Statistical mechanics of coil-rod structure in biopolymer gels

Due to the unique properties of biopolymer gels, they are extensively used in the food industry and biomedical applications such as drug delivery. Different from rubber-like materials, the constituting chains in many biopolymer gels randomly interlock with neighbouring chains by means of physical rather than covalent cross-linking. Such polymer networks are characterized by two principal regions: the disordered zone containing coiled chains and the ordered zone in the form of ion-mediated aggregation of macromolecules and/or helical structures. The ordered regions serve as junction zones between the disordered chains, and the size of these zones may alter as a result of zipping/unzipping phenomena. The entire polymer network can be envisaged as a collection of coil-rod structures serving as the building blocks, where the coil and rod are representative of the disordered and ordered zones, respectively. The present work aims to provide a rigorous formulation of coil-rod structure that can predict its mechanical behaviour including zipping/unzipping characteristics. The coil-rod structure is modelled by a rod attached to a freely jointed chain, where the length of the rod and the number of segments in the freely jointed chain are adjustable input parameters. The relationship between the force and end-to-end distance of the coil-rod structure is derived based on statistical mechanics. The formulation is extended to incorporate the zipping/unzipping mechanism with the aid of Boltzmann averaging. As an example of its applications, the model is implemented into the eight-chain model to describe the macroscopic mechanical response of the network. Another example is demonstrated where the zipping/unzipping mechanism is shown to be able to capture the unwinding of a double-stranded DNA under a tensile force. The formulation presented in this work paves the way for future studies that model biopolymer gel networks with potentially complex chain interactions.