GENERAL DISCUSSION

Dr. P. A. Winsor (Thornton Research Centre, Chester) said: Arora and Fergason write, " The essential question arises : are smectic B and similar states liquid crystalline or crystalline? In the broader sense of the word they are clearly mesomorphic but they are definitely more crystalline than liquid, and in fact, the existence is known of materials " (presumably they refer here to plastic crystals) " which are truly crystal- line but have very low yield stress and can be more deformable than smectic B in many cases. We believe that most confusion in nomenclature arises from the differentiation between plastic crystals and smectic B ".

The mesoniorphous, liquid crystalline character of plastic crystals has already been discussed. It is desirable to ensure that plastic crystals are defined as comprising a distinct class of mesophase-as distinct as the nematic, cholesteric and smectic mesophases themselves-characterized by rotational mobility of the constituent units about the lattice points. Plastic crystals apparently occur at the higher- temperature, lower-order end of the non-amphiphilic series of mesophases, whereas smectic B arises at the lower-temperature, higher-order end of the series. The clear differentiation between plastic crystals (even if we call them plastic mesophases or plastic liquid crystals) and smectic B is thus essential if we are to avoid serious con- fusion. If one demurs at calling smectic B " liquid crystalline '' one should keep to " mesomorphous " or even adopt " semicrystalline " but, in deference to Timmer- manns, let us reserve the term " plastic crystal " solely for rotational mesophases of the cubic (or occasionally hexagonal) type.

A further point of nomenclature involves the question of the usefulness of making a distinction between thermotropic (i.e., temperature-induced) and lyotropic (i.e., sclvent-induced) mesophases. All mesophases should be regarded as thermotropic since their limits of stability are dependent on temperature. Similarly, their limits of stability are highly dependent on the presence of even small amounts of solvents and on this account the mesophases should all be regarded as lyotropic.

In using the terms thermotropic and lyotropic a distinction is usually implicit between non-amphiphilic and amphiphilic mesophases respectively. But a virtually unlimited number of liquid crystalline (" fused ") amphiphilic mesophases are formed in complete absence of solvent, e.g., the M2 phases of the higher molecular weight, sodium sulphodialkylsuccinic esters at room temperatures, the neat phases of many branched chain anionic amphiphiles at room temperature, the cubic phase of calcium w-phenyl undecanoate at room temperature and, at higher temperatures, the neat soap phase of the fatty acid alkali metal soaps and the V, and M2 phases of the fatty acid alkaline earth soaps, both these classes of soap giving solid crystals at room temperature. These solvent-free mesophases cannot logically be called " lyotropic " but-like the non-amphiphilic mesophases they are able to take up continuously lesser or greater amounts of solvents (hydrocarbon, water etc.) before passing dis- continuously to a new phase-either amorphous or mesomorphous. On account of the above facts it seems misleading and undesirably divisive to draw a distinction between lyotropic and thermotropic mesophases. It would seem more helpful to classify mesophases as non-amphiphilic and amphiphilic-and to emphasize the similarities rather than the dissimilarities between these classes. The terms thermo- tropic and lyotropic might, perhaps usefully be retained to connote phase changes produced by temperature change or by the addition of solvent respectively. In

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G E N E R A L DISCUSSION 135

two-component phase diagrams (whether of non-amphiphilic or amphiphilic systems) those phase changes arising along lines parallel to the temperature axis and those arising along lines parallel to the composition axis would then be termed thermo- tropic and lyotropic phase changes respectively, i.e., the terms would be used purely descriptively and with no nuance of constitutional implication.

Prof. S . Chandrasekhar (Raman Research Znst., Bangalore) said : According to the model adopted by Humphries et al., the orientational order parameter at the nematic-isotropic transition temperature should have a universal value of 0.4292 for the pure compounds. It is interesting to note that the theory predicts that in the mixture the order parameters of the two components are different. I wonder if anything like an additivity rule that Madhusudana and I found in mixtures af p- azoxyanisole and p-azoxyphenetole is observed in this case also. The general anisotropic oscillator model for the dispersion energy of interaction between a pair of unlike molecules leads to an expression which is not a simple product of the anisotropies of the polarizabilities.2 Consequently the geometric mean approxima- tion is not exact. This may be partly responsible for the deviations between theory and experiment.

