Equation of state for polymer solution

The flow pattern through a cloud of polymer segments is obviously different from the flow pattern around a solid object. It can be shown theoretically, however, that the partial viscosity due to the cloud can take the same value as for a solid sphere with the radius of gyration of the cloud as its radius. The specific viscosity of polymer solution has been derived as 2.5(c/c_I), with c_I being the internal concentration associated with a polymer molecule. The internal concentration is the ratio of mass over the volume of gyration of segments in a polymer chain. A radius of gyration exists for any type of polymers, flexible or rigid, exhibiting different kinds of dependence on the molecular weight. From the expression of the specific viscosity, the intrinsic viscosity is shown to be equal to 2.5/c*, c* being the (minimum) internal concentration for the state of maximum conformational entropy. The equation for the specific viscosity, thus obtained, is expanded into a polynomial in c[η]. This formula is shown to agree with data for several kinds of polymers, with flexible, semi-rigid and rigid. The quantity 1/c_I can be interpreted as an expression for the chain stiffness. In polyelectrolytes, coulombic repulsive potentials affect the chain stiffness. The dependence of c_I on the effective population of polyions in the polyelectrolyte molecule is discussed. An equation of state for the polymer solution is formulated that included the internal concentration. The virial coefficients emerge as a result of c_I not always being equal to c*, and they are molecular weight dependent.