Mp. Taylor et Jeg. Lipson, A BORN-GREEN-YVON INTEGRAL-EQUATION THEORY FOR SELF-INTERACTING LATTICE POLYMERS, The Journal of chemical physics, 109(17), 1998, pp. 7583-7590
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].