Degree of swelling and extent of crowding of flexible polymer coils in low concentration region

At infinite dilution, a flexible polymer chain is an isolated coil swollen with solvent. The situation may be treated in a manner analogous to the swelling equilibrium of a lightly crosslinked network. From the thermodynamic relation, the degree of swelling of the polymer coil may be estimated (1, 2). This value, the degree of chain extension, was found to be somewhat larger than that estimated from intrinsic viscosity. This finding was interpreted to mean that the chain segments in the periphery of the coil are more extended than the average coil extension (1). In the present work the dilute but finite concentration range was examined. In this case a polymer coil is in equilibrium with solvent containing polymer chains of the same kind. As the concentration is increased, the excess extension of the chain segments in the periphery of the coil diminishes. With further concentration increase, the polymer coil continues to decrease in size to the size defined by the theta condition, when the free solvent disappears. At that concentration adjacent polymer coils begin to interpenetrate. This behavior is described quantitatively. The input data required for this calculation are the intrinsic viscosity of the polymer-solvent system of interest, that of the polymer at the theta condition, and the thermodynamic interaction parameter as a function of temperature, concentration, and molecular weight of the polymer. Thermodynamic equations and their derivations are described.