Relationships between linear expansion factors of polymer coils from viscosity and light scattering

The validity of several relationships which have been explicitly or implicitly proposed to describe the dependence of the linear expansion factor αη, as obtained from viscosity data, on the linear expansion factor αs, as given by light scattering measurements, was tested by applying standard statistical procedures to 133 pairs of αη and αs values. The results so obtained show that the simple identity αη = αs does not disagree with the experimental data. In limited ranges of αη values, however, a better fit is given by two relationships obtained by combining a theoretical equation by Tanaka et al., relating αs and the excluded volume variable z, with the empirical dependence between αη and z, as observed by the same authors. Following a similar empirical approach, a new realtionship is derived which describes the dependence of αη on αs, in the whole range of αη values, better than the identity; nevertheless the αη values calculated from αs through such a new relationship are always very close to αs, the differences being most probably smaller than the errors affecting the experimental determination of the expansion factors.