal internal force df acting on a spatial surface element da ¼ nda within the interior of that body, as shown in Fig. 2. For every internal surface element, we have df ¼ ξðx, t, nÞda ¼ σðx, t Þnda,

ð16Þ

where ξ is the traction vector measuring the force per unit area defined in the current configuration and σ is a symmetric spatial tensor called the Cauchy stress tensor. The internal force can be represented using quantities associated with the referred configuration Ω0, in which the surface element corresponding to da is denoted as dA ¼ NdA, so that df ¼ ΞðX, t, N ÞdA ¼ PðX, t ÞNdA

ð17Þ

where Ξ represents the nominal traction vector, which has the same direction as the Cauchy traction vector ξ but measures the force per unit area defined in the reference configuration, and P represents the first Piola-Kirchhoff stress tensor, which is a two-point spatial tensor and, in general, is not symmetric. Besides, for convenience of constitutive modeling, we can further define the second Piola-Kirchhoff stress tensor S, which is a symmetric stress tensor associated with the reference configuration but does not admit a physical interpretation in terms of actual surface tractions. According to the kinematics of deformation between the current and reference configurations, the stress measures defined above have the following relations [5]: σ ¼ J 1 PFT ¼ J 1 FSFT ,

ð18Þ

where J is the volume change between the reference and the current configuration and is equal to the determinant of the deformation gradient F:

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J ¼ detðFÞ:

ð19Þ

We limit our scope in this chapter to incompressible materials, for which the deformation can only be isochoric, and thus J remains equal to 1. The deformation of a continuum body causes the internal mechanical work which may be related to the different forms of stress tensors and the corresponding strain tensors. The rate of internal mechanical work (or stress power) per unit volume defined in the reference configuration Pint can be expressed as [5] _ Pint ¼ Jσ : d ¼ P : F_ ¼ S : E,

ð20Þ

_ and E, _ in which the stresses Jσ, P, and S are conjugate to the deformation rates d, F, respectively.

2.3

Thermodynamics

The goal of constitutive modeling is to derive quantitative relations between stress and deformation or strain. Since both stress and strain are tensors with multiple components, directly imposing functional relations between stress and strain may be challenging and, more importantly, may run the risk of violating basic physical principles such as the first and second laws of thermodynamics. It is critical to have a systematic procedure for deriving the stress-strain relations that conform to the laws of thermodynamics, especially for systems with significant dissipative behaviors, e.g., viscoelasticity of polymer networks with dynamic bonds discussed in this chapter. Here we briefly review this procedure which is well established in the area of rational mechanics. Let us start by considering the energy balance within a continuum body. The first law of thermodynamics requires the following energy balance equation to be satisfied: Π_ ¼ Pint  ∇X  Q

ð21Þ

where Π is the specific internal energy per unit volume defined in the reference configuration and ∇X  Q is the divergence of the heat flux vector Q also defined in the reference configuration. Note that Pint is the stress power which represents the rate of work done by the surrounding medium to a material point through internal forces. The energy balance equation in Eq. (21) indicates that the change of the internal energy can be attributed to two factors, the internal mechanical work and the flux of heat energy. The second law of thermodynamics requires that the Clausius-Duhem inequality [5] is satisfied:

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135



 Q  0, ηg ¼ η_  ∇X   T

ð22Þ

where T is the absolute temperature and ηg represents the entropy generation rate being equal to the difference between the change rate of the entropy η_ and the divergence of the entropy flow ∇X  (Q/T ). The Clausius-Duhem inequality in Eq. (22) indicates that any thermodynamic process can only occur spontaneously toward the direction of positive entropy generation. For reversible thermodynamic processes, ηg in Eq. (22) is equal to zero. Combining Eqs. (21) and (22), the following hybrid inequality is obtained: D ¼ Pint  Π_ þ T η_ þ ∇X T  ðQ=T Þ  0, |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} D1

ð23Þ

D2

where D is the total energy dissipation rate for all irreversible thermodynamic processes occurring in a continuum body. The energy dissipation D can be divided into two parts: the first part D1 represents the intrinsic dissipation induced by the irreversible energy conversion, and the second part D2 represents the thermal dissipation induced by the irreversible heat conduction. The intrinsic dissipation D1 can be written in a stronger form via the ClausiusPlanck inequality [5], in which the stress power Pint is represented as the specific form S : E_ and the existence of a Helmholtz free energy function per unit reference volume, ψ ¼ Π  Tη, is postulated: D1 ¼ S : E_  ψ_  ηT_  0:

ð24Þ

In order to describe the thermodynamic process associated with deformation, we select a set of independent state variables to characterize the present thermodynamic state, and the rest of the variables are considered as thermodynamic functions of these independent state variables. For example, the isothermal deformation of an elastic solid can be considered as a reversible thermodynamic process, where the Green-Lagrange strain tensor E can be used as the state variable to quantify the extent of deformation. For non-isothermal processes, the temperature T should also be a state variable. Both E and T are referred to as the external state variables. If dissipation occurs in the continuum body, additional state variables are required to quantify the irreversible thermodynamic processes, which are referred to as the internal state variables [33]. These internal state variables are collectively expressed by a vector χ . Therefore, the free energy ψ can be written as a function of the state variables T, E, and χ . Using the time derivative ψ_ ¼ ð∂ψ=∂T ÞT_ þ ð∂ψ=∂EÞ : E_ þ ð∂ψ=∂χ Þ  χ_ , the Clausius-Planck inequality in Eq. (24) can be rewritten as

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    ∂ψ ðT, E, χ Þ ∂ψ ðT, E, χ Þ _ ∂ψ ðT, E, χ Þ _  χ_  0: ð25Þ D1 ¼ S  :E ηþ T ∂E ∂T ∂χ This inequality must be satisfied at any instant of any deformation process, i.e., _ T, _ and χ_ , which can be leveraged to obtain constitutive arbitrary combinations of E, relationships by following the Coleman-Noll procedure [34]. For example, when both T_ and χ_ are equal to zero, Eq. (25) needs to be satisfied no matter whether E_ is positive or negative, and the only possibility is S¼

∂ψ ðT, E, χ Þ : ∂E

ð26Þ

Similarly, we can derive that η¼

∂ψ ðT, E, χ Þ , ∂T

ð27Þ

and a residual inequality D1 ¼ κ  χ_  0,

κ¼

∂ψ ðT, E, χ Þ , ∂χ

ð28Þ

where κ is the vector thermodynamically conjugate to the internal state variable vector χ . The vector κ can be considered as a generalized thermodynamic force and the vector χ_ as a generalized thermodynamic flux. The residual inequality in Eq. (28) indicates that the intrinsic dissipation originates from the evolution of internal state variables which characterize the irreversible thermodynamic processes occurring within the material. A kinetic law is essential to formulate the evolution equation of the internal state variables χ , which can be developed based on the specific physical mechanism underlying χ and in accordance with the thermodynamic constraint in Eq. (28). According to the derivations above, constitutive modeling of polymer networks with dynamic bonds can be achieved with two additional components. First, one needs to specify how the network free energy depends on the strain, temperature, and internal state variables, from which the stress tensor can be determined using Eq. (26). Second, appropriate internal state variables and the associated kinetic laws should be defined to capture the changes in the network topology due to dynamic bonds. Both components rely on some idealized physical pictures capturing the effects of dynamic bonds. In the following, we describe two different approaches of establishing such physical pictures in Sects. 3 and 4.

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137

3 Macroscopic Deformation Theory This section describes the model developed by Long et al. [25, 26] and later refined by Guo et al. [30], which is referred to as the macroscopic deformation theory (MDT). The theory will be introduced using the model material system shown in Fig. 1.

3.1

Continuum Model to Capture Chain Detachment and Reattachment

The MDT is based on a continuum description of the polymer network which does not include its detailed molecular structure. Therefore, an equivalent theoretical picture is needed to account for the effects of dynamic crosslinks on the macroscopic mechanics. For the model system in Fig. 1, Long et al. [25] proposed a picture with the following assumptions (see Fig. 3). 1. Macroscopically, the polymer is a homogeneous and incompressible solid. Microscopically, the network consists of two types of chains: permanent and temporary chains. The permanent chains are attached to two static crosslinks and remain connected to the network. The rest of the chains are temporary chains since they can detach from and reattach to the network upon dissociation and reformation of the dynamic crosslinks. The total free energy of the network is equal to the sum of contributions from all permanent and temporary chains. 2. The initial state (t ¼ 0) is defined as the instant when mechanical loading is applied. In the initial state, it is assumed that all temporary chains are connected and all chains are relaxed (see Fig. 3a). This initial state is taken as the reference configuration Ω0 and also the ground state for the network free energy ψ. 3. Under mechanical loading, the network’s deformation is quantified by the deformation gradient F. If all temporary chains remain attached, the total free energy of the network is ψ 0(F), which is specified by a hyperelastic model [4]. Moreover, the permanent and temporary chains have the same mechanical behavior, i.e., they carry the same free energy if they experience the same macroscopic deformation F. 4. When a temporary chain detaches from the network (see Fig. 3b, c), it instantaneously relaxes to the free state. This assumption neglects potential viscous drag to a detached chain, which is reasonable for hydrogels with low viscosity solvent. Detached temporary chain may reattach to the network (see Fig. 3d). Immediately after reattachment of a temporary chain, it is in a relaxed state. After that the reattached chain starts to accumulate deformation according to the macroscopic

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(a) Initial state

… Permanent chains: N1

(b)

:Chain detachment

…

…

…

Temporary chains: N2 (c)

(d)

:More chains detachment

…

…

…

…

: Chain reattachment Fig. 3 A one-dimensional (1D) schematic for the continuum model of chain detachment and reattachment. (a) Initial state with relaxed permanent and temporary chains. (b, c) The temporary chains may detach from the network upon dissociation of dynamic crosslinks. (d) Detached temporary chains may reattach to the network upon reformation of dynamic crosslinks

deformation history F(t). For example, a temporary chain reattached at time τ experiences the deformation history from its birth at τ to the current time t (t  τ), which is denoted as Fτ ! t. The case of τ ¼ 0 corresponds to the permanent chains and the temporary chains that existed in the initial state. This theoretical picture captures two essential physical mechanisms: relaxation due to chain detachment and self-healing due to chain reattachment. To quantify these two mechanisms, let N0 be the total number of chains (i.e., permanent and temporary) per unit reference volume at t ¼ 0. Among these chains, N1 is the number of permanent chains per unit reference volume and is a constant. In addition, N2(t) is the number of original temporary chains that existed at t ¼ 0 and survived at the current time t. According to this definition, N0 ¼ N1 + N20 where N20 ¼ N2(t ¼ 0). When t > 0, N2(t) is less than N20 because of the detachment of temporary chains. Some of the detached temporary chains can reattach to the network, and the rate of this process at time t is defined as γ(t), i.e., number of chains per unit reference volume that are reattached per unit time. Using these definitions, the total network free energy ψ at the current time t can be written as

Mechanics of Polymer Networks with Dynamic Bonds

N þ N 2 ðt Þ
0!t  ψ¼ 1 ψ0 F þ N0 
   p det F0!t  1 ,

Zt

139

γ ðτÞφB ðt, τÞ ψ 0 ðFτ!t Þdτ N0

0

ð29Þ

where φB(t, τ) is the fraction of the chains reattached at time τ that survived at the current time t, since the reattached chains may detach again at a later time and p is a Lagrange multiplier [5] to enforce the incompressible constraint: det(F0!t) ¼ 1. The first term on the right-hand side of Eq. (29) represents the contribution from the permanent chains and original temporary chains, both of which experienced the full deformation history, i.e., F0!t, while the second term represents the contribution from reattached chains.

3.2

Kinetics of Chain Detachment and Reattachment

This section describes the kinetic relations for the chain detachment and reattachment which are needed to complete the constitutive model. Motivated by experimental findings [21] for a dual crosslink PVA hydrogel [15], Long et al. [25] assumed that the kinetics of temporary chains is independent of the macroscopic deformation. For the detachment of original temporary chains, the following relation was assumed:    α d N2 1 N2 , ¼ dt N 20 t R N 20

ð30Þ

where tR is a characteristic time for the dissociation of dynamic crosslinks and α is a dimensionless parameter. If α ¼ 1, Eq. (30) would reduce to the first-order reaction kinetics which yields an exponentially decaying function for N2(t) with a single characteristic time tR. In reality, the statistical nature of amorphous networks implies that there may exist a spectrum of characteristic times, which can be empirically accounted for by setting α > 1. The solution of Eq. (30) with the initial condition that N20 ¼ N2(t ¼ 0) is N2 ¼ φð t Þ ¼ N 20

 1 þ ðα  1Þ

t tR

1 1α

:

ð31Þ

The function φ(t) determines the fraction of original temporary chains that survived until t. Following the same approach, the surviving fraction of reattached chains φB(t, τ) in Eq. (29) has a similar form, but the relevant time is measured from τ to the current time t:

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φB ðt, τÞ ¼

  1 t  τ 1αB 1 þ ðαB  1Þ : tB

ð32Þ

It was found that in order to fit experimental data [25], the kinetic parameters for the reattached temporary chains (i.e., αB and tB ) need to be different from those for the original temporary chains (i.e., α and tR). This kinetic assumption will be revisited in Sect. 3.4 where a physically more consistent picture proposed by Guo et al. [30] is described. The reattaching rate γ(t) is assumed to follow the following kinetic relation: γ ðt Þ ¼

nb ð t Þ , tH

ð33Þ

where tH is the characteristic time for chain reattachment and nb(t) is the total number of detached temporary chains per unit reference volume at time t. Since the total number of chains in a unit reference volume N0 consists of four parts at all times, permanent chains (N1), original temporary chains (N2), reattached chains that survived until the current time (nrb), and detached chains (nb), we can obtain the following equation: nb ðt Þ ¼ N 0  N 1  N 2 ðt Þ  nrb ðt Þ:

ð34Þ

Furthermore, nrb(t) can be calculated by integrating the reattaching rate multiplied by the surviving fraction φB(t, τ) given in Eq. (32), which is Zt nrb ðt Þ ¼

γ ðτÞφB ðt, τÞdτ:

ð35Þ

0

Using Eqs. (33)–(35), we can derive an integral equation for the reattaching rate γ(t): Zt t H γ ðt Þ ¼ N 0  N 1  N 2 ðt Þ 

γ ðτÞφB ðt, τÞdτ,

ð36Þ

0

which can be solved numerically to determine γ(t).

3.3

Constitutive Equations

The two components required for constitutive modeling, i.e., the network free energy function ψ and kinetic relations, have been established in the previous two sections.

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141

To reduce the number of parameters, define ρ ( N1/N0) as the molar fraction of permanent chain in the initial state and γ ( γ/N0) as the molar fraction of the reattached chains per unit time. Therefore, Eqs. (29) and (35) can be rewritten as


ψ ¼ ½ρ þ ð1  ρÞφðt Þψ 0 F

0!t



Zt þ

γ ðτÞφB ðt, τÞψ 0 ðFτ!t Þdτ

0


   p det F0!t  1 ,

ð37Þ

and Zt t H γ ð t Þ ¼ ð 1  ρ Þ ½ 1  φð t Þ  

  1 t  τ 1αB γ ðτÞ 1 þ ðαB  1Þ dτ: tB

ð38Þ

0

In the context of continuum mechanics, φ(t) and γ(τ)φB(t, τ) are internal state variables characterizing dissipative processes in the network, i.e., detachment of stretched temporary chains. More precisely, by discretizing the integral in Eq. (37), one can see that the internal variables at time t are φ(t) and γ(kΔτ)φB(t, kΔτ)Δτ, where k ¼ 0, 1, 2, . . ., t/Δτ, and Δτ is a small increment of τ. Note that even though the dynamic crosslinks are reversible, detachment of stretched temporary chains is a thermodynamically irreversible process, since the reattached temporary chains cannot be spontaneously stretched. By plugging Eq. (37) into the Coleman-Noll procedure illustrated in Eqs. (25)– (28), one can derive a constitutive equation for the stress tensor. Since the deformation gradient F is used in Eq. (37), we use Eq. (20) to replace S : E_ in Eq. (24) by _ which gives P : F, P¼

∂ψ , ∂F

ð39Þ

where F should be interpreted as the total deformation gradient at time t, i.e., F0!t. Further derivations require a specific form of ψ 0(F) in Eq. (37). As in Long et al. [25], the incompressible neo-Hookean model (or the ideal rubber model) is adopted: ψ 0 ðFÞ ¼

 μ
T  tr F F  3 , 2

ð40Þ

where μ is the shear modulus at infinitesimal strain if all temporary chains are attached to the network. Substituting Eqs. (37) and (40) into Eq. (39), we arrive at the following result for the first Piola-Kirchhoff stress tensor P:

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Q. Guo and R. Long


T P ¼ p F0!t þ μ½ρ þ ð1  ρÞφðt ÞF0!t Zt þμ


T γ ðτÞφB ðt, τÞFτ!t F0!τ dτ,

ð41Þ

0

where the following identities have been used: h i T ∂tr ðFτ!t Þ Fτ!t


T ¼ 2Fτ!t F0!τ ,

∂F
0!t 

T
0!t T ∂det F ¼ det F0!t F0!t ¼ F : 0!t ∂F 0!t

ð42Þ ð43Þ

Recall that the Lagrange multiplier p is required to enforce the incompressibility assumption and can only be determined from boundary conditions. In addition to the stress equation, it can be verified that Eq. (28) is satisfied for each of the internal variables. To summarize, for any three-dimensional (3D) deformation history represented by F, we can use Eq. (41) to evaluate the first Piola-Kirchhoff stress tensor P. The relevant kinetic functions φ(t) and φB(t) are given in Eqs. (31) and (32), respectively, and the reattaching rate γ(t) needs to be solved numerically from Eq. (38). There are seven material parameters in this model: • • • • •

Initial shear modulus μ Molar fraction of permanent chains ρ Kinetic parameters for the detachment of original temporary chains α and tR Characteristic time for chain reattaching tH Kinetic parameters for the detachment of reattached temporary chains αB and tB

Next we consider uniaxial tension as an example to demonstrate this model. Without loss of generality, the tensile direction is assumed to be along the e1 direction of a Cartesian coordinate system. Denote the stretch ratio along e1 as λ. Incompressibility and isotropy imply that the stretch ratios along e2 and e3 are both λ1/2. Therefore, the only non-zero components of F are F11 ¼ λ and F22 ¼ F33 ¼ λ1/2. The Lagrange multiplier p can be determined using the stressfree condition that P22 ¼ P33 ¼ 0. After some algebra, it can be shown that the nominal tensile stress (or the engineering tensile stress) is   Zt 1 P11 ðt Þ ¼ μ½ρ þ ð1  ρÞφðt Þ λðt Þ  2 þ μ γ ðτÞφB ðt, τÞ λ ðt Þ 0

λðt Þ λ ðτ Þ dτ:  2  2 λ ðτÞ λ ðt Þ

ð44Þ

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143

This equation is similar to the viscoelasticity model by Green and Tobolsky [35] which is also based on a physical picture of chain breaking and reforming. It should be noted that Green and Tobolsky [35] reported the true stress σ 11(t), which is equal to λ(t)P11(t), and used different kinetic relations from those described in Sect. 3.2. Although Eq. (44) is valid for any deformation history, it is useful to consider the special case of stress relaxation to facilitate comparison with experimental data. In stress relaxation tests, λ(t) ¼ λ0H(t), where H(t) is the Heaviside step function. The nominal tensile stress P11(t) reduces to ! 1 P11 ðt Þ ¼ μ½ρ þ ð1  ρÞφðt Þ λ0  2 λ0

ðStress RelaxationÞ:

ð45Þ

Since λ(t) is a constant for t  0, the contribution from reattached chains becomes zero. More interestingly, the relative decay of P11(t) is governed by the chain detachment kinetics, while the magnitude is governed by the macroscopic stretch. These two effects are combined in a multiplicative manner. Therefore, the following reduced tensile stress PR is defined to highlight the chain detachment kinetics: 3 1  7 6 P ðt Þ t 1α 7 6 PR ðt Þ ¼ 11 2 ¼ μ6ρ þ ð1  ρÞ 1 þ ðα  1Þ 7: tR 5 4 λ0  λ0 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 2



ð46Þ

φðt Þ

By fitting Eq. (46) to experimental data, one can determine four material parameters: μ, ρ, α, and tR. The other three parameters, tH, αB, and tB, should be determined from experiments under other deformation histories, e.g., constant stretch rate _ . An example of model parameter calibration using the dual crosslink λðt Þ ¼ λt PVA gel [25] is shown in Fig. 4. In practice, the loading phase of a stress relaxation test cannot be instantaneous. Therefore, experimental results for two relaxation tests with different loading times (i.e., 5 s and 10 s) are plotted in Fig. 4a. It is evident that the loading phase can affect the relaxation phase, but after t > ~ 3 s the two sets of data converge, and fitting was performed using the converged portion of the experimental data. With the calibrated model parameters, Long et al. [25] examined the predictive capability of the model by comparing it to the uniaxial tension data under a range of loading histories, some of which are shown in Fig. 5. The model predictions and experimental data agree well, except when the nominal stress P11 23.2

>6.02

>95

>95

Compressive properties Ec σ uc εuc (kPa) (MPa) (%) 140 >3.58 >95 (10)

0.141g

8.2 (1.2)

7.8 (1.1)

3.9 (9.7)

1.8 (2.4)

Fracture toughnessa (kJ/m2)

(continued)

[16, 17, 19] [23] [23] [23] [23] [23] [23]

[20]

[7, 8, 20]

[7, 8] [7, 8, 14, 20] [7, 8, 20]

Ref [7, 8, 10, 14, 21] [9] [7, 8, 10, 11] [9] [18, 22] [7, 8, 13, 14] [9] [7, 8, 10]

Hydrophobically Associating Hydrogels with Microphase-Separated Morphologies 169

DMA 92.6

83.9

77.6

91.8

82.5

86.9

9.9

9.6

5.2

5.5

3.1

NIPA

0.9

6.0

1.5

6.4

3.1

HEA 4.4

9.1

6.0

1.5

6.4

3.1

Cb 3.0

3.40

3.70

5.16

2.34

3.02

27.8

Copolymer properties Sd Tg Mn PDI (K) (kDa)

0.064 (0.002) 0.051 (0.005)

0.108 (0.005) 0.184 (0.018)

0.270 (0.020) 0.210 (0.020)

0.470 (0.050) 0.540 (0.030)

Tensile properties Ec,d σ uc,d (MPa) (MPa)

514 (74) 567 (41)

575 (11) 503 (46)

εuc,d (%) Toughnesse (kJ/m3)

310 (70) 400 (70)

1,080 (220) 1,580 (130)

12.1 (1.8) 10.3 (2.8)

34.5 (1.6) 26.5 (1.2)

80– 85

~85

~85

~85

Compressive properties Ec σ uc εuc (kPa) (MPa) (%)

0.119 (0.051) 0.052 (0.17)

0.188 (0.055)

Fracture toughnessa (kJ/m2)

c

b

Fracture toughness Cinnamate Tensile extension rate ¼ 30.5 mm/min; compression rate ¼ 1.5 mm/min; average value of 3–5 specimens unless indicated otherwise: standard deviation in parentheses d Measured at 23 C for DFx and at 5 C for NFx (because of volume phase change); multiple values from different studies e Material toughness (area under stress–strain curve) f Separate samples g Single specimen determination h This sample is referred to as DF15 in Refs. [12, 13] i This sample is referred to as DFm9 in Refs. [15, 16, 18]

a

Gel DFm0C3 DFm10C3 DFm10C6 DFm5C1.5 DFm5C6 DFm3C9

F (Fm) 0.0

Dry polymer composition (mol%)

Table 1 (continued)

[11, 12, 15] [11]

[11, 12, 15] [11, 12, 15] [11]

Ref [11]

170 B. D. Vogt and R. A. Weiss

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171

Fig. 2 SAXS curves for (a) DF9 and (b) NF5 as a function of hydration at 23 C and 10 C, respectively. The numbers in parentheses denote the swelling ratio of the gel. The curves labeled (0) are the compression-molded dry copolymers, and the ones labeled (0) represent copolymer films that were completely dried after swelling with water. The curves were shifted vertically for clarity. The solid curves represents the best fits of scattering data to the hard sphere model of Griffith et al. [27]. Reproduced from Ref. [9] with permission

Fig. 3 (a) Transmission electron micrograph of dry DF22 stained with rubidium tetroxide; (b) comparison of SAXS and fast Fourier transform of the TEM image

2.2

Preparation of Hydrophobically Associating Supramolecular Hydrogels

Films of the copolymers were prepared by compression molding at elevated temperatures, e.g., 150 C, or by casting a polymer solution. Although the copolymers containing more than 2 mol% fluoroacrylate monomer were generally insoluble in water, they did dissolve in methanol, isopropanol, butanol, cyclohexanone, dimethyl

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sulfoxide (DMSO), or mixtures of isopropanol and water containing at least 25 wt% isopropanol, though the solubility depended on the concentration of fluoroacrylate in the copolymer. Hydrogels were obtained by soaking the copolymer films in de-ionized water until they reached constant mass. Table 1 also lists the equilibrium water concentration of the hydrogels, reported as swelling ratio, S, where S  (mass of hydrogel)/(mass of dry copolymer). S can be converted to the mass fraction of water in the hydrogel, xw, by Eq. (1). xw ¼

S1 S

ð1Þ

Thus, a hydrogel with a swelling ratio of 2.0 is composed of 50% water by mass. Figure 1 also shows the SAXS data for the water-swollen hydrogels, and the persistence of the peak in the scattering pattern indicates that the microphaseseparated morphology remains for the hydrogel. Only the hydrophilic polymer segments are swollen by water. The hydrophobic nanodomains are the crosslink junctions in these gels, which notably exist as a separate phase.

