Concentration Dependence of the Polymer Diffusion Coefficient

The form of the concentration dependence of the polymer diffusion coefficient depends on the concentration of the polymer relative to the crossover concentration, c*, between the dilute and semidilute regimes. At concentrations below c* the diffusion is of a single polymer molecule. As the polymer concentration is increased the friction coefficient is increased, thus leading to a slowing down of the motion of individual molecules. A microscopic, hydrodynamic theory explains this behavior quite adequately.¹As the polymer concentration approaches c* the diffusion coefficient vs. concentration curve flattens out and, at concentrations above c* but still in the semidilute regime, the diffusion coefficient becomes a linearly increasing function of the polymer concentration.² Typically, scaling approaches are employed to explain the behavior in the semidilute regime. By examining static correlations near the 0 temperature, Daoud and Jannink³ have expressed the density-density correlation function in terms of a correlation length that is inversely proportional to the concentration. Brochard and de Gennes,⁴ using dynamic scaling arguments for 0 conditions, have shown that the diffusion coefficient is inversely proportional to the correlation length and is therefore directly proportional to the concentration.