A BORN-GREEN-YVON INTEGRAL-EQUATION THEORY FOR SELF-INTERACTING LATTICE POLYMERS

A Born-Green-Yvon (BGY) integral equation is constructed for the end-t o-end distribution function of an isolated polymer on a lattice. The p olymer is modeled as a self-avoiding walk for which nonbonded sites in teract via an attractive nearest-neighbor contact potential. The BGY e quation is solved analytically using a Markov approximation for the re quired three-site distribution function and a delta-function pseudopot ential to model the lattice contact potential. The resulting recursive algebraic equation is readily evaluated for a polymer on any Bravais lattice with equal length base vectors. Results are presented for the mean-square end-to-end separation as a function of chain length and co ntact energy for polymers on several two-, three-, and four-dimensiona l lattices. The variation of the scaling exponent 2 nu with contact en ergy is used to locate the theta energies for these lattices. (C) 1998 American Institute of Physics. [S0021-9606(98)50941-5].