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CRITICAL BEHAVIOUR ABOVE A NEMATIC TO SMECTIC A PHASE TRANSITION
D. d’Humières, L. Léger
To cite this version:
D. d’Humières, L. Léger. CRITICAL BEHAVIOUR ABOVE A NEMATIC TO SMECTIC A PHASE TRANSITION. Journal de Physique Colloques, 1975, 36 (C1), pp.C1-113-C1-116.
�10.1051/jphyscol:1975120�. �jpa-00215897�
JOURNAL DE PHYSIQUE Colloque C1, supplkment au no 3, Tome 36, Mars 1975, page C1-113
Classification
Physics Abstracts 7.130
CRITICAL BEHAVIOUR ABOVE A NEMATIC TO SMECTIC A PHASE TRANSITION
(*)D. D'HUMIERES and L. LEGER (**) Laboratoires d'Electronique et de Physique Appliquke
3, avenue Descartes, 94450 Limeil-Brevannes, France
Resumb. - Les fluctuations du param6tre d'ordre smectique au-dessus d'une transition smec- tique A-nematique donnent naissance a des anomalies pour certains des coefficients de friction du nkmatique. En utilisant la dynamique d'une transition de Fredericks, on a mesurk la dkpendance en tempkrature de la viscosite de torsion y 1 au-dessus d'une transition smectique A-nematique faible- ment ler ordre : y l diverge quand on approche de la transition, mais trop faiblement pour qu'on puisse en dkduire un exposant critique. On a aussi observk des effets prktransitionnels importants pour la constante Blastique de divergence KI.
Abstract. - The fluctuations of the local order parameter above a nematic to smectic A phase transition give rise to singularities in the elastic constants, and in the viscosities of the nematic.
We have used the dynamics of a Fredericks transition to measure the temperature dependence of the twist viscosity y I above a weakly first order nematic to smectic A phase transition. y I diverges as the transition temperature is reached, but too weakly to allow the determination of a critical exponent. We also observe a large pretransitional increase of the splay elastic constant K I .
1. Introduction. - Since the first observations of smectic order fluctuations in the nematic phase, there has been a considerable interest in the static and dynamic properties of nematics near a nematic to smectic A phase transition.
Theoretically, mainly two kinds of approach have been developed :
- Assuming the transition to be second order, De Gennes has related the critical behaviour of the bend and twist elastic constants to the smectic correlation length t ( T ) [I]. This correlation length is defined from a development of the free energy in powers of the order parameter $ = $, eiq a complex function of r, whose amplitude $, specifies the density of the layers and whose phase cp specifies the position of the layers.
q satisfies a conservation law because the funda- mental state is invariant by a translation of the layers as in the 1 transition of helium.
Assuming the same critical exponent as for helium, De Gennes has predicted :
F. Brochard has extended those considerations to dynamic properties of both the smectic and nematic
(*) Supported by DRME under contract no 73 34 778 00 480 75 01.
(**) Permanent address : Laboratoire de Physique des Solides, BLtiment 510 91405 Orsay, France.
phases in the hydrodynamic regime q< < 1, using dynamic scaling laws [2]. She predicts the divergence of some of the friction coefficients of the nematic.
Independent calculations, using mode-mode coupling approximation, have confirmed her results [3], and we expect the twist viscosity y , and one of the Leslie friction coefficients a, [41 to diverge as
At the same time, McMillan, developing a time- dependent Landau theory approach, has predicted the divergence of the same friction coefficients [5], but in the framework of a a mean field approximation which leads to :
d y , N 6a,
- -
(T - T,)-'.~.More recently, Ma, Halperin and Lubensky have pointed out the fact that, because of the strong coupling between the nematic director no and the smectic parameter $, the transition should always be, at least weakly, first order [6]. However, if the first order character of the transition is sufficiently weak, we still expect the behaviour of a second order transition, with an effective transition temperature T* smaller than T,.
