Plasmonics for Hydrogen Energy (SpringerBriefs in Energy) 3030882748, 9783030882747

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SPRINGER BRIEFS IN ENERGY

Katsuaki Tanabe

Plasmonics for Hydrogen Energy 123

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Katsuaki Tanabe

Plasmonics for Hydrogen Energy

Katsuaki Tanabe Department of Chemical Engineering Kyoto University Kyoto, Japan

ISSN 2191-5520 ISSN 2191-5539 (electronic) SpringerBriefs in Energy ISBN 978-3-030-88274-7 ISBN 978-3-030-88275-4 (eBook) https://doi.org/10.1007/978-3-030-88275-4 © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are solely and exclusively licensed 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

Contents

1 Hydrogen Energy Technology and Plasmonics . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2

2 Field Enhancement Around Spherical Metal Nanoparticles and Nanoshells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 9

3 Field Enhancement on Planar Metal Surface . . . . . . . . . . . . . . . . . . . . . . . 11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4 Field Enhancement at Sharp Metal Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5 Field Enhancement in Metal Nanogaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Hydrogen Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Hydrogen Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Hydrogen Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Hydrogen Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Nuclear Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33 33 35 36 37 37 40

v

Chapter 1

Hydrogen Energy Technology and Plasmonics

The hydrogen energy is currently a representative clean energy without polluting or greenhouse emission in its use, in contrast to the conventional fossil fuels. For the abundance of elements in Earth’s crust, in the unit of amount of substance, hydrogen takes third place to oxygen and silicon. Therefore, there is no concern about depletion as an energy resource for hydrogen. However, most of the hydrogen atoms on the earth exist in the form of seawater, and therefore industrial production of hydrogen molecules, or other usable hydrogen-containing molecules, is required for the use of hydrogen energy. It is also important to produce hydrogen in clean, renewable manners, to contribute to the solution of the environmental problems, such as atmospheric pollution and global warming, and of the depletion of energy resources. For the widespread use of hydrogen energy, technical developments particularly for hydrogen production [1–5] and storage [6–12] are highly sought after. Free electrons in metals, particularly around metal surfaces or interfaces with dielectric materials, exhibit a strong interaction with electromagnetic fields or light in the form of collective oscillation, named surface plasmons [13–21]. The electromagnetic field intensity around subwavelength-size metal particles can be highly localized due to the coupling between the incident photons and collective oscillation of free electrons at the metal surface, resulting in focusing of electromagnetic energy density, or namely local field enhancement. Surface-plasmon-induced electromagnetic field enhancement on metal surfaces [22–26] has been utilized for various applications, such as chemical and biomedical sensing [27–31], photodetectors [32–34], light-emitting diodes [35–38], nanolasers [39–43], solar cells [44–52], and optical cloaking [53–57]. We review the recent advancement in the field of hydrogen energy technologies that utilize plasmonics for their performance enhancement.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 K. Tanabe, Plasmonics for Hydrogen Energy, SpringerBriefs in Energy, https://doi.org/10.1007/978-3-030-88275-4_1

1

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1 Hydrogen Energy Technology and Plasmonics

References 1. Barreto L, Makihira A, Riahi K (2003) The hydrogen economy in the 21st century: a sustainable development scenario. Int J Hydrogen Energy 28:267–284 2. Turner JA (2004) Sustainable hydrogen production. Science 305:972–974 3. Penner SS (2006) Steps toward the hydrogen economy. Energy 31:33–43 4. Mueller-Langer F, Tzimas E, Kaltschmitt M, Peteves S (2007) Techno-economic assessment of hydrogen production processes for the hydrogen economy for the short and medium term. Int J Hydrogen Energy 32:3797–3810 5. Rajeshwar K, McConnell R, Licht S (eds) (2008) Solar hydrogen generation: toward a renewable energy Future. Springer, New York, USA 6. Stroud RM, Viano AM, Gibbons PC, Kelton KF, Misture ST (1996) Stable Ti-based quasicrystal offers prospect for improved hydrogen storage. Appl Phys Lett 69:2998–3000 7. Schlapbach L, Zuttel A (2001) Hydrogen-storage materials for mobile applications. Nature 414:353–358 8. Adams BD, Chen A (2011) The role of palladium in a hydrogen economy. Mater Today 14:282–289 9. Li GQ, Kobayashi H, Taylor JM, Ikeda R, Kubota Y, Kato K, Takata M, Yamamoto T, Toh S, Matsumura S, Kitagawa H (2014) Hydrogen storage in Pd nanocrystals covered with a metal-organic framework. Nat Mater 13:802–806 10. Ley MB, Jepsen LH, Lee YS, Cho YW, von Colbe JMB, Dornheim M, Rokni M, Jensen JO, Sloth M, Filinchuk Y, Jorgensen JE, Besenbacher F, Jensen TR (2014) Complex hydrides for hydrogen storage—new perspectives. Mater Today 17:122–128 11. Mohtadi R, Orimo S (2017) The renaissance of hydrides as energy materials. Nat Rev Mater 2:16091 12. Yamagishi R, Kojima T, Kameoka S, Okuyama D, Sato TJ, Nishimura C, Tsai AP (2017) Creating the hydrogen absorption capability of CeNi5 through the addition of Al. Int J Hydrogen Energy 42:21832–21840 13. Ritchie RH (1957) Plasma losses by fast electrons in thin films. Phys Rev 106:874–881 14. Raether H (1988) Surface plasmons on smooth and rough surfaces and on gratings. Springer, Heidelberg, Germany 15. Ebbesen TW, Lezec HJ, Ghaemi HF, Thio T, Wolff PA (1998) Extraordinary optical transmission through sub-wavelength hole arrays. Nature 391:667–669 16. Maier SA, Brongersma ML, Kik PG, Meltzer S, Requicha AAG, Atwater HA (2001) Plasmonics—A route to nanoscale optical devices. Adv Mater 13:1501–1505 17. Barnes WL, Dereux A, Ebbesen TW (2003) Surface plasmon subwavelength optics. Nature 424:824–830 18. Brongersma ML, Kik PG (eds) (2007) Surface plasmon nanophotonics. Springer, Dordrecht, The Netherlands 19. Maier SA (2007) Plasmonics: fundamentals and applications. Springer, New York, USA 20. Shahbazyan TV, Stockman MI (eds) (2013) Plasmonics: theory and applications. Springer, Dordrecht, The Netherlands 21. Bozhevolnyi SI, Martin-Moreno L, Garcia-Vidal F (eds) (2017) Quantum plasmonics. Springer, Cham, Switzerland 22. Kim S, Jin JH, Kim YJ, Park IY, Kim Y, Kim SW (2008) High-harmonic generation by resonant plasmon field enhancement. Nature 453:757–760 23. Tanabe K (2008) Field enhancement around metal nanoparticles and nanoshells: a systematic investigation. J Phys Chem C 112:15721–15728 24. Schuller JA, Barnard ES, Cai WS, Jun YC, White JS, Brongersma ML (2010) Plasmonics for extreme light concentration and manipulation. Nat Mater 9:193–204 25. Jeong S, Kim MW, Jo YR, Kim NY, Kang D, Lee SY, Yim SY, Kim BJ, Kim JH (2019) Hollow porous gold nanoshells with controlled nanojunctions for highly tunable plasmon resonances and intense field enhancements for surface-enhanced Raman scattering. ACS Appl Mater Interfaces 11:44458–44465

