Molecular orientational correlations in isotropic phases of nematogenic and smectogenic compounds

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Molecular orientational correlations in isotropic phases of nematogenic and smectogenic compounds

A. Gohin, C. Destrade, H. Gasparoux, Jacques Prost

To cite this version:

A. Gohin, C. Destrade, H. Gasparoux, Jacques Prost. Molecular orientational correlations in isotropic phases of nematogenic and smectogenic compounds. Journal de Physique, 1983, 44 (3), pp.427-432.

�10.1051/jphys:01983004403042700�. �jpa-00209615�

Molecular orientational correlations in isotropic phases

of nematogenic ^and smectogenic compounds

A. Gohin, ^C. Destrade, ^H. Gasparoux and J. Prost

Centre de Recherche Paul Pascal, ^Domaine Universitaire, 33405 Talence Cedex, ^France (Reçu ^le 22 juillet 1982, révisé le 29 octobre, accepté le 10 novembre 1982)

Résumé. - L’influence de la proximité ^d’une phase smectique ^{A sur les} phénomènes prétransitionnels ^en phase isotrope ^{est étudiée sur une série dans} laquelle ^{il est} possible ^{de faire varier} l’écart des températures de transition

TN1 - TNA (I

isotrope, ^N

nématique, ^A

smectique A) ^{et même} de l’annuler. La déviation au comporte-

ment champ moyen ^est imputée ^au couplage ^{entre les} fluctuations des ordres orientationnels et translationnels.

Abstract.

We report ^{on the} pretransitional behaviour in isotropic phases ^of compounds belonging ^{to chemical}

series such that the transition temperatures TN1 ^and TNA (I

isotropic, ^N

^{nematic, A}

^smectic A) ^{may be} brought ^close together, ^{sometimes even to} give ^a single T1A transition. The departure from mean-field behaviour is

interpreted ^{in terms of a} coupling between the fluctuations of the translational and orientational order.

Classification

’

Physics ^Abstracts

61.30

64. 70E

1. Introduction.

It is now well known that, upon

approaching ^{a nematic} phase ^{from the} isotropic ^side,

a nematogenic system ^exhibits strong angular ^corre-

lations which manifest their existence in _many diffe- rent ways [1] particularly ^{in the} divergence ^{of the} depolarized Rayleigh ^{cross section} according ^{to a} (T - TN,)-’ ^law [2, 3] (TN,, ^{the absolute} stability ^limit

of the isotropic phase, ^{is not} very different from the first order transition temperature TNI). ^{However, even}

in this early work, Stinson and Lister noticed a

departure from this mean-field behaviour close to the

NI transition [3].

Other techniques ^{also lead to} the conclusion that mean-field theory fails close to TNI [4, 5]. Although quite ^{a number of} theoretical explanations ^{have been} proposed [6, 7, 8], ^we felt that there was still a need for further experimental information. In particular, ^the

influence of smectic order had never been taken into account despite ^the proximity ^{of such} phases ⁱⁿ many

compounds [9]. ^We report ^{here on} results obtained Table I.

Transition temperature of the studied p-n-alkoxybenzilidene-p’-n-butylaniline ^series (n04) from fliissige ^{kristalle in tabellen} (D. Demus, ^{H. Demus and H.} Zaschke-Leipzig,1974).

I

Isotropic, ^N

^Nematic, SA

^{Smectic A,} [ ] ^{indicate a} monotropic transition, temperatures in celsius.

(*) ^{Estimate at 80.3.}

(**) ^This value is the one of TN, - T1A (IA is the smectic A-Isotropic transition).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01983004403042700

428

Table II.

Transition temperatures ^{in celsius} of the studied p-methoxy-p’-alkyl ^tolanes p-methyl benzilidene-p’- n-butylaniline (1-4) ^{and 7-5 one}

with the p-n-alkoxybenzilidene-p’-n-butylaniline ^series

n04 (n

1, 8), ^the p-methoxy-p’-n-alkyltolane ^series [10] (from ethyl ^to pentyl), ^{the 7-5 one :} p-n-heptylben- zoate-p’-n-pentanoylphenyl ^series [11] and the p-n-

butylaniline-p’-methyl-benzilidene ^series.

