Second virial coefficients of poly(ethylene glycol) in aqueous solutions at freezing point

The second virial coefficients B_ij (nm³) of poly(ethylene glycol) with molecular weight M = 600-10⁴ in water are measured by freezing point depression. B₁₂ represents the virial cross coefficient for two PEG solutes with different molecular weights M₁ and M₂. B₁₁ can be well described by the scaling law M^3v with v ≃ 0.60. That is, the good solvent behavior is observed even for such low molecular weight. In terms of the hard-sphere model, the effective diameter of PEG ranges from 1.3 to 7.9 nm. Since the second virial coefficient is generally increased with decreasing temperature, our results at freezing point provide an upper bound. The virial cross coefficient is found to follow B₁₂ = B₁₁[1 + (M₂/M₁)^v]3/8. This result indicates that the effective hard-sphere picture is also reasonable for dilute solutions of different polymer molecules in good solvents.