The spatial distribution of colloidal particles in a confined space is frequently a key issue to many phenomena of practical significance. This problem is investigated by considering the distribution of colloidal particles in a spherical cavity under the conditions of relatively large cavities, low cavity and colloidal particles potentials, and low monovalent electrolyte and colloidal concentrations. The analytical expression for the particle−cavity pair interaction energy is derived under various surface conditions. The results obtained are used to evaluate the direct correlation functions in the hypernetted chain approximation employed for the resolution of an Ornstein−Zernike equation. For a fixed particle number concentration at the center of a cavity, we make the following conclusions: (i) the spatial distribution of particles increases in an oscillatory manner with the distance away from the cavity surface, (ii) increasing the particle−cavity pair interaction energy has the effect of reducing the free space of particles inside a cavity, and (iii) the greater the pair interaction energy between two particles, the higher the average concentration of particles.
Journal of Physical Chemistry B 109(38), pp.18048-18054