Scaling Theory of Polymer Solutions: Viscosity, Chain Self-diffusion, and Osmotic Pressure

Understanding properties of polymers in solutions remains one of the fundamental problems of polymer science. We applied a scaling approach based on the relationship between the solution correlation length ξ=lg^ν/B and the number of monomers g per correlation volume to analyze viscosity, chain self-diffusion coefficient, and osmotic pressure of charged and neutral polymers in solutions. The B-parameters and scaling exponent ν are determined by the solvent quality for the polymer backbone and type and strength of monomer-monomer interactions at different length scales. In our analysis of dilute and semidilute solution regimes, we highlight differences in the B-parameters obtained from solution viscosity, chain self-diffusion, and solution osmotic pressure. The extension of this approach to the entangled solution regime allows us to obtain the chain packing number and complete the set of parameters that describe dynamics of polymers in solution. This method is implemented to characterize the statics and dynamics of charged and neutral polymers in solutions.