Micromechanics of dynamically cross-linked nematics

In soft nematic networks, flexible polymer chains coexist with stiff, rod-like constituents to yield a material with one hybrid soft-and-stiff phase. The resulting mechanical behavior is drastically different from that of either phase alone and may be different from that of a more typical composite material as well. This is because coupled interactions between the two phases are inherent to the microstructure and cannot be ignored. To account for this, we use a physical description of the material that accounts for each constituent and their naturally arising interactions at its foundation. We approximate a soft nematic network as a collection of 'hairy rods,' which consist of a stiff rod-like molecule connected by soft flexible polymer chains. We develop a statistical description of the network by considering the conformation of chains linking each unit. An assumption of affine motion at the level of the chain-rod unit is employed, but the motion of the rod itself is assigned its own degrees-of-freedom, akin to a Cosserat or higher-order continuum theory. Using this description, the motion of the rod is dictated by the forces and torques that are transmitted to it by the polymer network, which are defined using a statistically formulated free energy and resulting constitutive laws. Using this framework, we illustrate the unique mechanical properties of nematic networks, including soft elasticity and anisotropy, as well as additional time-dependency that arises when dynamic crosslinks are introduced.