Concentration and Solvency Effects on the Excess Amount and Surface Free Energy of a Colloidal Particle in a Solution of Nonadsorbing Polymer

Analytical expressions are derived for the polymer excess amount and the grand potential (surface free energy) of flat and spherical surfaces immersed in a solution of nonadsorbing polymer chains in the mean-field approximation. We start from a recent mean-field expression for the depletion thickness which takes into account not only the effect of the chain length N but also that of the polymer concentration b and the solvency . Simple expressions are obtained for the interfacial properties at a colloidal surface, using both the adsorption method and the osmotic route. For a sphere of radius a, the excess amount can be separated into a planar contribution = -b and a curvature correction c = -(2/12)bc2/a, where c is a "curvature thickness" which is close to (but smaller than) . The grand potential has a planar contribution = (2/9)b/ and a curvature part c = (/18)b/a. We test the results against numerical lattice computations, taking care that the boundary conditions in the continuum and lattice models are the same. We find good agreement up to a polymer segment volume fraction of 10%, and even for more concentrated solutions our simple model is reasonable. For spherical geometry we propose a new equation for the segment concentration profile which excellently agrees with numerical lattice computations. The results can be used as a starting point for the pair interaction between colloidal particles in a solution containing nonadsorbing chains, which is discussed in the following paper.