References

3

26. da Jornada FH, Xian LD, Rubio A, Louie SG (2020) Universal slow plasmons and giant field enhancement in atomically thin quasi-two-dimensional metals. Nat Commun 11:1013 27. Weber WH, McCarthy SL (1975) Surface-plasmon resonance as a sensitive optical probe of metal-film properties. Phys Rev B 12:5643–5650 28. Nie SM, Emery SR (1997) Probing single molecules and single nanoparticles by surfaceenhanced Raman scattering. Science 275:1102–1106 29. Haes AJ, Van Duyne RP (2002) A nanoscale optical blosensor: Sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles. J Am Chem Soc 124:10596–10604 30. Homola J (2008) Surface plasmon resonance sensors for detection of chemical and biological species. Chem Rev 108:462–493 31. Oliveira LC, Lima AMN, Thirstrup C, Neff HF (2019) Surface plasmon resonance sensors: a materials guide to design, characterization, optimization, and usage, 2nd edn. Springer, Cham, Switzerland 32. Shackleford JA, Grote R, Currie M, Spanier JE, Nabet B (2009) Integrated plasmonic lens photodetector. Appl Phys Lett 94:083501 33. Berini P (2014) Surface plasmon photodetectors and their applications. Laser Photon Rev 8:197–220 34. Echtermeyer TJ, Milana S, Sassi U, Eiden A, Wu M, Lidorikis E, Ferrari AC (2016) Surface plasmon polariton graphene photodetectors. Nano Lett 16:8–20 35. Vuckovic J, Loncar M, Scherer A (2000) Surface plasmon enhanced light-emitting diode. IEEE J Quantum Electron 36:1131–1144 36. Hobson PA, Wedge S, Wasey JAE, Sage I, Barnes WL (2002) Surface plasmon mediated emission from organic light-emitting diodes. Adv Mater 14:1393–1396 37. Okamoto K, Niki I, Shvartser A, Narukawa Y, Mukai T, Scherer A (2004) Surface-plasmonenhanced light emitters based on InGaN quantum wells. Nat Mater 3:601–605 38. Pillai S, Catchpole KR, Trupke T, Zhang G, Zhao J, Green MA (2006) Enhanced emission from Si-based light-emitting diodes using surface plasmons. Appl Phys Lett 88:161102 39. Bergman DJ, Stockman MI (2003) Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems. Phys Rev Lett 90:027402 40. Zheludev NI, Prosvirnin SL, Papasimakis N, Fedotov VA (2008) Lasing spaser. Nat Photon 2:351–354 41. Noginov MA, Zhu G, Belgrave AM, Bakker R, Shalaev VM, Narimanov EE, Stout S, Herz E, Suteewong T, Wiesner U (2009) Demonstration of a spaser-based nanolaser. Nature 460:1110– 1112 42. Oulton RF, Sorger VJ, Zentgraf T, Ma RM, Gladden C, Dai L, Bartal G, Zhang X (2009) Plasmon lasers at deep subwavelength scale. Nature 461:629–632 43. Berini P, De Leon I (2012) Surface plasmon–polariton amplifiers and lasers. Nat Photon 6:16–24 44. Hayashi S, Kozaru K, Yamamoto K (1991) Enhancement of photoelectric conversion efficiency by surface-plasmon excitation: A test with an organic solar-cell. Solid State Commun 79:763– 767 45. Ihara M, Tanaka K, Sakaki K, Honma I, Yamada K (1997) Enhancement of the absorption coefficient of cis-(NCS)2 Bis(2,2’-bipyridyl-4,4’-dicarboxylate)ruthenium(II) dye in dye-sensitized solar cells by a silver island film. J Phys Chem B 101:5153–5157 46. Rand BP, Peumans P, Forrest SR (2004) Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters. J Appl Phys 96:7519–7526 47. Schaadt DM, Feng B, Yu ET (2005) Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles. Appl Phys Lett 86:063106 48. Pillai S, Catchpole KR, Trupke T, Green MA (2007) Surface plasmon enhanced silicon solar cells. J Appl Phys 101:093105 49. Nakayama K, Tanabe K, Atwater HA (2008) Plasmonic nanoparticle enhanced light absorption in GaAs solar cells. Appl Phys Lett93:121904

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50. Atwater HA, Polman A (2010) Plasmonics for improved photovoltaic devices. Nat Mater 9:205–213 51. Tanabe K (2016) A simple optical model well explains plasmonic-nanoparticle-enhanced spectral photocurrent in optically thin solar cells. Nanoscale Res Lett 11:236 52. Shen T, Tan Q, Dai Z, Padture NP, Pacifici D (2020) Arrays of plasmonic nanostructures for absorption enhancement in perovskite thin films. Nanomaterials 10:1342 53. Pendry JB (2000) Negative refraction makes a perfect lens. Phys Rev Lett 85:3966 54. Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, Smith DR (2006) Metamaterial electromagnetic cloak at microwave frequencies. Science 314:977–980 55. Alu A, Engheta N (2008) Multifrequency optical invisibility cloak with layered plasmonic shells. Phys Rev Lett 100:113901 56. Xu Y, Fu Y, Chen H (2016) Planar gradient metamaterials. Nat Rev Mater 1:16067 57. Balci O, Kakenov N, Karademir E, Balci S, Cakmakyapan S, Polat EO, Caglayan H, Ozbay E, Kocabas C (2018) Electrically switchable metadevices via graphene. Sci Adv 4:eaao1749

Chapter 2

Field Enhancement Around Spherical Metal Nanoparticles and Nanoshells

To quantitatively discuss the plasmonic field enhancement effect, the field enhancement factor, defined as the ratio of the electromagnetic field intensity around the metal object to that in the absence of the object, or the original incident field, is calculated as follows. The field enhancement factor represents how much energy can be concentrated from the incident optical or electric power. The intensities of electromagnetic fields around subwavelength-size metal nanoparticles and nanoshells can be described by the formalism below in the quasistatic limit [1, 2]. Consider a homogeneous, isotropic sphere placed in a medium in which there exists a uniform static electric field E0 = E 0 eˆz , as schematically depicted in Fig. 2.1. If the permittivities or dielectric constants of the sphere and the medium are different, a charge will be induced on the surface of the sphere. The initially uniform field will be therefore distorted by the introduction of the sphere. The electric fields inside and outside the sphere, E1 and E2 , respectively, are derivable from scalar potentials 1 (r, θ ) and 2 (r, θ ): E1 = −∇1 , E2 = −∇2 ,

