The second virial coefficient of polymer solutions

Abstract

A theoretical calculation of the temperature dependence of the second virial coefficient of polymer solution is carried out, assuming the Lennard‐Jones potential, φ( S ) = φ 0 [( S 0 / S ) 12 − 2( S 0 / S ) 6 ], between two molecular segments of chain polymer molecules in the solution. The result gives a good explanation for the experimental relation between the second virial coefficient, A 2 and the temperature, T : A 2 = a + ( b / T ), where b > 0 for good solvents and b < 0 for poor solvents. According to this calculation, the theta point, θ, at which the second virial coefficient vanishes is given by the relation, φ 0 / k θ = 0.292., and the temperature gradient of A 2 at this point is determined by another molecular parameter, S M , where M 0 represents the molecular weight of the segment. The theoretical value of the second virial coefficient agrees well with the experimental data of Krigbaum and Flory for polyisobutylene in benzene near the theta point, and it gives a value of about S 0 = 10 A. for the dimension of a segment consisting of seven monomer units in the solution. Another method for calculation of the molecular parameters, which employs the experimental data of the second virial coefficient is described. Application of this method to the light scattering data of Outer, Carr, and Zimm, permits calculation of the molecular paramenters of polystyrene in several solvents.