The elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

Abstract

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau, and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random-fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

17 pages, 7 figures

References in corpus (3)

• Nematic-Isotropic Transition with Quenched Disorder
• Isotropic-Nematic Transition in Liquid-Crystalline Elastomers: Lattice Model with Quenched Disorder
• Statistical models of mixtures with a biaxial nematic phase

Cited by in corpus (6)

• Lattice statistical models for the nematic transitions in liquid-crystalline systems
• Enhancement of nematic order and global phase diagram of a lattice model for coupled nematic systems
• Hard-needle elastomer in one spatial dimension
• Modulated phases in a three-dimensional Maier-Saupe model with competing interactions
• Uniaxial and biaxial structures in the elastic Maier-Saupe model
• Tricritical behavior of soft nematic elastomers