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We introduce a simple mean-field lattice model to describe the behavior ofnematic elastomers. This model combines the Maier-Saupe-Zwanzig approach toliquid crystals and an extension to lattice systems of the Warner-Terentjevtheory of elasticity, with the addition of quenched random fields. We usestandard techniques of statistical mechanics to obtain analytic solutions forthe full range of parameters. Among other results, we show the existence of astress-strain coexistence curve below a freezing temperature, analogous to theP-V diagram of a simple fluid, with the disorder strength playing the role oftemperature. Below a critical value of disorder, the tie lines in this diagramresemble the experimental stress-strain plateau, and may be interpreted assignatures of the characteristic polydomain-monodomain transition. Also, in themonodomain case, we show that random-fields may soften the first-ordertransition between nematic and isotropic phases, provided the samples areformed in the nematic state.

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