Fortschritte der Physik / Progress of Physics: Band 30, Heft 10 [Reprint 2021 ed.] 9783112591086, 9783112591079

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FORTSCHRITTE DER PHYSIK HERAUSGEGEBEN IM AUFTRAGE DER PHYSIKALISCHEN GESELLSCHAFT DER DEUISCMEN DEMOKRATISCHEN REPUBLIK VON F. KASCHLUHN, A. LÖSCHE, R. RITSCHL UND R. ROMPE

HEFT 10 • 1982 • BAND 30

A K A D E M I E

ISSN 0015 - 8208

- V E R L A G

•

Fortschr. Phys., Berlin 30 (1982) 10, 507-582

B E R L I N

EVP 10,- M

31728

BEZUGSMÖGLICHKEITEN Bestellungen sind zu richten — in der DDR an eine Buchhandlung oder an den AKADEMIE-VERLAG, DDR-1086 Berlin, Leipziger Straße 3—4 — im sozialistischen Ausland an eine Buchhandlung für fremdsprachige Literatur oder an den zuständigen Postzeitungsvertrieb — in der BRD und Berlin (West) an eine Buchhandlung oder an die Auslieferungsstelle KUNST UND WISSEN, Erich Bieber OHG, D-7000 Stuttgart 1, Wilhelmstraße 4—6 — in den übrigen westeuropäischen Ländern an eine Buchhandlung oder an die Auslieferungsstelle KUNST UND WISSEN, Erich Bieber GmbH, CH-8008 Zürich, Dufourstraße 51 — im übrigen Ausland an den Internationalen Buch- und Zeitschriftenhandel; den Buchexport, Volkseigener Außenhandelsbetrieb der Deutschen Demokratischen Republik, DDR-7010 Leipzig, Postfach 160; oder an den AKADEMIE-VERLAG, DDR-1086 Berlin, Leipziger Straße 3—4

Zeltschrift „Fortachritte der Physik" Herausgeber: Prof. Dr. Frank Kaschluhn, Prof. Dr. Artur LOsche, Prof. Dr. Rudolf Ritsehl, Prof. Dr. Robert Rompe, im Auftrag der Physikalischen Gesellschaft der Deutschen Demokratischen Republik. Verlag: Akademie-Verlag, DDR-1088 Berlin, Leipziger Straße 3 - 4 ; Fernruf: 2236221 und 2236229; Telex-Nr.: 114420; Bank: Staatsbank der DDR, Berlin, Konto-Nr.: 6836-26-20712. Chefredakteur: Dr. Lutz Rothkirch. Anschrift der Redaktion: Sektion Physik der Humboldt-Universität zu Berlin, DDR-1040 Berlin, Hessische Straße 2. Veröffentlicht unter der Lizenznummer 1324 des Presseamtes beim Vorsitzenden des Ministerrates der Deutschen Demokratischen Republik. Gcsamtherstellung: VEB Druckhaus „Maxim Gorki", DDR-7400 Altenburg, Carl-von-Ossietzky-StraEe 30/31. Erscheinungsweise: Die Zeitschrift „Fortschritte der Physik" erscheint monatlich: Die 12 Hefte eines JahreB bilden einen Band. Bezugspreis je Band 180,— M zuzüglich Versandspesen (Preis für die DDR: 120,— M). Preis je Heft 15,— M (Preis für die DDR: 1 0 , - M). Bestellnummer dieses Heftes: 1027/30/10. © 1982 by Akademie-Verlag Berlin. Printed in the German Democratic Republic. AN (EDV) 57618

Fortschritte der Physik 30, (1982) 10, 507—582

Dielectric Behaviour of Liquid Crystals H . KRESSE

Sektion Chemie der Martin-Luther-Universität Halle, Halle (S.), DDR1) Abstract The influence of the molecule structure on the dielectric anisotropy of nematic liquid crystals was experimentally investigated and discussed'from the point of view of the Maier-Meier theory. Further, the reorientation time of the dipoles in different smectic phases was measured and correlated to the structure of the phases. Some technical aspects are discussed in connection with the dielectrie relaxation phenomenon.

Contents 1.

Introduction

508

2. 2.1. 2.1.1. 2.1.2. 2.2. 2.3. 2.4. 2.4.1. 2.4.2. 2.4.3.

Theoretical Part Dielectric Constant and Dielectric Loss Phenomenological Theory Molecular Theories Maier-Saupe Theory of the Nematic Phase Maier-Meier Theory of the Static Dielectric Constant of Nematic Liquid Crystals. . Hindrance of Rotation in Nematic Phases . Martin-Meier-Saupe Theory Dielectric Relaxation in the Isotropic Phase Relations between the Different Dipole Relaxations and the Elastic Relaxation in the Volume Phase

509 509 509 511 514 516 518 518 521

3. 3.1. 3.2. 3.3.