2.3

Hydrogel Microstructure

The hydrogels summarized in Table 1 are unique among other supramolecular and covalent hydrogels described in the literature in that these hydrophobically associating hydrogels exhibit microphase separation. Their microstructure consists of ~2–6-nm-diameter core–shell nanodomains dispersed in a continuous phase of water-swollen hydrophilic polymer [10, 16, 18–21, 24, 25]. The actual dimensions of the core–shell nanodomain structure vary with the choice of monomers and the hydrogel composition. The details of the microphase separation in DFx, NFx, and HF hydrogels were determined by small-angle neutron scattering (SANS) [10, 16, 20, 21, 24, 25]. The nanodomains, shown schematically in Fig. 4, consist of a 1–5-nm-diameter hydrophobic core composed of hydrophobically bonded fluoroacrylate groups (red circles) surrounded by a ~1-nm-thick shell of water-depleted hydrophilic segments (dark blue area). The light blue area in Fig. 3 is the continuous phase of water-swollen hydrophilic polymer. Since the fluoroacrylate groups in the core are covalently bonded to the hydrophilic groups, the nanodomains act as multifunctional crosslinks, and the hydrophilic polymer network chains are shown by the blue lines in Fig. 4 that connect fluoroacrylate groups in separate nanodomains. The origin of the microphase separation in the copolymers is the thermodynamic immiscibility of the hydrophobic fluoroacrylate groups and the hydrophilic polymer. The persistence of the nanodomain structure in the hydrogels is a consequence of the enhancement of the unfavorable mixing of the hydrophilic and hydrophobic parts of the copolymer due to the solubility of the hydrophilic polymer chains and the immiscibility of the hydrophobic groups in water. Note that one might reasonably

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173

Fig. 4 Schematic of water-swollen poly(alkyl acrylamide-co-fluoroacrylate) copolymer hydrogels. The numbers denote (1) the water-swollen poly(alkyl acrylamide) continuous phase and coreshell nanodomains with (2) fluoroacrylate core and (3) water-depleted poly(alkyl acrylamide) shell. The blue lines are the poly(alkyl acrylamide) network chains. Reproduced from Ref. [22] with permission

expect that similar immiscibility of the hydrophilic and hydrophobic moieties also occurs in other hydrophobically associating hydrogels, such as the hydrocarbonbased hydrophobic-modified hydrogels reported by Okay and coworkers [28–33], but neither they nor the authors of other papers concerning hydrophobically associating hydrogels [3, 34] explicitly reported microphase separation. The one exception is a study concerning a micellar hydrogel containing stearyl methacrylate by Can et al. [35]. X-ray diffraction measurements of that hydrogel revealed a highly ordered nanodomains, probably due to lamellar crystals of the C18 alkyl side chains. The results of that paper reinforce our belief that the microphase-separated microstructure of fluoroacrylate-hydrophobically associating hydrogels is not unique and that many or all hydrophobically modified hydrogels are also microphase-separated. The importance of that with respect to supramolecular hydrogels, in general, is the supramolecular network formed by microphase separation is distinctly different than one formed by simple reversible physical bonds between individual functional groups, as is assumed in the explanation of the origin of the mechanical properties by most authors studying physical hydrogels. In order to fully understand the mechanical behavior and self-healing properties of supramolecular hydrogels, it is essential that the nature and structure of the supramolecular network be clearly identified. Thus, microstructure characterization should be an important part of all research on supramolecular or self-healing hydrogels. A fundamental parameter for describing a network structure is the crosslink density, which can be calculated from the theory of rubber elasticity [36]. This theory, however, does not distinguish between covalent crosslinks and temporal crosslinks such as supramolecular bonds or chain entanglements, so for a physically associated polymer or hydrogel, the effective crosslink density, νe, depends on temperature and stress that lead to dissociation, breaking, or healing of supramolecular bonds or disentanglements of polymer chains. Accordingly, the values of νe for

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the fluoroacrylate hydrophobically associating hydrogels were generally calculated from the modulus of a hydrogel freshly swollen to equilibrium before any deformation was applied, using the following equation [36] G¼

E ¼ 3

  2 1=3 1  νe RTϕ2 f

ð2Þ

where G and E are the shear and tensile moduli, respectively, f is the crosslink functionality, ϕ2 is the volume fraction of polymer in the swollen hydrogel, T is absolute temperature, and R is the gas constant. Equation (2) assumes a Poisson ratio, ν ¼ 0.5, which is a reasonable assumption for flexible crosslinked networks. Experimental tensile measurements of the Poisson ratio for DF10 indicated that ν was dependent on the stretching rate, though within the linear region, where modulus was measured, ν varied from 0.5 to about 0.4 [24]. The tensile modulus was measured from the initial slope of a stress–strain curve (i.e., extrapolation to zero strain), where it is assumed that the physical bonds are intact or from a dynamic mechanical experiment in tension with a strain amplitude small enough so that the mechanical response was linear. ϕ2 is related to the swelling ratio, S, by the following equation,  1 ðS  1Þρ ϕ2 ¼ 1 þ d

ð3Þ

where ρ is the density of the of the dry copolymer and d is the density of the solvent (water). Since each FOSA or FOSM group is attached to two chain segments (unless the FOSA or FOSM group is located at a chain end), a FOSA–FOSA or FOSM–FOSM supramolecular bond produces four network chains. Thus the functionality, f, of a nanodomain crosslink is twice the number of FOSA groups within the nanodomain (Nagg). Values for Nagg, determined by small-angle neutron scattering for NFx and DFx hydrogels with x  2 at temperatures between 9 C and 13 C, varied from ~30 to 180, so values of f ¼ 2Nagg ranged from 60 to 360 depending on the fluoroacrylate concentration in the copolymer [37]. In that case, the 2/f term in Eq. (1) is small enough to be neglected, and the relationship between modulus, swelling, and crosslink density for these hydrogels becomes νe 

E 1=3

3RTϕ2

ð4Þ

Typical values of νe for the DFx, NFx, and HFx hydrogels ranged from 100 to 1,000 mol/m3 [12, 13, 17, 25], which is one to two orders of magnitude greater than values for covalently crosslinked hydrogels. The high crosslink density is responsible for the generally higher modulus of supramolecular hydrogels compared with covalent hydrogels.

Hydrophobically Associating Hydrogels with Microphase-Separated Morphologies

2.4

175

Direct Extrusion of Hydrogels

As a consequence of the non-covalent nature of the hydrophobic bonds, viscous flow of the hydrogel can be achieved at elevated temperatures and/or if a sufficiently high stress is applied to the gel. Below the Tg of the associated FOSA or FOSM groups, ~45 C, the fluorocarbon core of the nanodomains is in a glassy state, and the relaxation time of the physical network is very long. The hydrogel is strong and tough, and a prohibitively high stress is needed to achieve viscous flow. The hydrogel cannot be easily injected or reformed under those conditions. However, extrusion of the hydrophobically associating hydrogels can be achieved by raising the temperature above the Tg of the nanodomains, where the relaxation times of the physical network are greatly reduced and hydrogel becomes a viscoelastic liquid [12]. A similar result can also be achieved by plasticizing the FOSA nanodomains, e.g., by adding a small amount of an organic solvent to the water-swollen hydrogel. DMSO is an attractive plasticizer, since it solvates the hydrophobic bonds and it has low systemic toxicity [38]. Figure 5 shows the extrusion of a DF22 hydrogel at 65 C using a commercial melt flow indexer (MFI); see schematic in Fig. 5a. The fully hydrated hydrogel (S ¼ 1.67) was cut into small pieces that were loaded into the heated barrel (9.48 mm diameter) of the MFI and extruded using a force of 21.2 N, which provided a maximum shear stress at the wall of the capillary (2.09 mm diameter) of τw ¼ 19.6 kPa. The sample flowed continuously from the capillary at a rate of 18.9 mm/min (Fig. 5b). Extrusion results for the water-swollen DF22 hydrogel at four temperatures and a nominal shear stress of τw ¼ 19.6 kPa are summarized in Table 2. The fully hydrated

Fig. 5 Extrusion of a DF22 hydrogel (S–1.67) using a commercial melt flow indexer at 65 C and τw ¼ 19.6 kPa: (a) schematic diagram of the melt flow indexer; (b) hydrogel extrudate (arrow) exiting the melt flow indexer

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Table 2 Extrusion results for DF22 gels Sample/swelling solvent DF22/water DF22/20/80 (w/w) DMSO/water

Flow rate (mm/min)a 25 C 45 C b 0.12c 0 b 0 0.55

50 C 0.24 0.60

55 C 0.48 9.5

65 C 18.9 40.3

Unless indicated otherwise, τw ¼ 19.6 kPa τw ¼ 97.6 kPa c τw ¼ 29.5 kPa a

b

DF22 did not flow at temperatures below 45 C, even when a shear stress of 97.6 kPa was used. At 45 C, it did not flow with τw ¼ 19.6 kPa, but it did flow slowly, 0.12 mm/min, when τw was increased to 29.5 kPa. At 55 C, the hydrogel flowed at a rate of 0.48 mm/min for τw ¼ 19.6 kPa, and the flow increased to 18.9 mm/min at 65 C and τw ¼ 19.6 kPa. The effect of plasticization of the hydrogel with DMSO (1 part DMSO per 4 parts water) is also shown by the data in Table 2. In that case, extrusion was possible at 45 C using a shear stress of 19.6 kPa, and at higher temperatures the addition of the DMSO increased the flow rates appreciably.

2.5

Self-Healing Behavior

The concept of healing has multiple meanings with regard to a supramolecular polymeric system. From a macroscopic perspective, one is concerned with the healing of cracks, and from a microscopic perspective, the focus is on the healing of the microstructure. Self-healing of cracks for a homogenous physical hydrogel is not remarkable. That phenomenon is universal for any single-phase amorphous polymer or non-covalently crosslinked network for times greater than the terminal relaxation time. That is, the phenomenon of crack healing is due to the viscoelastic nature of the material, and under load (gravity may be a sufficient force) for times longer than the terminal relaxation time, the material is a liquid and exhibits viscous flow. Self-healing of liquids is ubiquitous, so it is not surprising that viscoelastic hydrogels can self-heal at finite time scales, though the actual time for a supramolecular polymer depends on the relaxation times of the physical bonds and may not be easily accessible if the bond strength is very high (i.e., long relaxation times). Healing may be accelerated by physically forcing the surfaces of the crack together. In that case, the healing mechanism may be simply diffusion and re-entanglement of the polymer chains. Thus, it may not be necessary to achieve the terminal relaxation time of the interactions. However, technically, that is not self-healing – perhaps, it should be called facilitated healing. Healing of a microstructure is a bit more complicated, if for no other reason than it cannot be visually observed, like the healing of a macroscopic crack. Nonlinear deformations of supramolecular hydrogels break physical bonds and may deform or disrupt the microstructure, which, coincidently, is the toughening mechanism for

Hydrophobically Associating Hydrogels with Microphase-Separated Morphologies

177

such hydrogels. A major question here is what actually constitutes healing for a multi-phase morphology. One criterion may be the restoration of the nanodomain structure, i.e., the dimensions and spacing. In that case, healing involves diffusion and translation of chain segments to reform the hydrophobic bonds and restore the nanodomain structure, though it is unlikely that one can unambiguously determine, or expect, that each hydrophobic group from a broken hydrophobic bond that pulls out of a nanodomain by the retractive force in the network chains returns to its original nanodomain and spatial position within the nanodomain. Although it is not possible to directly observe the changes and reformation of the nanodomain structure due to deformation, scattering experiments, SAXS and SANS, can provide that information. That approach for assessing healing has the caveat that quantitative interpretation of scattering data requires a morphological model, and there is no unique model for describing the microstructure of these hydrogels. SANS is a particularly useful technique for evaluating the microstructure of hydrogels, because the large differences in the scattering length density (SLD) between hydrogen and deuterium allow one to contrast-match different parts of the microstructure, e.g., the hydrophilic polymer or hydrophobic nanodomain phases by using mixtures of H2O and D2O with different compositions [39]. The details of contrast-matching SANS experiments of the DFx hydrogels are provided in Refs. [16, 20, 25] and are not reproduced here. Simultaneous deformation and scattering measurements (i.e., rheo-scattering) for hydrogels can be performed at a variety of international laboratories with SAXS or SANS capabilities. For example, for the work discussed in this chapter, simultaneous tensile stretching and SAXS experiments [24] were conducted at Brookhaven National Laboratory (BNL) in Upton, NY (USA), and stress relaxation–SANS experiments [16] were conducted at the National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR) in Gaithersburg, MD (USA). In general, rheo-scattering experiments showed that the nanodomain microstructure became anisotropic during large strain deformations [20], and although the structure relaxed following a large amplitude strain, it did so with different kinetics than the stress relaxation. Although the microstructure anisotropy decreased during relaxation, it did not appear to be on a trajectory to recover to the original dimensions in an accessible time scale [20]. An alternative and simpler criterion for healing is the restoration of the mechanical properties of the hydrogel. That is a less rigorous definition that allows the establishment of a new equilibrium distribution of the hydrophobic groups in the healed multifunctional nanodomain crosslinks. It is also a more practical criterion, since the experiments are easier to perform, and with regard to healing, the most important outcome is the restoration of the mechanical integrity of the material. In this case, dynamic mechanical testing of the viscoelastic properties of the hydrogel undergoing nonlinear deformation, followed by relaxation, was used to judge the reversibility of the properties of these hydrogels [12]. As described in the next two paragraphs, those experiments revealed that self-healing occurred in that the viscoelastic properties of the hydrogel were reversible, even when the strain amplitudes

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Fig. 6 Strain and time sweep cycles at 22 C for DF9: (a, c, e, g) time dependence of G0 and G00 with strain ¼ 0.5% and ω ¼ 1 rad/s; (b, d, f) strain dependence of G0 and G00 at ω ¼ 1 rad/s. Modified from Ref. [12]

were large enough to produce a transition of the hydrogel from a viscoelastic solid to a viscoelastic liquid, i.e., when G00 > G0 . The reversible mechanical behavior of the microstructure of a DF9 hydrogel is demonstrated by the viscoelastic data in Fig. 6 [12]. Figure 6a shows a time sweep at room temperature (~22 C) for a shear strain amplitude of 0.5% at a frequency of ω ¼ 1 rad/s, where the viscoelastic behavior is linear. Under those conditions, the physical bonds do not break and G0 and G” remain constant with time. The first strain sweep, Fig. 6b, shows that the mechanical response becomes nonlinear at a strain amplitude of ~1.5%, which is manifested as a decrease in G0 and a peak in G00 as the strain is further increased. Those changes in G0 and G00 are due to changes in the hydrogel microstructure, specifically the breaking of the reversible hydrophobic bonds that decreases the effective crosslink density of the hydrogel. Breaking of the bonds may also involve pulling fluoroacrylate groups out of the nanodomains. However, that is not a catastrophic event, since not all the bonds break or pull out at once due to the relatively random conformations of the network chains that produce a heterogeneous stress distribution in the network. SANS experiments show that the nanodomain microstructure persists during nonlinear mechanical stretching of the hydrogel [20], which confirms that only some of the bonds break during deformation. The nanodomains may contain ~100 associated hydrophobic fluoroacrylate groups [10], so unlike a single-phase supramolecular hydrogel, breaking some supramolecular crosslinks, even if some fluoroacrylate groups pull out of the nanodomains, does not destroy the network. It only reduces the crosslink density, which can reform (heal) after the stress dissipates. A second time sweep following the first strain sweep, Fig. 6c, indicates that the dynamic and loss moduli recovered to their original values very quickly when the nonlinear stress was removed (compare Fig. 6a, c). Figure 6d–g show that this selfhealing behavior can occur for multiple strain cycles. Only three cycles are shown in Fig. 6, but the healing behavior was reproducible for all subsequent strain time sweep cycles evaluated.

Hydrophobically Associating Hydrogels with Microphase-Separated Morphologies

2.6

179

Mechanical Behavior

In general, conventional single network, covalently crosslinked hydrogels are soft and flexible but are relatively weak and brittle elastic solids with an elastic modulus between 0.01 and 10 kPa [40]. In accordance with the theory of rubber elasticity [36], the modulus can be increased by increasing the crosslink density, but that also further embrittles the gel. The network chains in a hydrogel are already highly stretched in their swollen, unperturbed state, so further stretching of the gel is limited, and, in general, covalent hydrogels have poor mechanical strength (1.3 g water/g polymer, that these hydrogels prevent from freezing are unprecedented.

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Fig. 26 Origins of the non-freezing (nf) water as a function of FOSM concentration in HFmx hydrogels: total nf water (black circle); nf water due to hydrogen bonding (red circle); and nf water due to nano-confinement (blue circle). The datum point at [FOSM] ¼ 0 represents the average value for crosslinked HEA hydrogels with different crosslink densities (Cs,XLHEA ¼ 19.9  1.8 wt %) Reproduced from Ref. [25] with permission

Fig. 27 Fraction of nonfreezing water in HFmx hydrogels as a function of interdomain spacing determined from SANS. Reproduced with permission from Ref. [25]

3.5

Shape Memory Hydrogels

Shape memory polymers (SMPs) are stimuli-responsive materials that can change shape when exposed to an external stimulus [109]. The most common type of shape memory material is one for which the shape change is achieved by changes in temperature, i.e., a thermally induced shape memory effect. Such materials have a permanent shape, but they can be reshaped above a critical, switching temperature and fixed into a temporary shape when cooled under stress to below the switching

Hydrophobically Associating Hydrogels with Microphase-Separated Morphologies

201

temperature. The switching temperature is usually coincident or close to a characteristic transition temperature, e.g., a glass transition, melting point, or some other thermodynamic transition temperature. When reheated above the switching temperature, the material reverts back to the permanent shape. SMPs are used commercially as heat-shrinkable tubing and films, but they also have potential biomedical applications as smart medical devices, implants in minimally invasive surgery, sutures, and drug delivery and vascular and orthopedic devices [110, 111]. Shape memory behavior hydrogels have been considered for sensors, actuators, and artificial muscles [112]. The development of shape memory behavior requires two separate crosslinked networks: (1) a permanent network formed from covalent crosslinks or supramolecular bonds with relaxation times much longer than the characteristic time of the shape memory behavior and (2) a temporary network formed from supramolecular bonds that can reversibly disappear or reform upon application of a suitable external stimulus, such as temperature. Those criteria are satisfied by the hybrid DFmx-Cy hydrogels, which have a covalently bonded network and a physical multifunctional network formed by the microphase separation of FOSM nanodomains. The FOSM nanodomains undergo a reversible glass-to-liquid-like transition at ~45 C, above which the hydrophobic bonds are sufficiently weakened so that the network deforms upon application of an applied stress [14]. Figure 28 shows the shape-fixing and shape recovery process of the DFm10-C6 hydrogel. The sample was dyed to improve the visual clarity. A rectangular film of a DFm10-C6 hydrogel, Fig. 28a, was heated to 65 C and stretched to 72% strain, Fig. 28b, and that temporary shape was fixed by cooling to 10 C under stress. Figure 28c shows the sample in its temporary shape after removing the applied stress. In that case, the length of the sample did not change upon removal of the stress. However, the length did decrease with time, while the unstressed temporary shape was soaked in 65 C water, Fig. 28d, which was a consequence of some recovery of the original shape due to the residual stress in the network chains. The ability to fix the temporary shape of a SMP may be quantified by a fixity parameter, F(t), F ðt Þ ¼

lðt Þ  lo ls  lo

ð6Þ

where lo is the original length; ls is the stretched length; and l(t) is the time-dependent length of the hydrogel after removal of the stress. Note that perfect fixity, i.e., no change in the temporary shape, corresponds to F ¼ 100%. Figure 29 shows how the fixity of the Fm10-C3 hydrogel changed with time for a period of 10 days at 10 C [14]. The fit of a stretched exponential to the data in Fig. 28 gave an equilibrium fixity of ~71% and a relaxation time for the F(t) of 129 h. When the sample in the temporary shape was reheated to 65 C, the length recovered to 26.0 mm, which was within experimental error of the original length, Fig. 28e). That corresponded to a recovery efficiency, R(t) ~ 100%, where

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Rðt Þ ¼

ls  lr ls  lo

ð7Þ

and lr is the length of the sample after the shape recovery step.

Fig. 28 Shape memory behavior of the DFm10-C6 hydrogel (sample dyed to blue for clarity): (a) the original shape of the gel (length ¼ 26.3 mm, width ¼ 1.7 mm, thickness ¼ 1.1 mm); (b) gel heated in water to 65 C and stretched to 45.2 mm; (c) the temporary shape of the gel immediately after cooling to 10 C and removing the stress (F ¼ 100%); (d) after soaking unstressed sample in 10 C water for 24 h (F ¼ 87%); and (e) after reheating gel in water to 65 C (R ~ 100%) Reproduced from Ref. [14] with permission

Fig. 29 Shape-fixing efficiency at 10 C as a function of time for F10-C3. Each data point represents the average of three separate experiments using strains of 75–95%, and the error bars are the standard deviation. Modified from Ref. [14]

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4 Summary Supramolecular amphiphilic hydrogels (SAHs) based on water-swollen copolymers of a water-soluble monomer with a fluoro(meth)acrylate exhibit high stretchability, high stiffness, high strength, and extraordinary fracture toughness as a consequence of their microphase-separated morphology. The microstructure is composed of core– shell nanodomains of associated fluoroacrylate dispersed in a water-swollen polymer phase. The nanodomains serve as multifunctional crosslinks for a physically crosslinked network. The morphology of the network is relatively independent of the choice of the water-soluble monomer, but the specific dimensions of the core– shell nanostructure depend on the concentration of the fluoro(meth)acrylate used. The high modulus and strength values achieved with these hydrogels are due to their very high crosslink density, which is a consequence of the relatively high fluoro (meth)acrylate concentration in the copolymer (5–25 mol%). Those concentrations are much higher than the crosslink junction concentrations in conventional, covalently crosslinked hydrogels. Despite the high crosslink density, the SAH hydrogels can have fracture toughness values ~104 J/m2, which is comparable to some synthetic elastomers. This remarkable toughness is due to the reversible nature of the supramolecular hydrophobic bonds that form the crosslinks. That is, unlike conventional crosslinked hydrogels that have essentially no mechanism for dissipating strain energy, the hydrophobic bonds can break when stressed but reform once the stress has dissipated. However, the energy dissipation mechanism in these microphase-separated hydrogels is fundamentally different than that reported for non-microphase-separated, supramolecular hydrogels, in that the nanodomain structure is a multifunctional crosslink, and not all of the hydrophobic bonds within the nanodomains break simultaneously. Therefore, the nanodomain crosslink structure under stress persists, though the crosslink density is stress-, temperature- and timedependent. Note that the toughening mechanism for other supramolecular hydrogels may not actually be different from that of the SAHs, but no other researcher of hydrophobically modified hydrogels, as well as most other supramolecular hydrogels, has reported microphase-separated morphologies for their hydrogels. In light of the known microstructure of the SAHs, the details of the microstructure of the various other supramolecular hydrogels that have been studied are an important issue that needs to be resolved. Like other supramolecular hydrogels, SAHs are viscoelastic due to the finite relaxation times of supramolecular bond. The mechanical response is timedependent, and the hydrogel exhibits considerable hysteresis in loading and unloading experiments and a Mullins effect. That behavior is a consequence of the changes in the microphase-separated microstructure as hydrophobic bonds break and may be pulled out of the fluoro(meth)acrylate nanodomains. The breaking of physical bonds produces the high-energy losses that are responsible for the material’s extraordinary toughness. However, because of the reversible nature of the hydrophobic bonds, they may reform once the stress is dissipated or removed. The nanodomain network persists during the hydrogel deformation, and as a result, the

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internal restoring stresses in the network chains of the remaining network, due to rubber-like elasticity, also persist and produce changes in the microstructure. The molecular details of the microstructure recovery are not yet fully known, but the global microstructure of the gel eventually recovers. The supramolecular nature of SAHs allows the hydrogel to be dissolved by solvating the hydrophobic bonds with a suitable solvent, such as isopropanol or a mixed solvent of water and isopropanol or DMSO. The resulting solutions may be electrospun into micro- or nanofiber mats that may be used as scaffolds for tissue engineering or injected through a capillary (syringe) into a non-solvent medium to form a hydrogel in situ during a medical procedure. Alternatively, the hydrophobic bonds can be sufficiently weakened by either raising the temperature above the Tg of the nanodomains, 45 C, or by applying a sufficient stress to the hydrogel, so that the hydrogel itself can be extruded through a capillary. The SAHs have potential uses in many of the biomedical applications that have been discussed elsewhere for physical hydrogels, in general [110, 111]. However, their two-phase microstructure provides an extra degree of freedom in the development of controllable drug release media using these hydrogels. The antifreeze and shape memory characteristics of the SAHs, which may have a number of biomedical implications, are also advantageous consequences of the microphase-separated microstructure. A serious deficiency of the SAHs discussed in this chapter is that the fluoro(meth) acrylate monomers that were used are no longer commercially available, and although they were commonly use in commercial products (e.g., in Scotchgard, a former product of the 3 M company) when the work on SAHs was begun in the late 1990s, they are today considered to be a persistent organic pollutant (POP). As such, these hydrogels cannot and should not be further developed. Research on similar microphase-separated amphiphilic hydrogels where a hydrocarbon-based hydrophobic monomer replaces the fluoro(meth)acrylate monomers, however, is currently underway. Early results indicate that similar mechanical properties as described here for the fluorocarbon SAHs are possible, as well as controlled drug release, antifreeze, and shape memory properties. Acknowledgments This review was derived from the research and journal papers of the following MS and PhD students and postdoctoral research associates from the University of Connecticut and the University of Akron: Sung-Su Bae, Kaushik Chakrabarty, Debashis Debnath, Jinkun Hao, Xing Lu, Matthew Mullarney, Siamak Shams Es-Haghi, Jun Tian, Chao Wang, Fei Wang, Clinton Wiener, and Yiming Yang. We also acknowledge the contributions to this research by Prof. Thomas A. P. Seery (University of Connecticut); Prof. Colleen Pugh (University of Akron (now, Wichita State University); Dr. Masatumi Fukuto and Dr. Ruipeng Li (Brookhaven National Laboratory, Upton, NY); Dr. Christopher White, Dr. Yun Liu, and Dr. Derek Ho (National Institute of Standards and Technology, Gaithersburg, MD); and Prof. Kenneth Shull and Kazi Sadman (Northwestern University). The nanostructure characterization of these hydrogels was enabled by user facilities for SAXS [Complex Materials Scattering (CMS/11-BM) beamline, operated by the National Synchrotron Light Source II and the Center for Functional Nanomaterials, which are US Department of Energy (DOE) Office of Science User Facilities operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704] and SANS (Center for High Resolution Neutron Scattering, a partnership between the National Institute of Standards and Technology and the National Science Foundation under Agreement No. DMR-1508249).

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Adv Polym Sci (2020) 285: 211–242 https://doi.org/10.1007/12_2019_55 © Springer Nature Switzerland AG 2020 Published online: 29 February 2020

Triblock Copolymer Micelle-Crosslinked Hydrogels Jun Fu

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Triblock Copolymer Micelle-Crosslinked Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Effect of Solvent on Structures and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Multi-responsive Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Macroscopically Assembled Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Supramolecular Micelle-Crosslinked Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract This chapter reviews the preparation, structures, properties, and applications of tough and responsive hydrogels crosslinked by triblock copolymer micelles. An amphiphilic triblock copolymer, Pluronic F127, is functionalized with reactive groups. The functional F127 chains form polyfunctional micelles in aqueous solution, which are used for reaction with hydrophilic monomers or polymer chains to form hydrophobically crosslinked network. Free radical polymerization, host-guest interaction, and dynamic bonds have been utilized to connect the polymer chains with the reactive micelle coronae. The obtained polymer hydrogels show outstanding strength and toughness, with the micelles serving as energy dissipation centers. The structural evolution and energy dissipation mechanisms have been investigated in detail. By incorporating functional monomers into the network, a series of functional hydrogels responsive to pH, salt, electric field, and temperature have been developed. The hydrogels have been utilized as building blocks to fabricate soft actuators, shape-morphing devices, and biomaterials for tissue repair.

J. Fu (*) School of Materials Science and Engineering, Sun Yat-sen University, Guangzhou, China e-mail: [email protected]

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Keywords Hydrophobic association · Micelles · Pluronic F127 · Responsiveness · Shape morphing · Soft actuator · Tough hydrogels · Triblock copolymer

Abbreviations 2D β-CD AAm AMPS AZO CC gels DC DLS DMAEA-Q DMAEMA DMSO F127 F127DA HAAD HEMA IS NaMAA PAAm PAMPS PDMAEA-Q PEG PNIPAM SAXS SEM TEM

Two dimension β-Cyclodextrin Acrylamide 2-Acrylamide-2-methylpropanesulfonic acid 4-(Phenylazo)benzoic acid Chemically crosslinked hydrogels Direct current Dynamic light scattering (2-(Acryloyloxy)ethyl)trimethylammonium chloride 2-(Dimethylamino)ethyl methacrylate Dimethyl sulfoxide Pluronic F127, poly(ethylene oxide-propylene oxide-ethylene oxide) Pluronic F127 diacrylate Hydrazine-modified hyaluronic acid 2-Hydroxyethyl methacrylate Ionic strength Sodium methacrylate Polyacrylamide Poly(2-acrylamide-2-methylpropanesulfonic acid) Poly((2-(acryloyloxy)ethyl)trimethylammonium chloride) Poly(ethylene glycol) Poly(N-isopropylacrylamide) Small-angle X-ray scattering Scanning electron microscopy Transmission electron microscopy

1 Introduction Among the non-covalent interactions used to crosslink hydrophilic polymer chains into networks, hydrophobic association has been very widely and successfully used as the mechanism for crosslinking and energy dissipation [1–3]. Okay et al. used micelles of small molecular surfactants to create a nanometer-sized spot for the local polymerization and association of hydrophobic monomers to form hydrophobic crosslinks [4]. The nanometer-sized hydrophobic crosslinks could be mediated by using salt and other monomers [5]. It even allows for the formation of crystalline domains that further toughen the hydrogels and impart shape memory effects

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[6]. Wang et al. used the self-assembled nanoparticles of surfactants as reactive crosslinkers after exposure to gamma ray that generates free radicals of the nanoparticles to initiate free radical polymerization and synthesize highly resilient hydrogels [7, 8]. Amphiphilic block copolymers are a family of macromolecular surfactants that self-assemble in water into micelles at the length scale from a few to hundreds of nanometers, as driven by the thermodynamic gain from the separation of water and hydrophobic blocks [9–11]. Thus, the micelles are dynamic but quite stable at given concentrations and temperature. This dynamic nature of hydrophobic association is advantageous beyond the conventional rigid chemical crosslinkers since it is flexible to deform upon loadings, which may allow for efficient energy dissipation before the network fractures. Moreover, the micelles, once damaged, may be able to reform at ambient conditions, which is important for self-healing. This chapter reports on representative tough and responsive hydrogels crosslinked by functional triblock copolymer micelles. The toughening mechanisms will be discussed based on investigations of mechanical properties and in situ X-ray scattering studies on the structure evolution of micelles upon loadings. Recent updates on the applications of such hydrogels as building blocks for the fabrication of responsive hydrogel devices are presented.

