SEDIMENTATION AND BROWNIAN DIFFUSION-COEFFICIENTS OF INTERACTING HARD-SPHERES

Einstein (1905) derived an expression for the diffusion coefficient of an isolated spherical colloid. Since that work, there have been two g eneral methods for analyzing Brownian diffusion in colloidal suspensio ns at finite concentrations. One follows Einstein's thermodynamic argu ment postulating a gradient in chemical potential as being the driving force behind diffusion together with a thermodynamic analysis of sedi mentation-diffusion equilibrium (Batchelor, 1976). The other approache s diffusion in a statistical fashion, deriving the macroscopic diffusi on coefficient from a microscopic analysis of Brownian motion (Felderh of, 1978). In principle, both methods are correct and should give iden tical results, but the distinctly different approaches have produced s ome controversy. To test the various theories, of Brownian diffusion, experiments were conducted measuring the sedimentation and Brownian di ffusion 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 descr ibed by the Carnahan-Starling equation for hard spheres. The sedimenta tion coefficient of the silica spheres was measured over a wide range of concentration in a closed bottom container. A light extinction meth od was used to monitor the fall speed of the interface that develops d uring gravity sedimentation. The diffusion measurements were made usin g Taylor's hydrodynamic stability method. A laser optical-fiber system capable of direct monitoring of the penetration depth and concentrati on profile of the diffusing species along the diffusion column was dev eloped. The measurements were found to be in fair agreement with Batch elor's theoretical results for sedimentation and Brownian diffusion of hard spheres.