(2.1)

∇ 2 1 = 0, (r < a) ∇ 2 2 = 0, (r > a),

(2.2)

where

where a is the radius of the sphere. Because of the symmetry of the system, the potentials are independent of the azimuthal angle φ . At the boundary between the sphere and the medium, the potentials must satisfy: 1 = 2 , ε1

∂1 ∂2 = εm (r = a), ∂r ∂r

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 K. Tanabe, Plasmonics for Hydrogen Energy, SpringerBriefs in Energy, https://doi.org/10.1007/978-3-030-88275-4_2

(2.3)

5

6

2 Field Enhancement Around Spherical Metal …

Fig. 2.1 Schematic configuration of a metal (upper) nanoparticle or (lower) nanoshell in an electric field, considered for the calculations of field enhancement factors

r

E0

 a

E0

m 2 1

r



observing point

observing point

a1 a2 where ε1 and εm are the frequency-dependent complex permittivities or dielectric functions of the sphere and the surrounding medium, respectively. It is additionally required that lim 2 = −E 0 r cos θ = −E 0 z,

r →∞

(2.4)

that is, the electric field far from the sphere is the unperturbed original field. It can be derived that the potentials 1 = −

3εm E 0 r cos θ, ε1 + 2εm

2 = −E 0 r cos θ + a 3 E 0

ε1 − εm cos θ , ε1 + 2εm r 2

(2.5) (2.6)

satisfy Eqs. 2.2–2.4. These solutions for the potentials could be also derived rigorously by using Legendre polynomials. From Eqs. 2.1 and 2.6, the electric field outside the sphere can be expressed as: E2 = E 0

     a 3 ε1 − εm a 3 ε1 − εm 1+2 3 eˆr cos θ + −1 + 3 eˆθ sin θ , (2.7) r ε1 + 2εm r ε1 + 2εm

where eˆr and eˆθ are the unit vectors to r and θ directions, respectively, and thus:

2 Field Enhancement Around Spherical Metal …

 2  2      E 2  =  E0 

7

 2 2  3     cos2 θ + −1 + a ε1 − εm  sin2 θ .   r 3 ε1 + 2εm  m (2.8)

 3  1 + 2 a ε1 − εm  r 3 ε + 2ε 1

The electric field intensity will be therefore maximized at the direction θ = 0, π for most cases, and the field enhancement factor is defined as:  2   2   E2   a 3 ε1 − εm   . η ≡  2 = 1 + 2 3   r ε1 + 2εm   E0 

(2.9)

Note that η is defined as the ratio of field intensities and not field magnitudes. Equation 9 can be also written as:   η = 1 +

α 2  , 2πr 3

(2.10)

ε1 − εm . ε1 + 2εm

(2.11)

using the polarizability of the sphere: α = 4πa 3

It has also been known that nanoshells, concentric nanoparticles consisting of a dielectric core and a metallic shell, exhibit attractive features such as extremely large field enhancement and a wide tunability of the resonant frequency. Such distinctive characteristics can be understood to be a result of the strong interaction between the plasmons for a metal sphere and a metal-dielectric hollow cavity, whose hybridization forms a metal shell [3–7]. By adjusting the relative core and shell dimensions, we can widely tune the resonance frequency, or the peak wavelength for field enhancement, of a nanoshell, while the optical resonance is essentially a fixed frequency resonance, almost independent of their particle sizes for metal nanospheres. Also, nanoshells can exhibit significantly larger field enhancement than that for nanoparticles according to conditions. For the case of a concentric spherical core–shell structure consisting of an inner spherical core with a radius a1 and a dielectric function ε1 , and an outer spherical shell with a radius a2 and a dielectric function ε2 , the polarizability is formulated as: α = 4πa23

(ε2 − εm )(ε1 + 2ε2 ) + f 3 (ε1 − ε2 )(εm + 2ε2 ) , (ε2 + 2εm )(ε1 + 2ε2 ) + f 3 (2ε2 − 2εm )(ε1 − ε2 )

(2.12)

where f is the diameter ratio of the inner material to the outer material, f ≡ Therefore:

a1 . a2

8

2 Field Enhancement Around Spherical Metal …

Field enhancement factor

(-)

20 Ag Al Au Co Cr Cu Ni Pd Pt Sn Ti

15

10 1200

Al

1000 800

5

600 400 200

0 200

0 0

400

600

Ag 200

400

800

600

1000

Wavelength in vacuo (nm)

Fig. 2.2 Calculated field enhancement factors, η, of spherical metal nanoparticles of eleven metals in air or H2 . Reprinted with permission from Ref. [2]. Copyright 2008 American Chemical Society

2   a23 (ε2 − εm )(ε1 + 2ε2 ) + f 3 (ε1 − ε2 )(εm + 2ε2 )   η = 1 + 2 3 . r (ε2 + 2εm )(ε1 + 2ε2 ) + f 3 (2ε2 − 2εm )(ε1 − ε2 ) 

(2.13)

Note that the dielectric constants ε1 , ε2 , and εm are generally complex functions of wavelength and are expressed as ε j = εj + iεj ( j = 1, 2, m), where both of εj , and εj are real. As observed in Eqs. 2.9 and 2.13, the field enhancement factor for a subwavelength-size spherical nanoparticles or nanoshells depends simply on the relative distance from the center of the particle or the shell, r/a, and on the diameter ratio of the inner to the outer material, f , for a nanoshell, but not on the absolute size of the particle or the shell. As understood by the form of Eqs. 2.9 and 2.13, the largest field enhancement is obtained immediately adjacent to the metal particle surface, r = a, and therefore we calculated the field enhancement factors η for the point r = a, for both metal nanoparticles and nanoshells. Figure 2.2 presents the calculated η of nanoparticles of eleven metals surrounded by air or H2 [2]. The observed peaks are associated with the resonance or surface mode, characterized by internal electric fields with no radial nodes. Among these eleven metal elements, particularly the noble metals, Ag, Al, Au and Cu, show distinctively higher peaks of the field enhancement factor than the other metals due to their high electrical conductivities. Figure 2.3 presents the calculated dependence of η on the f factor (= a1 /a2 ) for Ag nanoshells with SiO2 core in air or H2 [2]. The resonant or the peak wavelength is found to be quite sensitive to the f factor and we can widely tune the peak wavelength through the ultraviolet region to the infrared by adjusting the f factor. The peak η becomes larger as the factor f becomes larger until the Ag shell becomes too thin to support strong plasmons. This result can be understood by considering the

