Thermodiffusion of charged colloids: Single-particle diffusion

An expression for the single-particle thermal diffusion coefficient of a charged colloidal sphere is derived on the basis of force balance on the Brownian time scale in combination with thermodynamics. It is shown that the single-particle thermal diffusion coefficient is related to the temperature dependence of the reversible work necessary to build the colloidal particle, including the core, the solvation layer, and the electrical double layer. From this general expression, an explicit expression for the contribution of the electrical double layer to the single-particle thermal diffusion coefficient is derived in terms of the surface charge density of the colloidal sphere, the electrostatic screening length, and its core radius, to within the Debye-HUckel approximation. This result is shown to explain experimental data, for both thin and thick double layers. In addition, a comparison with other theories is made.