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Rev. A 45, 5632 1992. 14 E. M. Aver'yanov and M. A. Osipov, Sov. Phys. Usp. 160, 89, 206 1990 Sov. Phys. Usp. 33, 365 1990 ; ibid., 206 1990 ibid., 880 1990 .
Character of the N D 2 D h (0,d ) phase transition in diskotic liquid crystals E. M. Aver’yanova) L. V. Kirenski Physics Institute, Siberian Branch of the Russian Academy of Sciences, 660036 Krasnoyarsk, Russia

~Submitted 22 November 1995! Pis’ma Zh. E´ksp. Teor. Fiz. 63, No. 1, 29–32 ~10 January 1996! The first experimental data on the orientational ordering of a diskotic reentrant nematic N D are presented. The data show that the phase transition N D 2D h(0,d) is a strong first-order transition with a large jump DS.0.2 in the orientational order parameter S of the molecules. This indicates an anomalously strong coupling between the columnar and orientational ordering of the molecules and explains the absence of fluctuational divergence of the elastic moduli K 11 and K 22 in the nematic phase near this transition. © 1996 American Institute of Physics. @S0021-3640~96!00601-8#

1. The character of the phase transition N D 2D h(0,d) remains an intriguing puzzle in the physics of liquid crystals ~LCs! in spite of the fact it must always be a first-order transition.1–3 On the one hand, the diskotic phase D h(0,d) can occur only for sufficiently large values of S;2 this is supported by the experiments of Refs. 4 and 5, which give S.0.9. For such values of S the susceptibility x of the nematic phase is low,6 and by analogy to the N2SmA transition in ordinary calamite liquid crystals7 one would expect that the jump DS at the point T ND of the transition N D 2D h(0,d) should be small. This corresponds to the recent results obtained with computer modeling by the moleculardynamics method,8,9 which predict a weak jump DS.0.01 with S(T ND )50.920.95. On the other hand, in the case when the transition N D 2D h(0,d) is close to a secondorder transition, a fluctuational increase of the elastic moduli K 11 and K 22 of the nematic phase should be observed near T ND ; 1,2,10 this is not confirmed experimentally.11,12 Finally, the mean-field molecular-statistical theory3 and Monte Carlo computer modeling of an athermal system of diskoid particles13 predicts a strong first-order N D 2D hd transition with a large jump in S. The experimental situation is not clear because there are no data on S in the N D phase of objects which possess a D phase. In the present letter we report the first experimental data on S in the reentrant nematic phase N D ; these findings can account for the above-noted discrepancy between theory and experiment. 2. The objects of investigation were two homologs of the derivatives of truxene 33

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LC-1

R: 2OC~O!C9H19

LC-2R: 2OC~O!C13H27

with the sequences of phase transitions12 68

81.34

138

280

LC21: K→ N D ↔ D rd ↔ D h0 ↔ I, 61

56

80.34

112

241

LC22: K → ~ D ↔ ! N ↔ D ↔ D ↔ I, hd D rd hd where the numbers indicate the temperature ~°C! of the corresponding transitions. Data on the refractive indices n o,e (l5589 nm! were used to determine S(T) in the N D phase.12 We now introduce the parameters A53( g t 2 g l )/( g l 12 g t ) and Q5 e a /( e¯ 21), where gW is the molecular polarizability tensor, the axis l is normal to the plane of the molecule, e j 5n 2j , e a 5 e o 2 e e , and e¯ 5( e e 12 e o )/3. In the absence of p -electron conjugation of the fragments of the rigid aromatic molecular core, the low values of the birefringence Dn5n o 2n e , 12 the spatially ramified position of the molecular fragments, and the substantially nonlocal character of the molecular polarizability make it possible to neglect the anisotropy of the tensor of the local field of a light wave in LC–1,2 when determining S. 14 The modulus S of the tensor order parameter S i j 5S(r i r j 2 d i j /3), where r i, j are the components of the director r, is given by the expression AS ~ T ! 5Q ~ T ! .

~1!

Since there is no p -conjugation of the molecular fragments, the possible changes induced in the conformation of the peripheral chains R by a change in T and S do not affect g¯ and have a negligible effect on g a and A. In the N D phase the temperature dependence Q(T) can be approximated by Haller’s formula15,16 Q ~ T ! 5Q 0 ~ 12T/T n ! b n ,

~2!

where the parameters Q 0 50.292,T n 5378.9 K, b n 50.174 for LC–1 and Q 0 50.206, T n 5362.1 K, and b n 50.136 for LC–2 correspond to the minimum standard deviation of the experimental values of Q from the values of Q calculated from Eq. ~2!. The curves Q(T) are displayed in Fig. 1. For A5const and S 0 51 ~Ref. 16! the ratios Q(T)/Q 0 give the temperature dependences S(T) displayed in Fig. 2. For both LCs within the reentrant N D phase the parameter S varies over the range 0.60–0.72, which is much lower than the typical values S.0.9 for the diskotic phases D h(0,d) . 4,5 For LC–2 near the transition N D 2D hd an anomalous increase of S, which is characteristic for first-order transitions N2SmA close to a tricritical point, does not occur.17,18 Therefore the transition N D 2D h(0,d) is characterized by a large change DS.0.2, it is a strong first-order transition, and it is not accompanied by strong pretran34

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FIG. 1. Q(1) versus t512T/T n in logarithmic coordinates for the reentrant nematic phase N D of the liquid crystals LC-1 ~h, top and left! and LC-2 (s, bottom and right!.