Experimental Methodology 523 Estimation of the Dielectric Constant and the Dielectric Loss in the Frequency Range 0 . 1 - 1 2 MHz 523 Low Frequency Measurements in a Micro Cell 525 High Frequency Measurements 525

4. 4.1. 4.1.1. 4.1.2. 4.1.2.1. 4.1.2.2. 4.1.2.3. 4.2.

Static Dielectric Constant Influence the Terminal Groups on the Static Dielectric Constant Influence of the Length of Alkyl Chain Influence of the Chemical Structure on the Dielectric Constant Azobenzenes Phenylpyrimidines Phenylbenzoates Influence of the Middle Group on the Static Dielectric Constants

!) DDR-4020 Halle (S.), Mühlpforte 1; GDR 1

Zeitschrift „Fortschritte der Physik", Bd. 30, Heft 10

522

525 525 525 526 527 529 532 535

508

5. 5.1. 5.1.1. 5.1.2. 5.1.3. 5.1.4. 5.2. 6. 6.1. 6.1.1. 6.1.2. 6.2. 6.2.1. 6.2.2. 7. 7.1. 7.2. 7.3.

H . KRESSE

Dielectric Behaviour of Liquid Crystalline Carboxylic Acids in the Pure Phase and Binary Systems Dielectric Behaviour of Pure Liquid Crystalline Carboxylic Acids trans-4-rc.-Alkyl-cyclohexanecarboxylic Acids 4-re-Alkylbenzoic Acids 4-n-Alkyloxybenzoic Acids 4-w-Alkylaminobenzoic Acids Dielectric Behaviour of Mixtures of Nematic Carboxylic Acids with non Liquid Crystalline Acids Dielectric Relaxation in Nematic Phases Dielectric Investigations at Unoriented Samples in the GHz-Region and Comparison with MHz-Measurements 4-n-Octyloxyphenyl 4-w-Pentyloxybenzoate 4-ra-Hexylphenyl 4-Methoxybenzoate and 4-ra-Butyloxyphenyl 4-m-Hexylbenzoate. Dielectric Relaxation at Oriented Samples in the MHz-Range Homologous 4-ra-Alkyloxyphenyl 4-Methoxybenzoates Employment of the "Theorem of Corresponded States" on the Relaxation Behaviour

537 537 537 539 540 543 544 548 548 548 549 551 551 552

7.5.

Dielectric Relaxation at Multi-Component Systems in the Nematic Phase Introduction 4-m-Octyloxyphenyl 4-ii-Pentyloxybenzoate (4)/2-Methylphenyl Benzoate (B) . . . 4-»-Hexyloxyphenyl 4-Methoxybenzoate (4)/Ethylhydrochinone l,4-bi-(4-ra-Hexylbenzoate) (B) 4-m-Butyloxyphenyl 4-re-Hexylbenzoate (4)/Hydrochinone l,4-bi-(4-?i-Hexylbenzoates) Technical Mixtures

8. 8.1. 8.2. 8.2.1. 8.2.2. 8.3. 8.4.

Dielectric Behaviour of Smectic Liquid Crystals Structure and Rotational Possibilities in Mesomorphic Phases Dielectric Behaviour of Smectic High Temperature Phases Smectic A Phases Smectic C Phases Dielectric Investigations in SB and SF Phases Dielectric Investigations in SG, SE and Sx Phases

563 563 566 566 568 570 571

9.

Influence of the Dielectric Relaxation on the Dielectric Orientation Effects . . . .

573

7.4.

554 554 555 557 559 561

1. Introduction The fantastic development of microelectronics in the last twenty years has given many impulses for technics and science. Of course, the new generation of electronic digital instruments needs new kinds of electrooptical displays. One of these are liquid crystalline displays, known for fifteen years. Liquid crystals have been a traditional sphere of research at the; university of E[alle from the beginning of this century. Using very simple geometrical models V O R L À N D E R and his coworkers have synthesized many liquid crystals. In about 1 9 4 0 M A I E R investigated the connections between the molecular structure and the dielectric behaviour of these substances. Since 1 9 5 5 these traditions have been continued in the synthetic group of S C H U B E R T and from the angle of physical behaviour, particularly in the field of polymorphism, in the group of SACKMANN. The peerless atmosphere in Halle, which is connected with these traditions, has allowed the author in the last then years to investigate the dielectric behaviour of liquid crystals taking a comprehensive approach. Contrary to the reviews by B Ô T T C H E R and B O R D E W I J K [2] as well as D E J E U [2] the author tries a more complex representation of his own results.

