Extrapolation formulas for polymer solution properties
Murugappan Muthukumar, Sam F Edwards · The Journal of Chemical Physics · 1982
We have derived general expressions for the average size of a labeled chain and the osmotic pressure of the polymer solution as functions of polymer concentration and the strength of the excluded volume effect both varying from very low to very high. By employing a combination of path integral and field theoretic techniques to treat the correlations of the density fluctuations, we have renormalized the excluded volume interaction and the chain step length in terms of a screening length. The renormalized step length and the screening length are coupled by integral equations. In the limit of these lengths being independent of wave vectors, they are related by algebraic equations. In the region of criticality, we recover scaling laws and the known results for low and high polymer concentrations, respectively. We have also obtained the various numerical prefactors in terms of the free chain prefactor. Our development provides extrapolation formulas for the screening length, effective step length, free energy of the solution, and the average size of a chain, for intermediate concentrations and for intermediate strengths of excluded volume effect.