On the existence of the thermomechanical terms of Akopyan and Zel’dovich in cholesteric liquid crystals

ABSTRACT

We revisit a theoretical paper of Akopyan and Zel’dovich about the thermomechanical coupling terms in nematic liquid crystals. We show that the expressions of these terms given by these authors must be corrected to satisfy the Onsager reciprocity relations, a point already stressed by Pleiner and Brand in 1987. We then extend this calculation to the cholesteric phase and show that there are no additional terms in the uniaxial approximation of this phase. Finally, we give the correspondence between the Akopyan and Zel’dovich terms and those calculated by Pleiner and Brand in 1996 by making a different choice for the forces and the fluxes in the theory.

Graphical Abstract

KEYWORDS:

• Cholesteric liquid crystals
• thermomechanical effects
• out-of-equilibrium thermodynamics

Acknowledgements

We thank Efim Kats for fruitful discussions and Alain Dequidt for pertinent and useful remarks about the group theory calculations.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. A gradient of an electric or chemical potential would produce the same effects, as was stressed by de Gennes in his book on liquid crystals [24].

2. In this case, the cholesteric phase is still described by a single director n which rotates along the helical axis.

3. Note that in Reference [24], the role of the fluxes and forces is reversed because de Gennes prefers to write the forces as a function of the fluxes, in opposition to our choice of writing the fluxes as a function of the forces. Nevertheless, our choice of forces and fluxes is completely equivalent to the convention of de Gennes because the swapping transformation and preserves the Onsager relations and the time-reversal behaviour of each quantity.

4. Note that in this equation, the second-order tensors D and are by convention flattened in one-dimensional vectors.

5. Several terms of the decomposition presented in the appendix were eliminated here because D is symmetric and traceless ().

6. Several terms of the decomposition presented in the appendix were eliminated here because .