2 Triblock Copolymer Micelle-Crosslinked Hydrogels Polymer chains are comprised of at least one hydrophobic block and one hydrophilic block usually form micelles in water since the hydrophobic block precipitates from water whereas the hydrophilic one dissolves or swells in water [11]. Thus, micelles with hydrophobic cores and hydrophilic coronae are formed to minimize the unfavorable contact between water and hydrophobic segments. The micelle conformation usually depends on the composition and volume fraction of the blocks. For triblock copolymers with two hydrophilic A blocks and one hydrophobic B block, or ABA triblock copolymer, nano-micelles with A coronae and B cores are formed in water (Fig. 1). The shape and stability of the micelles are determined by the molecular weight, volume fraction of B block, temperature, and concentration of the aqueous solution. The formed micelles are at the thermodynamic equilibrium state in dilute solutions and are quite stable unless the solvent quality, solution composition, or temperature changes. Fig. 1 Self-assembling of amphiphilic ABA triblock copolymer in water into micelles

water A

B

A

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Fig. 2 (a) The synthesis of Pluronic F127 diacrylate (F127DA) through end group modification of F127 triblock copolymer with acryloyl chloride. (b) TEM image of the self-assembled F127DA micelles

Pluronic polymers are a family of amphiphilic nonionic triblock copolymer surfactants that are widely used in industry, cosmetics, and pharmaceutics [12– 14]. Among these, Pluronic F127, or poly(ethylene oxide-co-propylene oxide-coethylene oxide) PEO65-PPO99-PEO65, is known to form micelles in water (Fig. 2). It is a thermo-responsive material that forms physical gels at high concentrations and elevated temperatures [15, 16]. The self-assembled hydrogels are not stable and weak. It is difficult to manipulate the structures and properties of such gels [15]. Instead, F127 micelles in dilute solutions are used as nano-crosslinkers to connect the hydrophilic polymer chains into 3D networks [17]. For this purpose, reactive hydroxyl end groups are functionalized with acrylates [17], aldehydes [18, 19], host/guest moieties [20], and others [21]. The reactive hydroxyl groups on both ends are readily modified with acryloyl chloride. Thus, the hydroxyl groups are converted into reactive double bonds, resulting in F127 diacrylate (F127DA, Fig. 2a) [17]. The small hydrophobic groups do not influence the micellization behavior of the triblock copolymer in water. F127DA chains self-assemble into micelles in aqueous solutions (Fig. 2b). In fact, the critical micellization concentration (CMC) of F127 and F127DA is almost the same. For given concentrations above CMC in water, the dimensions of F127DA and F127 are almost identical in the range from about 150 to 300 nm, depending on the triblock copolymer concentration. Presumably, the functional double bonds are located in the hydrophilic PEO coronae. The reactive micelles are utilized to synthesize polymer hydrogels by copolymerizing with monomers including acrylamide. As the mixtures of the multifunctional micelles and monomers, initiator, and accelerating catalyst are initiated at elevated temperature, polymer hydrogels are obtained without using any other crosslinking agents (Fig. 3a). The multifunctional micelles serve as macro-crosslinkers with the hydrophobic association in the cores, and the hydrogen bonding between polymer chains and physical entanglements of the polyacrylamide (PAAm) chains serve as additional non-covalent crosslinks. The obtained hydrogels are robust and ultra-stretchable. The hydrogel could be knotted and then stretched to

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Fig. 3 (a) The one-pot synthesis of polyacrylamide hydrogels crosslinked by F127DA micelles. (b) The obtained hydrogels are strong and stretchable and (c) replicate the topography of the molds. Modified from Ref. [17] with permission. Copyright 2014 American Chemical Society

very long elongations before fracture or sustain high pressure compression and then immediately recover to its original shape after load release (Fig. 3b). This one-pot synthesis is advantageous because the free radical polymerization could take place in any mold by injecting the precursor solution before initiation. As a result, the synthesized hydrogels nicely replicate the topography of the mold (Fig. 3c). This is beneficial for the synthesis of robust hydrogel devices with complicated structures.

2.1

Mechanical Properties

The micelle-crosslinked hydrogels show outstanding mechanical properties. Figure 4a shows representative tensile stress-strain curves of F127DA micellecrosslinked polyacrylamide micelles. The hydrogels show very high stretchability, with a fracture strain higher than 2,000% and fracture strength about 300 kPa. The fracture strength and strain are dependent on the acrylamide (AAm) concentration in the feed. At a relatively low AAm concentration (2 mol/L), the hydrogel shows a fracture strength of about 40 kPa and a very long fracture strain about 3,000%. With increasing AAm concentration, the fracture strength significantly increases to 150 and 280 kPa, whereas the fracture strain decreases to 2,500 and 2,000% (Fig. 4a). The slight decrease in stretchability and significant increase in fracture strength suggest an increase in fracture toughness or the energy dissipated until the failure of hydrogels. The fracture toughness is defined as the area underneath the tensile stress-strain curves. Figure 4b shows the fracture strength and fracture energy

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Fig. 4 (a) Representative tensile stress-strain curves of F127DA micelle-crosslinked hydrogels with different acrylamide (AAm) concentrations. (b) The dependence of fracture strength (σ) and fracture energy on the AAm concentration. Reprinted from Ref. [17]. Copyright 2014 American Chemical Society

of the micelle-crosslinked hydrogels with different AAm concentrations. Accompanying with the increase in fracture strength, the fracture energy simultaneously increases from 0.6 to 2.8 MJ/m3. It is very interesting to find that both the fracture energy (or toughness) and fracture strength increase with AAm concentration. This simultaneous reinforcement and toughening behavior are very unusual for conventional polymer materials. In the micelle-crosslinked hydrogels, the hydrophobic association, hydrogen bonding, and chain entanglements are three major mechanisms to dissipate energy during loadings. With given F127DA concentrations, the hydrophobic association remains constant. With increasing AAm concentration, the polymer chain length between crosslinks may increase, and thus the degree of chain entanglements and the hydrogen bonding between AAm segments will increase as well. The overall effect is the increase in physical crosslink density, which is manifested by the decreasing swelling ratio of gels with increasing AAm concentrations. For chemically crosslinked hydrogels, the increase in crosslink density usually results in higher modulus and strength. But the hydrogels become rigid and fragile. Herein, the increase in non-covalent interactions between polymer chains, together with the hydrophobic association, enables significantly increases in energy dissipation capability. Thus, the modulus, fracture strength, and fracture toughness of the micelle-crosslinked hydrogels simultaneously increase with AAm concentrations. In a certain F127DA concentration range, the strength and toughness of the micelle-crosslinked hydrogels increase with F127DA concentration, due to more crosslinking and energy dissipation centers. However, with very high F127DA concentrations, the strength and toughness slightly decrease, probably due to the separation of F127DA micelle from the network. On the other hand, the micelle-crosslinked hydrogels show outstanding compression strength, toughness, and fatigue resistance against cyclic loadings. Figure 5a shows representative compression stress-strain curves of the hydrogels. The hydrogels do not fail up to 98% strain (no higher strain was used to protect the

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Fig. 5 (a) Representative compression stress-strain curves of F127DA micelle-crosslinked hydrogels with different AAm concentrations. Cyclic compression loading-unloading curves of (b) micelle-crosslinked and (c) chemically crosslinked PAAm hydrogels. Reprinted from Ref. [17] with permission. Copyright 2014 American Chemical Society

load cell). The apparent stress at 98% strain (σ 0.98) increases from 28 to 75.5 MPa with AAm concentration increasing from 2 to 6 mol/L, and the corresponding compression toughness, or the area underneath the stress-strain curve, increases from 0.6 to 2.34 MJ/m3. The increasing strength and toughness suggest the formation of a denser network with increasing AAm concentrations, likely due to the formation of longer chains and more chain entanglements in addition to the hydrophobic crosslinking by the F127DA micelles. In order to determine the activation energy of the hydrophobic association, frequency-dependent rheological measurements have been performed at different temperatures [22]. The obtained modulus-frequency curves are superposed into a single master curve at a reference temperature of 21
C (Fig. 6a). The corresponding shift factors (aT) are plotted against the reciprocal of Kelvin temperature, showing a linear dependence. The apparent activation energy is derived from the slope of the fitting line, or 264.9 kJ/mol (Fig. 6b). This activation energy value is smaller than that of covalent bonds and close to those reported by Gong et al. for hydrogels crosslinked by triblock copolymer micelles [23].

2.2

Effect of Solvent on Structures and Properties

Usually, the mechanical properties of hydrogels are determined by the crosslink density, chain entanglements, and chain conformation of the network. For chemically crosslinked hydrogels, the crosslink density is fixed upon changes in solvent or environment conditions. In the case of hydrophobically associated hydrogels with

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C. (b) The lnaT-1/T plot for the shift factors (aT) derived from (a). Reproduced from Ref. [22] with permission. Copyright 2018 John Wiley and Sons

micelles as macro-crosslinkers, the association number and micelle dimensions are sensitive to solvent quality. The solvent-copolymer interactions, as well as the chain conformations, are sensitive to the solvent selectivity to specific chains. The influence of solvent quality on the structures and mechanical properties of F127DA micelle-crosslinked hydrogels has been systematically investigated by Xu et al. [24]. An organic solvent, dimethyl sulfoxide (DMSO), which is water soluble and less selective than water to the polymer chains, is used to tune the selectivity of solvent in the gels. A series of water/DMSO binary solvents are used to synthesize PAAm hydrogels crosslinked by F127DA micelles. In the binary solvents, F127DA forms micelles with similar size distributions and hydrodynamic size ξH, independent of the DMSO volume ratio ( f ) in water and DMSO mixture, according to dynamic light scattering (DLS) measurements. The ξH value ranges from 140 to 180 nm with no significant difference between each other. Free radical polymerization of acrylamide monomers and F127DA micelles in DMSO/water solvent takes place to produce hydrogels. Here, the DMSO volume fraction in the binary solvent ( f ) is increased from 0 to 0.5, 0.75, 0.9, and 1.0, and the obtained gels are correspondingly denoted as MFD0, MFD0.5, MFD0.75, MFD0.9, and MFD1. Figure 7a shows representative tensile stress-strain curves of the gels crosslinked by F127DA micelles with different f values. With increasing DMSO content in the gels, the fracture strength decreases from 137 to 135, 87, 68 and 32 kPa (Fig. 7b), while the corresponding fracture strain increases from about 700 to 750, 900, 1,200, and 2,800% (Fig. 7c). It is interesting that the fracture toughness, or the area below the stress-strain curves of these gels, is almost constant, independent on the volume fraction of DMSO (Fig. 7d). It has been established that the tensile toughness is primarily attributed to the hydrophobic association in the micelle cores

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[17]. Therefore, it is likely that the overall hydrophobic association in the gel networks almost remains unchanged, despite the different DMSO fractions. In order to explore the structures and mechanisms underneath the observations, SEM imaging of freeze-dried gels and in situ small-angle X-ray scattering measurements of the gels are performed. Figure 8 shows representative SEM images of fractured and freeze-dried surfaces of MFD0, MFD0.5, MFD0.9, and MFD1 gels. The MFD0 hydrogels swollen with water show typical porous structures, with smooth walls (Fig. 8a). With increasing DMSO content, no porous structures are observed at the fracture surface. Instead, the surface becomes rough, with small particles gradually appearing (Fig. 8b–d). The particle size increases with DMSO content. In the MFD1 gels, a lot of particles with dimensions ranging from tens of nanometers to about 100 nm are observed (Fig. 8d). These particles are smaller than the ξH of F127DA micelles formed in DMSO solutions. Similar formation of particles has been observed in other micellecrosslinked hydrogels and recognized as microphase separation structures [25– 27]. Here, the presence of DMSO promotes microphase separation of micelles from PAAm networks. This will be discussed later.

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Fig. 8 Cross-section SEM images of freeze-fractured and dried (a) MFD0, (b) MFD0.5, (c) MFD0.9, and (d) MFD1 gels. Reproduced from Ref. [24] with permission. Copyright 2019 John Wiley and Sons

The structural evolution of micelles in the gel matrix has been further investigated by using in situ small-angle X-ray scattering (SAXS) with a two-dimension (2D) detector to collect scattering photons. Chemically crosslinked PAAm hydrogels (CC gels) are used as control. Figure 9a shows representative 2D SAXS patterns of CC gels, MFD0 hydrogels, and MFD1 organogels obtained with the incident beam perpendicular to the stretching direction (Fig. 9b). The CC gel gives a dispersive

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Fig. 9 (a) 2D SAXS patterns of chemically crosslinked (CC) PAAm hydrogel, F127DA micellecrosslinked MFD0 hydrogel, and MFD1 gel at 0, 100, and 300% strains. (b) The incident X-ray beam is perpendicular to the stretching direction. The corresponding meridian scattering profiles of the gels at (c) 0, (d) 100%, and (e) 300% strains. (f) The long period of the gels at different strains as calculated from the scattering vectors q. Reprinted from Ref. [24] with permission. Copyright 2019 John Wiley and Sons

scattering halo, showing no peak scattering vector (Fig. 9c). There are no scattering structures in the CC gels. In contrast, the MFD0 hydrogel shows a typical isotropic scattering ring. In order to quantitatively characterize the structural features, the meridian profiles of the 2D SAXS patterns of unstretched gels are compared in Fig. 9c. The MFD0 hydrogel shows a peak scattering vector (q) of 0.17 Å1. The radius of scattering halo, as well as the corresponding q value, decreases with increasing DMSO content to 0.75 and 1.0 in the gels (Fig. 9c). The q value of MFD1 gel is much smaller than that of the MFD0 hydrogel, and the scattering intensity is much weaker as well. The corresponding long periods (L ) in the MFD0, MFD0.75, and MFD1 gels are about 37, 40, and 87 nm (Fig. 9f). The presence of DMSO significantly enhances the long periods and probably the micelle size in the gels. The scattering ring becomes anisotropic when the gels are stretched, whereas it remains unchanged for the CC hydrogels. The circular scattering rings of all the micelle-crosslinked gels become ellipsoidal, with the long axis perpendicular to the stretching direction (Fig. 9d, e). The maximal scattering vector in the meridian direction increases with stretching strain (Fig. 9a). The scattering pattern evolution suggests an orientation and/or deformation of micelles in the gels upon stretching. At 100 and 300% strain, the meridian long periods are slightly increased. During stretching, the deformation of micelles is apparently much less than the polymer

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chains in the gels. This is rational since the major deformation comes from polymer chains. In order to further examine the effect of solvent quality on the structures and properties of the micelle-crosslinked gels, solvent exchange experiments are conducted. The as-prepared MFD1 gels are immersed in water for 12 h to replace DMSO with water, and the MFD0 hydrogels are immersed in DMSO for 12 h to replace water with DMSO. The obtained gels are, respectively, denoted as MFD1,ex and MFD0,ex. It is interesting to find that the tensile stress-strain curves of the MFD1,ex gel overlap that of the MFD0 hydrogel, while the MFD0,ex gel overlaps that of the MFD1 gel (Fig. 10a). Moreover, SEM images reveal that after replacing DMSO with water, the MFD1,ex gel becomes porous with smooth walls (Fig. 10b), whereas MFD0,ex gel after replacing water with DMSO shows microphase separated particles in the polymer matrix (Fig. 10c). These results strongly suggest solventinduced structural changes in the polymer network and the micelles, and the structure changes have significant influences on the mechanical properties of the gels. In dilute solutions, the solvent-polymer interactions are measured by the FloryHuggins interaction parameter χ [28]. Here, the χ values between solvent and PAAm chains are calculated by approximately using the χ value of AAm for PAAm. Calculations yield a χ(AAm-DMSO) of 7.34 and a χ(AAm-H2O) of 0.23. These values suggest that water is a good solvent to PAAm, but DMSO is less compatible with PAAm. Therefore, the PAAm chains in DMSO will adopt a collapsed conformation and microphase separation. On the other hand, the χ(PPO-DMSO) is 0.55 and the χ(PPO-H2O) is 3.48. It is likely that the F127DA micelles may adopt a compact structure in water, while the micelles may become loose and expanded in DMSO. This thermodynamic analysis is consistent with observations based on SAXS patterns that the micelles become larger with the presence of DMSO. Therefore, the structures and mechanical properties of F127DA micellecrosslinked hydrogels are significantly influenced by the solvent quality. Essentially, the micelle structures and PAAm chain conformation are dependent on the

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interactions with solvent. DMSO is less compatible with PAAm chains and more compatible with the PPO blocks. Therefore, with increasing DMSO content in the gels, the F127DA micelles are swollen, whereas the PAAm chains adopt a collapsed conformation. As a result, the hydrophobic association in the micelles and network is weakened, resulting in lower tensile strength but larger stretchability. Since the overall F127DA content remains constant, the global hydrophobic association in the gels is not significantly changed. Therefore, the total energy dissipation capability remains constant, despite changes in solvent quality.

3 Multi-responsive Hydrogels Responsive hydrogels that change their volume or shape upon external stimuli have potential applications in soft actuators [29, 30], artificial muscles [31], drug delivery [32, 33], shape morphing [6, 34], and shape memory [35] devices. It is convenient to incorporate functional moieties, including ionic, chargeable [36], host-guest [31], magnetic [37], thermo-sensitive [38], and light-sensitive groups [39], into the polymer networks, to synthesize multi-responsive hydrogels. In history, however, it remains a challenge for most conventional responsive hydrogels for practical applications, primarily due to the poor mechanical properties. Some hydrogels even could hardly survive the volume changes induced by external stimuli. Recent developments in tough hydrogels have enabled the preparation of a series of responsive hydrogels with outstanding mechanical properties. Double network hydrogels [40] and nanocomposite hydrogels [41, 42] containing thermo-responsive poly(N-isopropylacrylamide) (PNIPAM) chains or segments experience reversible volume or shape changes, which have been employed for the fabrication of soft actuators and walkers. Hydrogels with intrinsic supramolecular recognition are sensitive to redox [43], small molecules [44], or radiation [31] that alters the supramolecular crosslinks and thus changes the volume or shape of hydrogels. Polyelectrolyte hydrogels with ionic or chargeable moieties are responsive to external stimuli that change the charge density inside the network or alter the osmotic pressure balance. To date, it is desired to create novel strategies to synthesize multiresponsive hydrogels with outstanding mechanical properties by using a versatile method that is applicable for many functional groups. The self-assembled F127DA micelles are compatible with most hydrophilic monomers, including ionic monomers. Since F127DA triblock copolymer is a nonionic macromolecular surfactant, its micelle solution is stable with the presence of ionic monomers [45]. The F127DA micelles remain their size and shape when mixed with ionic monomers, initiator, and catalyst. Polyelectrolyte hydrogels are easily obtained by free radical polymerization. Here, 2-acrylamide2-methylpropanesulfonic acid (AMPS) [46] and (2-(acryloyloxy)ethyl) trimethylammonium chloride (DMAEA-Q) [45] are separately copolymerized with AAm and F127DA micelles to produce anionic and cationic hydrogels.

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The obtained polyelectrolyte hydrogels show outstanding mechanical properties. Figure 11a shows the representative tensile stress-strain curves of micellecrosslinked cationic P(DMAEA-Q-co-AAm) hydrogels with different molar ratios of DMAEA-Q to AAm (QxMy). With increasing DMAEA-Q content, the apparent fracture strength, fracture strain, and modulus decrease. The corresponding fracture energy decreases as well. Similarly, Fig. 11b shows the typical tensile stress-strain curves of micelle-crosslinked anionic P(AMPS-co-AAm) hydrogels with different molar ratios of AMPS to AAm (SxMy). The tensile strength, fracture strain, modulus, and fracture toughness decrease with increasing AMPS content. These hydrogels sustain very high compression loadings to more than 98% strain without discernible failure (Fig. 11c, d). The gels recover their original shapes after unloading. Moreover, these polyelectrolyte hydrogels have outstanding fatigue resistance. When the gels are cyclically compressed to very high strains (e.g., 90% strain), the loading and unloading curves complete a hysteresis loop, and the successive loops fully overlap each other. No waiting time is needed between two adjacent cycles (Fig. 11e). The hysteresis loop indicates energy dissipation during loadings, while the overlapping of loops suggests an immediate and complete recovery of the energy dissipation mechanisms in the hydrogels after unloading. In comparison to their nonionic PAAm hydrogel counterparts, the F127DA micelle-crosslinked polyelectrolyte hydrogels show a bit lower strength and

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toughness. It is likely that the internal electrostatic repulsion between the polymer chains more or less weakens the energy dissipation. On the other hand, the intrinsic electrostatic repulsion largely determines the volume of the hydrogels. Changes in the pH, or ionic strength in the environment usually, alter the intrinsic electrostatic balance in the swollen network, leading to changes in the volume. Such volume changes are reversible when the environmental pH and ionic strength are reversed. Reversible swelling and deswelling take place for the cationic poly(DMAEA-Q) (PDMAEA-Q, QxMy) and anionic polyAMPS (PAMPS, SxMy) hydrogels crosslinked by F127DA micelles. Figure 12a shows representative swelling of QxMy hydrogels at pH 3 and deswelling at pH 11. At pH 7, the electrostatic repulsion (Fig. 12b) leads to swelling. As the pH becomes 11, the OH ions with negative charges shield the electrostatic repulsion (Fig. 12d) and thus the hydrogel shrinks. The swelling and deswelling are reversible as the hydrogels are shuttled between acidic, neutral, and alkaline solutions (Fig. 12c). Meanwhile, reversible swelling/shrinking takes place as the environmental ionic strength is cyclically changed. The as-prepared QxMy hydrogels swells in pH 7 solution with an ionic strength (IS) of 0.1 to equilibrium. Subsequent immersion of the gel in a neutral solution with ionic strength of 0.05 leads to further swelling. Then, as the swollen gel is taken back to the IS 0.1 solution, it deswells to the previous equilibrium volume. The hydrogel undergoes cyclic swelling and deswelling as it is repeatedly immersed in neutral solutions with different IS values (Fig. 13). It is interesting that the equilibrium volume at each condition almost

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Fig. 13 Reversible swelling and deswelling of the F127DA micellecrosslinked Q1M8 hydrogel cyclically immersed in solutions with ionic strength (I ) of 0.05 and 0.20. Reproduced from Ref. [45] with permission. Copyright 2015 Royal Society of Chemistry

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remains constant, indicating that the crosslinking based on hydrophobic association is quite stable in these solutions. Similarly, the anionic P(AMPS-co-AAm) (SxMy) hydrogels undergo reversible swelling and deswelling in response to changes in environmental pH and ionic strength. Polyelectrolyte gels are known as electroactive materials [47, 48]. Osada first reported the motility of a PAMPS hydrogel driven by electric field in ionic surfactant solutions [48]. Therein, when the PAMPS is immersed in a dilute solution of n-dodecyl pyridinium chloride containing 3  102 mol L1 sodium sulfate, an external electric field drives the electrokinetic surfactant assembly on the surface of hydrogel. The local osmotic pressure increases to cause shrinking at the assembly side. Consequently, the gel bends toward the assembly surface. This bending behavior is thus determined by the charge type of the surfactant and the gel, and the electric field direction. As the electric field direction is reversed, the gel bends oppositely. By hooking both ends of the polyelectrolyte gel strip to a polymer ratchet, it is even driven to “walk” along the ratchet. Recent studies have found that polyelectrolyte hydrogels can be actuated by electric field in small molecular surfactant (e.g., sodium dodecyl sulfate) and salt solutions. Ion migration in solutions induced by electric field is likely to guide the redistribution of free ions in the polyelectrolyte network, leading to the formation of opposite ionic bilayers at the gel surface. Thus, the local electrostatic balance and osmotic pressure are changed, leading to asymmetric swelling or deswelling at the surface. The rapid ionic migration in electric field makes the gel response rapidly and reversibly. Figure 14 schematically illustrates a typical electric field actuation setup. A reversible DC power supply is used to generate electric field between two graphite electrode plates that are immersed in a salt solution. The salt could be Na2SO4, ionic surfactants, or other ionic molecules. The polyelectrolyte hydrogel strip is fixed at

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Fig. 14 (a) Schematic illustration to the electric field actuation setup. Actuation of (b) the S1M5 and (c) Q1M5 hydrogels in the electric field. Adapted from Ref. [46] with permission. Copyright 2016 American Chemical Society

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one end to a holder, with the free end immersed in the solution. As the electric field is applied, the hydrogel starts to bend toward one of the electrodes. The bending direction is determined by the electric field direction and the charge type in the hydrogel. The P(AMPS-co-AAm) hydrogel with negative charges in the pendant groups swings toward the cathode (Fig. 14b), while the P(DMAEA-Q-coAAm) gel with positive charges in the dangling groups bends toward the anode (Fig. 14c). Figure 15 shows the cyclic actuation of the P(AMPS-co-AAm) and P(DMAEA-Q-co-AAm) hydrogels in the electric field. The P(AMPS-co-AAm) hydrogel bends toward the cathode, for example, at 20 V, with a 100 mm distance

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between the electrodes. The bending angle reaches about 20
in about 10 s. As the bias is reversed, the gel strip starts to bend backward and reaches an angle about 60
in less than 1 min (Fig. 15a). As the electric field direction is cyclically reversed, the gel strip swings between the electrodes. The bending angle is merely dependent on the actuation time. Similarly, the P(DMAEA-Q-co-AAm) gel is cyclically actuated in the electric field (Fig. 15b). The response of the hydrogel to the electric field is dependent on the salt concentration and electric field strength (voltage and distance between the electrodes). According to Shiga type bending theory [49] for gels driven by electric field, the bending degree   Y ¼ RC p ht L2 ð1  ht Þ =DE

ð1Þ

where E is Young’s modulus, D is the thickness, L is the length of the hydrogel strip before bending, Cp is the concentration of the free counterions to the polyions, h is the counterion’s migration rate, and t is the exposure time to an electric field. The bending behavior is described by the bending angle (θ) of the hydrogel strip from its original position (Fig. 14a). For a given hydrogel strip in an electric field, the bending angle increases almost linearly over time (Fig. 16a). There is a transition in the slope of the bending curve at about 60–70 s, independent on the angle of the gels. This slowdown behavior may indicate the migration saturation of counterions in the polyelectrolyte gels in about 1 min. The bending rate is sensitive to the salt concentration in the solution. With increasing Na2SO4 concentration in the solution, the bending rate of P(AMPS-coAAm) hydrogel becomes slower (Fig. 16a, b). In general, the bending behavior is a result of electric field-induced migration of free counterions in the gels. With increasing salt concentration or ionic strength in the solution, the electrostatic interaction of counterions might be partially screened or counteracted. This explains the slowing down of the actuation of gels by increasing salt concentration. With given Na2SO4 concentrations, the bending rate for P(DMAEA-Q-co-AAm) gel is faster than that of P(AMPS-co-AAm) gel (Fig. 16b). With given salt concentrations, the actuation rate increases with electric field (Fig. 16c). A higher electric field drives more free counterions to migrate and then the gel bends faster. In fact, the content of ionic groups fixed in the polymer network essentially determines the actuation rate of the gels. Figure 16d compares the actuation rates of P(DMAEA-Q-co-AAm) gels at different electric field strength. At each electric field strength, the actuation rate increases with increasing DMAEAQ contents. Similar dependence is also observed for the P(AMPS-co-AAm) gels actuated by electric field. During the electric field-driven actuations, no obvious shrinking has been observed. This is quite different from the actuation of polyelectrolyte hydrogels actuated by electric field with the presence of amphiphilic ionic organic surfactants. In those cases, the migration and adsorption of surfactants to the gel surface induce local deswelling. During cyclic actuation by reversing electric field direction, the

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Fig. 16 Electric field actuation behaviors of P(AMPS-co-AAm) (SxMy) and P(DMAEA-Q-coAMPS) (QxMy) hydrogels. (a) Bending angle over time at different Na2SO4 concentrations. (b) Dependence of actuation rate on Na2SO4 concentration. (c) Bending angle over time at different electric field strength. (d) Dependence of actuation rate on the electric field for hydrogels with different charge densities. Adapted from Ref. [46] with permission. Copyright 2016 American Chemical Society

hydrogels undergo repeated deswelling, which eventually causes structural damages and failure of most conventional fragile polyelectrolyte gels. Herein, the polyelectrolyte hydrogels crosslinked by F127DA micelles are stable in the salt solutions, and their outstanding strength, toughness, and fatigue resistance make them survive actuation for many cycles, without any damages. Besides, the migration of counterions in the gels is reversible. The actuation behavior is quite stable. No damping in the actuation rate or swing amplitude is observed for these hydrogels. Such electric field actuation of tough polyelectrolyte hydrogels may find applications in artificial muscles, soft actuators, or soft robotics [48, 50].