2 Field Enhancement Around Spherical Metal …

9

Fig. 2.3 Dependence of the field enhancement factor, η, on the f factor (= a1 /a2 ) for Ag nanoshells with SiO2 core in the air. Reprinted with permission from Ref. [2]. Copyright 2008 American Chemical Society

strong interaction between the sphere and the cavity plasmons for thin shells [4]. The maximum peak η is about 730 with f ~ 0.9 and peak η larger than 500 can be obtained in a wide range of wavelengths through 600 to 1100 nm. Also, the full width of the half maximum (FWHM) is as large as 800 nm (1.5 eV) ranging from 500 nm (2.5 eV) to 1300 nm (0.95 eV). However, uniform nanoshells with a single f can exhibit a FWHM less than 100 nm (< 0.3 eV). Therefore one can use a group of nanoshells with various f ’s for the applications requiring wide ranges of wavelength coverage for field enhancement. Such a wide-range tunability of the peak wavelength can be utilized for various kinds of hydrogen energy applications. For example, artificial photosynthetic systems would harvest more light with Ag/SiO2 nanoshells with f ~ 0.9 for Photosystems I and II for their narrow absorption bands around at 700 nm.

References 1. Bohren CF, Huffman DR (1983) Absorption and scattering of light by small particles. Wiley, Weinheim, Germany 2. Tanabe K (2008) Field enhancement around metal nanoparticles and nanoshells: a systematic investigation. J Phys Chem C 112:15721–15728 3. Oldenburg SJ, Averitt RD, Westcott SL, Halas NJ (1998) Nanoengineering of optical resonances. Chem Phys Lett 288:243–247 4. Prodan E, Radloff C, Halas NJ, Nordlander P (2003) A hybridization model for the plasmon response of complex nanostructures. Science 302:419–422

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5. Halas NJ (2005) Playing with plasmons: tuning the optical resonant properties of metallic nanoshells. MRS Bull 30:362–367 6. Hooshmand N, Jain PK, El-Sayed MA (2011) Plasmonic spheroidal metal nanoshells showing larger tunability and stronger near fields than their spherical counterparts: an effect of enhanced plasmon coupling. J Phys Chem Lett 2:374–378 7. Jeong S, Kim MW, Jo YR, Kim NY, Kang D, Lee SY, Yim SY, Kim BJ, Kim JH (2019) Hollow porous gold nanoshells with controlled nanojunctions for highly tunable plasmon resonances and intense field enhancements for surface-enhanced Raman scattering. ACS Appl Mater Interfaces 11:44458–44465

Chapter 3

Field Enhancement on Planar Metal Surface

Next, we present the calculation of the field enhancement factors on planar metal surfaces [1]. We adopted the scheme to derive the maximum field enhancement described in Ref. [2] by Weber and Ford. Having removed the noble-metal approximation in Ref. [2], we fully calculated the field enhancement factors for noble metals and hydrogen-absorbing transition metals. Figure 3.1 shows a schematic crosssectional view of the system under consideration. Let ε1 and ε2 be the frequencydependent complex permittivities or dielectric functions of the surrounding medium and the metal, respectively, and let θ be the incident angle. We assumed an incidence of a p-polarized plane wave as the original electromagnetic field and its coupling into a surface-plasmon mode to determine the maximum field enhancement factors. Following the procedure described in Ref. [2], the energy flux towards the x direction per unit length in the y direction (i.e., the Poynting vector) can be formulated as

PS P

c = 8π



∞ −∞



Re E S P × HS∗P



      + 2   k S P ε1 q1 + ε2 q2 ωε1  E S P 0  · xdz ˆ = Re , 16π |q1 |2 + |k S P |2 ε2 q1 q2 (3.1)

where c is the speed of light, E S P and HS P are the electric and magnetic fields of the surface-plasmon mode: HS P =Hy yˆ exp{i(k S P x − ωt) − q1 z}, z > 0 =Hy yˆ exp{i(k S P x − ωt) + q2 z}, z < 0,   c Hy iq1 xˆ − k S P zˆ exp{i(k S P x − ωt) − q1 z}, z > 0 E S P = ε1 ω   c = Hy −iq2 xˆ − k S P zˆ exp{i(k S P x − ωt) + q2 z}, z < 0, ε2 ω © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 K. Tanabe, Plasmonics for Hydrogen Energy, SpringerBriefs in Energy, https://doi.org/10.1007/978-3-030-88275-4_3

(3.2)

(3.3) 11

12

3 Field Enhancement on Planar Metal Surface

Fig. 3.1 Schematic spatial cross-sectional view of the material system considered for the calculations of field enhancement factors. Reprinted with permission from Ref. [1]. Copyright 2019 American Institute of Physics

Electromagnetic energy

Dielectric function 1

z

air/H2/vacuum or H2O Surface plasmon propagation

2

Metal x   H y is the amplitude of the magnetic field of the mode. E S P 0+ is the electric field at the metal surface. ω is the frequency of the field. q1 and q2 are the complex wave vectors in the z direction in the surrounding medium and the metal, respectively. k SP is the complex wave vector of the surface-plasmon mode in the x direction. The wave vectors are calculated by 1/ 2

−ε2j ω qj = ( j = 1, 2), c ε1 + ε2 kS P

ε1 ε2 1/ 2 ω = . c ε1 + ε2

(3.4)

(3.5)

The real and imaginary parts of complex quantities are indicated by primes and double primes, respectively. The energy dissipation flux of the surface plasmon mode is then       + 2   ESP 0   k S P ε1 q1 + ε2 q2 d PS P ωε 1   = α PS P = 2k S P PS P = k − Re , dx 8π S P |q1 |2 + |k S P |2 ε2 q1 q2 (3.6) where α is the absorption constant. On the other hand, the energy flux provided into the metal surface by the coupling of the external field into the surface-plasmon mode can be written as  2 c 1/ 2   ε1 cos θ  E0  (1 − R), (3.7) 8π

3 Field Enhancement on Planar Metal Surface

13

where E0 is the electric field of the incident wave, or namely the external field. R is the reflectivity at the metal surface. In the steady state, those two energy fluxes are equal to each other based on the conservation of energy, and therefore      + 2 ES P 0 

    2 k S P ε1 q1 + ε2 q2 ωε1  c 1/ 2   Re cos θ = kS P ε  E 0  (1 − R). 8π ε2 q1 q2 8π 1 |q1 |2 + |k S P |2 (3.8) We then come to derive the field enhancement factor:      + 2   ES P 0  c |q1 |2 + |k S P |2 cos θ (1 − R)  .  η≡ =  2 k S P (ε1 q1 +ε2 q2 ) 1/ 2    ωε k Re    E0  1 SP ε2 q1 q2

(3.9)

Weber and Ford used an approximation, ε2 μ0 ) Cnm exp − n + 2 n≥|m| m=−∞

(5.15)

∞ ∞   n≥|m| m=−∞

2 = F

(5.13) Dnm exp

∞ ∞  

F≡



cosh μ − cos η.

