Theory of Dilute Polymer Solution. II. Osmotic Pressure and Frictional Properties

Abstract

The osmotic second virial coefficient of flexible polymer solutions is calculated on the basis of the pearl-necklace model with continuous medium approximation. Proper account is taken not only of the intermolecular interaction but also of the intramolecular interaction of segments or the so-called ``excluded volume effect.'' Evaluation is carried out to the triple contact approximation. The results show that the intramolecular interaction has a marked influence on the molecular weight dependence of the coefficient. Then, theories of the intrinsic viscosity and frictional coefficient are developed on the same model as above, following the Kirkwood and Riseman scheme. The results show that, if α is the linear expansion factor of the polymer coil, the intrinsic viscosity is asymptotically proportional to α2 for the free-draining case and α2.43 for the impermeable case. This implies that even in the limit for impermeable molecule, the hydrodynamic radius of the polymer coil is not proportional to its statistical radius. Finally a thorough comparison of the present theories with experimental data is made, taking solutions of polystyrene in cyclohexane as an example. The results prove that the theories are very fitted for structural interpretation of experimental data.