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4 Macroscopically Assembled Devices To fabricate smart flexible devices from responsive and functional hydrogels, it is keen to integrate hydrogels with different properties or functionalities into single devices [51]. To date, numerous hydrogel devices based on bilayer structures have been reported. The classic bilayer architecture, pioneered by Hu et al. [52], is usually comprised of two hydrogel layers with different moduli or different responsiveness. Upon external stimulus, each layer swells or deswells differently, leading to different volume changes and internal stress. As a result, the gel bends to release the internal stress. Many responsive hydrogels, including thermo-, pH-, ion-, redox-, and lightresponsive hydrogels, have been utilized to fabricate bilayers. This fundamental principle of hydrogel bilayers has recently been widely extended to fascinating devices with abundant geometry or architectures that execute delicate movements. Bilayer flowers, grippers, and others have been demonstrated in literature to reversibly change shapes or grasp small objects. So far, most bilayer-based hydrogel devices are fabricated by sequential synthesis of the layers with different components and properties. This procedure is usually trivial and limited to simple structures. For practical applications, it is desired to develop novel simple and reliable methods to integrate hydrogel building block into devices. However, direct assembling [53] or gluing hydrogels together is challenging because most hydrogels are slippery and not adhesive to each other. Harada et al. utilize supramolecular recognition at the surface and interface of hydrogels to assemble small hydrogel cubes together [43, 44, 54, 55]. Shi et al. further demonstrate that the success of such macroscopic assembling based on supramolecular recognition is highly dependent on the rigidity of the gels [56]. It is difficult for gels with high modulus to assemble together since the macroscopic assembling requires the readjustment of surface topography to achieve a conformal contact. To tackle this problem, a soft and flexible surface coating is devised to allow for adaptive and conformal contact to enable macroscopic assembling [57]. These studies demonstrate the possibility to use hydrogels as building blocks to construct smart devices. But it remains a challenge to develop versatile strategies applicable for most hydrogels, particularly strong and tough hydrogels, for the fabrication of smart devices for practical applications. In comparison with the short-scale supramolecular recognition, electrostatic attraction has long-distance effects. In the polyelectrolyte hydrogels, the ionic functional groups are fixed on the network, acting as immobile charges, while the free counterions are recognized as mobile ions [58]. The free ions can migrate in electric field. In fact, as two polyelectrolyte hydrogels with opposite immobile charges are placed together, a transient electric field forms at the interface (Fig. 17a). The local electric field will drive migration and redistribution of mobile ions (Fig. 17b). As a result, a new local electrostatic field and electrostatic equilibrium are established (Fig. 17c). This concept of macroscopic assembling of hydrogels based on electrostatic attraction is examined by using F127DA micelle-crosslinked poly(sodium methyl

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Fig. 17 Local electric field evolution at the interface of two hydrogels with opposite charges. (a) The local electric field, (b) migration of free counterions, and (c) establishment of new electrostatic equilibrium at the interface. Reproduced from Ref. [58] with permission. Copyright 2018 Royal Society of Chemistry

acrylate-co-2-hydroxyethyl methacrylate) P(NaMAA-co-HEMA) hydrogels with negative charges and poly(2-(dimethyl amino)ethyl methacrylate-co-2-hydroxyethyl methacrylate) P(DMAEMA-co-HEMA) hydrogels with positive charges [58]. 2-Hydroxyethyl methacrylate (HEMA) is used to modulate the modulus of the hydrogels, and the concentrations of NaMAA and DMAEMA are changed to tune the immobile charges in the networks. As the hydrogels containing negative and positive charges are assembled together, the immobilized polyions form a robust interface. As the assemblies are pulled apart, one of the hydrogels is ruptured near the interface (Fig. 18a), and long fibers are pulled out at the interface (Fig. 18b). The tensile strength of the assemblies is used to measure the adhesion strength. Figure 18c shows that the tensile strength increases from 35.4 kPa to a maximum of 104.5 kPa at the CMAA of 0.125 mol/L and then decreases to 42.0 kPa at CMAA of 0.15 mol/L. It is likely that the increase of the –COO charge density in the network favors the interface strength. When the CMAA was over 0.1 mol/L, those counterions (Na+) remained inside the gels may screen the negative charges and thus reduce the interface strength. On the other hand, the effect of positive charge density or DMEAMA concentration in the gels on the interface strength is also investigated. Figure 18d shows the tensile strength of hydrogels with different CDMAEMA. The interface strength increases from 26.4 to 104.5 kPa as the CDMAEMA increases from 0.1 to 0.4 mol/L and then decreases to 76.1 kPa as the CDMAEMA further increases to 0.5 mol/L. With the CDMAEMA lower than 0.4 mol/L, the positive charge density increases with CDMAEMA, leading to the enhancement of interface strength. With the CDMAEMA higher than 0.4 mol/L, the free ions may partly shield the electrostatic interaction, resulting in the reduction of interface strength. The interface strength can be measured by using peel-off tests. In this method, two hydrogel strips with opposite charges are assembled together. The free ends of the bilayers are steadily pulled by using a tensile test instrument to separate the assembly apart (Fig. 19a). The force and displacement are recorded. Figure 19b shows representative force-displacement curve of the gels with different negative charge (NaMAA) contents in the network. The oscillating peaks on the curves indicate the gradual peeling-off at the interface.

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Fig. 18 (a) Photographs of tensile tests of assembled hydrogels with negative and positive charges. (b) SEM image of the fracture surface of the assembly. The tensile strength values of the assemblies with different (c) negative charges or NaMAA concentration and (d) positive charges or DMAEMA concentrations. Adapted from Ref. [58] with permission. Copyright 2018 Royal Society of Chemistry

Fig. 19 (a) Peel-off test and (b) representative peel-off force-displacement curves of hydrogels with different formulations. Adapted from Ref. [58] with permission. Copyright 2018 Royal Society of Chemistry

The interface strength is sensitive to the ionic strength of the solutions. As the assembly is immersed in salt solution, the ions may migrate into the interface and shield the electrostatic interaction. When the ionic strength or salt concentration

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Fig. 20 Effect of ionic strength on (a) the electrostatic interaction, (b) tensile strength, and (c) peeloff behavior at the interface. Adapted from Ref. [58] with permission. Copyright 2018 Royal Society of Chemistry

increases, the shielding effect may dominate and eventually overwhelm the electrostatic attraction between the immobilized polyions (Fig. 20a). As a result, the tensile strength decreases from about 90 kPa to less than 20 kPa (Fig. 20b), while the peeloff force decreases from about 0.38 N to undetectable levels (Fig. 20c) as the ionic strength gradually increases from 0.01 to 0.05 mol/L. The interface strength is sensitive to the solution pH. At low pH, the COO groups of the NaMAA moieties are protonated and become neutral. As the solution pH increases, the COOH groups start to lose proton and gradually become charged. Thus, the interface electrostatic interaction increases at pH < 7. Further increase in pH at pH > 7 leads to electrostatic shielding at the interface and thus decreases the interface strength (Fig. 21). Figure 21b shows the tensile strengths of the assemblies at different pH values. With the pH increase from 3 to 7, the interface strength increases from 16.8 to 83.2 kPa, probably due to the increase in charge density in the PNaMAA segments. Further increase of pH to 11 led to a gradual decrease of the interface strength to 0 N. The corresponding peel-off tests show that the peel-off force is larger than 0.15 N, 0.21 N, and 0.44 N at pH 3, 5, and 7. The peel-off force further decreases to 0.13 N at pH 9. Based on the robust electrostatic attraction at the interface, the polyanionic and polycationic hydrogels are assembled into bilayers and shape morphing devices with

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Fig. 21 Effect of pH change on (a) the electrostatic interaction, (b) tensile strength, and (c) peel-off force of the hydrogel assemblies. Adapted from Ref. [58] with permission. Copyright 2018 Royal Society of Chemistry

Fig. 22 Macroscopic assembling of polyelectrolyte hydrogels with opposite charges. (a–c) Bilayers and (d–h) microstructured assemblies. The assemblies undergo shape morphing upon external stimuli. Reprinted from Ref. [58] with permission. Copyright 2018 Royal Society of Chemistry

periodic structures. Figure 22 show representative macroscopic assemblies of P(NaMAA-co-HEMA) and P(DMAEMA-co-HEMA) hydrogels. First, a bilayer comprised of P(NaMAA-co-HEMA) and P(DMAEMA-coHEMA) hydrogel sheets (150  5  1.5 mm each) is fabricated (Fig. 22b). As the assembly is immersed in a solution of pH 5, the P(NaMAA-co-HEMA) layer remains unchanged, but the P(DMAEMA-co-HEMA) layer is swollen 1.5 times

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that at pH 7. The different swelling extent drives the bilayer to bend toward the P(NaMAA-co-HEMA) side, leading to the formation of a ring (Fig. 22c). Upon immersing in pH 7 solution, the bilayer slowly recovers to its original state. Second, the macroscopic assembling was further utilized to fabricate assembled devices with patterned structures (Fig. 22d). For example, the P(DMAEMA-coHEMA) patches (width ¼ 5 mm, thickness ¼ 1.5 mm) are periodically assembled on the P(NaMAA-co-HEMA) (200  10  1.5 mm) surface with an angle of 45
and a spacing of 5 mm (Fig. 22e). The periodic structures with different swelling properties produce an internal stress upon immersing in a solution of pH 5, which drives a transformation from planar shape to a helix in about 320 min (Fig. 22f–h). Herein, the internal stress is rendered by the periodic swelling contrast of polycationic and polyanionic gels [58]. The facile fabrication could be used for a convenient fabrication of 3D structures by properly engineering the hydrogel sheet dimensions and/or the periodicity and the size of the patches.

5 Supramolecular Micelle-Crosslinked Hydrogels The hydroxyl end groups of F127 triblock copolymer can be modified with many other functional groups. The modified F127 chains self-assemble in aqueous solutions into polyfunctional micelles. The obtained micelles are able to link with polymer chains through supramolecular recognition, dynamic bonds, and noncovalent bonding, just to name a few. It offers great opportunities to design the crosslinking method and particularly to tune the mechanical, self-healing, and recovery properties. Chen et al. functionalized the F127 copolymer by attaching aldehyde groups on both ends (Fig. 23) [18]. In aqueous solutions, the modified F127 chains selfassemble into micelles with abundant aldehyde groups in the coronae. Aldehydes are known to form dynamic acylhydrazone bonds with acylhydrazine groups [59]. The modified micelles were employed as multifunctional crosslinkers to bond with three-armed poly(ethylene glycol) (PEG) with acylhydrazine end groups, leading to the formation of hydrogels (Fig. 23). Different from the F127DA micellecrosslinked hydrogels, the use of aldehyde-functionalized F127 micelles and threearm polymers produces hydrogels crosslinked by hydrophobic association and chemical bonding. The dual crosslinking is coupled through the dynamic acylhydrazone bonds. Although the molecular weight of PEG is relatively low, the obtained hydrogels show an extremely high stretchability up to 117 times of its original length. The dynamic hydrophobic association and acylhydrazone bonding work together to provide a large amount of energy dissipation, as featured by the large hysteresis loops upon tensile loading-unloading tests. It is assumed that the chain sliding in the micelles may account for the extremely high stretchability. However, it takes about 3 days to achieve about 90% recovery at room temperature, presumably due to the re-establishment of the acylhydrazone bonds in the networks.

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Fig. 23 Aldehyde-functionalized F127DA micelles as macro-crosslinkers for the synthesis of ultra-stretchable and self-healing hydrogels based on hydrophobic association and dynamic bonds. Reprinted from Ref. [18] with permission. Copyright 2017 American Chemical Society

This strategy based on aldehyde-modified F127 micelles has been applied to crosslink hydrazine-modified hyaluronic acid (HAAD) via acylhydrazone bonds, leading to the formation of injectable, self-healing, and biocompatible hydrogels [60]. The hydrogels are applied to promote wound healing of deep partial-thickness burn of rat skin. Guo et al. further used aldehyde-modified F127 micelles to form dynamic bonds with the amino groups of quaternized chitosan, generating injectable and selfhealing hydrogels with outstanding antibacterial activity [19]. The hydrogels are adhesive to skin and tissues and promote the healing of full-thickness wound of rat skin. Moreover, Song and Li et al. modified both ends of F127 with azo groups, generating F127AZO that self-assembles into micelles in water (Fig. 24) [20]. The AZO groups in micelle coronae form inclusion complex with vinyl-functionalized β-cyclodextrin (β-CD), forming micelles terminated with double bonds. Such functional micelles are used to copolymerize with AAm, leading to hydrogels crosslinked by F127 micelles through supramolecular links (Fig. 24). The hydrogels show tensile strength up to 480 kPa and stretchability to more than 2,000% and sustain cyclic compression loadings with small loss of compression toughness. The supramolecular AZO/β-CD complex is sensitivity to UV light since the AZO group changes its trans-conformation to cis-conformation upon UV irradiation [31]. The cis-AZO has much lower complex constant with β-CD than that of the trans-AZO/β-CD pair. Therefore, the supramolecular AZO/β-CD links between

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Fig. 24 AZO-modified F127 micelles as macrocrosslinkers to crosslink β-CD terminated PEG chains through host-guest recognition, leading to the formation of ultra-stretchable and tough hydrogels. Reprinted from Ref. [20] with permission. Copyright 2018 American Chemical Society

polymer chains and F127 micelles could be cleaved upon exposure to 360 nm light, leading to reduction in tensile strength and stretchability. Subsequent irradiation by 480 nm light leads to partial recovery of the mechanical properties, probably due to the re-establishment of AZO/β-CD links in the networks.

6 Conclusions Triblock copolymer micelles have been successfully used as non-covalent crosslinking centers to prepare hydrogels with outstanding strength, toughness, and fatigue resistance. The nonionic triblock copolymer micelles are compatible with many functional monomers, which allows for very flexible design in the functionalities of the polymer hydrogels. By using ionic or chargeable monomers, a series of responsive hydrogels have been developed. Moreover, the responsive hydrogels are assembled through electrostatic attractions into soft devices with welldefined structures, which are able to undergo programmed shape morphing upon external stimuli. This strategy based on triblock copolymer micelles provides a variety of possibilities to construct novel high performance and functional hydrogels. Dynamic

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linkage between micelles and polymer chains based on different mechanisms, including supramolecular recognition and dynamic bonding, has been demonstrated to tune the stretchability, injectability, self-healing, and stimulus-responsiveness. These merits and properties are promising for applications as soft actuators and biomedical engineering. Acknowledgment This work is supported by the National Natural Science Foundation of China (51873224 and 21574145) and MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Zhejiang University (2018MSF04).

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Adv Polym Sci (2020) 285: 243–294 https://doi.org/10.1007/12_2019_59 © Springer Nature Switzerland AG 2020 Published online: 24 April 2020

Self-Healing Hydrogels Based on Reversible Covalent Linkages: A Survey of Dynamic Chemical Bonds in Network Formation Ruveyda Kilic and Amitav Sanyal

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Imine Bond Formation-Based Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Cross-Linking of Natural Polymers Using Imine-Based Linkages . . . . . . . . . . . . . . . . . . 2.2 Cross-Linking of Synthetic Polymers Through Imine Linkages . . . . . . . . . . . . . . . . . . . . . 3 Acylhydrazone Bond Formation-Based Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Cross-Linking of Synthetic Polymers Through Acylhydrazone Linkages . . . . . . . . . . 3.2 Cross-Linking of Natural Polymers Through Acylhydrazone Linkages . . . . . . . . . . . . . 4 Boronic Ester Bond Formation Based Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Cross-Linking of Synthetic Polymers Through Boronic Ester Linkages . . . . . . . . . . . . 4.2 Cross-Linking of Natural Polymers Through Boronic Ester Linkages . . . . . . . . . . . . . . 5 Diels-Alder Cycloaddition-Based Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Disulfide Bond Formation-Based Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Photo-Responsive Linkage-Based Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Dual-Responsive Self-Healing Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Over the past decade, the design of hydrogels has transformed from fabrication of static cross-linked materials to dynamic systems, which upon damage can potentially self-heal to their original state, either autonomously or through the help of external stimuli. This chapter highlights, through examples, the synthesis and

R. Kilic Department of Chemistry, Bogazici University, Istanbul, Turkey A. Sanyal (*) Department of Chemistry, Bogazici University, Istanbul, Turkey Center for Life Sciences and Technologies, Bogazici University, Istanbul, Turkey e-mail: [email protected]

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self-healing properties of hydrogels based on the various types of dynamic chemistries available for their fabrication. While the main focus of the chapter is on the chemistry of cross-linking and the conditions under which self-healing was achieved, a brief discussion on the method utilized to ascertain the extent of selfhealing through mechanical or rheological data, as well as possible applications of such materials, is explored. Keywords Click reactions · Cross-linked networks · Dynamic covalent chemistry · Self-healing hydrogels · Stimuli-responsive

1 Introduction Hydrogels are cross-linked polymeric materials that have gained a ubiquitous presence as indispensable materials in various biomedical applications [1– 3]. Hydrogels can either form the bulk of the functional material, e.g., injectable gels for therapeutic applications or tissue engineering scaffolds, or be present at the interface of diagnostic devices for biological assays, or act as functional coatings on implantable devices. In many of these applications, short- and long-term durability and stability under the biological environment are crucial for their performance. Depending on the application, hydrogels should not only be chemically stable under the environment but also be stable to the exposed mechanical stresses. Similar to self-healing of biological soft materials such as tissues, any damage incurred on the hydrogels should be repairable. Thus over the past decade, hydrogels have transformed from being static cross-linked materials to dynamic systems that upon damage can revert to their pristine state either autonomously or through the help of external stimuli [4–6]. Hydrogels maintain their network structure upon swelling in water through the presence of either physical or chemical cross-links. Most physical cross-links are dynamic in nature since they are based on crystallization, hydrophobic, electrostatic, or hydrogen-bonding interactions, which can reform upon damage. The dynamic nature of such physical interactions allows incorporation of energy dissipation modes into the hydrogel which makes them more tolerant to transient stress. Depending on the chemical composition and network structure, physically crosslinked hydrogels exhibit excellent mechanical properties suitable for many biological applications and have been of high interest in recent years [7–9]. Likewise, chemically cross-linked hydrogels have also been explored extensively over the past decades since their network structure, the nature of interchain linkages, and responsiveness to external stimuli can be fine-tuned through synthetic strategies [10]. Furthermore, chemically cross-linked hydrogels can possess very good mechanical properties over a wide range of environmental conditions. In case of chemically cross-linked hydrogels, damage results in rupture of chemical linkages that form the

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network structure. In general, chemical cross-links in hydrogels are often irreversible, e.g., those formed in photopolymerized gels. Once the interchain cross-links are broken, the network structure does not revert back to its original state, and the loss of mechanical and other related properties is irrecoverable. In recent years, it has been established that this problem can be addressed through utilization of cross-linking strategies that involve dynamic chemical linkages. These chemical bonds upon breakage can undergo reformation, and thus the original network structure can be restored. The reformation of the ruptured bond can occur in an autonomous manner, i.e., by itself without the need of any external stimuli, or in an externally triggered fashion which would require external stimuli such as heat or light, either to enable fast recovery or to recreate conditions necessary for bond formation. To date, most dynamic covalently cross-linked hydrogels undergo self-healing through application of external stimuli, which generally recreate the bond formation conditions that are often the same as the ones employed during their fabrication. A variety of reversible chemical linkages have been employed to date to install covalent cross-linkages required for network formation. The commonly used reversible bond formations involve heteroatom-based imine, acylhydrazone, boronate ester, disulfide bonds, along with carbon-carbon bonds formed through [4+2] Diels-Alder cycloaddition and [2+2] and [4+4] cycloaddition reactions (Fig. 1). The subsequent sections of this chapter are divided into parts that highlight the synthesis and self-healing properties of hydrogels based on the specific type of dynamic chemistry utilized to fabricate such gels through examples. While the main focus is on the chemistry of cross-linking and the conditions under which self-healing was achieved, a brief discussion on the method utilized to ascertain the realization of self-healing has also been provided by mentioning the mechanical or rheological data of these materials. Furthermore, information related to possible application of the hydrogels under investigations as provided by the researchers has also been included to provide the readers with intended or possible utility of such materials.

2 Imine Bond Formation-Based Hydrogels Dynamic imine bonds formed through reaction between an aldehyde and a primary amine group, also known as Schiff base reaction, have been widely exploited to install stimuli-responsive cross-links in hydrogels. Imine bond forms upon nucleophilic addition of the amine to the carbonyl of aldehyde through three types of reactions which are imine condensation, exchange, and metathesis. It is a favorable reaction for polymer cross-linking to obtain hydrogels since it does not involve any intermediate step. The cleavage and formation of the bond occur instantly within the hydrogel network allowing autonomous self-healing. The dynamic equilibrium of these hydrogels can be tuned by varying the electronic and steric nature of the carbonyl and amine groups involved, as well as through the choice of solvent, concentration, pH, and temperature of the environment [11].

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Fig. 1 Stimuli-responsive nature of dynamic covalent bonds that are commonly used to obtain selfhealing hydrogels

2.1

Cross-Linking of Natural Polymers Using Imine-Based Linkages

Natural polymers such as chitosan, gelatin, fibrinogen, and their derivatives, which are rich in amine groups, have been widely used to fabricate dynamic polymeric networks using imine chemistry. Likewise, aldehyde groups can be introduced into natural polymers such as dextran and pullulan through the oxidation of their pendant hydroxyl groups. As one of the earliest examples, Wei and coworkers reported several self-healing hydrogels cross-linked through imine linkages [12–14]. In most of their work, chitosan was reacted with a poly(ethylene glycol) bearing benzaldehyde groups at chain ends (DF-PEG) to yield gels with tunable physical properties for different applications. Using this chemistry, a chitosan-based dynamic hydrogel with good self-healing ability and quick recovery was synthesized for encapsulation and controlled release of small bioactive molecules such as lysozyme

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Fig. 2 (a) Synthesis of self-healing chitosan and DF-PEG hydrogels through imine cross-linking, (b) continuous step strain test (strain, 20–200%), (c) visual self-healing experiments of self-healing hydrogel and gelatin solution (control). Adapted with permission [12]. Copyright 2011, American Chemical Society

without compromising its bioactivity (Fig. 2) [12]. Using the same chemistry, the authors reported fabrication of a magnetic hydrogel which was deformed under high strain (200%) and could easily recover its initial mechanical property upon reducing the strain to 1% [13]. It was also demonstrated that small pieces of these magnetic hydrogels could combine together to yield a larger bulk gel under an external magnetic field. They employed the same chemistry for obtaining a chitosan-based hydrogel as an injectable cell therapy carrier which facilitates 3D encapsulation of HeLa cells with good viability (87% after the injection and 85% after 24 h) [14]. In this system glycol chitosan (GCS) derivative was used to improve the solubility of chitosan. In 2015, Tseng and coworkers synthesized an injectable, biodegradable, selfhealing hydrogel by cross-linking DF-PEG with glycol chitosan (GCS) in water to

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Fig. 3 (a) Synthesis, (b) continuous step strain tests of alginate and self-healing chitosan hydrogels. Adapted with permission [15]. Copyright 2015, Wiley-VCH

obtain hydrogels with stiffness suitable for the differentiation and growth of neural stem cells (NSCs) (
1.5 kPa) [15]. Additionally, conventional alginate hydrogels with similar physical properties were prepared with calcium chloride-based crosslinking for comparison of self-healing ability (Fig. 3a). Chitosan-based system formed gels within 200 s at room temperature and 100 s at 37 C, allowing enough time for drug/cell encapsulation and injectable formulation, while the alginate precursor formed solid gel immediately. Continuous step strain tests were carried out for both hydrogel systems, where strain was altered between 1 and 300%. The self-healing chitosan gel recovered back to its initial G0 value repeatedly, while recovery of the alginate gel was very limited (Fig. 3b). To test healing effect on neural development, murine NSCs were mixed in hydrogels. Self-healing hydrogel based on imine linkages allowed spheroid progenitors to maintain their original shape, while in the alginate gels, the cells grew away from the gel and spread along the cell plate. Instead of using a synthetic polymer-based cross-linker, a biopolymer containing the complementary reactive group can be employed for obtaining hydrogels. Along these lines, in 2016, Wei et al. designed a neuro-compatible, injectable, and selfhealing hydrogel which was obtained by mixing N-carboxyethyl chitosan (CEC),

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Fig. 4 (a) Synthesis of self-healing CEC-OSA-based hydrogels, (b) G0 of the CEC-l-OSA hydrogel from alternate step strain (strain, 1–1,000%) at 37 C. Adapted with permission [16]. Copyright 2016, Springer Nature

due to its improved solubility in aqueous media, and oxidized sodium alginate (OSA) in DF-12 (Dulbecco’s Modified Eagle Medium/Ham’s F12) medium of neural stem cell at 37 C (Fig. 4a) [16]. Stiffness of hydrogel was tuned by changing the chitosan concentration, and hydrogels with biomechanical properties similar to

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Fig. 5 (a, b) Hydrogel precursors, (c) schematic illustration of self-healing conductive hydrogels network, (d, e, f) macroscopic images showing self-healing property. Adapted with permission [17]. Copyright 2016, American Chemical Society

natural brain tissue (100–1,000 Pa) to support neural stem cell (NSC) growth and differentiation were obtained via the Schiff base reaction. The dynamic nature of the imine bonds ensured self-healing, as demonstrated through alternate step strain measurements. Strain was varied from 1 to 1,000% alternately and repeated several times. Recovery of the storage modulus (G0 ) to its initial value was observed when strain was reduced to 1% (Fig. 4b). This polysaccharide-based self-healing hydrogel was used as carrier for NSC transplantations. In 2016, Dong et al. synthesized a series of self-healing, injectable, conductive hydrogels by cross-linking chitosan-graft-aniline tetramer (CS-AT) with PEG-DA at 37 C (Fig. 5a–c) [17]. Two different cell lines were co-cultured in hydrogels, and viability of the cells was not changed after injection, besides, linear and tunable release profiles of cells were obtained by using different cell types or changing the initial number of embedded cells. Self-healing ability of CS-AT10 hydrogel was investigated by conducting visual and rheological experiments. Small pieces of hydrogel were injected through a needle in a mold first, and a bulk hydrogel was obtained within 2 h. The hydrogel obtained from reunification of injected fractures

