Sedimentation and brownian diffusion coefficients of interacting hard spheres

Abstract

Abstract Einstein (1905) derived an expression for the diffusion coefficient of an isolated spherical colloid. Since that work, there have been two general methods for analyzing Brownian diffusion in colloidal suspensions at finite concentrations. One follows Einstein's thermodynamic argument postulating a gradient in chemical potential as being the driving force behind diffusion together with a thermodynamic analysis of sedimentation-diffusion equilibrium (Batchelor, 1976). The other approaches diffusion in a statistical fashion, deriving the macroscopic diffusion coefficient from a microscopic analysis of Brownian motion (Felderhof, 1978). In principle, both methods are correct and should give identical results, but the distinctly different approaches have produced some controversy. To test the various theories, of Brownian diffusion, experiments were conducted measuring the sedimentation and Brownian diffusion coefficients of uncharged rigid spheres. Sterically stabilized silica spheres dispersed in cyclohexane were used as a model colloid. The osmotic compressibility of this system was found to be well described by the Carnahan- Starling equation for hard spheres. The sedimentation coefficient of the silica spheres was measured over a wide range of concentration in a closed bottom container. A light extinction method was used to monitor the fall speed of the interface that develops during gravity sedimentation. The diffusion measurements were made using Taylor's hydrodynamic stability method. A laser optical-fiber system capable of direct monitoring of the penetration depth and concentration profile of the diffusing species along the diffusion column was developed. The measurements were found to be in fair agreement with Batchelor's theoretical results for sedimentation and Brownian diffusion of hard spheres.