Improved expression of the mean-square radius of gyration, 2. Poly(1,1-disubstituted ethylene)s

The mean-square radius of gyration of poly(1,1-disubstituted ethylene)s is calculated according to a method already developed for poly(methyl methacrylate), poly(α-methylstyrene) and polyitaconate. During the derivation both the effect of side groups and the masses of skeletal atoms were taken into account. A hypothetical polymer chain was introduced, in which the mass of the substituents on every C^α was considered to be concentrated in their center of mass, and the virtual side bond vector runs from C^α to this center. The mean-square radius of gyration of poly(1,1-disubstituted ethylene)s consists of two parts, one of which is the mean-square radius of gyration of the hypothetical molecule described before and the other is related to the geometrical characteristics of the side groups. Numerical calculations indicated that the dependence of the mean-square radius of gyration of poly(1,1-disubstituted ethylene)s on the molecular weight is analogous to that of vinyl polymers, 〈S²〉 = aM^b, where a and b are constants characteristic of the polymer.