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Divergence of the bend elastic constant above a nematic to smectic a quasi second order phase transition
Volume 44A, number 7
DIVERGENCE
13 August 1973
PHYSICS LETTERS
OF THE BEND ELASTIC
CONSTANT
TO SMECTIC A QUASI SECOND ORDER
ABOVE
A NEMATlC
PHASE TRANSITION
L. LEGER Laboratoire de Physique des Solides, FacultPdes Centre d’Orsay, 91405 Orsay, France
Sciences,
Received 25 May 1973 Measurements of the Fredericks critical field and of the diamagnetic susceptibilities have been made on the whole nematic range of p-butoxy benzilidenep’-octyl aniline. The deduced bend elastic constant K, shows a critical behaviour in (T- T,(NA) )*.” above the nematic to smectic A transition. Measurements of the diamagnetic susceptibilities in the smectic A and B phases are also reported.
The presence of short range smectic order in the nematic phase, first observed by De Vries on X-rays diagrams [ 11, leads to an increase of the bend and twist elastic constants (Kg and K, respectively) as the smectic layers do not accept twist or bend deformations, because of their fixed thickness. This effect was first observed by Gruler [2]. From an analogy between smetic A and superconductors, De Gennes [3] has predicted that the K2 and K3 pretransitional enhancements should be proportional to (T- TJ-7/(2-n). Recently, Cheung and Meyer [4] have reported on measurements of K3 for a weakly first order nemat+smectic A phase transition, and determined a critical exponent v = y/(2-r)) = 1, significantly different from the prediction of 0.66 [3]. We present here preliminary results on another determination of K, near the transition. We have measured the well known Fredericks critical field from homeotropic to planar, H, = (n/d) dwa (d is the sample thickness, xa = xl1- x1 the anisotropic part of the diamagnetic susceptibility) over the whole nematic range of p-butoxy benzilidene-p’-octyl aniline (B.B.O.A.)*. This product has a nematic to smectic A phase transition at about 63”C, with a very weak latent heat (83 Cal/mole) [5]. The sample, observed between crossed polarisers, is enclosed in an over which temperature is regulated at at better than 10-20C, over one day. Good homeotropic orientation is obtained by treating the glass * The B.B.O.A. was synthetized in our lab by L. Liebert and L. Srezlecki.
plates with hexadecyltrimethyl-ammonium bromid 161, and is optically controlled. The magnetic field is increased very slowly (< 100 G/mn), and the critical fieldH, is taken as the field at which a sudden rise in the transmitted intensity is observed, corresponding to the tilt of the molecules in the middle of the slab. The rate of varying H is always controlled to be slow enough so that no difference can be noticed in H, whether H is increased or decreased. If working sufficiently closed to r,, a new magnetic field threshold is observed (larger than If,) above which a regular array of stripes parallel to H appears. The periodicity is of the order of the sample thickness, and the polarisation of the transmitted light indicates a molecular orientation out of the plane (If, no) (no is normal to the glass plates). In order to deduce the temperature dependence of K3 from the measurement of H,(T), we need a determination of xa. We have measured this anisotropy, using a P.A.R. vibrating sample magnetometer. Fig. 1 shows the temperature dependence of x,, (curve a) over the whole mesomorphic range. The applied magnetic field (8 kG) was sufficient to maintain the orientation of the molecules parallel to the field in the smectic phases, if obtained by slowly cooling from the oriented nematic. No discontinuities have been noticed at the nematic-smectic A or smectic A-smectic B transitions. Curve c shows the temperature dependence of xa, deduced form xa = $(x1, - jj) where jj is the diamagnetic susceptibility in the solid and in the isotropic liquid, which is observed to be temperature independent as in P.A.A. and M.B.A.A. [7]. 535
Volume
44A, number
7
PI IYSICS LETTERS
13 August
lY73
j”5
6
55
IPig.1. Temperature dependence of the diamagnetic suxeptibilities. curve a) susceptibility parallel to the molecules, curve b) observed susceptibility for a non oriented smectic sample, curve c) anisotropy of the diamagnetic susceptibility y;,. Fig. 7 shows the temperature dependence of K3. deduced from these measurements. We do observe a large increase of K, as the smectic transition is reached Assuming that, besides the divergent term, the normal contribution to K3 is proportional to the square of the order parameter (i.e. xi), we have tried to fit our Kj temperature dependence with the law K3 =AAT--V+B~~. We have varied B in reasonable limits. taking into account the values of K, far from T c(AN) ’ Then, we are able to fit the K, enhancement 6K, = K, ~ Bxi with a AT-’ law. For each sample used, the transition temperature was taken as the temperature at which the specific defects, corresponding to the bending of the smectic layers, begin to appear when slightly touching the upper glass plate enclosing the sample [8]. The inset of fig. 2 shows a typical loglog plot, for B = 4.5 X IO7 CGS. A linear behaviour is well observed up to AT = 2”C, giving a critical exponent v = 0.64. The main uncertainty in the determination of that exponent comes from the uncertainty in the determination of the background term Bxi. The maximum variation of B compatible with the experiments (4 X IO7
536
1:1g. 2. 1 empt‘raturc dependence bend elastic constant.
