Continuum limit of the rotational isomeric state model: Higher moments of the monomer–monomer distribution function

Abstract

In an earlier paper we established anomalies in the angular moments 〈PJ(cosϑn) 〉 of the monomer–monomer distribution function for flexible polymers. (PJ is the Jth Legendre polynomial, ϑn is the angle between the first and nth monomers, and the brackets denote a thermal average). We show here how these anomalies arise from the tetrahedral symmetry of the three-state rotational isomer model and how they disappear in the continuum limit of torsional conformations. We also relate the averages 〈rN2p〉 of the first few powers of the end-to-end distance rN to the angular moments and evaluate them in the continuum limit. It is concluded that the eighth and higher radial moments contain spurious contributions when calculated within the usual three-state model.