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was cut into two, and immediate healing of two pieces was observed when they were put together (Fig. 5d–f). Furthermore, to assess self-healing qualitatively, strain amplitude sweep test was applied on hydrogel where strain was alternated between 1 and 300%. A drastic decrease in G0 occurred under high strain (300%), and immediate recovery to original G0 was recorded upon reducing strain to 1%. This biodegradable and intelligent hydrogel possesses a great potential to be used as a cell therapy platform for cardiac tissue repair. Recently, using a related approach, Guo et al. reported an injectable self-healing conductive hydrogel formed by mixing CEC with dextran-graft-aniline tetramer (Dex-AT) oligomers in deionized water with a molar ratio of –NH2 to –CHO (1:1) with different AT concentrations [18]. Thus, obtained hydrogel’s self-healing ability was tested by continuous step strain method (Fig. 6a). Rheological characterization of Dex-AT3/CECS was carried out to define breakpoint of cross-linked structure. Furthermore, strain was increased from 1 to 300% to collapse gel. At high strain G00 (loss modulus) was higher than G0 (storage modulus) showing gel-to-sol transformation. After reducing the strain, G0 and G00 recovered to original values immediately (Fig. 6c). Besides, hydrogel was blended into small pieces and injected as a

Fig. 6 (a) Synthesis of polymers and preparation of Dex-AT/CECS hydrogel, (b) macroscopic illustration of cut pieces of Dex-AT3/CECS hydrogel, (c) rheological characterization. Adapted with permission [18]. Copyright 2019, Elsevier

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disk and allowed to heal for 12 h in humid atmosphere. Resulted hydrogel demonstrated almost the same G0 value as the in situ formed hydrogel, thus proving good self-healing ability. Macroscopic self-healing of two cut pieces is illustrated in Fig. 6b where two pieces of Dex-aT3/CECS hydrogel healed immediately after they were put in contact at room temperature. Several cell types including myoblast cell are encapsulated and released from the hydrogel with good viability and proliferation ability. This novel biocompatible self-healing hydrogel has a great potential as a cell delivery carrier for skeletal muscle or tissue repair. In 2017, Guo and coworkers used N-carboxyethyl chitosan (CEC) and PEG-DA to obtain self-healing hydrogel for local delivery of chemotherapeutic agent doxorubicin (DOX). CEC was synthesized by a green method in this work using water as a solvent. Hydrogels were obtained by mixing polymer solutions prepared in deionized (DI) water at 37 C, and rapid gel formation (within ca. 60 s) was recorded by using vial tilting method. Self-healing assessment was done by visual and quantitative experiments. In visual experiments, when four pieces of stained hydrogels were incubated at 25 C for 3 h, boundary disappearance was observed. In quantitative experiments, alternate strain test was carried out between 1 and 300% strain values for three cycles. Under high strain (300%), storage modulus (G0 ) of hydrogel decreased from 11 to 1.05 kPa showing strain-induced network deformation and unloading strain on hydrogel (1%) enabled recovery of G0 back to its initial value within 100 s [19]. Self-healing hydrogels containing a protein-based component were reported by Hsu and coworkers in 2017. They synthesized a chitosan-fibrin (CF)-based hydrogel in water and compared the self-healing property with fibrin and classical glyco chitosan (CS)-based gels with similar physical properties. The CF and CS hydrogel systems were optimized to obtain suitable stiffness (1.2 kPa) for blood capillary formation, and fibrin gel was used as a positive control. Fibrinogen gels were obtained in the presence of thrombin, which converts it to a fibrin network. To demonstrate macroscopic self-healing properties of resulted gels, the disappearance of a punctured hole in hydrogels was investigated. Fibrin gel did not self-heal, as expected, but the CF gel showed faster healing than the traditional CS hydrogel system (Fig. 7a). Aditionally, rheological tests were carried out, which indicated that the breaking strain of CF gel was higher than CS gel, yet, both CS and CF hydrogels showed quick recovery in continuous step strain tests where strain was alternated between 1 and 150% (Fig. 7b) [20]. The utility of such Schiff base-based hydrogels was expanded by a recent study by Zhao, Sun, and coworkers. They designed an injectable self-healing hydrogel as microwave ablation therapy agent by simply mixing GCS and difunctionalized DF-PEG in saline, at room temperature. The ionic hydrogel produced hightemperature hyperthermia upon a low power density microwave (2.0 W, 2.45 GHz) exposure because of the ions that are fixed through saline. Self-healing property of hydrogel is demonstrated by using a periodic step change of oscillatory strain between 300 and 1%. G0 of damaged hydrogel returned back to its initial value quickly upon reducing strain to 1% [21]. Another example utilizing similar combination was reported by Hsieh and coworkers in 2018, who designed a self-healing

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Fig. 7 (a) Macroscopic self-healing tests of fibrin and CS and CF hydrogels, (b) rheological selfhealing tests of CS and CF hydrogels. Adapted with permission [20]. Copyright 2017, Springer Nature

hydrogel system from PEGDA and GCS with optogenetic molecules for cytosolic gene delivery with excellent cell viability and a high efficiency. Neural stem cells (NSCs) and bacteriorhodopsin D94N-HmBRI (HEBR) plasmids were injected in chitosan-based (CS) hydrogel system. In situ transfection of HEBR to NSCs was achieved by seeding NSC in HEBR containing CS hydrogel and filling the mixture in a barrel and extruding the mixture through a needle. Transfection efficiency was 80% for the CS hydrogel and 20% for gelatin-based hydrogel which was injectable but not self-healable and was used as a comparison to demonstrate enhanced transfection. Furthermore, it was reported that the embedded cells proliferated and specifically differentiated into neurons in vitro and in vivo experiments. Self-healing property of the CS hydrogel was also demonstrated by continuous step strain test at

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37 C (strain between 1 and 300%). This chitosan-based hydrogel system has a potential to treat central nervous system disorders such as Parkinson’s disease, epilepsy, and stroke [22]. In 2017, Cheng and coworkers reported a pH- and temperature-sensitive self-healing hydrogel obtained by cross-linking aldehydecontaining pullulan (A-Pul), a highly water-soluble polysaccharide, with poly-lysine (PL) and branched polyethyleneimine (BPE) in aqueous media using the Schiff base reaction. Self-healing property of ɛ-PL45/A-Pul200/BPEI2 was demonstrated by continuous step strain test. Hydrogel was damaged by increasing strain from 1 to 500%, and upon decreasing strain to 1%, G0 returned to its original value in 150 s. Furthermore, rhodamine B and methyl orange-color containing hydrogels were prepared, and a hole was punched through both hydrogels. Self-healing ability was further assessed through the investigation of disappearance of boundary between colored semicircles and hole [23].

2.2

Cross-Linking of Synthetic Polymers Through Imine Linkages

Since utilization of natural polymers that possess multiple amine groups or functional groups that can yield aldehydes and ketones is quite practical, little effort has been devoted to utilize synthetic polymers. Hydrophilic polymers incorporated with appropriate functional groups to achieve cross-linking have been utilized as building blocks for self-healing hydrogels. Polymer architecture (linear, star, branched, etc.) is one of the factors that affects the nature of cross-linking and internal network structure of hydrogels. Synthetic polymers can be prepared with control over their architecture and thus provide a handle for tuning of properties. For example, homopolymers that were obtained through free radical polymerization of dendritic oligoethylene glycol (OEG) monomers show thermo-responsive property and can collapse to form hydrophobic envelopes heterogeneously. In 2018, Li, Zhang, and coworkers utilized first-generation OEG-based dendritic macromonomers (MG1) to yield stimuli-responsive self-healing hydrogels with enhanced mechanical properties [24]. First, dendritic macromonomer MG1 and 2-aminoethyl methacrylate hydrochloride were copolymerized to yield an amine group containing copolymer. Hydrogels were obtained through Schiff base reaction between the amine groups on copolymer and PEG-DA in buffer solution (pH 10.0) at room temperature within 1 min (Fig. 8a). Self-healing was demonstrated through the rejoining of cut pieces of stained hydrogel (6 h without any external intervention) (Fig. 8b). Rheological tests revealed that the G0 and G00 of self-healed hydrogel were almost the same as the original hydrogel (Fig. 8c). Reversible dynamic covalent linkages based on imine chemistry have been also exploited to formulate nanocomposite hydrogels. Instead of combing polymers with complementary groups, one can envision that appropriately functionalized organic or inorganic nanomaterials can lead to cross-linking. In a recent example,

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Fig. 8 (a) Preparation and (b) macroscopic self-healing tests of PG15A1, (c) rheological selfhealing tests showing storage modulus (G0 ) and loss modulus (G00 ) of original and self-healed hydrogel. Adapted with permission [24]. Copyright 2018, The Royal Society of Chemistry

Bhattacharya et al. reported fluorescent self-healing gels that are comprised of carbon dots (C-dots) and polyethyleneimine (PEI) (Fig. 9a) [25]. This seminal report uses C-dots as a hydrogel gel building block, as well as a fluorophore. The C-dots were synthesized from different carbonaceous precursors like glutaraldehyde, benzaldehyde, etc. Strain alternation experiment was conducted to demonstrate viscoelastic recovery of the C-dots/PEI gel. Upon reducing strain from 300 to 1%, the gel rapidly healed and returned to almost its original G0 value within 10 s. This process was repeated four times without resulting in any unrecoverable damage (Fig. 9b). As an interesting approach, Chen and coworkers employed Schiff base reaction to obtain a self-healing hydrogel that can be used to collect digital information for identification [26]. This system aims to print 3D finger friction ridges on a soft hydrogel surface and allow its disappearance after a certain time. For this purpose,

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Fig. 9 (a) Preparation of C-dots and C-dots/PEI hydrogel, (b) strain recovery tests of C-dots/PEI hydrogel. Adapted with permission [25]. Copyright 2019, American Chemical Society

amine functional groups bearing silica nanodots (SiND-NH2) were combined with benzaldehyde terminated triblock copolymer poly(ethylene oxide)-poly (propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO), in aqueous media to obtain hydrogels. Self-healing ability was demonstrated by cutting hydrogel into two halves and formation of a whole gel immediately after putting them in contact.

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3 Acylhydrazone Bond Formation-Based Hydrogels Another widely used linkage for fabrication of stimuli-responsive self-healing hydrogels involves the acylhydrazone bond, a type of imine bond that is obtained through the condensation of a hydrazine with an aldehyde or ketone. The acylhydrazone bond is more stable compared to an imine bond and is regarded as kinetically inert under neutral and basic conditions. However, under acid catalysis acylhydrazone bond can undergo hydrolysis, exchange, and metathesis reactions like imines [11]. In recent years, this pH-responsive chemical bond has been used to fabricate mechanically strong, pH-sensitive self-healing materials for various biomedical applications.

3.1

Cross-Linking of Synthetic Polymers Through Acylhydrazone Linkages

An early example of polymer gels based on dynamic acylhydrazone bonds was reported by Chen and coworkers in 2010. Gels were prepared by mixing bis-acylhydrazine functionalized PEO with tris[(4-formylphenoxy)methyl]ethane in the presence of catalytic amount of glacial acetic acid in dimethylformamide (DMF) for 16 h (Fig. 10) [27]. The pH-dependent sol-gel transition was demonstrated by using HCl and TEA and repeated for 8 cycles, but the stability of gels was lost during the transitions as deduced from rheological tests. Visual experiments showed that two pieces of freshly prepared hydrogels merged into one by keeping them in contact for 7 h. Linear or branched PEG, an FDA-approved biocompatible hydrophilic polymer, or its derivatives are widely used to fabricate cross-linked polymeric networks due to their high solubility both in organic and aqueous media, ease of functionalization, and conjugation. For instance, in 2017, Wang et al. reported an ultra-stretchable, self-healable hydrogel formed by mixing a three-armed PEO with acylhydrazine termini (G3) and a triblock copolymer PEO99-b-PPO65-b-PEO99 (PF127) with aldehydes at chain ends (G2) in phosphate buffer (pH 6.0) via dynamic acylhydrazone bonds (Fig. 11a) [28]. The amphiphilic triblock copolymer formed micelles (PF127) by self-assembling in water and acted as macro-cross-linkers. Due to the possibility of internal rearrangement of micelles under external force, hydrogels demonstrated improved mechanical properties and did not fracture at the largest strain (11,700%) with a stress of 297 kPa. The pH-sensitive tensile behavior of the hydrogels due to acylhydrazone bond was also demonstrated. When pH value changed to 6.5 or 5, lower fracture strain and stress were observed. Self-healing capability of the hydrogel was illustrated by using stress-strain curve. A sample was cut into two and placed in a mold to heal for 24 h. Self-healed hydrogel

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Fig. 10 Schematic illustration of dynamic acylhydrazone bond containing gel. Adapted with permission [27]. Copyright 2010, American Chemical Society

exhibited similar tensile stress curve as the original sample (fracture strain as 10,650% and stress 247 kPa) (Fig. 11b). As a result, combination of dynamic covalent with physical interactions generated a tough hydrogel with extremely high stretchability, high toughness, and good self-healing ability. Apart from using polymeric cross-linkers, small molecules have also been employed as functional cross-linkers. For example, in 2018, Liu et al. reported a slice-resistant, self-healing hydrogel by cross-linking calix[4]pyrrole-derivative bearing hydrazide (CPTH) groups with PEG-DA via acylhydrazone bond formation at neutral pH in H2O/EtOH mixture [29]. Self-healing was demonstrated by visual experiments where two hydrogels were prepared and dyed with rhodamine B and methylene blue, respectively. Each gel was cut into two halves and put in contact for 24 h under moist atmosphere at room temperature. Healed gels resisted stretching by a tweezer. Quantitative self-healing assessment was further investigated by tensile strength test to demonstrate that healed hydrogel showed similar tensile strength and recovered to 93% and 100% of the initial value after 24 h and 48 h, respectively. Singh and coworkers reported PEG-based self-healing hydrogels formed by cross-linking an eight-arm PEG polymer containing glyoxylic aldehyde termini with an eight-arm PEG hydrazine polymer in aqueous media at 37 C (Fig. 12a) [30]. Controlled release of covalently attached chemotherapeutic agent (DOX) from gel matrix was achieved for more than 40 days in a pH-responsive manner. Selfhealing property was examined by macroscopic experiments where two pieces of hydrogels (one piece containing DOX) are joined together after incubating in contact

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Fig. 11 (a) Hydrogel formation through acylhydrazone bond formation between PF127 aldehydes and G3, (b) tensile test curves of the original hydrogel (black curve) and the hydrogel self-healed for 24 h (red curve). Adapted with permission [28]. Copyright 2017, American Chemical Society

under humid atmosphere for 6 h (Fig. 12b). Self-healing ability of hydrogels with good mechanical properties (1,650 Pa) was also assessed by alternating strain test (strain between 1 and 1,000%) where each strain was applied for 60 s. Hydrogel regained its initial storage modulus instantly when stress was dropped (Fig. 12c). Disappearance of the seam and uniform distribution of PEG-DOX conjugate owing to the dynamic nature of hydrazone linkages also demonstrates self-healing. While most of the reports utilize polymers with reactive groups at their chain ends, it is also possible to employ polymers with reactive functional groups on their side chains. Reversible addition fragmentation chain transfer (RAFT)

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Fig. 12 (a) Preparation of PEG hydrogels from eight-arm PEG glyoxylic aldehyde and eight-arm PEG hydrazine, (b) self-healing characteristic of two hydrogel halves (with and without PEG-DOX loading), (c) G0 at alternating strains of 1 and 1,000%. Adapted with permission [30]. Copyright 2019, American Chemical Society

polymerization of acrylic monomers can give desired polymers and stimuliresponsive polymeric networks as demonstrated in the recent study by Zheng and coworkers [31]. A ketone-based acylhydrazone bond containing self-healing hydrogel for local drug delivery was reported to reduce the cytotoxicity caused by reactive aldehyde functional groups on gel precursors. Copolymer was obtained by RAFT polymerization of diacetone acrylamide and acrylamide (DAAM/AM), and hydrogel was synthesized by cross-linking the ketone-bearing polymer with hexanedihydrazide in DI water (Fig. 13a). Rheological tests were carried out to assess self-healing property by continuous strain test. Under low strain (1%), material showed gel-like behavior, while under high strain (1,500%) it turned into a sol state. Upon reducing strain to 1%, G0 immediate recovery was observed, and the process was shown to be repeatable (Fig. 13b).

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Fig. 13 (a) Synthesis of ketone-bearing polymer by RAFT polymerization of AM and DAAM and formation of hydrogels by acylhydrazone cross-linking, (b) alternate strain test (strain: 1–1,500%). Adapted with permission [31]. Copyright 2017, The Royal Society of Chemistry

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Fig. 14 (a) Schematic illustration of TPE- and PEO23 DNH-based hydrogel formation, (b) visual self-healing experiments showing light-emitting hydrogels under daylight (top) and UV (bottom). Adapted with permission [33]. Copyright 2019, Wiley-VCH

More recently, in 2018, An et al. designed a self-healing, thermo-responsive, degradable hydrogel by cross-linking a water-soluble copolymer of Nisopropylacrylamide, formylphenyl acrylate and N,N-dimethylacrylamide, P (NIPAM-FPA-DMA), with PEO dihydrazide in DI water [32]. Self-healing was demonstrated by punching a hole on the hydrogel and placing another hydrogel to fill the cavity. Two pieces were incubated for 24 h and the self-healed hydrogel stretched and twisted without falling apart. Furthermore, physically encapsulated hydrophobic chemotherapeutic agent DOX showed a controlled release profile over 12 h, both below and above cloud point (30 and 40 C). In an interesting example, Shen et al. reported a cross-linking-induced thermo-responsive and self-healing hydrogel with light-emitting property using ketone-based acylhydrazone dynamic covalent bonds [33]. Hydrogel was formed by cross-linking diacetone acrylamide/ acrylamide copolymer synthesized with tetraphenylethylene (TPE) containing RAFT agent with a naphthalene containing acylhydrazide (PEO23 DBH or PEO23 DNH) in DI water (Fig. 14a). TPE was used for aggregation-induced emission, while diacetone acrylamide acted as a main component to stimulate thermo-responsive gelation. Self-healing property was demonstrated by macroscopic healing experiments. Hydrogel was cut into two, and original or different pieces were put in contact in a moisturized desiccator for 24 h. Healed gels were stretched and bended without falling apart and were visualized under daylight and UV to observe the integration of different pieces (Fig. 14b).

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Cross-Linking of Natural Polymers Through Acylhydrazone Linkages

Natural polymers bear high potential for application in regenerative medicine and other related biomedical fields. They can be utilized as tissue engineering materials, bone repair/replacement, dental repair/replacement, controlled drug delivery, and skin repair materials. Natural polymers can be functionalized using various chemical transformations to carry hydrazine, aldehyde, or ketone moieties. Recently, Li et al. reported a hydrogel based on hydrazine-modified hyaluronic acid (HAAD), a natural polymer widely employed for wound healing applications and benzaldehyde modified biocompatible Pluronic F127 (BAF127) that can have a potential for promoting burn wound healing [34]. Hydrogel was synthesized in phosphate-buffered saline (PBS) at room temperature by utilizing acylhydrazone-based linkages. Micellization-based cross-linking was formed by telechelic aldehyde end-linked Pluronic F127, a nonionic triblock copolymer of PEO-PPO-PEO (Fig. 15a). Another hydrogel was also synthesized by using the same chemistry by cross-linking HA with four-armed PEG (TPEG) with benzaldehyde terminals to compare with the HA-az-TPEG. The continuous strain test was employed for both systems to compare self-healing property. The strain varied between 1 and 300% at 37 C, and both Gel3 and HA-az-TPEG hydrogels demonstrated similar rapid self-healing where the structures were collapsed under high strain and upon reducing strain to 1% G0 restored back to 95.0% of the original values (Fig. 15b). Also, visual experiments showing self-healing of gels by joining of hydrogel pieces were also undertaken (Fig. 15c). Another promising system was reported by Sharma et al., who fabricated an injectable self-healing hydrogel for pH-responsive release of a chemotherapeutic agent (DOX) up to 30 days [35]. Xanthan, a high molecular weight heteropolysaccharide, was oxidized to obtain the aldehyde groups needed for cross-linking. Hydrogel was obtained by cross-linking eight-arm PEG with oxidized xanthan in aqueous media at 37 C through hydrazone linkages. These hydrogels possessed excellent cytocompatibility in 2D and 3D culture of mouse fibroblasts (NIH-3T3). Self-healing studies were carried out by visual experiments where hydrogels were cut into two halves and put in contact at 37 C. Furthermore, continuous strain test showed that hydrogel lost its integrity under high strain (800%) and regained initial G0 value upon reducing strain to 1% in an alternating cycle for five times.

4 Boronic Ester Bond Formation Based Hydrogels Boronic ester bonds are formed between boronic acid derivatives and 1,2- and 1,3-diols by reversible condensation reaction in aqueous media. The stability of boronic ester bonds can be tuned by pH, and thus this reversible bond can serve as a

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Fig. 15 (a) Preparation of HA- and F127-based self-healing hydrogel, (b) continuous step strain measurements of HA-az-F127 (Gel3) and HA-az-TPEG hydrogels, (c) visual self-healing experiments of Gel3. Adapted with permission [34]. Copyright 2018, American Chemical Society

stimuli-responsive cross-linking motif to yield self-healing materials. Usually the boronic ester bonds are obtained at pH higher than the pKa of diol, which is usually greater than 8, which may limit certain application in biological systems. However, through the modification of boronic acid by addition of electron-withdrawing or -donating groups, the esterification equilibrium can be achieved across a range of pH values (~4–10) [36]. To date, a huge amount of research has been devoted in this area, both with natural and synthetic polymers, as outlined in the section below.

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Cross-Linking of Synthetic Polymers Through Boronic Ester Linkages

Diol-containing synthetic polymers such as poly(vinyl alcohol) (PVA)-, poly(dopamine) (PDA)-, and linear poly(ethylene glycol) (PEG)-based derivatives have been widely used to obtain hydrogels with boronic ester bond-based linkages. Also, the boronic acid functional group can be incorporated to polymer backbone through polymerization of boronic acid-containing monomers. The chemistry is not new, and boronic ester chemistry has been used for many years to obtain cross-linked polymers. For example, in 1991, Kitano reported a polymeric material obtained by crosslinking PVA and poly(N-vinyl-2-pyrrolidone) with pendent phenylboronic acid (PBA) moieties which undergoes sol-gel transition in a glucose-sensitive manner [37]. But in recent years, due to renewed interest in stimuli-responsive materials, the chemistry has resurfaced and has been a topic of intensive research over the past few years. For example, in 2011, He et al. reported a hydrogel formed through boronatecatechol complexation [38]. A hydrogel was synthesized by cross-linking 1,3-benzenediboronic acid with catechol-functionalized four-arm PEG under basic conditions (pH 9). Gel-to-sol transition was pH dependent, as demonstrated by lowering the pH to 3.0, after gel formation at pH 9.0. Self-healing of gel was investigated by rheological measurements, where G0 decreased and crossed with G00 under high strain (1,000%) and recovered back upon decreasing the strain to 5%. However, formation of boronate ester bond under harsh alkaline condition limits its application in biomedical fields. A solution to such problem was proposed in an early report, in 2007, where Kiser and coworkers reported pH-sensitive hydrogels that can be suitable for biological applications such as drug delivery [39]. They optimized the gelation at physiological pH by using salicylhydroxamic acid (SHA) which has a higher affinity for PBA at around pH 4–5. Polymers containing PBA or SHA were prepared by free radical polymerization of appropriate acrylic monomers with either acrylic acid (AA) or 2-hydroxypropylmethacrylamide (HPMA). Hydrogel was obtained by mixing aqueous solutions of PBA- and SHA-containing polymers at physiological pH. The study shows that the nature of the polymeric backbone such as neutral or charged plays an important role in the pH-based reversibility of interchain interactions. ###Recently, Deng et al. used dynamic boronic ester cross-linking to fabricate self-healing hydrogels at neutral and acidic pH by using 2-acrylamidophenylboronic acid (2APBA), an intramolecular coordinating boronic acid monomer [40]. They cross-linked the copolymer of N,N-dimethylacrylamide (DMA) and 2APBA with two different diol-containing polymers (either PVA or a catechol-functionalized copolymer, namely, P(DOPAAm-co-DMA)) in DI water or in a potassium biphthalate buffer at (pH 4.0) (Fig. 16a). Internal coordination between the carbonyl oxygen and boron helped to stabilize boronic ester at acidic and neutral pH. Visual self-healing experiments of P(2APBA-co-DMA) hydrogel demonstrated scar disappearance within 60 min (Fig. 16b). Self-healing properties of hydrogels formed from P(2APBA-co-DMA) and P(DOPAAm-co-DMA) or PVA at pH 4.0 were

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Fig. 16 (a) Synthesis of dynamic hydrogels through boronic ester bond, (b) visual self-healing experiments, (c) collapse and recovery behavior of G0 and G00 of P(2APBA-co-DMA)/P(DOPAAmco-DMA) (left) and P(2APBA-co-DMA)/PVOH (right) hydrogels under high (400%) and low strain (10%). Adapted with permission [40]. Copyright 2015, American Chemical Society

demonstrated by rheological tests under high strain (400%) or at linear viscoelastic region (LVE) (strain 10%). Strain-dependent crossover of G0 with G00 of both hydrogels recovered back to original values rapidly upon reducing strain to 10% (Fig. 16c). Anderson and coworkers recently reported a glucose-responsive, injectable, selfhealing PEG-based hydrogel system [41]. Hydrogels were formed by cross-linking multi-arm PEG macromonomers containing either PBA groups or a glucose-like diols in aqueous medium with different pH values (Fig. 17a, b). The effect of pH on gelation was examined (pH 6–8). Size-dependent glucose-responsive release of larger proteins along with 3D cell encapsulation (3T3 fibroblast cell line) and in vivo studies were carried out successfully. Step strain measurements were conducted to demonstrate self-healing properties of hydrogels. Strain was alternated between γ ¼ 500% and γ ¼ 0.05% (Fig. 17c). Under high strain G0 dropped drastically, and inversion of G0 and G00 occurred immediately, indicating straininduced failure. Upon reducing strain on gels, 100% recovery of both G 0 and G 00 was observed within a few seconds. Visual self-healing experiments carried out where two PEG-FPBA hydrogel pieces, prepared at pH 7.0, were combined together and resisted stretching (Fig. 17d). Shan and coworkers used similar approach to design self-healing, adhesive, and cytocompatible PEG-based hydrogels via reversible covalent phenyl borate ester bonds. Gels were obtained by cross-linking dopamine functionalized four-armed PEG with PBA-modified four-armed PEG in a

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Fig. 17 (a) Schematic illustration of dynamic cross-linking, (b) chemical structures of PEG macromers and PEG-diol, (c) step strain measurements (strain, 0.05–500%), (d) visual self-healing experiments of PEG-FPBA gel at pH 7.0. Adapted with permission [41]. Copyright 2015, WileyVCH

buffer (pH 9.0) at 37 C within 10 s [42]. Self-healing property of triple responsive (toward pH, glucose, and dopamine), degradable hydrogels was demonstrated by visual experiments. Simply, two pieces of cut hydrogels kept in contact, and they formed a uniform single piece gel within 30 s. Using a somewhat different synthetic approach, Tseng et al. synthesized a hydrogel system utilizing reversible nature of boronate ester linkages [43]. A glucose-sensitive self-healing hydrogel was formed through cross-linking poly(ethylene glycol)-diacrylate (PEGDA) and dithiothreitol (DTT) with borax via boronate ester linkages in PBS (Fig. 18a) as a sacrificial layer of branched tubular channels inside another non-sacrificial hydrogel (e.g., fibrin gel or chitosan gel) containing neural stem cells (NSCs). Self-healing ability was tested by continuous step strain; hydrogel did not lose its mechanical strength over repeated cycles (Fig. 18b). The boric acid in the structure of self-healing hydrogel is known to form complex with glucose, hence leading disintegration of gel to form complicated and interconnected hallow channels in bulk gel allowing endothelial cells to grow and form lumens while NSCs embedded in non-sacrificial construct form neurosphere-like structure.