of the
variations in u larger than 0.60 < v < 0.70. lo get free of that ambiguity. we are now undertaking measurements for AT< 0.1 “C. However. our data seems to show a critical behavio of K, in AT -“. with an exponent v = 0.65 f 0.05. c~ompatible with DC Gennes’ prediction of 0.66. and significantly different from Cheung and Meyer’s results. This last point may be explained by the fact that. in our case. the transition is closer to a second order phase transition than in their case.
References 12. de Vries, Jfol. Crystal and Liq. Crystal 10 (1970) 31: Acta Cryst. A25 (1969) 5 135. 121It. Gruler, Z. Naturforschg, to bc published. [ 31 P.G. De Gennes, Sol. St.‘Comm. 10 (1972) 753. 141 L. Cheung and R.H. Meyer, Physics Lett. 43A ( 1973) 261. [S ] G.W. Smith. to be published. [6] J.E. Proust, L. Ter-Minassian and E. Guyon, Sol. St. Comm. 11 (1972) 1227. [7) J. l’rost and 11. Gasparoux. (:.I<. Acad. SC. Paris 272 (1971 1168. [Xl M. Delaye, R. Kibotta and G. Durand, to be published. \ I ]
DIVERGENCE
13 August 1973
PHYSICS LETTERS
OF THE BEND ELASTIC
CONSTANT
TO SMECTIC A QUASI SECOND ORDER
ABOVE
A NEMATlC
PHASE TRANSITION
L. LEGER Laboratoire de Physique des Solides, FacultPdes Centre d’Orsay, 91405 Orsay, France
Sciences,
Received 25 May 1973 Measurements of the Fredericks critical field and of the diamagnetic susceptibilities have been made on the whole nematic range of p-butoxy benzilidenep’-octyl aniline. The deduced bend elastic constant K, shows a critical behaviour in (T- T,(NA) )*.” above the nematic to smectic A transition. Measurements of the diamagnetic susceptibilities in the smectic A and B phases are also reported.
The presence of short range smectic order in the nematic phase, first observed by De Vries on X-rays diagrams [ 11, leads to an increase of the bend and twist elastic constants (Kg and K, respectively) as the smectic layers do not accept twist or bend deformations, because of their fixed thickness. This effect was first observed by Gruler [2]. From an analogy between smetic A and superconductors, De Gennes [3] has predicted that the K2 and K3 pretransitional enhancements should be proportional to (T- TJ-7/(2-n). Recently, Cheung and Meyer [4] have reported on measurements of K3 for a weakly first order nemat+smectic A phase transition, and determined a critical exponent v = y/(2-r)) = 1, significantly different from the prediction of 0.66 [3]. We present here preliminary results on another determination of K, near the transition. We have measured the well known Fredericks critical field from homeotropic to planar, H, = (n/d) dwa (d is the sample thickness, xa = xl1- x1 the anisotropic part of the diamagnetic susceptibility) over the whole nematic range of p-butoxy benzilidene-p’-octyl aniline (B.B.O.A.)*. This product has a nematic to smectic A phase transition at about 63”C, with a very weak latent heat (83 Cal/mole) [5]. The sample, observed between crossed polarisers, is enclosed in an over which temperature is regulated at at better than 10-20C, over one day. Good homeotropic orientation is obtained by treating the glass * The B.B.O.A. was synthetized in our lab by L. Liebert and L. Srezlecki.