Experimentally a lot of work has been devoted to these transitions. For the static properties, several methods have been used to measure the bend and twist elastic constants close to the transition, and exponents of 0.66 have been reported [7, 8, 91. But
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975120
AND L. LEGER the controversy is still open, and other authors have
reported exponents of 0.5 [lo] which seem to depend on sample purity. For the dynamic properties the work seems more difficult : evaluations of the coeffi- cient Sy,
show that it is expected to be very small with respect to the non-divergent contribution to y , [2]. A pretran- sitional increase in y, has in fact already been observed [11], but the measurements were not done sufficiently close to T, to determine a critical exponent (AT = T
-
Tc > 0.3 OC).In this paper we report on measurements of the twist viscosity y, above a nematic to smectic A phase transition, using the dynamics of a Fredericks transi- tion [12], in a temperature range
2. Experimental conditions. - We have mainly worked on butyloxybenzylidene octylaniline (I) which has a nematic to smectic A phase transition at 63 OC with a small heat of transition (80 cal/mole). This compound is interesting for several reasons :
- From NMR measurements no jump in the orientational order parameter S can be detected at the transition, indicating very a weak coupling between S and the smectic order parameter $ [I 81.
- There is only one molecule per smectic layer, while there are certainly two in the more widely studied compound CBOOA [13].
- Strong planar anchoring can be achieved using oblique-incidence evaporation of silicon monoxide on the glass plates [15] ; no striations occur in the distorted sample, while they are present in CBOOA and prevent measurements for AT < 0.1 OC.
The temperature of the sample is controlled by means of an electronically regulated oven, with two successive heating stages 1161. The stability is evaluated as better than 2 x OC over the time of an experi- ment, and the lateral gradient in the useful part of the sample is of the same order of magnitude.
In order to measure the twist viscosity y,, we have chosen to follow the dynamics of the relaxation of the distorsion of the nematic when the magi~etic field H i s suddenly varied from values larger than the Frede- ricks critical field Hc to values smaller than Hc [12].
Two geometries can be used : the planar geometry (elsewhere called geometry 1) for which the molecules are oriented parallel to the glass plates, and the magnetic field applied normal to them, and the homeo- tropic geometry (geometry 3) for which the molecules are normal to the glass plates and H parallel to them.
(1) This compound was synthetized in the Laboratoire de Physique des Solides at Orsay by L. Liebert and L. Strzelecki.
The two corresponding Fredericks critical fields are respectively
(d is the sample thickness, X , the anisotropy of dia- magnetic susceptibility, K , and K3 the splay and bend elastic constants). If H is larger than Hc, a distorted configuration of the director appears. If H is suddenly decreased to a value smaller than Hc, the distortion relaxes exponentially, with a relaxation time
- 1 H2i x a -
$1,
z , ( H ) = ---
7"
where
1/7
is an effective friction coefficient which takes into account the effect of the hydrodynamic motion induced by the rotation of the director (backflow corrections). For geometry 1, those corrections are expected to remain always very small, even close toTc
(;;
- <1
, and we can neglect them, whilein geometry 3
:ly3
-- 0.8 far from T,.An easy way to follow the relaxation of the distortion is to record the transmitted intensity of a laser beam polarised at 450 with respect to the rest direction of the molecules no in geometry 1, or with respect to H for geometry 3. When the distortion relaxes to zero, this transmitted intensity passes through maxima and minima : the phase difference between the light polarized parallel and perpendicular to no(to H for geometry 3) is proportional to 8& (8, = (n,n,)) in the mid-plane of the nematic slab, and for large time t, the succession of the minima is given by an exponential law e-"'". Even very close to T, we have been able to record more than ten minima in the transmitted intensity (we use samples of thickness 240 pm), and we evaluate the relative accuracy for the determination of z at 2 %.
From the field dependence of z, we can deduce
~ i l y : and X ~ I Y ? .
