Computer Simulations of Semi-flexible Polymer Chains

Monte Carlo Simulations are performed to obtain the isotropic-nematic (IN) transition in systems with semi-flexible polymer chains of different lengths. The chains are modeled as spherical beads that interact via a square-well potential. Bonded beads are connected by strings chosen so that bond length varies between 1.01$\sigma $ and 1.05$\sigma $ (where $\sigma $ 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 2.02$\sigma $ and 2.1$\sigma $. The vapor-liquid coexistence and isotropic-nematic (IN) coexistence curves are obtained using computer simulations. An IN transition is found for N$_{b} \quad \ge $ 10. The density, at which the IN transition occurs, moves to higher values as N$_{b}$ is increased and then drops on further increase. This is analogous to the initial increase in the critical density for pure alkanes as the chain length is increased.