  When liquid-crystalline elastomers pass through the isotropic-nematic
transition, the orientational order parameter and the elastic strain vary
rapidly but smoothly, without the expected first-order discontinuity. This
broadening of the phase transition is an important issue for applications of
liquid-crystalline elastomers as actuators or artificial muscles. To understand
this behavior, we develop a lattice model of liquid-crystalline elastomers,
with local directors coupled to a global strain variable. In this model, we can
consider either random-bond disorder (representing chemical heterogeneity) or
random-field disorder (representing heterogeneous local stresses). Monte Carlo
simulations show that both types of disorder cause the first-order
isotropic-nematic transition to broaden into a smooth crossover, consistent
with the experiments. For random-field disorder, the smooth crossover into an
ordered state can be attributed to the long-range elastic interaction.
