MEAN-SQUARE RADIUS OF GYRATION OF POLYMER-CHAINS

The calculations of the mean-square radius of gyration for more than t hirty seas of polymer chains are reviewed on the basis of a unified ap proach. A general expression of the mean-square radius of gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square radius of gyr ation of a model chain, in which every side group, R, was considered t o be located in the centroid of the substituent flanking the related s keletal atom, and the second one is the total contribution of the squa re radius of gyration of every substituent around its centroid. Numeri cal calculations showed that the logarithmic relationship between the mean-square radius of gyration and the degree of polymerization become s linear when x is greater than 100, and the dependence of the mean-sq uare radius of gyration on the molecular weight can be expressed by th e general formula [S-2] = aM(b), which was supported by a number of ex perimental measurements. A comparison of our expression for the mean-s quare radius of gyration with that reported by Flory was made. The dif ference is obvious in the range of lower molecular weight, and gradual ly declines with increasing degree of polymerization.