Conformational origin of the molecular weight dependence of the characteristic ratio of the dipole moment in poly(A-B)

By poly(A-B) we denote a chain with repeating sequence -A-B-, such as polyoxymethylene. Here A and B stand for a single atom, e.g., -O-, or a group of atoms, e.g., -CH2-. All n bond vectors are of the same length, l, as are all bond dipole moment vectors, m. The manner in which the characteristic ratio of the dipole moment, Dn≡〈μ2〉0/nm2 approaches its asymptotic limit is related quantitatively to the behavior of subchains of various sizes in poly(A-B). Illustrative numerical calculations with rotational isomeric state (RIS) models for several polymers are consistent with the predictions. The approach of Dn to its asymptotic limit is sensitive to longer subchains than is the approach of the characteristic ratio of the end-to-end distance, Cn≡〈r2〉0/nl2, to its asymptotic limit, due to the differences in the connectivity of the bond vectors (head-to-tail) and the bond dipole moment vectors (head-to-head, tail-to-tail).