Nonlinear Elasticity of the Sliding Columnar Phase

Abstract

The sliding columnar phase is a new liquid-crystalline phase of matter composed of two-dimensional smectic lattices stacked one on top of the other. This phase is characterized by strong orientational but weak positional correlations between lattices in neighboring layers and a vanishing shear modulus for sliding lattices relative to each other. A simplified elasticity theory of the phase only allows intralayer fluctuations of the columns and has three important elastic constants: the compression, rotation, and bending moduli, $B$, $K_y$, and $K$. The rotationally invariant theory contains anharmonic terms that lead to long wavelength renormalizations of the elastic constants similar to the Grinstein-Pelcovits renormalization of the elastic constants in smectic liquid crystals. We calculate these renormalizations at the critical dimension $d=3$ and find that $K_y(q)\sim K^{1/2}(q)\sim B^{-1/3}(q)\sim (\ln (1/q){)}^{1/4}$, where $q$ is a wavenumber. The behavior of $B$, $K_y$, and $K$ in a model that includes fluctuations perpendicular to the layers is identical to that of the simple model with rigid layers. We use dimensional regularization rather than a hard-cutoff renormalization scheme because ambiguities arise in the one-loop integrals with a finite cutoff.

This file contains 18 pages of double column text in REVTEX format and 6 postscript figures

References in corpus (2)

• Sliding Columnar Phase of DNA-Lipid Complexes
• Elasticity, Shape Fluctuations and Phase Transitions in the New Tubule Phase of Anisotropic Tethered Membranes

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