sition fluctuations of the local diskotic ordering in the nematic phase. This explains the absence of fluctuational growth of the modulus K 11 near T ND . 11,12 The large magnitude of DS agrees qualitatively with the results of Refs. 3 and 13 and disagrees substantially with the data obtained from molecular-dynamics computer modeling,8,9 just as in the case of the magnitude and temperature dependence of S(T) near a transition N D 2I.16

FIG. 2. Temperature dependence of the orientational order parameter S of the molecules in LC–1 ~left side! and LC–2 ~right side!. The solid lines were calculated from Eq. ~2!. T ND is the temperature of the transition N D 2D rd . 35 JETP Lett., Vol. 63, No. 1, 10 Jan. 1996 E. M. Aver’yanov 35

3. For the transition N D 2D h(0,d) the order parameter S is noncritical, and the change DS(T ND ) is due to its interaction with the critical order parameter for this transition — W which fixes the two-dimensional lattice.1,2 The lowest-order the multcomponent vector c invariant taking this interaction into account in the thermodynamic potential of the D h phase, has the form DF(S i j , cW )52lS u cW u 2 ~Ref. 2!, where u cW u is the modulus of the vector cW , and l5const .0. For this reason, in the D h phase S5S N 1l x u cW u 2 , and the large magnitude of DS, together with the large S N (T*T ND ).0.7, the weak change in S N (T), and the low value of the nematic susceptibility x ~Ref. 6!, points to an anomalously large interaction constant l. This qualitatively distinguishes the transition N D 2D h(0,d) from the first-order transitions N2SmA, for which the analogous coupling constant between the nematic and one-dimensional smectic ordering of the molecules is small17 and high values of DS occur only near the transition N2I, with low values of S N , a strong temperature dependence S N (T), and a high susceptibility x . 6 The weak temperature dependence S(T) in the D h phase4,5 also indicates that u c (T ND ) u is close to saturation and that N D 2D h is a strong first-order transition. The anomalously high value of l is evidently associated with the presence of quite long peripheral chains R, a necessary condition for columnar ordering of molecules in real objects. Indeed, stratification of the N D phase at the N D 2D h transition, with segregation of the aromatic cores of the molecules and aliphatic chains, leads to a jump DS(T ND ) for the cores because the cores tend to be close-packed along the axis of a column, strongly restricting the freedom of orientational fluctuations of the molecular axes l relative to the column axis. The tendency toward stratification increases with the length of the chains R, and at the same time the existence region of the N D phase becomes smaller. This shrinking corresponds to an increase in l, 2 and for sufficiently long chains R and high values of l the D h phase arises directly from the isotropic liquid.2 This work was supported by Grant 5F0028 from the Krasnoyarsk Science Foundation. a!

e-mail: [email protected]

E. I. Kats, Zh. E´ksp. Teor. Fiz. 75, 1819 ~1978! @Sov. Phys. JETP 48, 916 ~1978!#. E. I. Kats and M. I. MonastyrskiŽ, JETP Lett. 34, 519 ~1981!. 3 G. E. Feldkamp, M. A. Handschy, and N. A. Clark, Phys. Lett. A 85, 359 ~1981!. 4 D. Goldfarb, Z. Luz, and H. Zimmermann, J. de Phys. ~Fr.! 42, 1313 ~1981!. 5 V. Rutar, R. Blinc, M. Vilfan et al., J. Phys. ~Paris! 43, 761 ~1982!. 6 E. M. Aver’yanov, Zh. E´ksp. Teor. Fiz. 97, 855 ~1990!. @Sov. Phys. JETP 70, 479 ~1990!#. 7 P. de Gennes, The Physics of Liquid Crystals, Clarendon Press, Oxford, 1974 @Russian translation, Mir, Moscow, 1977#. 8 M. D. de Luca, M. P. Neal, and C. M. Care, Liq. Cryst. 16, 257 ~1994!. 9 A. P. J. Emerson, G. R. Luckhurst, and S. G. Whatling, Mol. Phys. 82, 113 ~1994!. 10 J. Swift and B. S. Andereck, J. Phys. Lett. 43, L-437 ~1982!. 11 V. A. Raghunathan, N. V. Madhusudana, S. Chandrasekhar, and C. Destrade, Mol. Cryst.–Liq. Cryst. 148, 77 ~1987!. 12 T. Warmerdam, D. Frenkel, and R. J. Zijlstra, J. Phys. ~Paris! 48, 319 ~1987!. 13 J. A. C. Veerman and D. Frenkel, Phys. Rev. A 45, 5632 ~1992!. 14 E. M. Aver’yanov and M. A. Osipov, Sov. Phys. Usp. 160, 89, 206 ~1990! @Sov. Phys. Usp. 33, 365 ~1990!#; ibid., 206 ~1990! @ibid., 880 ~1990!#. 15 I. Haller, J. Solid State Chem. 10, 103 ~1975!. 1 2

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E. M. Aver’yanov, JETP Lett. 61, 816 ~1995!. M. A. Anisimov, JETP Lett. 37, 11 ~1983!. 18 E. M. Aver’yanov, P. V. Adomenas, V. A. Zhuikov, and V. Ya. Zyryanov, Zh. E´ksp. Teor. Fiz. 91, 552 ~1986! @Sov. Phys. JETP 64, 325 ~1986!#. 16 17

Translated by M. E. Alferieff

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