The n04 series was chosen for the large changes ^{in the}

nematic and smectic existence domains it provides (Table I) : ^{the lower} homologues ^{do not reveal} any smectic phase ^while exhibiting ^a large ^{nematic exis-}

tence range, whereas the higher homologues ^{show no}

or a small nematic existence _range. Thus, ^{one can} vary the difference ( T N, - TNA) ^from negative ^values (monotropic TNt) ^{in 804 to} large positive ^values (estimated > ^{50 °C for} 204).

The tolan series on the other hand does not contain any smectic phase (Table II). Finally, the 7-5 is cha- racterized by ^a negative ^{value of} TN, - TNA ^whilst

the 1-4 does not have _any mesomorphic phase ^at atmospheric pressure (Table II).

If the smectic pretransitional ^{order affects the} nematic angular fluctuations in isotropic phases, ^one

would expect ^this effect to be strong ^{for the} higher homologues of the n04 series (and 7-5), ^{weak for}

the lower homologues ^and negligible ^{in the case of}

1-4 (N.B., ^{a direct} isotropic-crystal ^involves very little

pretransitional phenomena). Expectations concerning

the tolan series are less obvious since although ^{we did}

not observe it, ^{we cannot} preclude ^{the existence of} monotropic ^smectic phases.

In the next section, ^we report ^the experimental

results and in the last one propose ^a theoretical inter-

pretation ^{based on a mode} coupling analysis ^which gives ^a satisfactory ^{account of our} observations.

2. Experimental ^results.

^The pretransitional

orientational order in the isotropic phase ^{of the above}

mentioned compounds ^has been estimated from depo-

larized light scattering measurements. Indeed, ^{in the} vicinity ^{of a} mesomorphic phase transition, or, ^more

generally, ^when angular correlations are very strong, other sources of depolarized scattering ^are negligible [ 1, 3].

Materials for this study ^were synthesized ^{from the} corresponding benzaldehyde ^and butylaniline following the usual Schiff base recipe. ^The synthesized

materials were purified by ^several recrystallizations ⁱⁿ dry ethanol. The liquid crystals ^were filtered into

optical fused-quartz cells of inside dimension 10 x 10 mm. The filtering ^{was carried out under} nitrogen pressure, slightly ^{above the} clearing point, through ^a sintering ^funnel (G7). ^{All the} filtering pro-

cess was performed ^{in a} nitrogen atmosphere ^{in order}

to avoid oxidation of the substances. The mesomor-

phic-isotropic transition temperature ^{was obtained} from direct observation both _upon heating ^and cooling ^the sample ^under study, ^{with no more than}

50 mK hysteresis. ^{We take this} figure ^{to be a measure}

of the high purity ^{of the home} synthesized compounds (Table I).

We used a home made scattering ^set up, the wave-

length of the incident _power being ^{546.1 nm} (an

OSRAM HBO 200 _mercury lamp) ^set up in the 90°

I,,H geometry [ 12]. ^The temperature ^{of the} sample ^was

determined and maintained within a 10 mK accuracy.

At all the studied temperatures, the scattered intensity

of the sample ^was calibrated with a toluene reference.

Close to the NI transition, ^the attenuation of the incident _power, due to scattering, ^{was taken into}

account, and led ^to corrections always smaller than 10 %. ^The TN, ^{drift was found to} be smaller than 100 mK, ^{and was found to be a few 100 mK for the} lower homologues (the ^least satisfactory ^case being

the 104) ^{over a} few weeks. In all cases, the overall

uncertainty ^{in the} IVH(T) ^{value was} kept ^{at the order} of2%.

’

From de Gennes theory, ^we expect [1] : T/IvIiT) oc (T - T:t) (1). ^{Our results} (Figs. ^{1 to} 4) ^do support this prediction ^{in most of the} investigated ^domains.

