Dynamic properties near the columnar-crystalline phase transition

2014 Dynamic quantities are computed near the transition from the columnar to the crystalline phase. The enhancement from order parameter fluctuations of the viscosities 03BD1 and 03BD3 is found to be proportional to the first power of the correlation length. We briefly describe how the 03C9-1/2 divergence of viscosities predicted in the columnar phase by Ramaswamy and Toner is suppressed near the transition to the crystalline phase. Tome 45 No 11 I 1~ JUIN 1984 LE JOURNAL DE PHYSIQUE LETTRES J. Physique Lett. 45 (1984) L-509 L-513 le’~ JUIN 1984, Classification Physics Abstracts 64.70M A columnar phase with D6h symmetry [1] was experimentally found by Chandrasekhar, Sadashiva, and Suresh [2]. Early work on the general properties of this phase and the transitions to other phases was due to Kats [3]. Based on the expression for the elastic energy given by Prost and Clark [4], a model which included coupling of the order parameter to elastic degrees was recently presented by the authors, and its static properties near the columnar-crystalline phase transition were discussed [5]. The hydrodynamics in the columnar phase was obtained by Prost and Clark [4]. Since the transition from the columnar to the crystalline phase is predicted to be second order [5], it is of particular interest to examine the dynamics near this transition. We focus on dynamic behaviour in this report. Compared with the columnar phase, the crystalline phase corresponds to the appearance of a density wave parallel to the C 6 axis, with wave vector qo p 2 ~ , where d is the lattice constant along C6 axis. Near the columnar-crystalline transition, fluctuations of the density with wave Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019840045011050900 L-510 JOURNAL DE PHYSIQUE LETTRES vectors q near + qo = (0, 0, + q II) become important and thus their coupling to the other variables should be taken into account. We will take the part of the density with wave vectors near + qo as our order parameter, m, where m(k, t) is the Fourier transform of the density, and the integral domain D is taken to be two small separated spheres centred at ± qo respectively. The total free energy of the system can then be written as