Polymolecularity correction formulae for the calculation of weight- and number-average mean square radii of gyration from experimentally determined [formula omitted] mean square radius of gyration

Abstract

The polymolecularity correction formulae are given for the exact transformation of the z-average mean square radius of gyration 〈 r 2 〉 z , as determined, e.g. by light scattering or neutron scattering techniques, into the weight- and number-average mean square radii of gyration 〈 r 2 〉 w and 〈 r 2 〉 n , respectively. The procedure based on the “Principle of Corresponding Averages” is outlined and can be applied to any other averages of the dimensions of macromolecules or to any other averages in polymer science, which stem from the fact that most polymers are polymolecular, i.e. exhibit a molar mass distribution (MMD). The importance of polymolecularity correction is stressed by numerical calculations of the polymolecularity correction factors q r n and q r n for the transformation of 〈 r 2 〉 z into 〈 r 2 〉 w and 〈 r 2 〉 n , respectively, for Schulz and logarithmic normal MMDs. It is seen that the errors introduced into the numerical values for the mean square radius of gyration by not considering the correction factor q r w are of the order of 10% for such small values of the polymolecularity index M w/ M n = 1.1 and that they are increasing to 20% by not considering q r n for the same value of M w/ M n = 1.1. For M w/ M n = 2, these errors increase to the order of 50–75%.