Mechanics of transiently cross-linked nematic networks

Polymeric networks are ubiquitous in biology and are vital components to some of the key functions of life. Composite networks of stiff and flexible polymers such as the actin-filamin network of the cytoskeleton posses novel mechanical properties that arise from physical interactions, geometry and topology of the network. Particularly, (a) the cross-linking chains in these networks dynamically break and reform in time that drive their rheological properties, and (b) stiff rod-like polymers have been found to show liquid crystalline phases including nematic alignment. Models of such transient nematic networks are either phenomenological or computational thereby lacking the simplicity of physics-based models in elucidating the key physical mechanisms. We present here a modelling framework using the statistically-based transient network theory to describe the rate-dependent mechanics of nematic networks. The model bridges continuum mechanics quantities to statistical measures of chain distribution in the network such as the conformation tensor. We show that the model degenerates to classical theories of anisotropic solids when the bonds are permanent and to anisotropic fluids when the bond exchange is rapid. The effect of the interplay between the bond dynamics and geometry of the network on its emergent mechanics is explored and illustrated using the example of a thin-walled tube under pressure. The generality of the framework and its potential to describe continuum level mechanics based on a variety of local physical interactions and network geometries is discussed.