509

Dielectric Behaviour of Liquid Crystals

2. Theoretical Part 2.1. Dielectric Constant and Dielectric Loss 2.1.1. Phenomenological Theory According to the classical electrostatic an electrical field E induced a dipole moment in every part of a volume of a non-conductor. The quotient of the induced electrical moment and the volume is the polarization P . Both of these vectors are connected by

P = (e*-l)eE

(1)

(E — 8.85 • 10" 12 Fm" 1 ; E* = complex (relative) dielectric constant). Microscopic theories [3—7] distinguish between the induced polarization P1 and the orientational part P 2 which arise from the atoms and molecules. The problem with this consideration is the estimation of the so-called "internal field" U; the field which is acting directly on the particles, because the macroscopic field E is modified by the atoms and molecules. This difficulty has been solved by different theoretical models. Often they are useful only for special problems. One of these possibilities, the Onsager theory, will be presented in chapter 2.1.1. A differentiation between and P2 is possible because of the different molecular dynamic behaviour. So, the reorientation of the induced polarization is much faster than 10~ 11 s because of the high mobility of the electrons in a molecule. If we neglect the atomic polarization and the dispersion of refractive index [6], we can write at high frequencies e* = £oo (P |] E) (2) or according to Maxwell

Soo = n2- (n: refractive index).

(2a)

The orientational part P2 arises from the partial orientation of the permanent molecular dipole moments in the direction of the external electrical field. This process is connected with a rotation of parts of the molecules or even the whole molecule and it takes place more slowly. The temporal change of P2 after switching off a constant electrical field can be described by the equation [6] d PS) dt

=

PS) T

or

P2(i)=P20exp

0

H )

.

(3)

In (3) T0 means the (macroscopic) relaxation time and P 2 0 the orientational part of P before switching off the electrical field. The equation (3) is very useful for a clear interpretation of the relaxation time: the relaxation time r 0 is that time in which the orientational part of the polarization is decreased to 1/e of the original value. The delay of P 2 in relation to an external electrical field can be detected experimentally as a phase shift between voltage and current. This method has the advantage that the frequency dependence of the complex dielectric constant in (1)

e* =e' - is"

(4)

is relatively easy of access and e as well as e" can be estimated from measurements of capacity or else cbnductivity. The phenomenological theory gives relations between the real component of the dielectric constant e', the imaginary part e" and the frequency /. Therefore, let us regard an external 1*

510

H. KRESSE

electrical field with the amplitude E0 and the circular frequency to = 2nf E =

E0 e x p (ia>t).

(5)

If the frequency of the electrical field is small enough, the orientational part of the polarization can follow the electrical field without any delay and we measure the total polarization P0. On the other hand, we find at high frequencies only the induced polarization. Both of these borderline cases can be written in the equations P0 = e(e0 — 1) E Pi

=

e(e0o -

resp.

(6a)

1 )E.

(6b)

e0 is the so-called static dielectric constant and the high frequency limit of relative dielectric constant. Equation (6) can be also written in scalar form, because the imaginary part of s* disappears in these cases. The change of the orientational part of polarization P2{t) in (3) can be described also in the following way [6] * ™ = ± [ P , at r0

P

- P

l

t

m

.

(7)

From (5), (6), and (7) follows Q/V

TQ

TQ

The differential equation (8) can be solved [5] and the integration constant is determined by the conditions a> 0, P2{t) ~> P 0 — P1: P,(t) =

f°~.eco)E. 1 + %a>r0

(9)

e(

Multiplication of numerator and denominator with (1 — ia>r0) and addition of P } gives P(t)

=

eE

/

(Soo -

1\

1) +

I

,

®0

, . . .

1 + coV

~

•

'•

®0

1 + w V

(10)

If we compare (10) with (1) and (4) follows , £

. +

=

«0 Eoo 1+coV'

„ =

e0 eoo 1+coV

WT

°-

,1 1. ( U )

The variation of a' and e" with the logarithm of frequency is shown in fig. 1. The dielectric loss e" has at the relaxation frequency /* =

(/* =

0 3

G H z in

!)

(12)

a maximum, whereas e' decreases by (e0 — fioo)/2. Another possibility of evaluation of eq. (11) is a graphical description of e" as a function of e' with the frequency as parameter (fig. 2). This so-called COLE-COLE plot [9] gives for a Debye relaxation mechanism [3] a semicircle.

511

Dielectric B e h a v i o u i of Liquid C r y s t a l s

Often, the experimental results can be represented in the form of e*

= ' e ~ + 11 +_ ! °( rÎ C O T£ Q u-.) «

(13)

which distinguish themselves from (11) by the Cole-Cole distribution parameter