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Mechanical study of the ferroelastic smectic A to smectic C phase transition
R. Bartolino, Geoffroy Durand
To cite this version:
R. Bartolino, Geoffroy Durand. Mechanical study of the ferroelastic smectic A to smectic C phase transition. Journal de Physique, 1984, 45 (5), pp.889-893. �10.1051/jphys:01984004505088900�. �jpa- 00209822�
Mechanical study of the ferroelastic smectic A to smectic C phase transition
R. Bartolino (*) and G. Durand
Laboratoire de Physique des Solides, Université de Paris-Sud, 91405 Orsay, France (Reçu le 24 octobre 1983, accepté le 9 janvier 1984)
Résumé. 2014 Nous mesurons la relation entre les contraintes et les déformations instantanées normales aux couches, dans le cristal liquide butyloxyphènyl nonyl benzoate (40P 90B) autour de la transition de phase smectique A ~ smectique C. De la dépendance en température des déformations et contraintes critiques qui induisent mécanique-
ment le changement de phase, nous déduisons les paramètres de Landau de la transition. La compression critique
de flambement moléculaire en phase A est 30 % plus grande que la dilatation critique pour réaligner les molécules du C normalement aux couches. Cet effet inattendu pourrait s’expliquer par un écart au modèle de champ moyen,
ou une influence non symétrique de défauts.
Abstract 2014 We measure the instantaneous stress/strain relationship associated with layer compression in the
smectic liquid cristal butyloxy phenylnonyl oxybenzoate (40P 90B) across the smectic A ~ C phase transition.
The temperature dependence of the critical stress and strain required to induce mechanically one phase from the other, allows the Landau parameters of the transition to be determined. The critical compressional stress of mole-
cular buckling in phase A is unexpectedly 30 % larger than the critical dilative stress in the C phase which realigns
the molecules normal to the layers. This could be accounted for by a departure from the mean field, or by a non symmetric influence of defects.
Classification
Physics Abstracts
61.30 - 62.20
Smectic A liquid crystals (SA) are layered systems, with molecules normal to the layers. Many SA com- pounds undergo when lowering their temperature,
a second order phase transition towards a smectic C
phase (Sc), with the same layered structure, but with molecules tilted inside the layers [1].
The SA -+ Sc transition has been mostly studied by optical methods [2, 3], or by X-rays [4, 5]. In fact,
the SA --+ Sc transition is a ferroelastic transition, and should be very sensitive to mechanical fields. For
instance, when the molecules tilt inside the layers, they change the layer thickness, so that a thin « home- otropic » sample, with layers parallel to fixed boundary glass plates, is subjected to normal dilative stresses.
It is well known [7, 8] that a uniaxial stress normal
to the layers can produce a large shift of the A - C transition temperature. In this paper, we present a mechanical study of a second order SA -+ SC phase
transition. We measure essentially the stress-strain
relationship [9] for layer compression or dilation,
versus the temperature, around the transition tempe-
(*) Unical Liquid Crystal Group-Fisica, Univ. Calabria,
87100 Cosenza, Italy.
rature T AC. In principle from such data, we should
be able to deduce the parameters of the Landau free energy describing the transition.
To describe the transition, we use the classical [1]
Landau free energy density :
where 0, the molecular tilt with respect to the normal
to the layer, is the order parameter. We neglect VO
terms, assuming that the tilt remains uniform in the
sample. The last two terms represent the standard
expansion of f in powers of 0. Bl, assumed to vary like a (T - T AC) (a > 0), induces the A -+ C transi- tion at T = TAC* The first term represents the elastic energy stored in a layer compressive strain E. cx 02
represents the coupling between molecular tilt and
layer compression, in the presence of fixed boundary plates. As previously explained [3], a % 1 is a molecular rigidity factor expressing the departure of the mean
molecular conformation from a rigid rod for which
a = 1. B and C are elastic moduli independent of
the temperature T.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01984004505088900
890
This description is valid for a perfect smectic, without defects. In fact, it is known [10] that, in a reasonably short time, the internal stresses induced by the molecular tilt can be relaxed by, say, the emission of edge dislocations. It is always possible, however, to apply a rapid enough normal strain g(t)
on the sample and to measure the instantaneous induced stress a(t), so that the relaxation process has no time to develop. To give a realistic description
of what happens close to the transition, one must distinguish now between the two initial situations :
a) Unstressed sample in the smectic A phase (T > TAC). For a rapidly applied strain, one can
calculate the instantaneous induced stress from (1),
without considering any relaxation process. Mini-
mizing f versus 02, one finds an angular tilt 0 induced
by the applied strain 8 :
In fact, the condition ()2 > 0 implies 8 8th with
Eth is negative. It corresponds to the compression
which induces the C phase [7].
