Single-particle thermal diffusion of charged colloids: Double-layer theory in a temperature gradient

The double-layer contribution to the single-particle thermal diffusion coefficient of charged, spherical colloids with arbitrary double-layer thickness is calculated and compared to experiments. The calculation is based on an extension of the Debye-Hückel theory for the double-layer structure that includes a small temperature gradient. There are three forces that constitute the total thermophoretic force on a charged colloidal sphere due to the presence of its double layer: i) the force FW that results from the temperature dependence of the internal electrostatic energy W of the double layer, ii) the electric force Fel with which the temperature-induced non-spherically symmetric double-layer potential acts on the surface charges of the colloidal sphere and iii) the solvent-friction force Fsol on the surface of the colloidal sphere due to the solvent flow that is induced in the double layer because of its asymmetry. The force FW will be shown to reproduce predictions based on irreversible-thermodynamics considerations. The other two forces Fel and Fsol depend on the details of the temperature-gradient-induced asymmetry of the double-layer structure which cannot be included in an irreversible-thermodynamics treatment. Explicit expressions for the thermal diffusion coefficient are derived for arbitrary double-layer thickness, which complement the irreversible-thermodynamics result through the inclusion of the thermophoretic velocity resulting from the electric- and solvent-friction force.