Journal of Physical Chemistry, Vol.100, No.24, 10408-10413, 1996
Equations of State and Virial-Coefficients for Rigid Linear-Chains
The study of isotropic-nematic phase transition in a system of rodlike molecules requires an accurate equation of state for the isotropic phase. In this paper, generalized Flory-dimer (GF-D) theory is extended to fluids composed of rigid linear chains, and its predictions of the compressibility factor and virial coefficients are compared with simulation results available in the literature. A simplified equation of state is derived which eliminates the need to evaluate exclusion volumes. Compressibility factor predictions for linear tangent hard-sphere (LTHS) trimers, linear fused hard-sphere (LFHS) trimers, LTHS tetramers, and planar T- and Y-shaped tangent hard-sphere tetramers are in excellent agreement with simulation results. For LFHS 6-mers and 8-mers, with the ratio of bond length I to hard-sphere diameter d of 0.5, GF-D predictions are in good agreement with simulation results only for volume fractions less than about 0.4. At higher densities, GF-D theory first underpredicts and then slightly overpredicts the compressibility faster for both LFHS 6-mers and 8-mers. However, the modified Wertheim equation of state overpredicts the compressibility factor over the entire density range for these fluids. For LFHS 8-mers (l/d = 0.6), the agreement between GF-D predictions and simulation results is good only up to a volume fraction of about 0.33, after which the theory overpredicts the compressibility factor. This breakdown is attributed to an isotropic-nematic phase transition. Examination of the virial coefficients for LTHS chains and LFHS (l/d = 0.5) chains reveals that GF-D theory benefits from a cancellation of errors caused by overprediction and underprediction of the individual virial coefficients.
Keywords:DIRECTIONAL ATTRACTIVE FORCES;THERMODYNAMIC PERTURBATION-THEORY;INTRAMOLECULAR STRUCTURES;CHEMICAL-EQUILIBRIA;MOLECULAR-DYNAMICS;POLYATOMIC FLUIDS;HARD DUMBBELLS;BHS THEORY;SIMULATION;SPHERES