For values of I s 1, smaller than 18th I (8 > 8th)
the sample behaves as a normal smectic A, with a layer compression modulus B. Let us compute the apparent compression modulus B’ of the induced Sc phase, for 8 8th. From (2) and (1) after differentiation with respect to s, we obtain for the stress the expression:
with
and
B’ is smaller than B, because of the induced molecular tilt above the threshold stress alh-
b) Unstressed sample in the Sc phase (T TAc).
In the C phase, we assume that edge dislocations have
completely relaxed the internal stresses created by
the molecular tilt, for zero applied strain. The tilt
now has its equilibrium value :
without any quenching from fixed plates parallel to
the layers. This quenching, however, will be efficient
for a rapidly applied strain s(t). We can write the
new (instantaneous) equilibrium tilt 0’(s) as :
The compressional term of (1) is now written for small tilt angles as :
Minimizing the new free energy with respect to 6 one obtains
which corresponds to (2) for 00 = 0. Note that 6 is positive for compression as expected. Equation (10)
is valid as far as we remain in the Sc phase. Comparing (10) and (7) shows the correspondence between a
temperature change and a layer strain.
If the strain becomes too large (and positive), the Sc-S A transition is induced. The smectic behaves
now as a normal SA material, of layer elastic constant B.
The threshold (dilative) strain is now given by :
For strains smaller than 8th’ the apparent layer come pression modulus obtained from (1), (9) and (10) is again B’. The threshold stress is always :
symmetrical through the transition.
The experimental set-up used in this experiment
has already been described [9]. Because of the relaxa- tion processes already discussed, we measure the
transmitted stress through a homeotropically aligned sample submitted to a rapidly varying step-like strain.
The rise time of the strain is shorter than 100 gs. The
sample we use is 40P 90B [II], which gives a mono- tropic second order SA-SC phase transition [12],
when cooling from the SA phase at TAC = 62°C.
The homeotropic orientation is obtained by silane coating. The sample thickness is d = 50 J.1m. The maximum plate dilation created by a voltage excita-
tion of 400 V on the piezoelectric ceramics is 2 000 A,
which results in maximum strains of about 4 x 10-3.
The sample holder is placed in an oven, with an
electric temperature control better than 5 x 10-2 °C.
The good quality of the sample can be checked opti- cally under a polarizing microscope.
We first start with the sample in the A phase, a
few degrees above TAC, Applying small strains
(s - 10-4) we measure the corresponding instanta-
neous stress a, by the method explained in [9], i.e.
we apply a step like strain of amplitude s. The trans-
mitted stress is a damped exponential-like signal.
We measure the initial (zero delay) amplitude 6 of
this time dependent stress. We obtain the value of the elastic constant Bfor the SA phase : B=2.6 x 10-’ dyn./
cm’. We now increase the amplitude of the strain and
keep measuring u(s). For large positive values of s (i.e. corresponding to the sample dilation), we keep
observing the same linear dependence 6 = Bs as
for small strains (until we eventually reach the layer
undulation instability [8] threshold which is not
represented here). For compressive strains, on the
other hand, we observe a sudden decrease of slope of
the a(s) plot, for a critical strain e.h as shown on
figure 1. We have reproduced the same experiment at
different temperatures. Within our present accuracy, the small signal measured B is temperature inde-
Fig. 1. - Stress-strain curves. The results for the smectic A phase are sketched on the left at two different temperatures : dots are for T - T AC = 0.2 OC, squares for T - TAC = 0.5 °C. The results for the smectic C phase are drawn on the right,
T - TBc = - 0.2 oC (black squares) and T - TAC = - 0.5 OC (crosses).
pendent, up to 5 °C above TAC’ On the other hand,
Eth (and the associated threshold stress 6th3) varies linearly with temperature, as shown in figure 2 for
8th and in figure 3 for Qth. From these data, we find
Fig. 2. - Threshold strain Eth versus temperature, in smectic A (right) and smectic C (left).
I
Fig. 3. - Threshold stress Qte versus temperature. Negative
values are for smectic A and positive for smectic C.
and
which results in B = 2.6 x 10’ dyn./cm2, in agreement with the value previously deduced from the low signal slope.
892
Fig. 4. - Compressibility modulus B versus temperature. On the right B measured in the smectic A phase. On the left B’
measured in the smectic C phase.
