Isotropic-genesis nematic elastomers (IGNEs) are liquid crystalline polymers (LCPs) that have been randomly and permanently cross-linked in the high-temperature state until they form an elastically rigid network. Thus, instead of being free to diffuse throughout the entire volume as is the case for nematogens in a liquid, the nematogens in an IGNE are mobile only over a lengthscale controlled by the density of cross-links. We address the effects that such network-induced localization has on the liquid crystalline characteristics of a system that is measured in the high-temperature regime. In contrast to the case of pure liquid nematics, these characteristics of IGNEs are influenced by both thermal and quenched disorder.

To study the IGNE, we consider a microscopic model of dimers that are randomly and permanently cross-linked via Hookean springs, and the dimers interact via orientational and positional excluded-volume forces.

Using the replica formalism, we derive two types of correlators that diagnose the local nematic order: the disorder-averaged thermal fluctuation correlator and the disorder-averaged glassy correlator of the local nematic order. These correlators enable us to predict that for sufficiently large disorder strength, the glassy and thermal fluctuation correlators oscillate as they decay with separation distance.

By utilizing a two-statistical ensemble approach that takes into account the thermodynamic states of the system at the instant of cross-linking and at the instant of measurement long after cross-linking, the model also enables us to determine how the strength with which an IGNE memorizes the nematic alignment pattern present at the instant of cross-linking varies with the density of cross-links and the temperature at which the system was cross-linked.