(5.16)

φ ext is the potential for the external electric field, Y n m (cosη, φ) is the spherical harmonics, and An m , Bn m , C n m , and Dn m are constants to be determined by the boundary conditions. φ ext is expressed by:

26

5 Field Enhancement in Metal Nanogaps

ext = −E 0 (z cos θ0 + x sin θ0 cos φ0 + y sin θ0 sin φ0 ),

(5.17)

where E 0 is the amplitude of the external electric field, and θ 0 and φ 0 are the polar and azimuthal angles of the direction of the external electric field relative to the z- and x-axes, respectively, as indicated in Fig. 5.1. The spherical harmonics are expressed by [10]: 

2n + 1 (n − |m|)! |m| P (cos η)eimφ , 4π (n + |m|)! n

(5.18)

[ n−m 2 ] m  1 (−1) j (2n − 2 j)! 2 2 t n−2 j−m . = n 1−t 2 j!(n − j)!(n − 2 j − m)! j=0

(5.19)

Ynm (cos η, φ)

Pnm (t)

= (−1)

m+|m| 2

An m , Bn m , C n m , and Dn m can be determined, via Eqs. 5.9–5.12, through the following equations. For m = 0, A0n = −Bn0 ,

(5.20)

Cn0 = −Dn0 ,

(5.21)

 Cn0 = {exp[(2n + 1)μ0 ] − 1}A0n − F0 cos θ0 4π (2n + 1),

(5.22)

Un0 A0n + Vn0 A0n−1 + Wn0 A0n+1 = Sn0 ,

(5.23)

Un0 = χ sinh μ0 {1 − exp[−(2n + 1)μ0 ]} + (2n + 1) cosh μ0 {1 + χ exp[−(2n + 1)μ0 ]},

(5.24)



2n − 1 (5.25) exp(−μ0 ){1 + χ exp[−(2n − 1)μ0 ]}, 2n + 1  2n + 3 0 Wn = −(n + 1) (5.26) exp(μ0 ){1 + χ exp[−(2n + 3)μ0 ]}, 2n + 1  4π 0 {cosh μ0 − (2n + 1) sinh μ0 }, Sn = 2F0 cos θ0 χ exp[−(2n + 1)μ0 ] 2n + 1 (5.27) √ F0 ≡ a E 0 2, (5.28) Vn0 = −n

χ≡ For m = 1 and –1,

[ε0 − ε(λ)] . [ε0 + ε(λ)]

(5.29)

5 Field Enhancement in Metal Nanogaps

27

±1 A±1 n = Bn ,

(5.30)

1 A−1 n = − exp(2iφ0 )An ,

(5.31)

Cn±1 = Dn±1 ,

(5.32)

Cn−1 = − exp(2iφ0 )Cn1 ,

(5.33) 

Cn1 = {exp[(2n + 1)μ0 ] + 1}A1n + F0 sin θ0 exp(−iφ0 )

4π n(n + 1) , 2n + 1

Un1 A1n + Vn1 A1n−1 + Wn1 A1n+1 = Sn1 , Un1 = χ sinh μ0 {1 + exp[−(2n + 1)μ0 ]} + (2n + 1) cosh μ0 {1 − χ exp[−(2n + 1)μ0 ]},

(5.34) (5.35) (5.36)



(n + 1)(n − 1)(2n − 1) exp(−μ0 ){1 − χ exp[−(2n − 1)μ0 ]}, (5.37) 2n + 1  n(n + 2)(2n + 3) 1 Wn = − (5.38) exp(μ0 ){1 − χ exp[−(2n + 3)μ0 ]}, 2n + 1  4π n(n + 1) 1 Sn = 2F0 sin θ0 sinh μ0 χ exp(−iφ0 ) exp[−(2n + 1)μ0 ] . (5.39) 2n + 1

Vn1

=−

For other integer values of m, An m , Bn m , C n m , and Dn m are zero. An m , Bn m , C n m , and Dn m also become zero for m = 1 and –1 when the external electric field is parallel to the z-axis (θ 0 = 0), and for m = 0 when the external electric field is perpendicular to the z-axis (θ 0 = π/2). For n = 0 and nmax , the maximum value of n, Eq. 5.23 becomes: U00 A00 + W00 A01 = S00 ,

(5.40)

Un0max A0n max + Vn0max A0n max −1 = Sn0max .

(5.41)

For n = 1 and nmax , Eq. 5.35 becomes: U11 A11 + W11 A12 = S11 ,

(5.42)

Un1max A1n max + Vn1max A1n max −1 = Sn1max .

(5.43)

For each condition of the system, we need to solve the simultaneous equations of Eqs. 5.23 and 5.35 with a sufficiently large nmax , for the convergence of

28

5 Field Enhancement in Metal Nanogaps

m m m Am n , Bn , C n , and Dn , and the below-mentioned field enhancement factor. Their convergence becomes laborious as the two particles become closer to each other, and nmax of about 100 was required for the case D/R0 = 0.01, for example. m m m Am n , Bn , C n , and Dn determined by Eqs. 5.20–5.39 satisfy Eqs. 5.9–5.12. After determining An m , Bn m , C n m , and Dn m , we calculate the electric field components E μ , E η , and E φ with the scaling factors hμ , hη , and hφ as follows:

1 ∂0 (i = μ, η, φ), h i ∂i

(5.44)

hμ =

a , cosh μ − cos η

(5.45)

hη =

a , cosh μ − cos η

(5.46)

hφ =

a sin η . cosh μ − cos η

(5.47)

