Computer simulations of stiff and semiflexible polymer chains have been of continuing interest for the past sixty years primarily because of the ability of these materials to form liquid crystal phases. Our interest in these materials arises in the context of a new class of stiff poly (benzimidazole) polymers, which have been proposed for use in high temperature battery applications. These materials do not suffer the water management problems, which are a source of continuing problems in Nafion based materials. Rather, these materials, where phosphoric acid is the charge carrier, are distinguished from other classes of polymers used in battery applications in that they readily form gels thus encapsulating as much as 95% by weight of phosphoric acid. This phosphoric acid is thought to play the role of the electron transport thus obviating the role played by water. As a first step to understanding the unusual charge transport behavior in these materials we constructed a polymer model, which is particularly, amenable to study chain dynamics, which we believe underlies the ability of these materials to form reversible gels with liquid crystalline domains.

Monte Carlo simulations were performed on semiflexible polymer chains with the goal of delineating their isotropic-nematic (IN) and gas-liquid coexistence envelopes. The chain monomers are spherical beads that interact via a square-well potential with all other beads. Bonded beads are connected by strings chosen so that bond length varies between 1.01σ and 1.05σ (where σ is the hard sphere diameter). The stiffness of the molecules is controlled via a potential between beads separated by two bonds; this potential restricts the distance between these beads to be between 2.02σ and 2.1σ. The vapor-liquid coexistence and IN coexistence curves are obtained using computer simulations. An IN transition is found for 10 ≤ N _b ≤ 30 (where N_b is the number of beads per chain). Both the density at which the IN transition occurs and the location of the gas-liquid coexistence go through a maximum with increasing N_b. For longer chains, behavior expected from theory is found and both of these coexisting densities decrease with increasing length.

Discrete Molecular Dynamics/Collision Dynamics has been employed to study the formation of a physical gel by semi-flexible polymer chains. The formation of a geometrically connected network of these chains is investigated as a function of temperature. As the temperature is lowered, a percolated homogeneous solution phase separates to form a non-percolated nematic fluid and upon further decrease in the temperature, it goes back to a percolated gel state. The gelation, at lower temperatures, is due to the dynamic arrest of chains, preventing them from completing the phase separation process. The cooling rate also plays an important role in deciding the final outcome. Quenching the system, to the final temperature, at a faster rate yields gelation while slower quenches result in phase separation.