The most drastic assumption in the theory would appear to be the one concerning the pair distribution function. In effect, it is assumed that the molar volume of the mixture is independent of the composition and temperature. The Maier-Saupe theory shows that a 2 % change in volume results in some 20-30 % change in the order parameter of a pure compound. The free energy will also change corre- spondingly, and since the temperature of transition is determined by equating the free energy to zero, this assumption may lead to serious errors. How far it is justified in the specific cases studied by Humphries et al. can be judged only if the densities are known.

Dr. G. R. Luckhurst (University of Southampton) said : In reply to Chandrasekhar, in my paper with Humphries and James, the nematic-isotropic transition point for binary mixtures of nematogens was calculated from approximate expressions, given by eqn (3.1) and (3.2), for the pseudo-potentials of the two components. These equations may also be used to estimate the orientational order P, for the individual components as a function of the composition of the mixture. The results of such calculations would, of necessity, be approximate since we know that to obtain exact agreement with the experimental order in the pure mesophase the pseudo-potential must contain the term with L = 4. However, retention of these higher order terms for multicomponent systems results in the introduction of several arbitrary parameters. We have sought to avoid this by using eqn (3.1) and (3.2), together with the geometric mean rule to calculate the orientational order for the complete composition range of a mixture of nematogens (I) and (11) at 494.2 K. The results of these calculations are plotted, as lines (a) and (c), in the figure as a function of the reduced temperature for the mixture rather than its composition which, in this context, has less theoretical significance. As we might expect, the order for the component with the higher nematic-isotropic transition is greater at any given reduced temperature. Included in the figure, as line (b), is the degree of order predicted by the Maier-Saupe theory

S. Chandrasekhar and N. V. Madhusudana, J . Phys., 1969,30,C4-24.

1969), chap. 2. * H. Margenau and N. R. Kestner, Theory of Intermolecular Forces (Pergamon Press, London,

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136 G E N E R A L DISCUSSION

86.5 a9 92 95 90 loo

100 T* FIG. 1.-The orientational order F,<a) for component (I) and (c) for component (11) in their binary mixture plotted as a function of reduced temperature. Curve (b) is the orientational order for a

pure mesophase conforming to the Maier-Saupe theory.

for the pure mesophase and this line falls in between the values for the two com- ponents. We have also calculated a weighted average of the two orientational orders from the expression

The results for this composite order parameter are not shown in the figure since they are virtually identical with the curve predicted by the Maier-Saupe theory for single- component systems. Our theory of multi-component systems would seem, therefore, to justify an empirical relationship proposed by Chandrasekhar and Madjusudana on the basis of their analysis of optical studies by Chatelain and Germain.2 It is unfortunate that, unlike nuclear magnetic resonance experiments, such optical measurements are unable to provide values for the degree of order for the separate components with which to test the theory further.

It is important to realise that the geometric mean rule which we use to calculate the mixed energy parameter c12 is not a part of our molecular field theory of multi- component liquid crystalline systems. The rule is proposed simply to remove all arbitrary parameters from a particular expression for the orientational Helmholtz function. Indeed, as we say in the paper, it is departures from the geometric mean approximation which account so well for the observed deviations from linearity of the nematic-isotropic transition in the phase diagrams.

The assumption concerning the pair distribution function in both mixed and pure nematic mesophases is clearly the most suspect part of the theory and one which we are seeking to remove. However, this approximation is expected to be quite reliable for nematogens, such as those discussed in the paper, which have similar structures. The approximation may even be better than Chandrasekhar implies, for we are only concerned with the properties of the systems at the nematic-isotropic transition which is a corresponding temperature for the pure mesophases and their binary mixtures.

