Liquid Crystals

3Thermomechanical Effects in Liquid Crystals

Patrick OSWALD¹, Alain DEQUIDT² and Guilhem POY¹

¹Laboratoire de Physique, ENS de Lyon, France

²CNRS, SIGMA Clermont, Clermont Auvergne University, Clermont-Ferrand, France

3.1. Introduction

Any unconstrained thermodynamical system tends to spontaneously evolve in such a way as to homogenize its intensive variables.

Let us take a concrete example. In a conducting fluid containing a solute, for instance, these variables are the temperature, the pressure, the velocity, the chemical potential of the solute and the electric potential. The thermodynamic equilibrium state of this system is reached when all these variables are constant and the free energy is minimal. However, these variables vary in space and time during the equilibration phase. Thus, a non-homogeneous distribution of temperature will result in the appearance of a heat flux. Similarly, a gradient of chemical potential will produce a flux of solute, while a gradient of electric potential and/or velocity will generate an electric current and/or a flux of momentum.

To each of these irreversible phenomena is associated a transport coefficient, which enters into a transport law of the type

[3.1]

where J_k is the flux of the property k, γ_k is the associated transport coefficient and X_k is the gradient force that acts on this property.

In the previous example, these laws were known ...