Universal ratios of characteristic lengths in semidilute polymer solutions

We use experimental and simulation data from the literature to infer five characteristic lengths, denoted ξ_s, ξ_f, ξ_∏, ξ_φ, and ξ_D of a semidilute polymer solution. The first two of these are defined in terms of scattering from the solution, the third is defined in terms of osmotic pressure, the fourth is defined by the spatial monomer concentration profile, and the last is defined by cooperative diffusion. In a given solution, the ratios of any of these five lengths are expected to be universal constants. Knowing these constants thus allows one to use one measured property of a solution as a means of inferring others. We calculate these ratios and estimate their uncertainties for solutions under Θ as well as good solvent conditions. The analysis is strengthened by use of scattering properties of isolated polymers inferred from computer simulations.