S. Chandrasekhar and N. V. Madhusudana, J. Physique (C4), 1969,30,24. P. Chatelain and M. Germain, Compt. Rend., 1964, 239, 127. D. H. Chen, P. G. James and G. R. Luckhurst, Mol. Cryst. Liquid. Crysf., 1969, 8,71.

pimixture) - - X P y ’ + (1 - X ) F i 2 ’ .

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GENERAL DISCUSSION 137

Dr. E. R. Smith (The Open University, Bletchley) (communicated): The paper by Luckhurst et al. notes at several points that the energy of intermolecular interaction is due to pairwise additive interactions. Since a large fraction of the intermolecular interaction is due to dispersion forces, the non-pairwise additive forces may be signifi- cant. Careful descriptions of the dependence of the transition temperature upon model pair interactions may ignore entirely the dependence of the transition tempera- ture on multiparticle interactions. Because of the relatively large size of the molecules characteristically occurring in liquid crystals, it should be possible to get reasonably accurate results for the dispersion energy of the system by using the Lifshitz theory. The application of this theory to multilayer systems indicates that 50 % and more of the dispersion energy comes from non-pairwise additive sources. There is no reason to expect that the non-pairwise additive energies should be any smaller in cylindrical arrays than they are in multilayer systems. It would be possible to estimate the dispersion energy of a nematic crystal by calculating the energy of a regular array of model cylindrical molecules. The bulk energy calculated would only be that of a model, but it would show whether the non-pairwise additive effects are large. The spacing between molecules would be taken from experimental data. The description of dispersion energies given by the Lifshitz theory is "parameter independent ". The energies calculated for the model would depend only upon the bulk frequency dependent dielectric susceptibilities and the geometries of the model molecules. Thus, there should be no adjustable parameters in the dispersion energy of the system.

Dr. G. R. Luckhurst (University of Southampton) said : In reply to Smith, clearly, if non-pairwise additive forces are important then our theory for multicomponent systems, and indeed all theories of pure nematogens, would require drastic revision. However, the qualitative and quantitative success of the various theories, based as they are on pairwise additivity, might be taken to imply that the effects of non- additivity are not as important as Smith would have us believe.

Dr. G. R. Luckhurst (University of Southampton) said: In reply to Leadbetter, the magnitude of the thermal fluctuations for the director in a nematic mesophase may be obtained from an electron resonance experiment.l Since the correlation time for these fluctuations is about s a spin probe dissolved in the nematic mesophase simply experiences a static distribution of the orientations of the director. The effect of this static distribution on the electron resonance spectrum of the probe i s to make the line shapes asymmetric. By analyzing this asymmetry we have found that for 4,4'-dimethoxyazoxybenzene the root-mean-square fluctuations of the director decrease from 10" near the nematic-isotropic transition to about 6" in the supercooled mesophase. In marked contrast, the magnitude of the molecular fluctuations with respect to the director can be as large as 50".

Prof. J. A. Janik (Krakow) said: Could Luckhurst explain what is the interpreta- tion of the time ca. s which he measures by the e.s.r. method?

Dr. G. R. Luckhurst (University of Southampton) said: In reply to Janik, the correlation time which is measured in an electron resonance experiment, such as the one I have hinted at, is that for molecular rotation which modulates a second rank tensor. This is in contrast to the dielectric relaxation measurements described by

S. A. Brooks, G. R. Luckhurst and G. F. Pedulli, Chem. Phys. Letters, 1971,11,159.

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138 G E N E R A L DISCUSSION

Meier, where the rotational correlation time for fluctuations in a first rank tensor is determined. The value for the correlation time of the paramagnetic probe dissolved in the mesophase is rather small and similar to that found in the isotropic melt. Presumably molecular rotation in the two phases is not so dissimilar, provided correct allowance is made for the anisotropic ordering potential.