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Fig. 18 (a) Preparation of PEGDA/DTT/borax-based self-healing hydrogel, (b) continuous step strain (strain, 1–150%). Adapted with permission [43]. Copyright 2017, Elsevier

Another study utilizing borax-based cross-linking was reported in 2018 by Chen et al., who showed shapeable and recyclable agarose/PVA-based double network hydrogels which exhibit excellent self-healing property both in air and underwater [44]. Hydrogels were obtained by mixing agarose/PVA solution in hot water with borax solution. Dynamic PVA-borate network provided self-healing to hydrogel, while H-bonding interactions in agarose supported mechanical strength. Healed hydrogel at room temperature for 10 s was stretched to test the tensile strength and showed almost the same stress-strain behavior with the original one. The tensile stress of hydrogel healed under water for 60 s revealed 70% recovery, indicating agarose/PVA hydrogels exhibit a fast self-healing property underwater as well. Visual experiments were conducted to demonstrate self-healing of PVA-boraxbased hydrogel containing 1 wt % of agarose. In 2018, Pasparakis and coworkers reported multi-responsive, self-healing, and cytocompatible hydrogels by cross-linking a copolymer (P1) of NIPAAm and 3-(acrylamido)phenylboronic acid (APBA) with PVA via boronate ester bonds in PBS (pH 7.4) at 25 C in less than 10 min (Fig. 19a) [45]. Furthermore, optically active gel nanocomposites were prepared by mixing P1 with colloidally stable poly (vinylpyrrolidone)-coated gold nanoparticles. Hydrogels undergo gel-sol transition owing to the disruption of the boronate ester thermally (heating above 37 C) or optically (irradiation with green light). Alternate step strain measurements (between 10 and 200%) demonstrated self-healing behavior of P1-PVA hydrogel and repeatability of this process for several times without significant loss of the mechanical properties (Fig. 19b). Visual self-healing experiments were carried out under heat (39 C) and light and without any external stimuli. Images showed that the hydrogels can fully recover their mechanical properties within minutes (Fig. 19c, d).

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Fig. 19 (a) Representative synthesis of self-healing hydrogels, (b) step strain tests of P1-PVA (at 25 C), (c) thermally (P1-PVA) (top) and optically (P1-PVA-AuNP) (bottom) self-healed hydrogels, (d) self-healing of P1-PVA (top) and P1-PVA-AuNP (bottom) hydrogels at 25 C without external stimuli. Adapted with permission [45]. Copyright 2018, The Royal Society of Chemistry

Recently, Li and coworkers synthesized poly(vinyl alcohol)/poly(dopamine)/ graphene (PVA/PDA/GO)-based hydrogels by partially reducing graphene oxide under the oxidative self-polymerization of dopamine and mixing with prepared PVA aqueous solution and sodium tetraborate aqueous solution [46]. Hydrogels possessed conducting ability due to the presence of partially reduced graphene oxide and rapid self-healing ability due to boronic ester bonds. Alternate step strain sweeps were conducted to show self-healing performance of hydrogel. Strain was changed between 1 and 300%. Under high strain, gel structure collapsed into quasi-liquid state and exhibited rapid restoration of G0 and G00 even after four cycles. Tensile tests of self-healing hydrogels were carried out to calculate the effectiveness of mechanical property and revealed that hydrogels recover 92.89% of the original tensile strength within 1 min, because of the dynamic breakage and reformation of the diolborate ester bonds in the hydrogel network. Narain and coworkers have reported a series of hydrogels by utilizing benzoxaborole-diol complexation for several biomedical applications [47–49]. By using the same chemistry, a self-healing and injectable hydrogel based on triblock hydrophilic glycopolymer (PLAEMA-b-PDEGMA-b-PLAEMA abbreviated as PLDL) and benzoxaborole-containing copolymer (P(AAm-st-MAABO) abbreviated as PAB) was reported in 2019 (Fig. 20a) [50]. PLDL was a diol containing robust polymer that can avoid undesired oxidation and synthesized via a two-step atom transfer radical polymerization (ATRP) with varied ratios of sugar groups.

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Fig. 20 (a) Schematic illustration of hydrogel formation through benzoxaborole-diol complexation, (b) the decrease and recovery of G0 and G00 under high (500%) and low (1%) strain. Adapted with permission [50]. Copyright 2018, American Chemical Society

Hydrogels were obtained through dynamic benzoxaborole-sugar complexation in PBS solutions with different pHs (7.4, 8.4, 9.4) within 3 min after mixing copolymer solutions. Resulting hydrogel was investigated using rheological tests where strain was increased from 0.1 to 500% to break the gel structure. Hydrogel recovered back to its initial G0 and G00 values within 300 s after reducing the strain to 1% (Fig. 20b). In their most recent work, in 2019, Narain, Hall, and coworkers reported a novel hydrogel fabrication that utilizes the traditional sugar-based boronic ester and a novel nopoldiol-based benzoxaborolate bonds to yield a dual cross-link network (DCN) system (Fig. 21a) [51]. This method yielded a catalyst/light free rapid in situ formation of hydrogels within 26 s, with stimuli (reactive oxygen species)responsive degradation, wide self-healing pH range (8.5–1.5), exceptional stability under acidic condition, and polyol solutions. Hydrogels were capable of pH-responsive drug release (DOX) and for cell (HeLa) encapsulation. Combining reversible sugar (GAEMA)-benzoxaborolate cross-links allowed self-healing, while reaction between nopoldiol and 5-methacrylamido-1,2-benzoxaborole (MAAmBO) moieties endows a rigid but slightly reversible network to provide an acid and polyol resistance hydrogel structure. Strain sweep tests with γ ¼ 1% and 400% were carried out to demonstrate modulus recovery upon gel failure (Fig. 21b). Visual experiments

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Fig. 21 (a) Representation of synthesis of polymers (PB and PNG) and DN hydrogel, (b) step strain test and (c) visual self-healing experiments of 10 w/v % PBNG hydrogel at pH 7.4. Adapted with permission [51]. Copyright 2019, American Chemical Society

were conducted to assess self-healing ability by putting two halves of PBNG hydrogels (DOX loaded and unloaded) in contact for 20 s (Fig. 21c).

4.2

Cross-Linking of Natural Polymers Through Boronic Ester Linkages

Natural polymers offer many advantages in terms of abundancy, low cost, excellent biocompatibility, biodegradability, nontoxicity and non-immunogenicity. Because of the great potential of stimuli-responsive hydrogels in biomedical applications, facile methods to obtain natural polymer-based self-healing hydrogels with reversible linkages such as boronate ester bonds have been developed. For instance, guar gum, a high molecular weight natural polysaccharide with plentiful side chains, and hyaluronic acid are commonly preferred in these studies due to the presence of abundant hydroxyl groups. It was mentioned earlier that ionic polymers can improve gelation via boronic ester complexation at physiological pH [39]. By utilizing this advantage of ionic polymers, Tarus et al. synthesized stable hydrogels via phenylboronic ester bonds at

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Fig. 22 (a) Preparation of HA hydrogels, (b) dynamic rheological tests showing collapse and recovery of G0 . Adapted with permission [52]. Copyright 2014, Wiley-VCH

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physiological pH by using hyaluronic acid (HA), a high molecular weight negatively charged polysaccharide (Fig. 22a) [52]. Dynamic hydrogels were formed by crosslinking maltose and PBA-modified HA in aqueous media at pH 7.4. Self-healing property of hydrogel was demonstrated by rheological test as well as visual experiments. Upon applying an oscillatory stress above the LVE region, hydrogel structure was deformed (50% decrease in G0 ), and recovery of G0 occurs (within less than 10 min) without a significant loss in G0 value when stress was reduced for five repeating cycles (Fig. 22b). Another example utilizing guar gum was reported by Chen and coworkers to fabricate a multi-responsive self-healing hydrogel by cross-linking it with borax in aqueous media at room temperature [53]. This reformable and injectable gel possessed rapid and repeatable self-healing ability, as demonstrated by continuous strain test to assess the changes in G0 and G00 under high strain (100%) and low (10%) strain. Strain-induced decrease in G0 by 66% was recorded under high strain (100%) which regained its original value immediately upon reducing strain to 10% G0 over a cyclic test. Additionally, several visual experiments where two different hydrogels were cut, rejoined, stretched, bended, and remolded were demonstrated.

5 Diels-Alder Cycloaddition-Based Hydrogels Diels-Alder cycloaddition reaction between a diene and dienophile is highly specific and has been extensively exploited in fabrication of self-healing polymeric materials [54]. It is thermally reversible due to the instability of Diels-Alder product under high temperature. Diels-Alder reaction has been utilized to fabricate thermally healable materials that heal on demand by applying the appropriate thermal treatment. The seminal contribution in the area of self-healing materials was made in 2002 by Wudl and coworkers, who utilized Diels-Alder cycloaddition chemistry to obtain mechanically strong and thermally re-mendable materials by mixing multi-furan and multi-maleimide monomeric precursors [55]. Re-mending upon damage was examined through compact tension test where two pieces of fractured polymeric material were held together for 2 h at 120–150 C under nitrogen and cooled to room temperature. A quick survey of reports on self-healing materials shows that most of the work reported to date have investigated self-healing properties of non-hydrophilic cross-linked networks. For example, several self-healing gel systems based on furan-containing methacrylate polymers cross-linked using bismaleimide linkers have been reported [56]. Although interesting, utilization of high temperatures to achieve self-healing can be a limitation in many applications. It can be anticipated that the maleimide functional group will undergo decomposition through hydrolysis and ring opening to a certain extent upon heating in aqueous environment. One of the advantages that the Diels-Alder reaction offers for fabrication of hydrogels is that it can be carried out in water, is catalyst-free, has tolerance toward

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Fig. 23 (a) Preparation of Dex-l-PEG hydrogels through Diels-Alder reaction, (b) continuous step strain test (strain, 1.0–1,000%), (c) visual self-healing experiments (12 h in a sealed box at 37 C). Adapted with permission [57]. Copyright 2013, Wiley-VCH

oxygen, and lacks by-product formation. However, it is still a concern to these systems in biomedical applications due to the toxicity of furan derivatives and requirement of relatively high temperatures for retro-Diels-Alder reaction. To overcome these limitations of Diels-Alder reaction-based systems, Wei et al. designed a dextran-based self-healing hydrogel (Dex-l-PEG) using the Diels-Alder reaction between fulvene-modified dextran and dichloromaleic-acid-modified PEG in PBS at 37 C (Fig. 23a) [57]. Continuous step strain measurements were carried out to demonstrate self-healing property. Strain was increased from 1.0 to 1,000% and each strain kept for 300 s. Under low strain, G0 was larger than G00 indicating solid-like hydrogel. Upon increasing strain, G0 and G00 inverted and decreased showing deformation of gel structure and transformation to liquid-like state (Fig. 23b). Visual experiments were carried out to demonstrate self-healing of two cut pieces incubated at physiological temperature (37 C for 12 h) without any external intervention, and healing kinetics was monitored by scanning electrochemical microscopy (Fig. 23c).

6 Disulfide Bond Formation-Based Hydrogels Utilization of disulfide-based linkages to cross-link hydrogels has gathered increasing interest in recent years. Unlike most of the commonly used linkages that are pH responsible, the disulfide bond is stable under a wide range of pH but undergoes cleavage in the presence of a thiol or thiolate anion. Requirement of such a specific trigger makes these hydrogels quite selective in displaying responsive behavior.

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Additionally, the disulfide bond scission can occur in the presence of a tripeptide, namely, glutathione, found in elevated amounts in cancerous tissues and cells. Cleavage of disulfide bond in the presence of thiol-containing molecules occurs through a disulfide-thiol exchange reaction. The exchange reaction does not require any catalyst, UV irradiation, or heat to be triggered. Due to aforementioned advantages, this chemistry has been utilized to yield self-healing hydrogels which may possess a potential as redox-sensitive smart materials especially for drug delivery and tissue engineering systems. The concept of designing self-healing polymeric materials via the thiol-disulfide redox reversible exchange reaction has been known for almost a decade. Matyjaszewski and coworkers disclosed self-healing polymer films based on thioldisulfide exchange reaction [58]. Poly(n-butyl acrylate) multi-arm star polymers were synthesized and further used as macroinitiators for chain extension by ATRP of bis(2-methacryloyloxyethyl) disulfide to yield a disulfide cross-linked gel. This disulfide cross-linked macroscopic gel was reduced to obtain thiol (SH)-bearing polymers in solution. Thereafter, available SHs on the periphery of polymers were oxidized by either I2 or FeCl3. Disulfide cross-linked film was obtained upon reformation of disulfide bonds by oxidation of thiol-functionalized polymers. Scratches with different width and depth ranging from nanometers to micrometers were formed on the surface of the film, and rapid self-healing behavior without external intervention was reported, as deduced from analysis with atomic force microscopy. A few years later, in 2015, Waymouth and coworkers reported self-healing hydrogels that contained disulfide linkages and could be formed under neutral conditions [59]. They utilized 1,2-dithiolanes, i.e., five-membered cyclic disulfides, to obtain reversible linkages. Hydrogels were synthesized from water-soluble ABA triblock copolymers which contained a central poly(ethylene oxide) block and terminal dithiolane blocks (p(TMCDT-PEG-TMCDT)). To obtain cross-linked network, p(TMCDT-PEG-TMCDT) copolymer was mixed with a dithiol, namely, ODT, in water (Fig. 24a). Dynamic strain tests were carried out to demonstrate self-healing using alternating strain between 1 and 800% for a 10 wt % hydrogel at 25 C. Strain-induced deformation was recovered immediately (80%). They are strongly viscoelastic and have a high toughness (fracture energy of 1,000–4,000 J/m2), a high

T. L. Sun (*) South China Advanced Institute for Soft Matter Science and Technology, South China University of Technology, Guangzhou, China e-mail: [email protected] K. Cui Laboratory of Soft and Wet Matter, Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Sapporo, Japan

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modulus (0.01–8 MPa), a high failure strain (150–1,500%), and a failure stress (0.1–2 MPa), together with 100% self-recovery and a high self-healing efficiency behavior. These excellent mechanical performances are comparable to that of rubbers, most tough double-network hydrogels, and soft bio-tissues. The extensive experimental studies show that these multiple mechanical properties are related to the formation of dynamical features of inter- and intra-chain ionic bonds, and this study opens a common strategy to develop tough and self-healing hydrogels. Keywords Ionic bond · Polyampholyte hydrogel · Self-healing · Toughness · Viscoelastic

1 Introduction Hydrogels are a class of cross-linked polymer network swollen with a large amount of water. Their high permeabilities to small molecules make hydrogels undergo the reversible volume change by imbibing or exuding water in response to change in temperature, light, pH, ionic strength, etc. [1–7]. The reversible volume changes have been used to develop sensors and actuators. Furthermore, hydrogels bear some similarities to biological tissues as a result of their soft and wet nature and have been investigated for use in medical applications, such as extracellular matrix, drug delivery, and tissue regeneration [8–10]. However, conventional hydrogels are often brittle and weak, and thus little attention was paid to them as structural materials, which substantially limit the scope of their applications [11–13]. For example, recent advances in soft device such as loudspeakers, touch pads, electroluminescent displays, electronic skins, etc., require the hydrogels with highly stretchable, mechanical tough, and fatigue resistance behavior [14–20]. In the past two decades, many efforts have been made to synthesize strong and tough hydrogels, such as slide-ring gels, tetra-PEG gels, nanocomposite hydrogels, double-network hydrogel (DN) hydrogels, etc., which has largely changed these traditional view that hydrogels are very weak and thus broadened their applications [21–26]. Among them, the most successful work is the DN hydrogels that show extraordinarily high strength and toughness. DN gels consist of interpenetrating brittle and ductile networks. When hydrogels are loaded in tension, the brittle network breaks progressively into fragments, which dissipates substantial amounts of energy and prevents catastrophic crack propagation, while the elasticity of ductile network forces them to return to its original configuration [22, 27]. Thus, the chemical cross-linked brittle network by covalent bonds serve as “sacrificial bond” that effectively toughen the sample. They show a high toughness (fracture energy of 1,000–1,000 J/m2), a high stiffness (0.1–1 MPa), a high failure tensile strain (1,000–2,000%), and a failure tensile stress (1–10 MPa) although they have 80–90 wt% of water at an equilibrium state. The excellent mechanical behaviors

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of DN hydrogel are comparable to some soft load-bearing tissues. Using the state-of-the-art double-network approach to enhance the mechanical toughness has successfully resulted in a series of tough hydrogels and elastomers, such as polyethylene-oxide/polyacrylic acid double-network gels, tough double-network hydrogel from biopolymers, multiple network elastomers, etc. [28–31]. However, a disadvantage of DN gel is that the sample shows permanent softening after experiencing large deformation since the rupture of the brittle networks is the breaking of the covalent bonds. Thus, DN hydrogels show excellent mechanical performance but lack self-healing behavior, compared to the loading-bearing bio-tissues [27]. To address this problem, alternatively it is possible to replace the irreversible covalent bonds in the brittle network by the dynamic bonds, including reversible physical bonds and reversible covalent bonds [32]. These reversible bonds serve as the reversible sacrificial bonds. When the sample is loaded, the reversible bond is broken to dissipate energy, imparting the toughness of the sample. When the sample is unloaded, the ruptured reversible bonds are able to re-form, imparting the internal and surface self-healing of the damaged materials. Along this line, several tough hydrogels with partial or full self-healing behavior have been fabricated using either the reversible physical bonds or covalent bonds. For example, the reversible physical bonds have been used to design self-healing materials, including agar/ polyacrylamide double-network hydrogel and supramolecular hydrogel from the association of ureidopyrimidinone units based on hydrogen bonds [33–37]; polyion complex hydrogel, polyampholyte hydrogel, and metal-ion-cross-linked alginate/polyacrylamide double-network hydrogel based on ionic bonds [38– 40]; poly(dodecyl glyceryl itaconate)/polyacrylamide double-network hydrogel, poly(stearyl methacrylate-co-acrylamide) hydrogel, and poly(dococylacrylate-coacrylamide) hydrogel based on hydrophobic interaction [41–43]; supramolecular hydrogel from the cyclodextrins based on host-gust interaction [44–46]; the healable supramolecular polymers based on π – π packing [47, 48]; and so on. The reversible covalent bonds are used to design self-healing materials, including poly(ethylene oxide)/tris[(4-formylphenoxy)methyl]ethane supramolecular hydrogel based on acylhydrazone bonds [49], self-healing gels from copolymerization of n-butyl acrylate based on trithiocarbonate units [50], self-healing gels based on diarylbibenzofuranone units [51], etc. Recently, we develop a tough and self-healing hydrogel from polyampholytes (PAs) that bears the cationic groups and anionic groups distributed along the main chain [39]. The random copolymerization process makes the ionic monomers randomly distributed along the backbones, resulting in the formation of ionic bonds with a wide strength distribution via inter- and intra-chain complexation in the polymer network. These ionic bonds were divided into two groups, weak ionic bonds (dynamic bonds) and strong ionic bonds (Fig. 1a), according to the competition between bonds strength and experimental observation time. The strong ionic bonds can maintain the integrity of the hydrogel over much longer time scale, imparting the elastic behavior, while the weak ionic bonds can break to dissipate energy to give toughness and re-form to enable self-healing behavior. Therefore, polyampholyte hydrogels are very strong and tough with failure tensile stress of

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(a)

(b)

MPTC

DMAEA-Q

Cationic monomer

Anionic monomer

NaSS

AMPS

Fig. 1 (a) Schematic illustration of polyampholyte networks with ionic bonds of different strength. (b) The chemical structures of cationic monomers MPTC and DMAEA-Q and anionic monomer NaSS and AMPS are used to design the polyampholyte hydrogels. Reproduced with permission from Ref. [39]

0.1–2 MPa, failure tensile strain of 150–1,500%, work of extension of 0.1–7 MJ/m3, Young’s modulus of 0.01–8 MPa, 100% self-recovery behavior, and a high selfhealing efficiency. They have a fracture energy of 1,000–4,000 J/m2, comparable to that of filled rubbers, tough double-network hydrogels, and soft tissues. In this review paper, we firstly optimize the compositions of tough hydrogels, including the charge ratio of cationic monomer and anionic monomer, monomer concentration, cross-linker concentration, chemical structures, etc. Secondly, we discuss the role of dynamical ionic bonds on the mechanical behavior of hydrogels, including the self-healing, viscoelastic, and fracture behavior. Thirdly, we elucidate the toughening mechanism of PA hydrogel. Fourthly, we simply summarize the recent applications of PA hydrogel. Finally, conclusions are given in the last part.

2 Synthesis and Optimized Structure PA hydrogels are synthesized from the one-step random copolymerization of cationic monomer and anionic monomer with a described molar ratio, monomer concentration, and initiator concentration in the presence of or without chemical

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0.5 0.4 0.3 0.2 0.1 0.0

0

6 12 18 24 30 Norminal strain (mm/mm)

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Fig. 2 (a) Images of a tough PA hydrogel. (b) Uniaxial tensile stress-strain behavior of PA hydrogels

cross-linkers under UV irradiation for several hours. After polymerization, the hydrogels at the equilibrated state are obtained by immersing the as-prepared gel in a large amount of water to remove the excess mobile counterions and residual chemical reagents from the as-prepared gel. This process will substantially stabilize the formation of inter- and intra-chain ionic bonds [39]. The approach to synthesize PA hydrogels is quite general and has been found effective to many kinds of ionic monomer combination, as shown in Fig. 1b. Two typical examples, the one made from the polymerization of sodium p-styrenesulfonate (NaSS) and 3-(methacryloylamino)propyl-trimethylammonium chloride (MPTC) and the other made from the polymerization of NaSS and methyl chloride quarternized N,N-dimethylamino ethyl acrylate (DMAEA-Q), are used to discuss this review. Hereafter, we denote the samples using the code Cm-f-x after the names of the copolymers, where Cm (mol/L) is total molar concentration of monomers, f is the anion monomer molar fraction, and x (mol%) is the molar ratio of the chemical cross-linker N,N0 -methylenebisacrylamide (MBAA) relative to Cm in the precursor solution. Figure 2a shows a photo of tough PA hydrogel P(NaSS-co-DMAEA-Q) 2.0–0.52–0.1% under stretching by hands, and the transparent sample can sustain a large deformation without fracture. Figure 2b shows a typical tensile stress-strain behavior of this hydrogel with a low Young’s modulus of 0.09 MPa, high failure tensile strain of 2,900%, failure tensile stress of 0.42 MPa, and work of extension of 4.7 MJ/m3. To obtain tough hydrogels, the compositions including charge ratio, chemical cross-linker density, total ionic monomer concentrations, and chemical structures of ionic monomers are optimized.

2.1

Charge Ratio

Firstly, PA gels were synthesized with different f at fixed Cm ¼ 2.0 M and x ¼ 0.1 mol%. The gels swell (volume swelling ratio Qv > 1) at f < 0.51 and

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Fig. 3 The effect of NaSS molar fraction on the volume swelling ratio, the weight swelling ratio, Young’s modulus, and compressive fracture stress of PA hydrogel P(NaSS-coDMAEA-Q) 2.0-f-0.1%. Reproduced with permission from Ref. [52]

f > 0.525 due to the large charge imbalance which is induced by the counterion osmotic effect of the net polymer charges and the polymer segments elongate. And at the very narrow region at f ¼ 0.51–0.525, the gels shrink (Qv < 1) as the Coulomb attraction prevails over the repulsion for neutral polyampholytes and the polymers collapse to a globule state (Fig. 3). The corresponding fracture stress dramatically increases at this region and reaches a maximum value at f ¼ 0.52. The optimized tough gel has ~50 wt% water content, which is quite close to that of biological tissues but lower than those of conventional hydrogels (>80 wt%). It was confirmed that the gel prepared from the precursor solution at f ¼ 0.52 has an exactly balanced charge ( ftrue ¼ 0.5) by element analysis [52].

2.2

Total Ionic Monomer Concentration

Secondly, PA gel P(NaSS-co-DMAEA-Q) with various monomer concentration Cm was prepared at f ¼ 0.52 without any chemical cross-linkers. When the sample was synthesized at low Cm (> KOH/urea aqueous solution [67, 68]. Different from that in other solvents mentioned above, the dissolution process in alkali/urea systems needs a low temperature treatment procedure (precooling the solvent [65] or freezing/thawing the mixture [66]), which arises as a fast dynamic self-assembly process among solvent small molecules (NaOH, urea, and water) and the cellulose macromolecules. The widely accepted mechanism of the dissolution of cellulose is that hydrogen bond acceptors (N–O, Cl, OAc, etc.) and/or donors (–NH2 in urea or thiourea) of the solvent break up the intra- and intermolecular hydrogen bonds in the biopolymer chains upon stirring, heating, or low temperature treatment [64, 74]. Notably, cellulose hydrogels can be formed via destructing the stability of cellulose solution in 7 wt% NaOH/12 wt% urea system by increasing the temperature to 50 C or reducing it to 20 C [64]. The irreversible gelation behavior of cellulose solution is very sensitive to temperature change and cellulose molecular weight and concentrations. In the NaOH/thiourea system, the sol-gel transition of cellulose is partially reversible in the range from 10 to 30 C. The formed gels at 30 C can be transformed to the liquid state at 5 C after stirring for a long period of time, which is caused by the reversible hydrogen-bonding networks between cellulose and solvent [75]. Thus, either at a higher temperature or a longer time, the gelation of cellulose solution can occur but only obtain weak hydrogels by using the preparation method from pure cellulose solution.

2.1.4

Hydrogels Prepared Directly from Bacterial Cellulose

Bacterial cellulose (BC) is formed by aerobic bacteria, such as acetic acid bacteria of the genus Gluconacetobacter, producing a thick gel composed of cellulose microfibrils and ~97% water, called pellicle [76]. The BC is proved to be a very pure cellulose with a high weight-average molecular weight (Mw), high crystallinity, excellent water-holding capacity, and good mechanical stability, which expand the wide range of applications of BC-based hydrogels in the biomaterials fields, such as

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tissue engineering scaffold, meniscus implants, and dental implants [76–78]. Putra et al. [79] synthesized a tubular BC gel with proper fibril orientation created by culturing BC in oxygen-permeable silicone tubes with inner diameter 10 kPa), rapid sol-gel transition ( Al3+ > Cu2+ > Zn2+ > Ca2+). Cationcarboxylate interactions are proposed to initiate gelation by screening of the

Fig. 11 (a) Photos of the CNF aqueous dispersion and the free-standing gels formed by addition of metal salt solutions to the carboxylated CNF dispersions. (b) Schematic illustration of metal ion-mediated CNF transient network in covalently cross-linked hydrogels. (c) Possible coordination modes in mussel-inspired cellulose nanocomposite tough hydrogel networks. From [176–178] with permissions from the American Chemical Society

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repulsive charges on the nanofibrils and to dominate gel properties through ionic cross-linking. Binding energies of cations with carboxylate groups were calculated from molecular models of CNF intrafibril and interfibril bonding to validate the correlation and provide further insight information for the cross-linked network structure. Taking advantage of their native biocompatibility and dynamic metalligand cross-linked network structure, the cellulose nanofibril-based hydrogels present promising biomedical applications as a tissue engineering substrate with physically adsorbed and covalently attached fibronectin protein onto the hydrogel surface to improve cell adhesion [183]. Utilization of reversible metal-ligand coordination interactions as sacrificial bonds in biopolymers is critical for the integral synthesis of mechanically superior biological materials. On the basis of the sacrificial bond theory, Yang et al. [177] designed cellulose nanofibrils (CNFs)-reinforced covalent polyacrylamide (PAAm) composite hydrogels by immersing into various multivalent cation aqueous solutions to form metal-ligand coordination association among CNFs, leading to the ionic-covalent cross-linked hydrogels (Fig. 11b). The cations promote the formation of porous networks of nanofibrils by screening the repulsive negative charges on CNF surface, dominating the superior mechanical properties with excellent tensile strength and toughness. Another advantageous feature of metal-ligand coordination is its ability to undergo repeated association to endow excellent self-recovery ability of the obtained ionic gels. The in situ Raman spectroscopy during stretching is utilized to corroborate the stress transfer medium of CNF in the microscopic deformation behavior of the gels. The microscopic morphologies of stable crack propagation validate that the multiple toughening mechanisms occur in a balanced energy dissipation manner, enabling synergistic combination of stiffness and toughness. Moreover, the creep behavior of the ionic gel in indentation test also suggests that the CNF ionic coordination contributes simultaneous improvement in hardness and elasticity compared to those pristine gels. This work provides a facile and straightforward ionic cross-linking strategy for CNF-based hydrogels with tunable dynamic properties, which may enrich exploration in biomedical field of highbearing cellulose-based soft materials. Dynamic nature of reversible coordination interactions not only toughens the mechanical performance via a sacrificial manner but also effectively heals the damage by reversible break and reform. Physical gels can realize self-healing process autonomously but often suffer from poor mechanical properties; thus constructing the fully physically cross-linked network without covalent bonds is an ideal strategy for integrating gels with efficient self-healing property and good mechanical performance. A few pioneering efforts on self-healing nanocellulosebased metallogel design have been made [178, 184]. For example, Yang et al. developed a simple one-pot strategy to prepare a fully physically cross-linked nanocomposite hydrogel through the formation of the hydrogen bonds and dual metal-carboxylate coordination bonds within supramolecular networks [184]. The iron ions (Fe3+) and TEMPO-oxidized cellulose nanofibrils (CNFs) acted as dual cross-linkers and led to the improved mechanical properties with excellent fracture strength (1.37 MPa), fracture elongation (1803%), and toughness (11.05 MJ/m3).

