Improved expression of mean-square radius of gyration. I. Vinyl polymers

Abstract

Taking account of the effect of large side groups, the mean-square radius of gyration of vinyl polymer chains has been deduced by the method of matrix algebra. According to previous approaches to the computation of conformational energy, every substituent of vinyl polymer is confined to an orientation in which the conformational energy is minimum, i.e., its plane is approximately perpendicular to the one defined by the skeletal bonds flanking the Cα atom. This model facilitates the derivation of mean-square radius of gyration. Neglecting the effect of side groups, the expression for mean-square radius of gyration given in this work reduces to be that reported by Flory. Numerical calculations indicate that for tactic polypropylene, polystyrene, poly(methyl acrylate), and poly-1,2-butadiene the dependence of mean-square radius of gyration on molecular weight can be expressed as 〈S2〉=aMb, which is in agreement with the experimental data.