Dr. C . I(. Yun (University of Strathclyde) said: Does Meier et al. agree that their relaxation equation is derived or derivable from the Liouville’s equation? If the Liouville’s equation is multiplied by each of the mass and the angular momentum of a particle and integrated partially for a uniform and stationary system, we obtain

af+v. (vf) = 0 at

cvf+V( f k T ) - M f = 0 dt

where the particle inertia is neglected and proper definitions of and M are introduced and where V = a/ad and d = g/p. Assumptions, M = -Vu and u = uN+uE and a definition P = f’exp {u,/kT), change (A) to

, D = -V(%)+V.

What do these authors assume about the induced dipole moment of a molecule? The magnitude of its anisotropy may not be negligible as compared with the per- manent moment. It is interesting to consider it because its relaxation time is com- parable to that of the permanent moment. A generalization can be made as follows. Assume that

(C) - uN fkT = *Ax2 + O(x4), - u,/kT = fly + +ay2 + O(y3, E3), where x = d. I,, y = d . e, e = z / E , p = bE and cc = aE2 and where b and a are material properties. This leads to

(D) aF

22,- = (AxVX + V) . (- PFVy - MFJJVY + VF) EE TF, at

and

neglecting O(p2, ap, or2). TFo = O - F , = 1+py++ay2,

When E 11 L, we have y = x and therefore D . V F = (1 -x2)F”-rF‘ = V F , Y = 2x-Ax( l - x 2 ) , (F)

The case E I L is similar if one makes same assumptions as in the paper.

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G E N E R A L DISCUSSION 139

I was a little confused about their eqn (3.18) because it is difficult to accept a set of computed numerical values as a proof. In my opinion, (3.18) comes from (El and (H) ;

Fo = Fm+o * b, = cMBM, aM = cMAM- (1) Thus, (3.18) is not an independent condition to be proved but a consequence that should hold if both (E) and (H) are true.

Can they justify the following assumption made in (3.14) and (3.19) when E I L? F = 1 +g cos 4, g = g(x, t ) (J)

Separation of variables with F- 1 = h(t)$(x)L(4) gives 8F at 1-x

22,- = vF G 2zoh‘ +ch = ;1”+m2;1 = (1 -x2>$”--r$’ +( c - Z 2 ) $ = 0, (K)

such that (J) seems equivalent to assuming that, among the engenfunctions 3, = ;1(4), only cos 4, which corresponds to the eigenvalue m2 = 1, is important. Is this reasonable especially when the field is alternated?

Dr. G. Meier (Freiburg i. Br.) (communicated): In answer to the question of Yun, our relaxation equation is indeed derivable from Liouville’s equation, since the latter is a continuity equation. The polarization due to the induced dipole moment exhibits a dispersion at frequencies which are orders of magnitude higher than the relaxation frequency of the permanent dipole moment. Therefore the induced dipole moment is of no importance for the relaxation times considered in our paper. Moreover, the generalization proposed by Yun introduce terms of higher order in E which were outside the scope of our paper.

It is true that the appearance of BM as a coefficient of xM in eqn (3.17) is not acci- dental, since for o = 0 and Eo = E, the F of eqn (3.17) must coincide with the t = 0 value of the F of eqn (3.13). Moreover, the coefficient of cu in the denominator of eqn (3.17), 2ro/cM, is obtained by considering directly eqn (2.10) for the alternating field case. However, even though eqn (3.18) is expected to hold, it is not a mathe- matically trivial relation. In particular, it is not immediately obvious to what extent it can be reproduced by the first few eigenfunctions. The M = 1 eigenfunction of the 4-dependent part of the separated equation (2.1 1) is in fact the only one that contributes. This result is exact and is due, in the static case, to the initial condition eqn (3.16) or, equivalently, to

F(t = 0) = 1 +(,uE/kT)sin 0 cos 4. The result is also exact for the alternating field case, since for o = 0 the static limit must be obtained.

Dr. C. K. Yun (University of Strathclyde) (communicated) : Concerning Meier’s reply to my question, I would make the following points. It is well known that the induced dipole moment exhibits a dispersion at frequencies in the optical range. Neglect of this dispersion has already been implied by assuming that a = a/E2 is a constant in eqn (C) of my comment. However, there exists another dispersion of the induced moment (or, rather, of its anisotropy) in the frequency range of our interest. Eqn (H) exhibits a term i02z0 in the permanent against icu4z0 in the induced contri- butions to F, which show that their effects on the dispersion are hardly separable.