We now cool down the sample into the smectic C
phase and reproduce the same experiment. The a’(s’) data are plotted in figure 1. We have plotted in figure 4 the observed B and B’, versus AT = T - TAC.
In phase A, B is constant, within our present accu- racy. In the C phase, B’ is almost constant for AT
- 0.3 °C. B’ = 6.0 x 106 dyn./cm2, which results in
B’/B = 0.23. Closer to Tc, we observe a small increase of B’. We know that the temperature gradient inside
the sample is of the order of 5 x 10-2 °C, much
smaller than 0.3 °C. This increase of B’ could be accounted for by a departure from the mean field
behaviour close to TAC, as observed recently on
another compound [2]. We now increase the applied
dilative strain. We note (Fig. 1) that the cr’(8’) diagrams
show an angular point as expected. The coordinate I
at th of this angular point depends on AT, as shown
on figure 3. We note that the 6th plot is almost conti-
nuous through the transition. However, Qth is no longer exactly linear in AT close to TAC. This may also be an effect of departure from mean field theory,
or to a temperature dependence of a. Within our
present accuracy, we can approximate at’h by the
linear variation :
30 % smaller than I C1th [ in the SA phase. We have also plotted on figure 2 the corresponding values of Eth which, with the same accuracy, can be represented by :
coherent with B’ = 6 x 106 dyn./cm2 already mea-
sured with small strains.
We can now calculate the parameters of the Landau free energy. Using B’IB = 0.23 gives (BIC) ot2= x22 3.35, i.e. : C/a2 - 3.9 x 106 dyn./cm2.
We know, from a previous independent optical
and X ray measurement [3] on the same compound,
that the tilt angle is : e2 - - [1.2 x 10-2/°C] AT =
- BJ_IC. Using the two experimental values of alh and
atth, we find C = 5.8 x 105 dyn. /CM2 , B 1. = [6.9 x 103/oC].1 T dyn./cm2 and a = 0.39 for the A phase, and
C= [2.8 x 105 dyn. /CM2 B 1. = [3.4 x 103 dyn./cm/°C] AT
and a = 0.27 for the C phase.
We must compare the present values to the one
already measured [3] on the same compound a = 0.51.
This value compares much better with a = 0.39 calculated in the A phase than with a = 0.27 from the C phase. A possible explanation could be a change in
the density and nature of defects when cooling the sample down to the C phase. Optically, the C sample
appears less homogeneous, because of the azimuthal
degeneracy of the molecular tilt. This could induce
a change of B across the transition and account for the unexpected difference between 6,h and ’
We believe that the data obtained from the SA phase are more reliable.
In conclusion, we have measured the stress/strain relationship associated with layer compression across
a smectic A to smectic C ferroelastic phase transition.
Combined with the previous determination of the molecular tilt in the layers (the order parameter),
our measurements allow the determination of the parameters (elastic and saturation constants) which
allow the simplest Landau description of the SA -+ Sc
transition. We find a lack of symmetry in our data
between the A and the C phase, which can be explained by the fact that the transition is not mean field, or
by some change of the defect nature or density across
the transition.
Acknowledgments.
We thank Dr. Malthete from College de France,
for the supply of the 40P 90B sample.
References
[1] DE GENNES, P. G., The Physics of Liquid Crystals (Oxford Press) 1975.
[2] GALERNE, Y., Thèse d’Etat, Orsay (1983).
GALERNE, Y., J. Physique Lett. 44 (1983) L-461.
[3] BARTOLINO, R., DURAND, G., DOUCET, J., Ann. Phys.
Fr. 3 (1978) 389.
[4] DOUCET, J., Thèse d’état, Orsay (1978).
[5] GUILLON, D., SKOULIOS, A., J. Physique 38 (1977) 79.
[6] RIBOTTA, R., MEYER, R. B., DURAND, G., J. Physique
Lett. 35 (1974) L-161.
[7] RIBOTTA, R., DURAND, G., J. Physique 38 (1977) 179.
[8] BARTOLINO, R., DURAND, G., Phys. Rev. Lett. 39
(1977) 1346.
[9] BARTOLINO, R., DURAND, G., Ann. Phys. Fr. 3 (1978)
257.
[10] DURAND, G., J. Chim. Phys. 80 (1983) 119.
[11] MALTHETE, J., BILLARD, J., CANCEILL, J., GABARD, J., JACQUES, J., J. Physique Colloq. 37 (1976) C3-1.
[12] BARTOLINO, R., MALTHETE, J., BARRA, O., J. Physique
41 (1980) 365.
