Concentration dependence of static and hydrodynamic screening lengths for three different polymers in a variety of solvents

We have used small angle neutron scattering and dynamic light scattering to measure the static and hydrodynamic screening lengths of polystyrene, polymethylmethacrylate and polydimethylsiloxane solutions ranging from marginal to good solvent quality. A universal plot is found for the scaled static screening length when the concentration is scaled using the second virial coefficient in the way suggested by renormalization group theories. The same concentration units do not produce a universal plot for the hydrodynamic screening length at the molecular weights that we have studied (all around 1–2×105 g/mol). However, when the concentration is expressed in terms of kDc, where kD is the virial expansion coefficient for the cooperative diffusion coefficient and c is the concentration, most of the variation between different polymer–solvent combinations is eliminated. The ratio of hydrodynamic screening length to static screening length increases with concentration for all of the polymer solvent pairs studied, and its value differs for different polymer solvent pairs.