plates with hexadecyltrimethyl-ammonium bromid 161, and is optically controlled. The magnetic field is increased very slowly (< 100 G/mn), and the critical fieldH, is taken as the field at which a sudden rise in the transmitted intensity is observed, corresponding to the tilt of the molecules in the middle of the slab. The rate of varying H is always controlled to be slow enough so that no difference can be noticed in H, whether H is increased or decreased. If working sufficiently closed to r,, a new magnetic field threshold is observed (larger than If,) above which a regular array of stripes parallel to H appears. The periodicity is of the order of the sample thickness, and the polarisation of the transmitted light indicates a molecular orientation out of the plane (If, no) (no is normal to the glass plates). In order to deduce the temperature dependence of K3 from the measurement of H,(T), we need a determination of xa. We have measured this anisotropy, using a P.A.R. vibrating sample magnetometer. Fig. 1 shows the temperature dependence of x,, (curve a) over the whole mesomorphic range. The applied magnetic field (8 kG) was sufficient to maintain the orientation of the molecules parallel to the field in the smectic phases, if obtained by slowly cooling from the oriented nematic. No discontinuities have been noticed at the nematic-smectic A or smectic A-smectic B transitions. Curve c shows the temperature dependence of xa, deduced form xa = $(x1, - jj) where jj is the diamagnetic susceptibility in the solid and in the isotropic liquid, which is observed to be temperature independent as in P.A.A. and M.B.A.A. [7]. 535
Volume
44A, number
7
PI IYSICS LETTERS
13 August
lY73
j”5
6
55
IPig.1. Temperature dependence of the diamagnetic suxeptibilities. curve a) susceptibility parallel to the molecules, curve b) observed susceptibility for a non oriented smectic sample, curve c) anisotropy of the diamagnetic susceptibility y;,. Fig. 7 shows the temperature dependence of K3. deduced from these measurements. We do observe a large increase of K, as the smectic transition is reached Assuming that, besides the divergent term, the normal contribution to K3 is proportional to the square of the order parameter (i.e. xi), we have tried to fit our Kj temperature dependence with the law K3 =AAT--V+B~~. We have varied B in reasonable limits. taking into account the values of K, far from T c(AN) ’ Then, we are able to fit the K, enhancement 6K, = K, ~ Bxi with a AT-’ law. For each sample used, the transition temperature was taken as the temperature at which the specific defects, corresponding to the bending of the smectic layers, begin to appear when slightly touching the upper glass plate enclosing the sample [8]. The inset of fig. 2 shows a typical loglog plot, for B = 4.5 X IO7 CGS. A linear behaviour is well observed up to AT = 2”C, giving a critical exponent v = 0.64. The main uncertainty in the determination of that exponent comes from the uncertainty in the determination of the background term Bxi. The maximum variation of B compatible with the experiments (4 X IO7
536
1:1g. 2. 1 empt‘raturc dependence bend elastic constant.
of the
variations in u larger than 0.60 < v < 0.70. lo get free of that ambiguity. we are now undertaking measurements for AT< 0.1 “C. However. our data seems to show a critical behavio of K, in AT -“. with an exponent v = 0.65 f 0.05. c~ompatible with DC Gennes’ prediction of 0.66. and significantly different from Cheung and Meyer’s results. This last point may be explained by the fact that. in our case. the transition is closer to a second order phase transition than in their case.
References 12. de Vries, Jfol. Crystal and Liq. Crystal 10 (1970) 31: Acta Cryst. A25 (1969) 5 135. 121It. Gruler, Z. Naturforschg, to bc published. [ 31 P.G. De Gennes, Sol. St.‘Comm. 10 (1972) 753. 141 L. Cheung and R.H. Meyer, Physics Lett. 43A ( 1973) 261. [S ] G.W. Smith. to be published. [6] J.E. Proust, L. Ter-Minassian and E. Guyon, Sol. St. Comm. 11 (1972) 1227. [7) J. l’rost and 11. Gasparoux. (:.I<. Acad. SC. Paris 272 (1971 1168. [Xl M. Delaye, R. Kibotta and G. Durand, to be published. \ I ]