POLYMER BORN-GREEN-YVON EQUATION WITH PROPER TRIPLET SUPERPOSITION APPROXIMATION - RESULTS FOR HARD-SPHERE CHAINS

A site-site Born-Green-Yvon (BGY) equation is derived for polymeric fluids. This relates the pair and triplet site distribution functions, and superposition approximations for the latter are analyzed. It is shown that the pair functions to be superposed are uniquely determined by the exact normalization equations and asymptotic conditions. The Kirkwood superposition of pair distribution functions is shown to be valid only for the case of sites on three different polymers; for the cases of two or three sites on the same polymer different pair functions must be superposed. The polymer BGY equation is derived for a soft bonding potential between adjacent sites; the result for infinitely stiff bonds is given as a limiting case. Numerical results are obtained for soft and stiff tangent hard-sphere chains, and comparison is made with simulations for packing fractions up to 0.4 and chains with up to 12 sites. © 1995 American Institute of Physics.