An Equation of State for the Isotropic-Nematic Phase Transition of Semiflexible Polymers

Based on the thermodynamic perturbation theory for polymer, a new equation is proposed by incorporating a wide range of molecular flexibility and perturbative interactions to describe the isotropic-anisotropic (nematic) phase transition phenomena of the semiflexible polymers. In the new equation, the framework of the Helmholtz free energy of the system is the same as the Onsager-like theory. The entropy loss due to the orientation is estimated by the Khokhlov-Semenov (KS) theory. With regard to the configurational free energy, the polymer is envisioned as a series of subchains. The Parsons-Lee approximation is used to account for the higher virial coefficients of the subchain and Yu equation for the hard-sphere-chain fluid is adopted to modify the defect of the first order approximation in dealing with the associating points. An analytical expression of the perturbative term is obtained by employing the "square peg in a round hole" potential function and the mean-field approximation. The hard-core part of the equation reduces to the Dupre-Yang theory when the stiffness of the molecule is high. When the model approaches the limit of the random coil, a modified equation of the hard-sphere-chain fluid is obtained. The present theory has been used to predict the isotropic-nematic phase equilibrium for real semiflexible polymers with two adjustable parameters. The agreements between the theoretical results and experimental data are much better than that of previous theories.