Repulsive Forces between Spherical Polyelectrolyte Brushes in Salt-Free Solution

Interaction forces between two colloidal spherical polyelectrolyte brushes in salt-free solution are calculated within Derjaguin approximation on the basis of self-consistent field Poisson-Boltzmann theory of a planar polyelectrolyte brush (E. B. Zhulina, O. V. Borisov, J. Chem. Phys. 107 (1997) 5952). It is demonstrated that at large separations the force-distance curve has a universal form which is independent of the charge density of the brush. At small separations the repulsive force is controlled by osmotic pressure of the counterions confined inside compressed brush. The crossover between these two regimes corresponds to the distance between the surfaces comparable to (double) thickness of a brush and occurs either continuously or with abrupt variation in the magnitude of the repulsive force. The latter is the case if the interacting brushes are found in the osmotic regime, that is, most of the counterions are retained in the intra-brush volume.