Ei =

Finally, we calculate the electromagnetic field enhancement factor I by: I =

E μ E μ∗ + E η E η∗ + E φ E φ∗ E 0 E 0∗

,

(5.48)

where the superscript * denotes the complex conjugate of each field component. We calculated the electromagnetic field enhancement factors at the points on the x–z plane at y = 0, i.e., φ = 0, with the external electric field parallel to the plane, i.e., φ 0 = 0. As a cross-check for the correctness of our numerical calculations, we obtained results consistent with the those for Ag presented in Ref. 1 [8]. In the calculation results for the dependence of the field enhancement factor on the polarization angle θ 0 , we observed that [8], for other polarization angles than θ 0 = 0, the field enhancement becomes weaker, as commonly known for the single-particle case [11]. Therefore, we mainly focus on the case θ 0 = 0, corresponding to the external electric field parallel to the line between the centers of the two metal particles, in this chapter. The variation in the position of the observing point between the particles, d/D, was observed to have a relatively small influence on the field enhancement [8], indicating a preferable spatial flexibility for applications. Figure 5.2 presents the calculated electromagnetic field enhancement factors for Pd particles in air or H2 , for the condition θ 0 = 0, d/D = 0, and λ = 365 nm, which is the resonant wavelength [8], with various θ and D/R0 . In other words, this calculation rotationally tracks the field enhancement on the surface of the particle (d/D = 0) for the angular dependence of the observing point (θ ). The calculation result of the field enhancement factors for the condition D/R0 = 100 approximately corresponds to those for the monopartite case [11], with a periodic angular evolution equivalently peaking at θ = 0 and π. For D/R0 = 0.1,

5 Field Enhancement in Metal Nanogaps

29

Fig. 5.2 Calculated electromagnetic field enhancement factors for Pd particles in air or H2 , for the condition θ 0 = 0, d/D = 0, and λ = 365 nm, with various θ and D/R0 . Reprinted with permission from Ref. [8]. Copyright 2021 Elsevier

which is the regime of gap plasmon, it is observed that the field enhancement factor has a sharp peak at θ = π, whose value is significantly larger than that at θ = 0, in contrast to the case of D/R0 = 100. Reflecting this result, hereafter we focus on the case θ = π, corresponding to the observing point locating on the line between the centers of the two metal particles. We summarize the calculation results for hydrogen-absorbing transition metals Pd, Ti, and Ni and noble metals Au, Ag, and Cu traditionally studied in the field of plasmonics. Figures 5.3 and 5.4 presents the calculated spectra of electromagnetic field enhancement factor for various metal particles in air or H2 , for the condition θ 0 = 0, θ = π, D/R0 = 0.1, 0.01, and d/D = 0.5 (in the middle of the gap). For all kinds of metals, for each of the conditions D/R0 = 0.1 and 0.01, the field enhancement factor did not largely vary with the value of d/D, 0 or 0.5 [8], again indicating the spatial insensitivity in the gap. Such a similarity is presumably because even the location in the middle of the two metal particles is strongly influenced by both metal surfaces for the case of very narrow inter-particle gaps. For each condition of D/R0 and d/D, the peak field enhancement factors in the spectra for Pd, Ti, and Ni do not compete with those for Au, Ag, and Cu. However, for the longer-wavelength or lower-frequency region, the field enhancement factors of all the metals converge and are comparable to one another. For the entire wavelength region, the field enhancement factors for Pd, Ti, and Ni exhibit values as large as several hundred and ten thousand for the cases D/R0 = 0.1 and 0.01, respectively. These field enhancement factors observed are significantly larger than those for the single-particle case [11], owing to the effect of gap plasmons. Interestingly, Ti is observed to be somewhat advantageous relative to other metals in the microwave regime. As a final remark, a combination of the gap plasmon effect discussed in this chapter with the nanoshell effect of Chap. 2 and/or the lightning-rod effect (sharp tips) of Chap. 4 would provide further field enhancement.

30 Fig. 5.3 Calculated spectra of electromagnetic field enhancement factor for various metal particles in air or H2 , for the condition θ 0 = 0, θ = π, D/R0 = 0.1, and d/D = 0.5. Reprinted with permission from Ref. [8]. Copyright 2021 Elsevier

Fig. 5.4 Calculated spectra of electromagnetic field enhancement factor for various metal particles in air or H2 , for the condition θ 0 = 0, θ = π, D/R0 = 0.01, and d/D = 0.5. Reprinted with permission from Ref. [8]. Copyright 2021 Elsevier

5 Field Enhancement in Metal Nanogaps

References

31

References 1. Aravind PK, Nitzan A, Metiu H (1981) The interaction between electromagnetic resonances and its role in spectroscopic studies of molecules adsorbed on colloidal particles or metal spheres. Surf Sci 110:189–204 2. Inoue M, Ohtaka K (1983) Surface enhanced Raman scattering by metal spheres: I cluster effect. J Phys Soc Jpn 52:3853–3864 3. Tanaka K, Tanaka M (2003) Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide. Appl Phys Lett 82:1158–1160 4. Dionne JA, Sweatlock LA, Atwater HA, Polman A (2006) Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization. Phys Rev B73:035407 5. Ward DR, Huser F, Pauly F, Cuevas JC, Natelson D (2010) Optical rectification and field enhancement in a plasmonic nanogap. Nat Nanotechnol 5:732–736 6. Zhou W, Dridi M, Suh JY, Kim CH, Co DT, Wasielewski MR, Schatz GC, Odom TW (2013) Lasing action in strongly coupled plasmonic nanocavity arrays. Nat Nanotechnol 8:506–511 7. Ludwig M, Aguirregabiria G, Ritzkowsky F, Rybka T, Marinica DC, Aizpurua J, Borisov AG, Leitenstorfer A, Brida D (2020) Sub-femtosecond electron transport in a nanoscale gap. Nat Phys 16:341–345 8. Nakashima Y, Tanabe K (2021) Nanogap plasmonic field enhancement on hydrogen-absorbing transition metals. Int J Hydrogen Energy 46:14581–14591 9. Morse PM, Feshbach H (1953) Methods of theoretical physics. McGraw-Hill, New York, USA 10. Jackson JD (1998) Classical electrodynamics, 3rd edn. Wiley, Hoboken, USA 11. Tanabe K (2008) Field enhancement around metal nanoparticles and nanoshells: a systematic investigation. J Phys Chem C 112:15721–15728

