Contraction of swollen coil of flexible polymer chain below theta temperature

In our previous study on thermodynamic equilibrium at infinite dilution, chain segments at the periphery of a polymer coil were shown to be more extended than the average expansion of the coil. This is because such segments are in contact with pure solvent, whereas inside the coil there is a concentration of the segments. In a subsequent work examining the low concentration range, this excess extension of the segments was shown to diminish as the concentration was increased. Having more and more neighboring coils, the chain segments at the periphery of the coil have less and less excess extension, because the concentration difference between the inside and the outside of the coil decreases. In the present work the range below the theta temperature is examined; for polymers of finite molecular weights there are soluble ranges including partial and critical miscibility. When the limits of miscibility are approached either by lowering the temperature at a constant concentration or by increasing concentration at a constant temperature, the excess extension of the chain segments at the periphery of the coil disappears. The calculation makes use of a modified Maron theory. The required input data are intrinsic viscosity and polymer-solvent interaction parameter as a function of polymer concentration. These parameters must be known as functions of temperature and molecular weight. The example used in this work is the polystyrene-cyclohexane system.