Close to the nematic-isotropic transition, ^as expected,

a departure ^from linearity ^{is observed with} many

compounds. However, ^{it is} striking ^{to note that with}

204 no such departure exists : the linear domain extends over more than 30 degrees ! ^{On the other} hand, it is clear from observations of figures ^{la and 16}

that the region ⁱⁿ which mean-field theory ^fails

increases strongly ^{when the} difference TNI - TNA

decreases. It is most pronounced ^{in 704} (TN, - TNA ^’

2.5 K), ^{and 804} (TN, - TNA - ^0.5 K) and extends

over practically ^{10 K. A} comparison between the results obtained with 1-4 and 7-5 (Fig. 2) again ^reveals

the importance ^{of the} coupling between smectic-like

( 1) ^Minor corrections are discussed in [12].

Fig. ^la.

Temperature dependence ^{of the} T/IvH ^ratio (IVH ^scattered intensity, incident beam vertically polariz- ed ; scattered beam horizontally polarized) in the n04 series.

The curves are vertically shifted for clarity’s sake. The TN,

values are given in table I. Note the increase of the non-

linear domain with increasing alkyl ^chain length, together

with an odd-even effect.

and nematic-like fluctuations : the direct isotropic- crystal transition of 1-4, should not lead to smectic like fluctuations, and it thus seems natural to observe

a strict linearity ^of T/IvH (due ^{to the} proximity ^{of a}

Fig. 1 b. - Plot of the departure ^of IGQ ^from linearity

versus temperature for the different compounds ^{of the n04}

series (n

^1, 8). ^Note the increase of the non-linear domain with the alkyl ^chain length.

Fig. ^2.

Temperature dependence ^{of the} T/IIH ^{ratio in the}

7-5 and the 1-4 derivatives.

monotropic ^nematic phase). ^{On the other hand, the}

direct smectic-isotropic transition of 7-5 shows _up as a very strong effect detectable as far as 20 K from the

Fig. ^3.

Slope ^{of the} (T /IvH)

f(T) ^curves (in ^{their linear} part) ^{versus the} alkyl chain carbon number in the n04 series.

Fig. 4. - Plot of the experimental (AN - AN) - V ^value (e.g. departure ^of Tyn ^from linearity Fig. lb) ^versus tempera-

ture. AN is estimated from the linear part, AN ^{from the}

exact value of the same ratio at a given temperature. ^The quasi linearity ^obtained with y

1/2 and y

2/3 ^{is in} good agreement ^{with the} theory (16). ^{Note that one can} extrapolate : TN, - Tgj rr ^{3.3 K,} TN, - TNA Na ^{5 K} (7 ^K

if non-classical exponent ^are retained).

430

extrapolated TNI temperature. The tolane results are

less demonstrative presumably because of undetected monotropic ^smectic phases. Finally, ^{let us} point ^out

the existence of sizeable odd-even effects in the slope

of the T/I,,H(T) ^{curves, in} the n04 series (Fig. 3). ^This

confirms the importance ^{of the} alkyl chain confor- mation in the de Gennes-Landau parameter values,

as already pointed ^out theoretically by Marcelja [13].

3. Interpretation.

^It is clear that a satisfactory analysis ^{of the} figures reported ^{above has to include a} coupling between smectic and nematic order _para- meters. Experiments reported ⁱⁿ [9] suggest ^{the same}

necessity. ^{Such a} coupling ^{is known to be} important

in the description ^{of the} nematic-smectic A transi- tion [15, 16]; ^{its effects on the} isotropic-nematic

transition have been discussed in [16] but the result

(obtained) ^there is affected by the omission of the lowest order coupling ^{term. The} approach ^we propose here constitutes the simplest ^{extension to mean-field} theory which allows an understanding of the results.

We integrate ^{out smectic} fluctuations, following ^a technique ^used by Halperin, Lubensky ^{and Ma, to}

discuss the influence of gauge-field fluctuations on the normal-conductor to superconductor transition in type ^I superconductors [ 17J. ^{It is an} approximate

treatment, in that it does ^not consider smectic and nematic fluctuations on an equal footing. ^Smectic

fluctuations are integrated ^out first, whereas the nematics order is kept ^{in the} mean-field approximation.

