End-point distribution and structure function of polymers

Abstract

The coefficients in the expansion of the structure function S(k) as small momentum transfer k can be related to universal ratios 〈 r 2 m 〉/〈 r 2〉 m , and 〈 r 2 n 〉 = ( l/ N 2) σ N Mn 〈( R m − R n ) 2 n 〉. where R m denotes the position of monomer m. N is the monomer number and the average is taken over the configurations of the polymer. We show that the moments 〈r 3m〉 calculated using the end-point distribution P N ( r) = A N ( r/ N n r 0) n exp[−( r/ r 0 N n ) n ]. where r is the correlation length exponent. σ = (1− v) −1, and A N a normalization constant give universal ratios in disagreement with Monte Carlo results in two and three dimensions.