My insistence on keeping the term O(E2) is better explained when EIIL, in which case eqn (C) is equivalent to

- u/kT = px +*(a + A)x2 + O(x3).

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140 G E N E R A L DISCUSSION

Here, I see no a priori reason for discriminating a term of O(x2) against another of the same order. Neglect of the term +ax2 is perhaps justifiable for a class of materials, in which I a I < I p I for a reasonable range of E. Tsvetkov and Marinin deter- mined the values of a = a/E2 and b = p / E for seven different compounds, every one of which becomes nematic when melted, by measuring the Kerr constants of their dilute solutions. Their results indicate that the magnitudes of I a I and I p I are comparable in each case.

There may yet be another dispersion that the theory should be able to explain. Williams and Heilmeier observed a dielectric dispersion in nematic p-azoxyanisole in the range co/27c < 10 s-l. They also observed some other ferroelectric properties of the sample, contrary to Davies’ remark on the paper by Meier et al.

Dr. G. R. Luckhurst (University of Southampton) said: In their paper, Martin et al. have shown how the Debye theory might be extended to extract the rotational correlation time from dielectric relaxation experiments with a nematic mesophase. I would ask the authors if they have used their analysis to determine the temperature dependence of the relaxation time zo in a nematic mesophase? My question is prompted by the results which my colleagues and I have obtained from an electron resonance investigation of molecular motion in 4,4’-dimethoxyazoxybenzene. One reason for employing this technique is that it is possible to achieve an unambiguous separation of effects caused by thermal fluctuations in the director, and those due to molecular reorientation with respect to the d i r e ~ t o r . ~ In contrast, such a separation is not possible in nuclear magnetic resonance studies of spin relaxation in the meso- phase. An unexpected feature of our results is the decrease in the rotational correla- tion time for the paramagnetic probe, vanadyl acetylacetonate, from 1.0 x s at 129°C to 0.45 x 10-lo s at 102°C. This temperature dependence is opposite to that found for the isotropic melt. Presumably the increase in orientational order with decreasing temperature facilitates molecular motion and so reduces the rotational correlation time.

Dr. G. Meier (Inst. Angew. Festkorperplzysik, Freiburg) said: In reply to Luck- hurst, experimental investigations on dielectric relaxation times in nematic meso- phases were made by W. Maier and G. Meier (ref. (2)), H. Weise and A. Axmann (ref. (3)), F. Rondelez (ref. (4)), F. Rondelez, D. Diguet and G. Durand (Mol. Cryst. Liq. Cryst., 1971, 15, 183), all showing an increase of the relaxation time with decreas- ing temperature. In our paper we did not quantitatively evaluate the temperature dependence of the retardation factor, but according to our theory the potential parameter A grows larger as the temperature decreases. Therefore, a larger retarda- tion factor and consequently a larger relaxation time, is predicted for lower tempera- tures.

Dr. J. A. Janik (Krakow) said: I do not undertsand the reason for the second (high frequency) maximum of 8’; in the paper by Meier et al. It seems to me that the only motions which are sufficiently fast to give the high relaxation are those con- nected with rotational around the long axis. If so, they should contribute rather to 8; than to E;. I would also ask Meier what is the relation of his results to Tsvetkov’s

V. N. Tsvetkov and V. Marinin, Zhur. Ekspt. Teuret. Fiz., 1948, 18, 641 ; (Chem. Abstr., 43, 3675d). R. Williams and G. Heilmeier, J. Chem. Phys., 1966, 44, 638. S. A. Brooks, G. R. Luckhurst and G. F. Pedulli, Chem. Phys. Letters, 1971,11, 159.