Within this scheme, ^the non-monotonous behaviour of the scattered intensity ^versus temperature reported

in [4, 9] ^cannot be accounted for. A more rigorous

solution considering simultaneously nematic and smectic fluctuations will be reported elsewhere. The reasonable ^success of de Gennes’ mean-field theory ^of

the nematic-isotropic transition, together ^{with the} good agreement ^{with our} experimental results, justify

our current approach.

The Landau free _energy to be used in this problem

must include the free energies of the nematic isotropic

and of the smectic-isotropic transitions together ^with coupling ^terms between smectic and nematic order parameters (resp : FN, Fs and FNS). They ^can directly ^be

written in Fourier _{space :}

+ higher ^{order terms in} Sii

^{( 1 )}

+ higher ^{order terms in p ,} (2)

(the ^summation convention ^on i and j ^is used).

The expression ^{for F is} exactly the de Gennes free energy of the nematic-isotropic transition : the nematic order parameter Sij ^is represented by ^the anisotropic part ^of any second rank ^tensor properly

normalized :

T*, would be the absolute stability ^{limit of the} isotropic phase, ^{if there were no smectic} coupling (note ^that

it is always ^{different from the actual} transition tem-

perature TN,, ^{even in the absence} of smectic coupling

due to the first-order nature of the nematic isotropic transition). L1 ^and L2 ^are the elastic constants of the nematic order parameter

nematic correlation lengths).

The expression ^for Fs ^{is the correct} covariant gene- ralization of de Gennes smectic energy [14]. ^{It has}

full isotropic symmetry ^{in the absence} of the nematic

coupling. p(k) is the Fourier component ^{of the mass}

density : AS - as(T - TSI) ⁽⁵⁾

TSI is the mean-field smectic A-isotropic ^transition temperature ^{in the absence} of the nematic coupling.

2 n/ko is the natural smectic layer spacing, ^and 03BE2

4 ko ClAs ^{the « bare » smectic} correlation

length.

Finally ^{the terms contained in} FNS express the

coupling ^between translational and orientational order; ^{the first} one, measured by ^{the constant r,} specifies ^the layer ^{direction at the} nematic-smectic A

transition, ^and gives ^{rise to a} Rodbell Bean type ^of effect [14] ; ^its importance is clear from the experimen-

tal evidence of tricritical points ^{due to the} proximity

of TNA ^and TNI [17, 18]. The second one, allowed

by symmetry, ^{is the one} kept ^{in reference} [16] : ^it

does not specify orientational correlation between

smectic and nematic orders, but rather the _compa-

tibility ^{between them} (for instance, it has been used

to explain ^{cases of reentrant behaviour} [20]).

The effective nematic free _energy FN ^{dressed by the}

smectic fluctuations is obtained by taking ^{the func-}

tional integral ^{over all} possible ^p fluctuations :

(In ^{(6) we use the commonly accepted notations for}

functional integrals ; /3

l/kB T).

The inverse scattered mtensity ^{is a measure of the}

effective coefficient IN ^{of the} _Sij harmonic term;

that is :

(without any summation on i and j ^{in this} expression).

Differentiating (6) ^with respect ^to Sij(O) gives :

and a further differentiation yields

Noting ^that

^and keeping ^the mean-field approximation ^for Sij :

where the average ( > p ^is understood to be taken over the _p fluctuations alone.

With

one finds :

and taking ^{account of the} p average isotropy :

Note that a perturbation expansion ^{of the} right hand side of (6) in powers of FNS ^would give ^{the same} result, owing ^{to the connected} cluster theorem. In the harmonic approximation :

and

one thus expects ^the following temperature dependence :

432

The experimental existence of tricritical points ^{of the}

Mac Millan’s type [18, 19], suggests ^that !’ 2 ko/9 As

may be of the order of unity, ^{when T -} Ts, ^{is of the}

order of a few degrees. This leads to the possibility ^of

a corrective term A2 I(T - TSI)3/2 of the order of a

few 106 _erg cm-3 if 03BEs - ^{10 - 6 cm, and 2} n/qo - ^{3 x} 10-’ _cm, which is indeed of the right ^{order of} magni-

tude to explain ^the experimental results. The

X/(T - TSI)1/2 ^{term, which is not} related with directly

observable phenomena ^{in the smectic} phase, ^{is more}

difficult to estimate. It could be either positive ^or negative.