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The proposed toughening mechanism hypothesizes that the hydrogen bonds within gel networks tend to preferentially break prior to the coordination bonds and the survived coordination bonds with dynamic feature also serve as sacrificial bonds to dissipate another amount of energy after the rupture of hydrogen bonds, which collectively maximized the contribution of sacrificial bonds to energy dissipation while affording elasticity. Additionally, the synergy of hydrogen bonds and coordination bonds act as dynamic but highly stable associations, leading to the effective self-healing efficiency over 90% after damage. It is expected that this facile strategy of incorporating the biocompatible and biodegradable CNFs may enrich the avenue in exploration of dynamic and tunable cellulosic hydrogels to expand their potential applications in the biomedical field. Yang’s subsequent work [178] was based on dynamic coordination bonds that mediated the tannic acid-coated cellulose nanocrystals (TA@CNCs) as building blocks. This study was focused on addressing the inherent contradiction between excellent self-healing and mechanical properties because of the dynamic cross-links for healing and steady cross-links for mechanical strength. The hydrogel was prepared by constructing synergistic interfacial dynamic coordination bonds among tannic acid-coated CNCs (TA@CNCs), poly(acrylic acid) chains, and metal ions in a covalent polymer network. The TA@CNC acting as a dynamic connected bridge endows the ionic gels with hierarchically porous network crosslinked by multiple reversible coordination bonds (Fig. 11c), leading to the significant mechanical reinforcement of ionic gels. Reversible nature of dynamic coordination interactions contributes excellent recovery property as well as reliable mechanical and electrical self-healing property without any assistance of external stimuli. Intriguingly, the ionic gels display durable and repeatable adhesiveness ascribed to the presence of catechol groups from the incorporated tannic acid, which can be adhered directly on human skin and employed as flexible strain sensors to monitor human motions, expanding the potential applications of dynamic cellulose-based conductive hydrogels in wearable electronic sensors and healthcare monitoring. By taking advantage of the strong and dynamic metal-ligand coordination, Alizadehgiashi et al. [185] used a microfluidic approach to fabricate an ion-scavenging nanocolloidal microgel material with the chemical cross-linking of cellulose nanocrystals and graphene quantum dots. By immobilizing the nanocolloidal building blocks through with imine formation, the hydrogels, with tunable pore size and structure, sufficiently high mechanical strength, and good permeability, were formed. Due to the large surface area and abundance of ion-coordinating sites on the surface of nanoparticle building blocks, the microgels exhibited a high ion-sequestration capacity. The microgels were recyclable and were used in several ion-scavenging cycles. In addition, Hai et al. [186] explored the application of invisible security probe for the selective detection, protection, and storage of fingerprint information based on the luminescent TbIII-carboxymethyl cellulose (CMC) complex-binding aptamer hydrogels with reversible responsive to ClO/SCN. The imaging information of the fingerprint can be detected quickly under UV light, where ClO/SCN regulation results in reversible on/off conversion of the luminescence signals for the encryption

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and decryption of multiple levels of information. This study opens new avenues for multilevel imaging, data recording, and security protection of fingerprint information with tunable fluorescent hydrogels.

3.2.4

Electrostatic Interactions

The dynamic ionic cross-links occur via the reversible electrostatic interactions between a charged cross-linked polymer chain and an oppositely charged polymer chain or oppositely charged ions, which introduce the smart behavior on natural biopolymer hydrogels [26, 187, 188], such as environmental sensitivity and selfhealing behavior. Particularly, there has been significant attention on dynamic cellulose-based hydrogels cross-linked by the electrostatic interactions. Chang et al. [189] synthesized a novel ampholytic hydrogel with pH and saltresponsive properties by cross-linking quaternized cellulose (QC) and carboxymethyl cellulose (CMC) with epichlorohydrin (ECH) in NaOH aqueous solution, where QC and CMC were employed as the polycations and polyanions, respectively. In addition to the chemical cross-links, the electrostatic interactions formed by the acidic (–COO) and basic groups (–(CH3)3N+) within the obtained polysaccharide hydrogel network led to the multiple responsive behaviors, including pH and salt. The results revealed that CMC mainly contributed to the increasing swelling as a result of strong water adsorption, whereas QC played a domain role in pH sensitivity by controlling the charges in the QC/CMC system. Subsequently, Chang’s group [190] reported an interface compatible nanocomposite hydrogel prepared by introducing quaternized tunicate cellulose nanocrystals (Q-TCNCs) into chemically cross-linked poly(acrylic acid) (PAA) networks (Fig. 12a). Notably, the electrostatic interaction between the positive charges of Q-TCNCs and negative charges of PAA chains improved their interface compatibility, resulting in improved mechanical strength, toughness, and recoverable ability. Similarly, Chang’s group [192] continued to investigate tough and selfrecoverable hydrogel reinforced by quaternized tunicate cellulose nanocrystals (Q-TCNCs) in dual physically cross-linked nanocomposite networks. Q-TCNCs acted as both interfacial compatible reinforcements and multifunctional crosslinking agents to form first loosely cross-linked network through the electrostatic interactions between –N(CH3)3+ on the surface of Q-TCNCs and –COO on the side chains of poly(acrylic acid-co-acrylamide) (PAAAM), whereas the second compacted cross-linking was built by the formation of ionic coordination between Fe3+ and –COO of PAAAM. Reversible physical bonds (electrostatic interactions and coordination bonds) in the dual physically cross-linked networks served as the reversible sacrificial bonds to effectively dissipate energies, which contributed to the integration of high tensile strength, high ductility, and high toughness. Importantly, the nanocomposite hydrogels displayed excellent self-recoverability after immersing in FeCl3 aqueous solution. The reversible physical interactions endowed TCNCreinforced hydrogels with excellent mechanical properties and recovery properties, which provided a universal strategy for construction of tough cellulose-based hydrogels.

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Fig. 12 (a) Fabrication process and network structure of Q-TCNC/PAA composite hydrogel. From [190] with permission from Elsevier. (b) pH-responsive behavior of cellulose nanocrystal (CNC)based gels formed by CNC-CO2H and CNC-NH2. From [191] with permission from the American Chemical Society

Recently, Weder’s group has shown that sulfonated CNCs can be used as a stimuli-responsive filler to create mechanically adaptive polymer nanocomposites in a range of different polymer matrices [193–198]. Thus, the nanocomposite stiffness can be controlled by switching on/off the attractive interactions between the CNCs. Altering the surface chemistry of CNCs allowed access to pH-switchable mechanically adaptable aqueous dispersions and nanocomposites which was demonstrated by Way et al. [191]. The functionalization of the surface of cellulose nanocrystals (CNCs) with either carboxylic acid (CNC-CO2H) or amine (CNC-NH2) moieties renders the CNCs’ pH-responsive behavior (Fig. 12b). The amine groups of CNC-NH2 are protonated at low pH, forming aqueous dispersions in water owing to the electrostatic repulsions of the ammonium moieties to inhibit

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aggregation, while CNCs functionalized with carboxylic acids (CNC-CO2H) exhibit an increase in modulus at low pH and form gels. In both cases, the neutral or little charged CNCs show better mechanical reinforcement than their highly charged counterparts. Thus, this work suggests for the first time that it is possible to alter the surface chemistry of the CNCs and therefore change the stimulus that can be used to alter the CNC interactions and thus the mechanical properties of their corresponding suspensions, gels, and nanocomposites. Based on the electrostatic interactions, Lin et al. [199] developed a biocompatible hydrogel with a double-membrane structure from cationic cellulose nanocrystals (CCNC) and anionic alginate as novel drug carrier. The presence of CCNC in the inner membrane can enhance the structural stability of the hydrogel through electrostatic interactions between cationic nanoparticles and anionic alginate. The thickness of the outer layer can be tuned by the adsorption duration of neat alginate, and the shape of the inner layer can directly determine the morphology and dimensions of the double-membrane hydrogel. The biocompatibility and nontoxicity derived from natural polysaccharide components as the building blocks can be preserved for the double-membrane hydrogel, which contribute to the complex drug release with the first quick release of one drug and the successively slow release of another drug.

4 Summary and Outlook Hydrogels based on biopolymer cellulose are a unique functional soft material with a cross-linked hydrophilic network entrapping large amounts of water and thus possess a great variety of properties. The combination of versatile physicochemical properties allows cellulose-based hydrogels to have a wide range of industrial and biomedical applications, attracting great scientific and industrial interest across the globe. Given the renewable, biocompatible, and biodegradable characteristics, cellulose and its derivatives with fascinating structures and properties offer a versatile platform for rational design of cellulose-based functional hydrogels. Much fundamental research has been conducted on the preparation of cellulose-based hydrogels, such as the development of solvent systems for hydrogels prepared directly from a native cellulose solution, hydrogel formation from cellulose derivatives by physical or chemical strategies, and cellulose-based composite hydrogels made by mixing natural biopolymers, synthetic polymers, or inorganics with cellulose or its derivatives to achieve a new structural design and functional properties integrated with the advantages of both components. In fact, more attention is paid on the development of the dynamically cross-linked cellulose-based hydrogels. The dynamic chemical cellulose-based gels contain reversible dynamic covalent bonds that can break and reform, such as imine bonds, disulfide bonds, Diels-Alder (DA) bonds, and disulfide bonds. Dynamically physical cellulose-based gels re-establish networks through dynamic formation of attractive non-covalent interactions, including hydrogen bonds, host-guest interactions, metal-ligand coordination, hydrophobic interactions, and electrostatic interactions. Dynamic chemistry provides a fascinating strategy to

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prepare dynamically cross-linked cellulose-based hydrogels with dynamic stimuliresponse or self-healing behaviors. For future outlook, more explorations should be focused on (1) “green” (safe solvents, none, or nontoxic cross-linkers), solvent systems for cellulose and low-energy processing for hydrogel preparation; (2) injectable cellulose-based hydrogels forming by physical cross-links within the body for applications of targeting drug release or tissue engineering; (3) pH- or enzymatic-sensitive cellulose-based gel by dynamic cross-links for drug release; (4) high-strength hydrogel reinforced from nanocellulose for tissue replacement; (5) self-healable cellulosebased gel to prolong the lifetime and improve the durability; (6) development of multifunctional integrated hydrogel on the basis of the structure and property of cellulose as an economical way to improve efficacy, selectivity, or recycling during water purification; (7) design of cellulose composite hydrogels with dynamic crosslinks and dissipation properties in a sacrificial manner; and (8) development of cellulose to prepare novel hydrogels with unique characteristics such as photonic properties. Undoubtedly, hydrogels based on cellulose and their derivatives still offer abundant promising opportunities in various fields, although significant challenges would need to be overcome before commercialization, and thus fundamental research into the nature of these systems should also continue.

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Adv Polym Sci (2020) 285: 355–378 https://doi.org/10.1007/12_2019_57 © Springer Nature Switzerland AG 2020 Published online: 29 February 2020

Self-Healing Collagen-Based Hydrogel for Brain Injury Therapy Raquel de la Cruz and David Díaz Díaz

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Collagen and Collagen Hydrogels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 In Vitro Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 In Vivo Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Hydrogels derived from biopolymers, also called biohydrogels, have shown potential for brain injury therapy due to their tunable physical, chemical, and biological properties. Among different biohydrogels, those made from collagen type I are very promising candidates for the reparation of nervous tissues due to its biocompatibility, noncytotoxic properties, injectability, and self-healing ability. Moreover, although collagen does not naturally occur in the brain, it has been demonstrated that collagen type I, which resides in the basal lamina of the subventricular zone in adults, supports neural cell attachment, axonal growth, and cell proliferation due to its intrinsic content of specific cell-signaling domains. This chapter summarizes the most relevant results obtained from both in vitro and in vivo studies using self-healing biohydrogels based on collagen type I as key component in the field of neuroregeneration.

R. de la Cruz and D. D. Díaz (*) Departamento de Química Orgánica, Universidad de La Laguna, La Laguna, Tenerife, Spain Instituto Universitario de Bio-Orgánica Antonio González, Universidad de La Laguna, La Laguna, Tenerife, Spain Institut für Organische Chemie, Universität Regensburg, Regensburg, Germany e-mail: [email protected]

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Keywords Brain therapy · Central nervous system · Collagen · Hydrogel · Regeneration

Abbreviations 2D 3D BBB bFGF BMSC CLG3/HLP CNS cRGD CSPG DGEA DRG ECM EGF ESC FAK FGF-2 FITC FN G3P GDNF GRP HA hMSC LG3 LN LP MCAO MSC mTGase NeuN NGC NGF NPC NSC PC12 PCR PNS ReNcell RGD RGDT SAPNS

Two dimensional Three dimensional Blood-brain barrier Basic fibroblast growth factor Bone marrow-derived mesenchymal stem cell Collagen-binding LG3/histidine-tagged LP Central nervous system Cyclo(RGD-D-Phe-Val) Chondroitin sulfate proteoglycans Aspartic acid-glycine-glutamic acid-alanine Dorsal root ganglion/ganglia Extracellular matrix Epidermal growth factor Embryonic stem cell Focal adhesion kinase Fibroblast growth factor-2 Fluorescein isothiocyanate Fibronectin Glyceraldehyde 3-phosphate Glial cell line-derived neurotrophic factor Human glial-restricted precursor Sodium hyaluronate (hyaluronic acid) Human marrow stromal cell Peptide LG3 Laminin Peptide FNTPSIEKP Middle cerebral artery occlusion Mesenchymal stem cell Microbial transglutaminase Neural nuclear protein Nerve guidance channel Nerve growth factor Neural progenitor cell Neural stem cells Pheochromocytoma cell Polymerase chain reaction Peripheral nervous system Neural progenitor cell Arginylglycylaspartic acid Arginylglycylaspartic acid-threonine Self-assembling peptide nanofiber scaffolds

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SC SEM

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Schwann cell Scanning electron microscopy

1 Introduction The central nervous system (CNS) is crucial for performing motor, sensory, and autonomic functions, including somatic injury repair. Unfortunately, the CNS has limited capacity for regeneration, resulting in the formation of glial scars and cysts. This makes the effects of neurotrauma, ischemia, hemorrhage, or neurodegenerative diseases displeasing and, very often, irreversible [1]. This is mainly due to the intrinsic properties of neural parenchyma (i.e., insufficiency of progenitor neural cells in the adult nervous system and slow ability of mature neural cells to regenerate, proliferate, and migrate [2]) and the heterogeneous microenvironment generated by the damage. This can lead to destruction of the blood-brain barrier (BBB), cytotoxicity (e.g., due to release of proteases and free radicals from necrotic cells), and trophic and oxygen deprivation. Many therapeutic strategies designed for enhancing endogenous repair mechanisms of the nervous system have become unsuccessful due to the short half-life and systemic effects of injectable growth factors, as well as the poor survival, differentiation, and migration of transplanted stem cells. One of the most promising approaches to overcome these issues is the use of three-dimensional (3D) hydrogel networks with tunable physical and chemical properties [3]. In the context of brain tissue regeneration, such hydrogels must support both viscous flow under shear stress (shear-thinning during injection) and time-dependent recovery upon relaxation (self-healing after injection at the injury site) in order to achieve a minimally invasive surgery [4]. Moreover, many other features such as biocompatibility, biodegradability, porosity, cell adhesion ability, low cytotoxicity and immunogenicity, lack of mutagenicity, and lack of swelling, are also critical aspects that should be considered to develop hydrogel scaffolds suitable for clinical applications in neuroregeneration [5]. Hydrogels can serve as local transport systems for the delivery of drugs and signaling molecules specifically to the injury site and as 3D scaffolds providing appropriate physical support, substrates for cell adhesion, optimal nutrient and oxygen exchange, and protection to host and graft cells, thus facilitating extracellular matrix (ECM) formation [6]. Within this context, the main role of hydrogels in neuroregeneration is to exert control over the host neural tissue and grafted cell fate by sustaining attachment, neurite outgrowth, proliferation, migration, differentiation, and viability. Among many types of hydrogels, biohydrogels derived from preexisting components of body tissues, such as collagen, constitute promising biomaterials for brain injury therapy due to their biocompatibility, noncytotoxic properties, self-healing ability, and intrinsic content of cell-signaling domains that can efficiently promote cell growth [7]. Usually, biological materials such as collagen are turned into mechanically stable hydrogels by either cross-linking processes (i.e., chemical cross-linking, photochemical cross-linking, enzymatic cross-linking, thermal cross-linking) or mixing with other

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polymers. Moreover, in order to use these biomaterials in brain injury therapy, we should consider that neural progenitor cells (NPCs) receive instructive cues from chemical and physical sources which affect differentiation and growth. Therefore, conjugation of specific bioactive molecules/peptides onto the culture surface constitutes a good strategy to gain control on the signals that cells receive from external stimuli. In this sense, a logical design of materials for tissue engineering applications, including regeneration of damaged brain tissues, involves the incorporation of adhesive peptide sequences and cytokines into material constructs to promote cell penetration and host tissue integration by enabling cell–matrix and cell–cell interactions. In this chapter, we summarize key results obtained in this field using self-healing biohydrogels based on collagen type I, including both in vitro and in vivo studies.

2 Collagen and Collagen Hydrogels Collagen is the main structural protein found in the ECM of connective tissues in the body. It is the most abundant protein in mammals, and it represents approximately 30% of the whole-body protein content [8]. From a chemical point of view, collagens are trimeric molecules composed of three polypeptide α-chains, which contain the repeating sequence (G-X-Y)n, where X is normally proline and Y is hydroxyproline. Such repeating pattern allows the formation of a triple helix, so-termed tropocollagen, which is the most characteristic structural feature of the collagen protein family. It is well established that subsequent stabilization upon further packing of the tropocollagen subunits into fibrils eventually forms a 3D collagen hydrogel. There are 29 collagen types reported in the literature, which differ in size, structure, and functions [9]. Collagen [10] and hyaluronic acid (HA) [11] are the most common natural polymers in neural tissue engineering. In particular, it has been reported that collagen hydrogel scaffolds infused with nerve growth factor are capable of improving cell viability in vitro [12]. Moreover, neurons cultured in collagen hydrogels have been found to retain their capacity to generate spontaneous post-synaptic potentials, demonstrating functional synapse formation [13]. Importantly, collagen hydrogels without additional topographical features have also been used to treat spinal cord injury in rats in vivo. The results have showed that these gels are biocompatible, support axonal growth, and can improve limited functional recovery. In addition, collagen-based hydrogels have also been used to differentiate NPCs into neurons and glial cells and to support neurite outgrowth of CNS neurons [14]. Collagen type IV is widely presented in the adult nervous system where it forms basement membranes of the BBB and neuromuscular junctions, being also associated to neurogenesis in the embryonic and adult brain. Collagen type I (hereinafter referred to as collagen I) is one of the collagen types found in fractone, an extracellular matrix structure, which is present in the lateral wall of the ventricles. This is relevant because such location constitutes one of the main neural stem cell (NSC) niches in the adult brain [9]. As NSCs retain the ability to self-renew and produce the major cell types of the brain, they have been on the focus of restorative therapy for

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neurodegenerative disorders. Although collagen does not naturally occur in the brain, it has been proved that collagen I, which resides in the basal lamina of the subventricular zone in adults, supports neural cell attachment, axonal growth, proliferation, and guidance in neural development [15]. Collagen I also forms the dura mater (i.e., the thick membrane that surrounds the brain and spinal cord) and leptomeninges [16]. Collagen I is routinely obtained from rat tails, porcine, and bovine skin, and several research groups have demonstrated that the collagen source influences significantly the properties of the hydrogels that can be formed [17]. Due to its role in CNS development, as well as the self-healing capacity of its hydrogels, collagen I is considered to be a good candidate for brain tissue regeneration [15]. For instance, neural progenitor cells isolated from the rat embryonic CNS have been found proliferate and differentiated rapidly into both neurons and astrocytes in collagen I hydrogels [8]. Furthermore, the neurons in these hydrogels were found to develop neuronal features, including neuronal polarity, neurotransmitters, ion channels/receptors, and excitability. Several reviews have been reported in the literature regarding the use of different biopolymers to repair nerve injuries [9, 18].

3 In Vitro Studies In 2007, Brannvall and co-workers developed a two-component collagen I-HA scaffold (1:1 volume mix) matrix to enhance the differentiation of mouse embryonic, postnatal, and adult NSCs and PCs (progenitor cells) [19]. The gel formation of the scaffold used in this study takes place during physiological conditions and is caused by the physical aggregation of collagen. The resulting network was found to retain hyaluronan and provided the stability required for culturing cells in 3D. It is worth noting that the formation of mature neural cells from NSC/PC depends on its intrinsic machinery but also on external factors and signals derived from the ECM. Both components of the 3D matrix, when used separately, were found to be compatible with culture of cells from the nervous system. The authors demonstrated that their combination constitutes a favorable condition for neuronal differentiation of NSC/PC. By raising the temperature to 37
C, gel formation of the collagen scaffold can be induced, and such property would be advantageous for tissue replacement after traumatic brain injury, where a cavity in the brain parenchyma is formed. By mixing cells with the scaffold at temperatures below 37
C, the cellmatrix mixture may fill the cavity with ECM components and new cells. Specifically, stem cells isolated from different ages of CNS tissue were seeded in the presence of the 3D bio-scaffold and cultured in medium containing the mitogens epidermal growth factor (EGF) and fibroblast growth factor-2 (FGF-2), a condition that stimulates NSC/PC proliferation. In general, the results showed that progenitor cells from the embryonic brain had the highest proliferation rate, and adult cells the lowest, indicating a difference in mitogenic responsiveness. NSC/PC from postnatal stages downregulated nestin expression more rapidly than both embryonic and adult

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NSC/PC, indicating a faster differentiation process. In particular, after 6 days of differentiation in the 3D scaffold, NSC/PC from the postnatal brain had generated up to 70% neurons, compared with 14% in a two-dimensional (2D) culture. The reason for the relatively high percentage of apoptosis is most likely dead cells being trapped in the 3D scaffold, compared with 2D culture, in which dead cells are detached from the surface and washed out during medium exchange. Another contributing factor could be a difficulty with exchange of gases and nutrients into the core of the matrix, compared with the corresponding 2D culture, which is only one cell layer thick. However, NSC/PC from other ages gave rise to approximately the same proportion of neurons in 3D as in 2D (9–26% depending on the source for NSC/PC). In the postnatal NSC/PC cultures, the majority of βIII-tubulin-positive cells expressed glutamate, g-aminobutyric acid, and synapsin I after 11 days of differentiation, indicating differentiation to mature neurons in the biocompatible hydrogel (Fig. 1). Bozkurt and co-workers compared in vitro a cross-linked porcine collagen scaffold with a fibrin hydrogel-based system for the ability to support neurite outgrowth in the rat dorsal root ganglion (DRG) [20]. It is important to highlight that although DRG studies deal with the peripheral nervous system (PNS), they can provide valuable data for regeneration of the relevant adult neurons. The nerve guide described in this work showed a high degree of porosity and, more importantly, a remarkable degree of orientation, with channel sizes between 20 and 50 μm. Such collagen guidance channels were manufactured using a series of chemical and mechanical treatments with a patented unidirectional freezing process (Fig. 2). Hemisected rat DRGs were positioned such that neural and non-neural elements could migrate into the collagen scaffold (Fig. 3). After 21 days, S100-positive Schwann cells (SCs) migrated into the scaffold and aligned within the guidance channels in a columnar fashion, resembling “Bands of Büngner.” Overall, the microstructural properties of collagen scaffold and the in vitro data after DRG loading make this scaffold a good candidate to be considered for promoting oriented nerve fiber regeneration in the PNS. Around the same time, a study on DRG carried out by Blewitt and co-workers [21] revealed that hydrogels with low collagen concentrations (0.4–1.0 mg/mL) helped to achieve the longest neurite extension. Hydrogels with higher collagen concentration and thus higher stability required modifications with adhesive recognition peptides to exhibit similar properties. The aim of this study was to investigate the effects of inhibitory molecules on nerve growth in 3D environments as compared to 2D surfaces. Thus, soluble peptide sequences were used as competitive inhibitors of neurite extension in collagen gels. In order to determine the effect of collagen gel properties on neurite extension, dissociated DRG cells were seeded into an array of collagen gel concentrations. E9 chick dorsal root ganglion cells were seeded within collagen gels as well as onto collagen-coated glass and were exposed, for 24 h, to one of three experimental peptide sequences, namely, arginine-glycine-aspartic acid-threonine (RGDT), cyclo(RGD-D-Phe-Val) (cRGD), or aspartic acid-glycineglutamic acid-alanine (DGEA) (Fig. 4). In 3D collagen gels, only the cRGD peptide sequence reduced neurite extension across a variety of gel concentrations. In contrast, on 2D surfaces, both RGD peptides reduced the number of cells expressing

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Fig. 1 P6 NS/PC grown in 3D express GABA, glutamate, and synapsin I upon growth factor withdrawal (WD). (a) GABA-positive neurons are formed after 5 days of WD, and, after 11 days of WD, most bIII-tubulin-positive neurons are GABA immunoreactive. Signal from βIII-tubulin removed; arrows indicate neurons. 3,200. (b) Neurons expressing βIII-tubulin are not synapsin I positive after 5 days of withdrawal. After 11 days of withdrawal, most βIII-tubulin-positive cells are synapsin I positive (blue). Signal from βIII-tubulin removed; arrows indicate neurons. 3,200. (c) After 11 days of withdrawal, mature neurons expressing NF-H (red) are expressing GABA (blue left, right arrowhead). Cells are also expressing glutamate (red right, arrow). Signal from EGFP has been removed. 3,200. Adapted with permission from reference [19], Copyright 2007 John Wiley & Sons

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Fig. 2 Scanning electron microscopy (SEM) of the microscopic structure of the collagen matrix. Pore sizes ranged between 20 and 50 μm (a, left, longitudinal section): extensive fenestrations interconnected the longitudinal guidance channels. (b, right, cross-section): Top view-longitudinal guidance channels pass from one end of the scaffold to the other. Scale bars (a) 50 μm (b) 100 μm. The orientation of the sections is indicated by the schematic diagrams. Adapted with permission from reference [20]. Copyright 2007 Mary Ann Liebert

Scaffold

DRG

500 µm Acc.V Spct Magn Del WD 10.00 kV 4.0 35x SE 11.5 EME UKA 06-264-4

Fig. 3 Scanning electron microscopy (SEM) example of a dorsal root ganglion (DRG) loaded onto the collagen matrix. Scale bar ¼ 500 μm. Adapted with permission from reference [20]. Copyright 2007 Mary Ann Liebert

neurites, but cRGD still exhibited superior inhibition of neurite expression (Fig. 5). Therefore, it seems that 2D substrate assessments for DRG growth do not accurately mimic growth in a 3D environment. Deister and co-workers investigated neurite extension from explanted dorsal root ganglia cultured within co-gels made from laminin, fibronectin, collagen I, and HA [22]. In contrast to previous results, this research showed that apparently neither collagen nor HA concentration had effects on neurite outgrowth and length. The

