Influence of polymolecularity on the second virial coefficient of polymers

Scaling theory is applied to derive expressions describing the influence of polymolecularity on the second virial coefficient, A₂, as obtained from osmotic pressure and light scattering measurements. Numerical values of polymolecularity correction factors are calculated for Schulz-Zimm and logarithmic normal distributions of the molecular weight, different qualities of the solvent and several ratios of the weight-average and the number-average molecular weights M̄_w/M̄_n. It is found that in the equation $ A_2 = K_{A_2 } cdot M_{{rm av}}^{a_{A_2 } } $ the weight-average molecular weight is a good approximation for M_av if A₂ is measured via light scattering, while the number-average molecular weight can be inserted for M_av if A₂ stems from osmotic pressure measurements.