Prediction and measurement of the interparticle depletion interaction next to a flat wall

A theoretical and experimental study was performed to investigate the depletion interaction between two colloidal particles next to a solid wall in a solution of nonadsorbing macromolecules. By calculating the change in free volume available to the macromolecules upon approach of the two particles, a relatively simple expression was developed for the interparticle depletion attraction in hard sphere systems as a function of the particle-particle and particle-plate spacing. Perhaps the most useful result obtained from this analysis was that the wall has no effect whenever the ratio of the particle radius to the macromolecule radius is greater than four. (In charged systems, this ratio would apply to the effective particle and macromolecule sizes.) A series of experiments was then performed in which the hydrodynamic force balance (HFB) apparatus was used to measure the shear force needed to separate a colloidal doublet consisting of two particles trapped in a secondary energy well formed by a repulsive electrostatic force and an attractive depletion force. The macromolecules used here were small, nanometer-sized spheres of either silica or polystyrene. Agreement between the measured separation forces and those predicted using the force balance model of J. Y. Walz and A. Sharma (J. Colloid Interface Sci. 168, 485 (1994)) was within a factor of 1.3 using no adjustable parameters and accounting for polydispersity and uncertainty in the macromolecule size. It is shown that this remaining discrepancy could be caused by the Brownian (stochastic) nature of the doublet breakup process.