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Fig. 4 Qualitative examination of cells on 2D substrates with various peptide treatments. All cultures were initially incubated 24 h (a) before peptide supplementation (imaged live). After subsequent 24 h incubation, cultures with RGES (c), DGEA (d), and no peptide added (b) exhibited similar networking and attachment. Cultures supplemented with RGDT (e) and cRGD (f) exhibited reduced networking and overall neurite expression. Reproduced with permission from reference [21]. Copyright 2007 Springer

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Fig. 5 Average neurite length after 24 h for each collagen gel concentration. Statistical differences ({) were noted between lengths in 1.5 and 2.0 mg/mL gels and those in the range from 0.4–1.0 mg/ mL. Error bars are SEM, n  100 for each sample type. Adapted with permission from reference [21]. Copyright 2007 Springer

model used in this study used primary neurons that are actively involved in peripheral nerve injury. Briefly, the collagen I concentration of the hydrogels varied between 1 and 2.5 mg/mL, and neurite outgrowth and length were analyzed, while hydrogels made with a lower collagen concentration (0.5 mg/mL) were found to be mechanically unstable to be used in these experiments. Laminin showed a strong, dose-dependent effect on both neurite length and outgrowth, whereas fibronectin displayed a slightly inhibitory effect on neurite extension. Similarly, the concentration of collagen I and HA showed no significant effects on neurite extension. Overall, the combinatorial effects observed among the four components of the formulations were additive rather than synergistic. The optimum co-gel formulation found in this study included 1.5 mg/mL of laminin and 1.5 mg/mL of collagen I (Fig. 6). In 2009, Kofron and co-workers proceeded to guide neuritis using the surface patterning of a 3D collagen I hydrogel matrix with laminin (LN) and chondroitin sulfate proteoglycans (CSPG) [23]. LN and CSPG were chosen as representative molecules because LN is known to promote neuronal adhesion, migration, and neurite extension, while CSPG is an inhibitor of neuronal growth. By placing the DRG layer uniformly between collagen I hydrogel and either LN- or proteoglycan-covered glass, the authors confirmed laminin’s micropatterning ability to guide DRG neurites on the surface of collagen (Fig. 7). In contrast, proteoglycan patterning did not lead to extension of DRG neurites. These results are relevant toward understanding how neurons integrate local structural and chemical cues to make net growth decisions. In the same year, Hiraoka and co-workers investigated collagen-based hydrogel effects on rat fetal NSCs [24]. During this study, the authors demonstrated that the viability of neurosphere-forming cells embedded in a collagen hydrogel can be improved by incorporating a LN-derived cell-adhesive peptide involving glyceraldehyde 3-phosphate (G3P) in the hydrogel (Fig. 8). Because the viability of most cells

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Fig. 6 Representative micrographs from DRGs cultured in gels made with (a) 1.5 mg/mL laminin and 1.5 mg/ml collagen I, (b) 1.5 mg/mL collagen 1 only (control), and (c) 1.5 mg/mL fibronectin and 1.5 mg/mL collagen I. Scale bar is 200 μm. The laminin-containing gels (a) had significantly more neurite outgrowth and greater length than the collagen I only gel (b). The fibronectincontaining gels (c) had significantly less neurite outgrowth and shorter neurites than the collagen I only gel (b). Adapted with permission from reference [22]. Copyright 2007 Taylor & Francis

largely relies on adhesion signaling, the improved viability is plausibly the consequence of enhanced cell adhesion in the hydrogel networks. G3P was originally identified by Kim and co-workers as a ligand for α3β1 integrin expressed on epithelial cells [25]. This peptide is contained in a G3 domain of a LN α3 chain, a component of a LN-5 isoform. The interaction between LN-5 and α3β1 integrin was reported to have an antiapoptotic effect in a variety of epithelial cells [26]. Moreover, LN-5 is abundantly found in epithelial basement membranes [27] and also expressed in developing brain tissues [28]. Therefore, the collagen matrix bound with G3P as reported in this study can be regarded as a biomaterial that mimics in part the native basement membrane. Importantly, live/dead assays (Figs. 8 and 9) showed that a larger number of neurosphere-forming cells survived in collagen hydrogels containing G3P than in pure collagen hydrogels. The authors were unable to distinguish necrotic cells from apoptotic ones, and possibly both mechanisms were involved in observed cell death. Regarding necrotic conditions, if any, cells were equally affected in both hydrogels, and cell viability may be improved by optimizing culture conditions such as oxygen and

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Fig. 7 In interface cultures, DRG explant growth patterns varied with interface cue. (a–c) 2D summations of maximum projections of a confocal stack of DRG explants grown for 3 days in interface cultures with no cue (a), micropatterned LN (b), or micropatterned CSPG (c) and stained for anti-neurofilament immunocytochemistry. (d, e) Coverslips removed from separate interface cultures with micropatterned LN (d) and micropatterned CSPG (e) and immunostained for anti-LN (d) and anti-CSPG (e). Top scale bar, 500 μm; bottom scale bar, 200 μm. Reproduced with permission from reference [23]. Copyright 2009 Institute of Physics Publishing

nutrient supply. For the observed difference in viability, the authors assumed that this was due to antiapoptotic signaling cascades activated in the cells in consequence of an interaction between G3P and α3β1 integrin. Indeed, integrin subunits α3 and β1 are both expressed on the neurosphere-forming cells, being in good agreement with previous reports for neural stem cells [29], cerebral cortex neurons [30], and differentiating neuroblastoma cells [31]. In 2010 Yao and co-workers reported the ability of collagen I-based hydrogel to support neurite outgrowth in rat pheochromocytoma cells (PC12) [32]. Collagen scaffolds were prepared using different concentrations of a fluorescent labeledlaminin peptide (PPFLMLLKGSTR). Although the results of this study indicated that there is not a significant difference in neurite length on the LN-containing collagen hydrogel when compared with a native collagen scaffold, neurites showed a preferential growth orientation toward the high level of the LN peptide gradient on the collagen hydrogel (Fig. 10). This observation suggests the existence of different mechanisms involved in the regulation of neurite extension and neurite orientation. In 2011, Lee and co-workers investigated the abilities of LN- and fibronectin (FN)-modified collagen to stimulate neuro-induction of rat BMSCs (bone marrowderived mesenchymal stem cells) [33]. The effects of the 3D gel conditions on the differentiation of MSCs into nerve cells were evaluated through observation of the

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Fig. 8 Results of cell culture assays in collagen hydrogels with or without incorporated nG3PCBD. (a, b) Phase-contrast microphotographs of cells cultured for 48 h in (a) a pure collagen hydrogel and (b) a collagen hydrogel containing nG3P-CBD. Bars: 100 μm. (c, d) Fluorescent microphotographs of cells cultured for 48 h in (c) a pure collagen hydrogel and (d) a collagen hydrogel containing nG3P-CBD. Cells were stained with calcein-AM (live cells in green) and propidium iodide (dead cells in red). Bars: 100 μm. Adapted with permission from reference [24]. Copyright 2009 The American Chemical Society

Fig. 9 The viability of cells cultured for 24 and 48 h in (open circle) collagen hydrogels containing nG3P-CBD or (filled circle) pure collagen hydrogels. Data are expressed as mean  standard deviation for n ¼ 4. Statistically significant ( p < 0.05, Tukey’s HSD test). Reproduced with permission from reference [24]. Copyright 2009 The American Chemical Society

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Fig. 10 Neurite growth on collagen scaffold with laminin peptide gradient. (a) Neurite growth on collagen scaffold without laminin peptide gradient. Neurite growth on (b) native collagen scaffold and on (c) cross-linked collagen scaffold with laminin peptide gradient. Scale bar: 100 μm. Adapted with permission from reference [32]. Copyright 2010 Wiley Periodicals

cellular morphology and protein and molecular assays. The adhesive proteincontaining hydrogels induced neuronal cell differentiation of BMSCs without the use of chemical differentiation factors, presumably due to the low stiffness of the 3D collagen microenvironment mimicking native brain tissue. The principal fate of MSCs is self-renewal without amplification and/or differentiation when cultured on a normal 2D culture dish without a supply of neurogenic medium, such as nerve growth factor (NGF), and this was also observed in the present study. Immunofluorescence staining, Western blot, and fluorescence-activated cell sorting analyses demonstrated that a large population of cells was positive for neural nuclear protein (NeuN) and glial fibrillary acidic protein, which are specific to neuronal cells, when cultured in the 3D collagen hydrogel. The dependence of the neuronal differentiation of MSCs on the adhesive proteins containing 3D gel matrices is considered to be closely related to focal adhesion kinase (FAK) activation through integrin receptor binding, as exposed by an experiment showing no neuronal outgrowth in the FAK knockdown cells and stimulation of integrin b1 gene. In 2012, Swindle-Reilly studied dissociated E9 chick DRG cells in a collagen I hydrogel modified with LN at concentrations of 0, 1, 10, or 100 μg/mL [34]. This study revealed that low-concentrated unmodified collagen hydrogels (0.4–1.5 mg/mL) supported a typical bimodal neurite growth more than the LN-modified variant. Expression of integrin subunits, α1, α3, α6, and β1, was confirmed by polymerase chain reaction (PCR) and immunolabeling in the 3D scaffolds. As expected, the increase in collagen concentration increased the stiffness of the gels (Fig. 11). Although confocal microscopy showed LN following the collagen fibers (Fig. 12), the addition of LN caused minimal changes on the stiffness of the scaffolds at any concentration of collagen. In 2013, Koutsopoulos and co-workers compared viability and differentiation of the mouse adult NSCs in peptide nanofiber hydrogels, Matrigel™, and collagen [35]. Preliminary studies performed by the same group showed that self-assembling peptides support neuronal cell attachment and extensive neurite outgrowth and

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Fig. 11 Mechanical stiffness increases with increasing concentration of collagen; however, the addition of LN did not alter the stiffness. Mechanical stiffness of collagen gels with added LN was measured by the overall modulus, G with oscillatory shear rheometry within the linear viscoelastic range. Significance ( p < 0.05) is noted by the symbols for plain gels only:  compared to 0.4 mg mL1 collagen gels, # compared to 0.6 mg mL1 collagen gels, @ compared to 0.8 mg mL1 collagen gels, + compared to 1.0 mg mL1 collagen gels, % compared to 1.25 mg mL1 collagen gels, and & compared to 1.5 mg mL1 collagen gels. No differences were noted with added LN within any concentration of collagen. Adapted with permission from reference [34]. Copyright 2012 Institute of Physics Publishing

promote active and functional synapse formations when neural cells were plated on the surface of preformed peptide hydrogel matrices. In this research, neural stem cells from the subventricular zone of an adult mouse were used. To stimulate extensive self-renewal of the neural stem cell population, human FGF-2, human EGF, and insulin in the stem cell propagating medium were also added. The authors found that continuous provision of both FGF-2 and EGF was necessary to sustain nonadherent neurosphere formation of neural stem cells. Tissue cultures in collagen I hydrogel were characterized by low cell migration, cell clustering, and limited neural stem cell differentiation. This may be due to the biological incompatibility between neural cells and collagen I, a substance not found in mammalian brain tissue. It is known that neural cells (especially differentiated neurons and immortalized neural cells) survive in collagen I in the presence of a cocktail of growth factors. Nevertheless, such studies are performed for short periods of times (i.e., up to 2 weeks), and they are characterized by low cell migration and differentiation. When neural tissue cultures were investigated for longer periods of time, the authors found enhanced cell survival rates in peptide nanofiber hydrogels compared to Matrigel™ and collagen I, suggesting that the beneficial effect of Matrigel™ on tissue cultures is mainly due to non-quantified growth factors and cytokines that are present in the material (Fig. 13). It is clear that when these chemical stimuli are removed, the material itself is not suitable to support a viable neural tissue culture. This is yet

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Fig. 12 Representative confocal images for DRG neurons growing on a 2D LN surface (a) or within 3D collagen (1 mg mL1) gels with or without 100 μg mL1 LN (b) are shown. In (a), the neurons growing on the LN surface were stained for α3, neurofilament, and nuclei, with the merge shown on the right. The images show that the α3 subunit is expressed within neurons and glial/ fibroblast support cells. In (b), neurons growing within the 3D scaffolds were stained with antibodies that are specific to the integrin receptor subunits, α1, α3, α6, and β1 and neurofilament antibody specific for neurons, with the merge shown on the right. Scale bar is 20 μm. Adapted with permission from reference [33]. Copyright 2012 Institute of Physics Publishing

another indication of the important role of the matrix environment in inducing neural stem cells into diverse differentiation pathways. In addition, rheological measurements of the peptide hydrogels, Matrigel™, and collagen I were performed to determine their mechanical properties. Matrigel™ and collagen I concentrations

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Fig. 13 Cell survival as a function of time. Live/dead assay of 3D neural cell tissue cultures in modified peptides shows increased cell survival compared to the unmodified ac-(RADA)4CONH2 hydrogel, Matrigel™, and collagen I. Adapted with permission from reference [35]. Copyright 2013 Elsevier

used in these experiments resulted in hydrogels with flow properties resembling those of the peptide hydrogels. Therefore, differences in cell behavior in different matrices could not be due to differences in the mechanical properties of the hydrogels.

4 In Vivo Studies Despite the promising results reported so far in in vitro studies, it is also important to determine whether these results correlate with what occurs in in vivo conditions. In this context, Yu and co-workers have used tissue engineering to implant transient MCAO (middle cerebral artery occlusion) rats with commercially available biodegradable 3D porous collagen I sponges containing rat embryonic NSCs to develop a therapy for cerebral ischemic injury [36]. As expected, the results obtained in this study confirmed that collagen has good cell and tissue compatibility. Indeed, its long-term safety, stability, and efficacy in vivo have been adequately established in humans [37]. Experimentally, NSCs from E14 d rats were dissociated and cultured by neurosphere formation in serum-free medium in the presence of basic fibroblast growth factor (bFGF), then seeded onto collagen to measure cell adhesive ability. Wistar rats (n ¼ 100) were subjected to 2 h middle cerebral artery occlusion. After 24 h of reperfusion, rats were assigned randomly to five groups: NSCs-collagen repair group, NSCs repair group, unseeded collagen repair group, MCAO medium group, and sham group. Neurological, immunohistological, and electronic microscope assessments were performed to examine the effects of these treatments. Scanning electronic microscopy (SEM) showed that NSCs assembled in the pores of collagen. At 3, 7, 15, and 30 days after transplantation of the NSC-collagen complex, some of the engrafted NSCs survive, differentiated, and formed synapses in the brains of rats subjected to cerebral ischemia. Six days after transplantation of the NSC-collagen complex into the brains of adult ischemic rats, the collagen gel

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began to degrade, and 30 days after transplantation, the collagen had degraded completely. Herein, it was concluded that the beneficial effect of the complexes is mediated by a neuroprotective rather than a regenerative mechanism. In the same year, Zhong and co-workers carried out a study in a photothrombotic stroke murine model [38]. The stroke cavity provides an ideal target for transplantation because it is a compartmentalized region of necrosis, can accept a high volume transplant without tissue damage, and lies directly adjacent to the most plastic brain area in stroke. However, direct transplantation into the stroke cavity usually causes massive death in the transplant. To overcome these limitations, the authors tested stem/progenitor transplants within a specific cross-linked biohydrogel matrix made of hyaluronan, heparin, and collagen I to create a favorable environment for transplantation into the infarct cavity after stroke, and the results were compared to those obtained from direct injection of stem cells without hydrogel support. In this study, both embryonic cortex-derived NPCs and ESC (embryonic stem cell)-derived NPCs were used. Overall, hyaluronan-heparin-collagen hydrogels were found to promote the survival of NPCs derived from both the fetal cortex and ESCs, with no effect on cellular differentiation or migration of the cells from the stroke site. Quantitative analysis of the transplant and surrounding tissue indicates diminished inflammatory infiltration of the graft with the hydrogel transplant. In this respect, the beneficial effect of the hydrogel was found to be at least twofold higher than that obtained with NSCs in the absence of the gel matrix. In 2013, Hoban and co-workers provided evidence for collagen I as a noncytotoxic and self-healing hydrogel in situ [39]. The researchers injected the striatum of sham rats with glial cell line-derived neurotrophic factor (GDNF)overexpressing rat bone marrow MSCs (GDNF-MSCs) encapsulated in a collagen hydrogel cross-linked with 4S-StarPEG (PEG ether tetrasuccinimidyl glutarate) (Fig. 14). In vitro studies confirmed that the collagen I hydrogel was nontoxic to neural cells or MSCs seeded within it and also permitted diffusion of GDNF from GDNF-MSCs into the cell culture medium. More importantly, it significantly reduced the host brain’s response to the cells by reducing the recruitment of both microglia and astrocytes at the site of delivery. Although the hydrogel prevented micro- and macrogliosis compared to the medium-injected control group, the scaffold poorly supported MSCs survival and decreased in volume several days post gelation both in vitro and in vivo. At the same time, Liang and co-workers developed a set of injectable hydrogels with variable HA:gelatin:PEG diacrylate ratios and used them to encapsulate C17.2 NSCs (mouse immortalized NSCs), human ReNcells (human immortalized NPCs), and human GRPs (glial-restricted progenitor cells) [40]. The gelation properties of the hydrogel were first characterized and optimized for intracerebral injection, resulting in a 25 min delayed injection after mixing the hydrogel components. To determine the optimal time for hydrogel delivery into the brain, the authors compared the resulting morphology of the hydrogel scaffold in vivo following an immediate or delayed injection. It was found that delayed injection produced optimal results, without leakage of gelatin into the brain tissue. The authors showed that an increase in gelatin content extended the gelation time, while HA promoted survival of all cell lines. In contrast,

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Fig. 14 Overall design of the study. Bone marrow-derived MSCs were extracted from the femora and tibiae of GFP transgenic Sprague-Dawley rats and transduced to overexpress human GDNF using a murine leukemia virus (in the photomicrograph, GDNF and nuclei are stained in red (immunofluorescence) and blue (DAPI), respectively). These were suspended in a type 1 collagen hydrogel prepared from bovine Achilles tendon, which was kept on ice to prevent gelation. The cellseeded collagen hydrogel was then subjected to a number of in vitro validation studies (i.e., impact of the hydrogel on astrocyte viability, MSC viability, and GDNF release) which were followed by in vivo studies in the adult rat brain to determine the host’s response to the hydrogel and the impact of the hydrogel on the survival of, GDNF release from, and the host response to the GDNF-MSCs. In the in vivo studies, the striatum was infused bilaterally at coordinates AP ¼ 0.0, ML  3.7 (from bregma) and DV 5.0 below dura. Adapted with permission from reference [39]. Copyright 2013 Elsevier

gelatin promoted survival and proliferation only in ReNcells and C17.2 cells. The hydrogels suppressed the innate immune response and improved viability of ReNcells injected into the striatum of immunodeficient mice. Interestingly, it was also found that hydrogel implantation can evoke a hitherto unreported immune response in the brain of immunocompetent animals. Since its innate immune system is still intact, activation of microglia and infiltrating leukocytes into the needle track may still be found in the control animals. In contrast, only a mild response occurred in the hydrogel scaffold groups. These findings suggest that the hydrogel suppresses the innate immune response induced by implanted human cells. Nakaji-Hirabayashi and co-workers also studied a collagen hydrogel with or without laminin-derived peptides with rats in vivo [41]. Poor viability of cells

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transplanted into the brain has been a critical problem associated with stem cellbased therapy for Parkinson’s disease. To overcome this problem, a collagen hydrogel incorporating an integrin-binding protein complex was prepared and used as a carrier for neural stem cells. The protein complex consisted of two polypeptides containing the G3 domain of a laminin α1 chain and the C-terminal oligopeptide of a laminin γ1 chain. These polypeptides were fused with α-helical segments, which spontaneously formed a coiled-coil heterodimer and with the collagen-binding peptide that facilitated the binding of the heterodimer to collagen networks. Through in vivo studies, the authors demonstrated that infiltration of microglial cells was physically blocked by the collagen hydrogel and the apoptotic cell death could be minimized by ligating integrins with the collagen-binding LG3 (CLG3)/histidine-tagged LP (HLP) complex incorporated in the collagen hydrogel. Accordingly, cell viability was significantly improved at the early stage after transplantation into the striatum (Fig. 15). This effect is caused by two antiapoptotic effects: integrin ligation and the suppression of microglial infiltration. It is considered that the inflammatory response in the brain is caused by microglia activated by foreign substances such as graft cells. The activated microglia infiltrates

Fig. 15 Number of living cells determined 3 h, 3 days, and 7 days after transplantation into the rat brain. Cells were suspended in collagen hydrogels (closed bar) with or (open bar) without the CLG3/HLP complex, or (hatched bar) in medium. The number of EGFP-expressing cells relative to that of transplanted cells (1.5  106 cells) was determined, and the data are expressed as the mean  standard deviation (day 0, n ¼ 3; day 3, n ¼ 10; day 7, n ¼ 9). The symbols  and { indicate statistical significance (Tukey’s HSD test,  p < 0.05 and { p < 0.01). Adapted with permission from reference [41]. Copyright 2013 The American Chemical Society

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into the graft regions to release various cytotoxic cytokines. It was previously reported that the use of materials such as hydrogels would be beneficial to the protection of transplanted cells from inflammatory responses in the brain. NakajiHirabayashi’s results demonstrated that the infiltration of microglia is inhibited at the early stage after transplantation, most likely due to the effect that the collagen hydrogel acts as a physical barrier against microglial infiltration. Although a collagen hydrogel itself may also initiate inflammation, it was speculated that this is overwhelmed by the effect of isolating graft cells from microglia.

5 Concluding Remarks In conclusion, taking advantage of their tunable physical, chemical, and biological properties, 3D biohydrogels made of collagen type I have shown great potential for brain injury therapy. Among other features, these hydrogels are biocompatible, noncytotoxic, and self-healable after injection, which is a major requirement for in vivo applications in neuroregeneration. Although collagen does not naturally occur in the brain, it has been demonstrated that collagen type I, which resides in the basal lamina of the subventricular zone in adults, supports neural cell attachment, axonal growth, and cell proliferation due to its intrinsic content of specific cellsignaling domains. The results derived from the studies summarized in this chapter illustrate the importance of several aspects such as (1) the necessary optimization of cell systems before attempting cell replacement in vivo, (2) the combination of the gel matrix with adhesive peptide sequences and proteins with appropriate cell attachment sites, (3) the use of SCs and their alignment within the guidance channels for the regeneration process, and (4) the appropriate stiffness, growth factor sequestering ability, and injectability feature of the biohydrogel system. Despite the promising results obtained during the last decade in both in vitro and in vivo models, more detailed mechanistic studies are still necessary to understand the function of collagens in the brain, which should be correlated to the effects obtained during the use of their hydrogels in brain therapy. For instance, additional studies are still necessary to visualize the interactions of collagens with other ECM molecules, cell surface receptors, and downstream signaling pathways, which is critical to understand the underlying connection between the presence of collagen and certain pathogenesis in the nervous system. Furthermore, future studies involving specific functionalization of the collagen hydrogel would be important to release on demand biological cues, glial scar modulating enzymes, or pro-survival factors for in vivo therapy. In addition, advances in microfabrication techniques will likely expand the use of biohydrogel scaffolds in neuroregeneration. In any event, any new developed collagen-based hydrogel should be thoroughly tested for immuno-/ allergenicity prior to their use in clinical applications.

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Acknowledgments D.D.D. thanks the University of Regensburg (Germany) and the University of La Laguna (Spain) for financial support and the Ministry of Science, Innovation and Universities (Spain) for the Senior “Beatriz Galindo” Distinguished Researcher Award.

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Index

A Amphiphilic copolymers, 167–174

B Brain therapy, 375

C Cellulose, 35, 322–331, 333–349 Central nervous system, 254, 357 Click reactions, 112 Collagen, 4, 70, 357–375 Continuum mechanics, 128–136, 141 Cross-linked networks, 88, 95, 273, 331, 346

D Dynamic bonds, 2, 18, 127–163, 235, 236, 238, 297, 303, 305, 312, 313 Dynamic chemistry, 245, 289, 330–348 Dynamic covalent chemistry, 25, 285 Dynamic networks, 63–122

H Hydroge, 1–19, 21–42, 44, 51, 53, 71, 112, 114, 160, 180, 182, 187, 189, 193, 199, 215, 216, 220, 224, 228, 230, 244, 247, 251, 267, 269, 274, 287, 289, 296–298, 312–315, 321, 324, 326–328, 330, 331, 334, 336, 337, 339, 347–349, 357–359, 364, 368, 372–375 Hydrogel, 1, 4, 25, 29, 33, 35, 39, 45, 49, 53, 114, 130, 172, 174, 177, 180, 182, 186,

190, 204, 216, 221, 223, 226, 251–253, 258, 263, 265–271, 273–289, 295–306, 308, 310–312, 315, 321, 324, 327–329, 331–334, 336–349, 357, 366–368, 371, 372, 375 Hydrogen-bonding interactions, 25, 244, 339–340 Hydrophobic association, 29, 36, 38, 39, 47, 54, 55, 166, 212–216, 219, 221, 223, 226, 235, 236, 338

I Ionic bond, 25, 35, 129, 130, 166, 297–299, 301, 303–308, 310, 313, 314

M Mechanical properties, 3, 4, 18, 24–26, 44, 46, 49, 51, 52, 55, 64, 65, 70–72, 92, 112, 173, 188, 204, 213, 215–218, 222–224, 237, 244, 249, 254, 257, 259, 268, 277–279, 282, 283, 289, 303, 310, 328, 333, 335, 339–341, 344–346, 348, 370 Mechanical reinforcement, 2, 67, 68, 116–119, 345, 348 Micelles, 36–40, 43, 45, 46, 54, 55, 212–215, 217–223, 225, 227, 229, 235–238, 257, 279, 337 Microphase separation, 168, 172, 173, 181, 190, 195, 201, 219, 222 Modelling, 65, 68, 76–86, 122 Molecular kinetics, 129, 162

379

380 N Nanocomposites, 67–70, 116, 118, 119, 122, 268, 337, 339, 340, 347, 348

P Physical hydrogels, 25, 27–30, 35, 39, 47, 51, 54, 173, 176, 204, 340 Pluronic F127, 214, 263 Polyampholyte hydrogel, 25, 184, 186, 187, 297, 298 Polymeer network, 23, 68, 70, 73, 77, 79, 80, 89, 101, 127163, 222, 228, 296, 301, 307, 308, 328, 335, 345 Polymer materials, 64, 65, 67, 72, 122, 216

R Regeneration, 296, 325, 331, 357–360, 375 Responsiveness, 230, 283, 333, 359

S Self-healing, 23–27, 31, 32, 35, 36, 44, 46, 47, 49, 70, 72, 114, 120, 129, 173, 176, 177, 236, 250, 252, 257–290, 295–315, 331–336, 339, 341, 342, 344, 355–375 Self-healing hydrogels, 26, 36, 44, 55, 129, 243–290, 295–315, 333 Semicrystalline hydrogels, 36, 47, 49, 50, 52, 54, 55

Index Shape morphing, 223, 233, 234, 237 Simulation, 65, 67–69, 73, 74, 76, 79, 81–86, 88, 93–95, 100, 102, 103, 105–109, 111–113, 117–120, 129 Soft actuator, 223, 229, 238 Stimuli-responsive, 71, 129, 200, 245, 246, 254, 257, 264, 265, 271, 333, 334, 341, 347 Supramolecular hydrogels, 166, 171, 173, 174, 176, 179–181, 183, 184, 187, 188, 193, 203, 341, 342

T Tough hydrogel, 33, 180, 187, 223, 230, 237, 258, 296–299, 303, 314 Toughness, 2, 23, 36, 49, 67, 70, 71, 111, 120, 129, 166, 169, 170, 179, 180, 182, 189, 193, 216–218, 224, 225, 236, 258, 263, 296, 297, 301, 310, 313, 314, 344, 346 Transient crosslink, 3, 7–9, 11–13, 16, 18

V Viscoelastic, 6, 14, 26, 37, 54, 55, 66, 71, 92, 114, 129, 143, 160, 175, 176, 178, 188, 266, 275, 298, 305, 307, 308, 310, 314, 341, 369 Viscoelasticity, 3, 6, 122, 129, 134, 143, 160, 163, 314