3. Results and discussion. - The temperature depen- dence of y h w e have deduced from those z measure- ments and from independer measurements of X , [9]
is shown on figure 1. For geometry 1 the backflow corrections are negligible, and y: gives a measurement of the twist viscosity y,. For both geometries a diver- gence is observed, but it remains a rather small effect : even for AT = 8 x OC, the pretransitional increase of y , is not larger than the background term roughly evaluated by extrapolating the temperature dependence of y , for AT > 5 OC. In such conditions it seems completely hopeless to deduce a critical expo- nent from those measurements as long as we cannot accurately determine the background term.
Thus we have tried to, at least, determine if the observed behaviour of y , corresponded to a mean
CRITICAL BEHAVIOUR ABOVE A SA-NEMATIC TRANSITION C1-115
FIG. 1. - Temperature dependence of the effective viscosities
yT.3 for planar and homeotropic geometries. The difference between the two curves comes from backflow corrections which are negligible for geometry 1 and not for geometry 3. A divergence is observed as AT = T- Tc goes to zero, but is too weak to
determine a critical exponent.
FIG. 2. - Temperature dependence of K3/y3* obtained from the relaxation time of the distorsion in zero magnetic field. The inset shows a comparison of the experimental results for K3Iyf with different curves calculated from
In the four curves A = 0.53 x 10-6, a =: 1.4 (c. g. s. units) ; v l = 0.66, v2 = 0.33. The two full curves correspond to B = 0.38, b = 0.4 and the two dotted lines curves to B = 0.44,
b = 0.2 (c. g. s. units).
field approximation or not, by comparing it to K,.
In principle, MacMillan predicts K3/yl to remain constant close to T,, while with a behaviour similar to the il transition of helium we expect K3/y1 to diverge like t1l2.
The temperature dependence of K,/~: deduced from extrapolation of z,(H) at zero field is shown on figure 2.
In the inset, the measured values for AT < 2.5 OC are compared to values calculated from
with v, = 0.66 and v, = 0.33.
K3(T), determined from the same z3(H) measure- ments is compatible with a 0.66 exponent [9], and allows a rather accurate determination of A and a : A = 0.53 x a = 1.4.
B is adjusted to obtain the right value in the K3/yl background term, and b to obtain the right K3/yl value for AT = 1 O C : B = 0.38 and b = 0.4 (c. g. s. units).
Our K3/y, measurements seem to agree better with a twist viscosity diverging as AT-'.^^ than
but this is not at all a determination of the critical exponent of y
,,
as the uncertainty in the determination of b is rather large. The only thing we can say is that, even for a reduction of 15 % of the background whichFIG. 3. - Transitional increase of the splay elastic constant K1, deduced from the Fredericks threshold field in geometry 1.
C1-116 D. D'HUMI&RES AND L. LGGER leads to dividing b by a factor 2, our results are not
compatible with yl and K3 diverging in the same way.
This last point contradicts recent measurements of KJy, by Salin and Durand [17] in CBOOA.
Figure 3 shows a more surprising result we have obtained by measuring the Fredericks critical field for geometry 1. An important pretransitional increase in K, is observed, and the ratio K J y , remains almost constant in the whole temperature range studied. Up to now we have no theoretical explanation for this behaviour.
4. Conclusion. - We have measured the twist viscosity y , for 40.8, using the dynamics of a Frede-
ricks transition, very close to a nematic to smectic A phase transition (AT > 8 x OC). We have observed a pretransitional divergence, which was too weak to allow the determination of the critical exponent. A comparison of y , to the bend elastic constant K, (K3/yl can directly be deduced from the relaxation time of the Fredericks distorsion in zero magnetic field), seems to indicate that K, diverges more rapidly than y,, and is more favourable to the predictions of dynamical scaling laws than to the time dependent Landau theory approach.
A pretransitional increase of the splay elastic constant K, has also been observed, and remains unexplained up to now.
References
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[I31 DELOCHE, B., CHARVOLIN, J., to be published (same confe- rence).
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