Since the plot ^{of the} experimental ^value T/IvH(T)

is a direct measure of IN ^{one can} readily compare formula (16) ^to experiment. It is clear that, this expres- sion gives ^{at least a} qualitative description ^{of the} AN(T )

bending down close to TNI (provided ^K F 2k 2 lAs,

if K > 0, ^or with K 0). ^For large ( T - TNI), (T - TSt) ^{is also} large and the decrease of 4N ^is

negligible. On the other hand the closer to TN, ^one gets, the smaller (T - Ts,) is, and thus the larger ^the

decrease in AN. ^If TNA is far from TN,, ^{the correction}

will never be sizeable, which is the case with 204. We chose to undertake a quantitative comparison ^of

formula (16) ^{with our 704} experimental ^{results, which}

are the most demonstrative and ^accurate data.

Figure ⁴ shows that a power law with an exponent between - 2 and - 1.5 is indeed appropriate ^for describing the results.

Note that a power law with exponent - 0.5, which corresponds ^{to a} coupled ^order parameter centred around _{a q}

0 wavevector (or ^{the K term}

of formula (15)) ^is clearly ^{ruled out : this further}

establishes ^the smectic character of the coupling

which is responsible ^{for the non} conventional beha- viour of angular fluctuations close to TN,.

In conclusion, ^{we stress we have} given ^{both theo-}

retical and experimental evidence that the proximity

of smectic phases ^does modify the critical behaviour

of mesogens ^{in their} isotropic phases. ^Other couplings

have the potentiality ^of leading ^to qualitatively ^similar effects, thus only ^a conjunction ^{of chemical} physics

and theory ^{allows us to draw a} conclusion. It is also

clear, ^that the theoretical description ^we propose here requires ^further attention, ^{and would} certainly

break down in the case of large smectic and nematic fluctuations.

Acknowledgments.

^{One of us} (J. Prost) ^acknow- ledges stimulating discussions with P. G. de Gennes,

E. Guyon ^{and E.} Dubois-Violette.

References

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193.

[2] STINSON, T. W. and LISTER, ^J. D., Phys. Rev. Lett.

25 (1970) ^503.

[3] STINSON, ^T. W., LISTER, ^{J. D. and} CLARK, ^N. A.,

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[4] LALANNE, ^J. R., POULIGNY, ^{B. and} COLES, ^{H. J. and} MARCEROU, ^J. P., ^Mol. Phys.- To ^be published.

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[9] ^{With the} exception ^{the work} by COLES, H. J. and

STRAZIELLE, C., J. de Phys. ⁴⁰ (1979) ^{895. The}

main line of their approach is identical to ours;

however, ^{the series we} study ^differs from theirs

together ^{with the} analysis of the results.

[10] MALTHETE, J., LECLERCQ, M., DVOLAITZKY, M., GABARD, J., BILLARD, J., PONTIKIS, ^{V. and} JACQUES, J., ^Mol. Cryst. Liq. Cryst. ²³ (1973) ^233.

[11] NGUYEN HUU TINH, ^Thèse d’Etat, ^Bordeaux (1978)

n° 57.

[12] The detailed description ^{of the} set-up ^{and the corres-} ponding analysis ^{is to} be found in : GOHIN, A., Thèse de spécialité, ^{Bordeaux n° 1487} (1979).

[13] MARCELJA, S., Solid State Commun. 13 (1973) ^759.

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[15] HARDOUIN, F., ACHARD, ^{M. F. and} GASPAROUX, H., Solid State Commun. 14 (1974) ^453.

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ROUX, H., ^Solid State Commun. 22 (1977) ^343.

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