Studies on the validity of the Einstein viscosity law and Stokes' law of sedimentation

Abstract Ultracentrifugal studies on polystyrene latex particles (PSL) in solutions of different densities prepared either from mixtures of H 2 O and D 2 O or from various concentrations of sucrose in water yielded a value, by interpolation, of 1.0520 for the density of solution in which the particles neither sediment nor float. Considerations of these results plus the nature of the particles lead to the conclusion that the partial specific volume of the polystyrene latex particles is (1/1.0520) cc./g., a value in agreement with the bulk specific volume of solid polystyrene. Evidence is presented for PSL to support the view that the effective hydrodynamic volume is equal to the partial specific volume, so that volume fractions can be determined from the partial specific volume and the dry weight concentration. Measurements of the viscosity of suspensions of polystyrene latex particles over a broad concentration range showed that the intrinsic viscosity was 2.5, in confirmation of the theory of Einstein. At concentrations above 2% by volume a square term in concentration, with coefficient about 10, and also a cubic term are needed to satisfy the data. From the partial specific volume of the latex particles and the value of the sedimentation coefficient extrapolated to infinite dilution, a value of 2640 ± 12 A. was calculated for the diameter of the particles from Stokes' law. This value is in excellent agreement with values obtained by electron microscopy, light scattering, and low angle x‐ray scattering. This agreement amounts to a satisfactory test of Stokes' law for particles not much larger than some of the viruses. Studies of the dependence of sedimentation coefficient on concentration indicate that existing theories are not completely satisfactory and that the influence of backward flow of liquid during the sedimentation of the solute particles is appreciable.