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GENERAL DISCUSSION 141

results published last year in Vest. Leningr. Gos. Univ.? If I remember rightly, Tsvetkov introduces a hindrance of molecular rotations which in some way must correspond to Meier’s retardation parameter.

Dr. G. Meier (Inst. Angew. Festkorperphysik, Freiburg) said: Referring to the question of Janik on the dispersion of the dielectric constants at microwave frequencies in our paper we treated the case of a dipole moment parallel to the long molecular axis. In a real molecule, such as p-azoxyanisole, we have to take into account two points : (i) the reorientation of the dipole components associated with the end groups is not appreciatively influenced by the nematic potential since these groups can rotate independently of the main body of the molecule. Therefore the contribution of these dipole components to the dielectric polarization exhibits the ordinary Debye relaxation in the microwave frequency region. (ii) The dipole component that is fixed in the body of the molecule can be split into a component pII parallel to the long molecular axis and a component pI perpendicular to it. In our paper it is argued that the reorientation of p, is not significantly affected by the nematic order. The p, contribution to the dielectric constants therefore shows the usual dispersion at microwave frequencies. In conclusion, in a real nematic liquid crystal there will be two dielectric dispersion regions : the usual Debye relaxation in the microwave frequency region and the relaxation process at radio frequencies caused by the nematic potential.

Janik also mentioned the work of V. N. Zwetkoff (Vestnik Leningr. Univ. Phys. Chem., 1970, 25, ser. 1, no. 4, 26 and Sou. Phys.-Crystallogr., 1970, 14, 573) on the theory of the dielectric anisotropy in nematic liquid crystals. This author tried to explain the static dielectric properties by introducing two parameters of the hind- rance to molecular rotation and adjusting these parameters to give the dielectric constants that are observed experimentally. This procedure is not free of arbitrariness and contradicts the theory of Maier and Meier (W. Maier and G. Meier, 2. Natur- forsch., 1961, 16a, 615) who assumed the full polarization to be present below the first dispersion region. In fact, at d.c. or low frequencies, there is no reason why the dipoles should not be distributed according to the Boltzmann factor. Any hindrance to the reorientation of dipoles does not affect the static distribution but is important for relaxation phenomena.

Dr. P. L. Nordio (University of Padua) (communicated) : We have derived a solution of the diffusion equation, in the presence of both nematic and electric field, which allows us to take into account more general forms of the orientational potential and the effect of the diffusion tensor anistropy. In the “ static ” case, the equation for F ( 0 , t ) becomes

or, in operator form : 1 aF Q F = --

D, at’

The nematic pseudopotential UN is expanded as a series of Legendre polynomials :

UNJRT = ZC~L,P,(COS j?).

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142 G E N E R A L DISCUSSION

The matrix representation of Q in the basis of the eigenfunctions D{',(aPr> of the angular momentum operator for the symmetric top VA, is

QYr' = - j(j+l)+ - -1 t n 2 djk+ r (::>I & x A n [ j ( j + l ) - k ( k + l ) - n ( n + l ) ] C ( n , k , j ; 0, l)C(n, k , j ; 0, m).

n

The general solution is

F ( 0 , t ) = 1 xji exp (sit> . X ; ' C ~ ~ ( O ) D / , , ( ~ > ,

where cci and xi are the eigenvalues and eigenvectors of the matrix Q(lm).

to be the usual Maxwell-Boltzmann distribution function. (2) considered by Martin, Meier and Saupe, we find

The coefficients cp(0) are fixed by the initial conditions, which require F(Q, 0) For the cases (1) and

P2E p,(t) = - C X j i exp (ai l ) X,'(D&,)[C(j, 1, n ; 0. O)J2, kT

Here a and Xrefer to the matrix Qoo, p and Y refer to the matrix elo. The averages (D&,) are performed over the undisturbed nematic distribution. (Work in progress, by P. L. Nordio, G. Rigatti and U. Segre, University of Padua).

