Self-diffusion of small molecules in colloidal systems

Abstract

The self-diffusion of small molecules in colloidal systems is calculated using the cell model to describe the effect of varying concentration of colloidal particles. The relevant boundary conditions are found using arguments from the thermodynamics of irreversible processes. From a general description of the self-diffusion in systems with spherically symmetrical particles we derive expressions for the concentration dependence of the effective self-diffusion coefficientD ^eff for several cases of practical importance. It is shown that when the molecule studied is strongly attracted to the particle a minimum inD ^eff is expected around volume fractionΦ=0.35. It is also shown that the often made distinction between free and bound molecules is often problematic and a more general description is proposed. The obstruction effect generated by the excluded volume is discussed both for spherical and spheroidal systems. It is pointed out that the often used formula due to Wang ((1954) J Amer Chem Soc 76:4755) is incorrect for self-diffusion and for the obstruction factor for spheres we obtain (1+0.5Φ)⁻¹. This expresion is tested both by experiments on water diffusion in systems containing latex particles and through computer simulations and it is found valid over a wide concentration range. For prolate ellipsoids the obstruction factor is not greatly different from that for spheres, while for oblate aggregates the limiting obstruction factor of 2/3 can be obtained at low concentrations. It is demonstrated that this effect can be used to distinguish between different aggregate shapes. It is also shown that the disorder present in a solution of colloidal particles leads to a decrease in the obstruction effect.