MEAN-SQUARE INTRACHAIN DISTANCES IN A SELF-AVOIDING WALK

An investigation is undertaken of the second-order moments associated with the distribution of intrachain elements in a self-avoiding-walk model of chain polymer. The mean-square distance of an element of the chain from an end point of the chain, (Qn2), and the mean-square distance of an element of the chain from the centre of mass, (Sn2), are enumerated exactly on various two- and three-dimensional lattices for short chains of links. It is conjectured that as n→∞, the limiting values of (Qn 2)/Rn2 and (Sn2)/(Rn2), Rn 2 being the mean-square end-to-end distance of the chain, depend on dimensionality rather than on lattice structure. Estimates for these limiting values in two and three dimensions are given.