Chapter 6

Applications

6.1 Hydrogen Production Hydrogen production from water, or so-called water splitting, by using photocatalysts is intensively studied [1–3]. Enhancement of the hydrogen production rate by focusing the optical energy into the photocatalytic materials by utilizing the localized surface plasmon resonance effect is an effective scheme [4–18]. Liu et al. demonstrated plasmonic enhancement of the water splitting rate under visible illumination at 532 and 633 nm by TiO2 photocatalyst plates coated with Au nanoparticles [4]. The plasmonic field enhancement increases the electron–hole pair generation rate at the surface of the TiO2 , where is the interface with H2 O, thus increasing the amount of photogenerated charge contributing to catalysis (Fig. 6.1). This mechanism of enhancement is particularly effective because of the relatively short diffusion length of the excitons or minority carriers in TiO2 , which otherwise limits the photocatalytic performance. Ingram and Linic demonstrated plasmonic enhancement by Ag nanocubes for the water splitting rate on TiO2 photocatalyst under visible illumination in the range of 350 – 650 nm [5]. Seh et al. demonstrated the use of noncentrosymmetric Janus Au–TiO2 photocatalysts for efficient visible-light hydrogen generation, owing to plasmonic field enhancement at the Au/TiO2 interface [6]. The plasmonic near-fields around the Au/TiO2 interface are coupled to optical transitions involving localized electronic states in TiO2 , leading to enhanced optical absorption and the generation of electron–hole pairs for photocatalysis. Mubeen et al. realized a solar water-splitting device based on a Au nanorod array covered by TiO2 and Pt nanoparticles in which essentially all charge carriers involved in the oxidation and reduction steps arise from the hot electrons resulting from the excitation of surface plasmons in Au (Fig. 6.2) [10]. Zhu et al. used Au/La2 Ti2 O7 nanostructures sensitized with black phosphorus to prepare a broadband solar response photocatalyst for hydrogen production [14]. In this system, the broad absorption of black phosphorus and plasmonic field enhancement by Au contribute to the enhanced photocatalytic activity with efficient interfacial electron transfer from excited black phosphorus and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 K. Tanabe, Plasmonics for Hydrogen Energy, SpringerBriefs in Energy, https://doi.org/10.1007/978-3-030-88275-4_6

33

34

6 Applications

Fig. 6.1 Schematic of the experimental setup for photocatalytic water splitting. Reprinted with permission from Ref. [4]. Copyright 2011 American Chemical Society

Fig. 6.2 Structure and mechanism of operation of the autonomous plasmonic solar water splitter. (Left) Schematic of the cross-section of an individual photosynthetic unit showing the inner gold nanorod, the TiO2 cap decorated with platinum nanoparticles, which functions as the hydrogen evolution catalyst, and the Co-OEC material deposited on the lower portion of the gold nanorod. (Right) Energy level diagram superimposed on a schematic of an individual unit of the plasmonic solar water splitter, showing the proposed processes occurring in its various parts and in energy space. CB, conduction band; VB, valence band; EF, Fermi energy. Reprinted with permission from Ref. [10]. Copyright 2013 Springer-Nature

6.2 Hydrogen Dissociation

35

Fig. 6.3 Schematic diagram of the energy band structure, plasmonic resonance, and electron transfer pathway in the MoS2 /TiO2 heterojunction. Reprinted with permission from Ref. [15]. Copyright 2018 Royal Society of Chemistry

Au to La2 Ti2 O7 . Guo et al. reported nonmetal plasmonic MoS2 /TiO2 heterostructures for efficient photocatalytic hydrogen generation (Fig. 6.3) [15]. Nonstoichiometric metal-chalcogenides can exhibit plasmonic absorption owing to charge collective oscillation on the metal-chalcogenide surface propagated by numerous anion (sulfur, in this case) vacancies within the crystal lattice. Such a plasmon-enhanced photocatalytic hydrogen production system based on low-cost, earth-abundant materials may be effective in view of practicality.

6.2 Hydrogen Dissociation Zhou et al. employed Al nanocrystals and their localized surface plasmon resonance as a photocatalyst for a hydrogen dissociation reaction, H2 + D2 - > 2HD, at room temperature and atmospheric pressure [19]. They observed peaks of the hydrogen dissociation rate at illumination wavelengths around 460 and 800 nm, corresponding to the localized surface plasmon resonance mode of the Al nanocrystals, and the interband transition in Al, respectively (Fig. 6.4). A photocatalytic reaction mechanism is then proposed that hot electrons generated in the Al nanocrystals, from the surface plasmon decay and from direct photoexcitation of the Al interband transition, transfer to hydrogen molecules, populating their antibonding orbitals and weakening the H − H bond, and thus facilitate their dissociation.

36

6 Applications

Fig. 6.4 Wavelength dependence of HD generation on an Al nanocrystal/γ-Al2 O3 photocatalyst. HD production (red circles) on photocatalyst illuminated by monochromatic light as a function of excitation wavelength. The calculated absorption cross section of a single Al nanocrystal surrounded by a porous γ-Al2 O3 shell is shown as black curve. Reprinted with permission from Ref. [19]. Copyright 2016 American Chemical Society

6.3 Hydrogen Storage The plasmonic field enhancement effect may potentially be also applied to hydrogenstorage technology. Because the dissociative adsorption of gaseous hydrogen molecules is the rate-limiting process among the whole hydrogen transport processes in hydrogen absorption into metals or alloys in many metal-hydrogen systems [20– 22], an active dissociation of hydrogen molecules into atoms or plasma by an applied electric field can, for instance, significantly enhance the total hydrogen absorption velocity into solid metals [23]. In this scheme, the applied electric field will be particularly enhanced in the vicinity of the metal surfaces, where the atomic dissociation occurs most efficiently for the subsequent surface adsorption due to the surfaceplasmon effect. In addition, it is indicated that hydrogen plasma enables supersaturation loading of hydrogen in metals [24, 25]. Losurdo et al. demonstrated that plasmonic antennas of Ga nanoparticles on α-Al2 O3 (sapphire) promote hydrogen absorption in the system, owing to the transverse and longitudinal localized surface plasmon resonances coupling light to activate hydrogen dissociative adsorption on Ga and reactive transfer into α -Al2 O3 , respectively [26]. Sytwu et al. designed a crossed-bar Au-PdHx antenna-reactor system that localizes the optical energy of the incident laser, by plasmonic field enhancement, on the side facet in the middle of a PdHx nanorod contacting a Au bar, and away from the tips of the PdHx nanorod [27]. They then demonstrated an increase in the hydrogen desorption rate on the side facet

6.3 Hydrogen Storage

37

Fig. 6.5 Schematic representation of the plasmonic Au nanoantenna-enhanced hydrogen sensing via hydrogen absorption in Pd. (Left) A Pd nanoparticle is placed at the nanofocus of a Au resonant antenna. (Right) Hydrogen absorption by the palladium nanoparticle changes its complex dielectric function, and a resonance shift (λ) of the Au antenna is optically detected. Reprinted with permission from Ref. [37]. Copyright 2011 Springer-Nature

of the PdHx nanorod, to a rate significantly higher than that at the tips, realizing an opposite situation to the inherent.

6.4 Hydrogen Sensing Hydrogen sensing is an important technical component in practical hydrogen use [28– 30]. The plasmonic field enhancement effect on metal surfaces can also be utilized for the enhancement of the sensitivity of hydrogen detection [31–45]. Langhammer et al. introduced a plasmonic hydrogen sensing scheme by detecting the induced electronic and structural changes in Pd during the hydridation process [34, 45]. Liu et al. demonstrated plasmonic Au nanoantenna-enhanced hydrogen sensing via hydrogen absorption in Pd [37]. They placed a Pd nanoparticle at the nanofocus of a Au resonant antenna (Fig. 6.5). When hydrogen absorption by the palladium nanoparticle changes its complex dielectric function, a resonance shift of the Au antenna can be optically detected. Baldi et al. realized in-situ detection of hydrogen-induced phase transitions in individual Pd nanocrystals by electron energy-loss spectroscopy [41].