Prof. Manse1 Davies (University College of Wales, Aberystwyth) said : Much could be added to our appreciation of molecular behaviour in liquid crystals if the usual optical measurements were accompanied by electric permittivity studies. Commer- cially available bridges allow a discrimination of 1 in lo6 in c0 whose increment above n i reflects the molecular dipole strength and orientation. In view of the pronounced orientational order, e.g., in the nematic phase, it is perhaps surprising that little sign of ferro-electric character appears in most liquid crystal systems : cf. P.A.A. ; co-6.0. This implies that over the measured samples a close approach to antiparallelism in the dipole elements along any axis is attained statistically. The antiparallelism is not only established with respect to the optic axis, but also for the dipole components (which could in chosen examples be large) orthogonal to that axis (fig. 1). The double randomization of the polar elements for such polarizable molecules in such anisotropic fields must be regarded as a special cir- cumstance in liquid crystal structures. The size of the units achieving dipole ran- domization, i.e., controlling the net effective dipole polarization observed, could lie between the molecular pair and some much larger aggregate. Are the dimensions of the non-dipolar aggregates established and do we understand why the polarizability elements are so well ordered whilst the dipoles are effectively in the random state of normal liquids ?

I also present some results of Dr. T. Krupkowski, obtained in Prof. Piekara's laboratory (Laboratory of Chemical Physics Al. Zwirki i Wigury 101, Warsaw). Short duration (ca. 1 ms) adjustable voltage pulses are accompanied by permittivity measurements at 3 MHz in the same directions as the applied field. Normal polar liquids (chlorobenzene, diethyl ether, etc.) would show a non-linear response at these fields (i.e., up to 25 kV cm-') equivalent to a Inaximum change in permittivity from the low field value of [ - Ac(HF)] ca. 1 x 10 '.

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GENERAL DISCUSSION 143

The much larger effects [ - A&(HF)] ca. 1000 x illustrated in fig. 2 are not due to electric current, heating or other adventitious effects as they virtually disappear at the nematic--+isotropic transition temperature (135°C). The 3 MHz frequency can be accepted as giving essentially go (cf. fig. 12 of Martin, Meier and Saupe). The enormous [-A&(HF)], e.g., at 119"C, up to 5 kV cm-l, is in the sense of a '' dielectric saturation " effect and implies that a high degree of orientation of the dipolar units giving rise to the c0 21 6.0 value in P.A.A. is achieved at especially low fields. This is unlikely to be the orientation of individual molecules. More probably it is the approach to complete orientation of much larger aggregates, i.e., domains or sub-domains within the nematic phase, the electric field between such domain

E/(kV cm-')

- Q02

-0.04

4 -0.06

- 4Os

-0,m

-0.12

d = 1.51 IIUII

FIG. 1.

units being effectively much lower than that between a polar molecule and its neigh- bours in the liquid state. This is understandable as the domains themselves are organized in such a way that their net electric effect approaches that of a non-dipolar unit (uide, absence of ferro-electricity). The non-rigidity of the domain structure (i.e., the imperfections in the alignment along the optic axis) leads to an enhanced degree of orientation of molecular units within the domains at higher fields; this effect can only come in at field strengths approaching or exceeding that between the molecular units. (These are not necessarily individual molecules, although that is one possibility.) The enhancement of alignment of molecular units along the direction of the applied high field and/or the decoupling of anti-parallel dipoles within the domains will lead to the positive A&(HF) effect which comes in at fields above 10 kV cm-I. In the latter (decoupling) form the effect is well established by Piekara in such polar liquids as nitrobenzene (cf. J. Chern. Phys., 1956, 25, 795).

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144 G E N E R A L DISCUSSION

As the temperature rises the polarity due to the residual dipole anisotropy in the domains (or sub-domains) decreases so that the initial fall [A&(HF)] is less; and the domains also bccorne internally less rigid in their molecular organization so that the positive effect comes in at lower fields. As the transition to the isotropic phase is approached all the features due to the domain structure are reduced but there is still a very large [ - A&(HF)] - 500 x at 10 kV cm-l near the transition temperature which disappears abruptly at that point.

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1971

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:04.

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