COMPUTER-SIMULATION STUDY OF THE APPROXIMATIONS ASSOCIATED WITH THE GENERALIZED FLORY THEORIES

The chain increment method and configurational bias Monte Carlo method s are used to test the approximations made in the derivation of the ge neralized Flory-Dimer (GF-D) theory for tangent hard sphere chains. In sertion probabilities and residual chemical potentials are calculated for hard chain fluids containing chains of length n=4, 8, 16, and 32 a t monomer densities, rho(M), up to 0.8. We find that the largest error s in the GF-D theory are those associated with assuming that the proba bility of inserting a monomer into a chain fluid is approximately equa l to the probability of inserting a monomer into a monomer fluid, as p redicted by the Carnahan-Starling equation of state. The errors in the incremental compressibility factors of the second segment associated with assuming that the conditional probability of inserting a second b ead next to the first bead in a chain fluid is approximately equal to the probability of inserting a second bead next to the first bead in a dimer fluid as predicted by combining the Carnahan-Starling and Tilde sley-Streett equations of state are relatively small. Consistent with the findings of Mooij and Frenkel, we find that these two approximatio ns lead to an overprediction of the incremental contributions to the c ompressibility factor. Despite the overprediction of the incremental c ontributions to the compressibility factor of the first segment, the G F-D equation of state accurately predicts the compressibility of hard chains; this accuracy is traced to (1) the insensitivity of the compre ssibility factors to errors in the insertion probability adn (2) cance llation of errors in the incremental compressibility factor of the fir st segment with small cumulative errors in the incremental compressibi lity factors of the third and subsequent segments. (C) 1996 American I nstitute of Physics.