6.5 Nuclear Fusion Laser fusion technology can potentially provide an ideal energy source for humans [46–52]. One of the most crucial issues hindering its practical realization at present is the low energy-coupling efficiency between the heating laser and the fuel target. Energy focusing into the fuel targets, achieved by attaching metallic cone guiding

38

6 Applications

materials in the vicinity of targets, was implemented to some extent [47, 48, 52], but further focusing, particularly inside the targets, is required. The possibility of realizing compact nuclear fusion reactors using deuterium-absorbed metals has also been investigated [53–58]. The density of the triggering energy supplied to deuterium– metal systems to activate the nuclear fusion reaction may be one of the key factors for producing a smooth and reproducible initiation of the reaction. The plasmonic field enhancement effect could be potentially also applicable to nuclear fusion technologies, as a scheme to increase the nuclear reaction rate by focusing the supplied electromagnetic field or laser on the fuel material containing hydrogen isotopes. A potential application for such scenario of nuclear fusion phenomenon supported by the plasmonic field enhancement effect is illustrated as follows. Once an initial nuclear fusion reaction occurs in the highly concentrated energetic “hot spot” region around a metal surface, the heat locally generated by the nuclear reaction induces subsequent reactions around the region and thus effectively initiates heat-mediated chain reactions to spread throughout the fuel material. Such “hot spots” can trigger an initial nuclear fusion reaction to locally generate large amounts of heat and induce subsequent reactions by supplying the necessary activation energy, thereby leading to a complete fusion ignition of the entire fuel material. The local energy-focusing effect thus significantly increases the probability of the initial nuclear reaction, even if the total power supplied to the fuel material remains the same, and therefore, may effectively reduce the input power threshold [23]. For laser fusion, an efficient ignition system comprising metal nanoparticles or nanoshells embedded in conventional deuterated polystyrene fuel targets was proposed and analyzed (Figs. 6.6 and 6.7) [59, 60]. The wide tunability of the resonant frequency of metal nanoshell allowing it to be matched with the wavelength of the incident heating laser may offer a significant practical advantage. It was numerically shown that the field enhancement factors for hydrogen-absorbing transition metals, such as Pd, Ti, and Ni, can surpass those for noble metals in the microwave region [23, 61]. Such plasmonic electromagnetic field enhancement effects for hydrogenabsorbing transition metals further indicates an additional scheme for a novel type of fuel target for deuterium- or tritium-absorbed transition-metal-based materials. It should be noted that a combination of the plasmonic field enhancement scheme with the existing metal-cone guiding scheme [47, 48, 52] may potentially enhance the overall energy-coupling efficiency even further.

6.5 Nuclear Fusion

39

Fig. 6.6 Spatial profile of the time-averaged electromagnetic energy density in the deuterated polystyrene ((C8 D8 )n or simply CD) fuel target with 10 randomly distributed Ag nanoparticles by a finite-element frequency-domain calculation. The regions of the CD fuel target, vacuum surrounding the CD target, and the perfectly matched layer (PML) for computation are labelled. The positions of the Ag nanoparticles are indicated by arrows. The inset shows a close-up view for the energy profile around a Ag nanoparticle. The dotted line indicates the cross section for the one-dimensional plot in Fig. 6.7. Reprinted with permission from Ref. [59]. Copyright 2016 Institute of Physics

Fig. 6.7 Cross-sectional plots of the time-averaged electromagnetic energy density at the uniaxial position relative to the center of the CD fuel target, along a cross-sectional line including three Ag nanoparticles as indicated by the dotted line in Fig. 6.6, for the cases with and without the Ag nanoparticles. Reprinted with permission from Ref. [59]. Copyright 2016 Institute of Physics

6 Applications

Time-averaged energy density (arb. u.)

40

w/ Ag nanoparticles

w/o Ag nanoparticle (x 10) -30

-20

-10

0

10

20

30

Position ( m)

References 1. Fujishima A, Honda K (1972) Electrochemical photolysis of water at a semiconductor electrode. Nature 238:37–38 2. Liu C, Colón BC, Ziesack M, Silver PA, Nocera DG (2016) Water splitting–biosynthetic system with CO2 reduction efficiencies exceeding photosynthesis. Science 352:1210–1213 3. Takata T, Jiang J, Sakata Y, Nakabayashi M, Shibata N, Nandal V, Seki K, Hisatomi T, Domen K (2020) Photocatalytic water splitting with a quantum efficiency of almost unity. Nature 581:411–414 4. Liu ZW, Hou WB, Pavaskar P, Aykol M, Cronin SB (2011) Plasmon resonant enhancement of photocatalytic water splitting under visible illumination. Nano Lett 11:1111–1116 5. Ingram DB, Linic S (2011) Water splitting on composite plasmonic-metal/semiconductor photoelectrodes: Evidence for selective plasmon-induced formation of charge carriers near the semiconductor surface. J Am Chem Soc 133:5202–5205 6. Seh ZW, Liu SH, Low M, Zhang SY, Liu ZL, Mlayah A, Han MY (2012) Janus Au-TiO2 photocatalysts with strong localization of plasmonic near-fields for efficient visible-light hydrogen generation. Adv Mater 24:2310–2314 7. Lee J, Mubeen S, Ji XL, Stucky GD, Moskovits M (2012) Plasmonic photoanodes for solar water splitting with visible light. Nano Lett 12:5014–5019 8. Zhang ZH, Zhang LB, Hedhili MN, Zhang HN, Wang P (2013) Plasmonic gold nanocrystals coupled with photonic crystal seamlessly on TiO2 nanotube photoelectrodes for efficient visible light photoelectrochemical water splitting. Nano Lett 13:14–20 9. Tanaka A, Sakaguchi S, Hashimoto K, Kominami H (2013) Preparation of Au/TiO2 with metal cocatalysts exhibiting strong surface plasmon resonance effective for photoinduced hydrogen formation under irradiation of visible light. ACS Catalysis 3:79–85 10. Mubeen S, Lee J, Singh N, Kramer S, Stucky GD, Moskovits M (2013) An autonomous photosynthetic device in which all charge carriers derive from surface plasmons. Nat Nanotechnol 8:247–251 11. Zheng ZK, Tachikawa T, Majima T (2014) Single-particle study of Pt-modified Au nanorods for plasmon-enhanced hydrogen generation in visible to near-infrared region. J Am Chem Soc 136:6870–6873

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