End-to-end distribution functions for polymers having a most probable molecular weight distribution

End-to-end chain distribution functions for a polymer with a most probable molecular weight distribution are obtained by assuming the end-to-end distribution for each molecular weight species is Gaussian and the degree of polymerization is large. The resulting radial distribution functions using the most probable number and weight species distributions are:

W_n (r,p) = k²re-^kr and W_w (r,p) = k³r²/2 e^?kr

respectively, where k is a function of the short-range effects and the extent of the reaction is p. The first and second moments of these functions are identical with those obtained by taking the number and weight averages of the moments for the monodisperse case. The most probable values of r, which cannot be obtained by the latter method, are found to be 1/k and 2/k, respectively, using the above distributions.