Concentration and solvency effects on the pair interaction between colloidal particles in a solution of nonadsorbing polymer

We present a simple analytical mean-field theory for the pair interaction between two colloidal particles, based upon a recent mean-field equation for the depletion thickness δ which depends on the chain length N, the bulk concentration φb, and the solvency χ. Only in the extremely dilute case is (in mean field) the interaction independent of χ. At relevant concentrations a better solvency leads for two flat plates to a stronger attraction at contact (∼φb/δ) and a smaller range of attraction. This range is 2δ_i, where the "interaction distance" δ_i is in semidilute solutions larger than δ. In the dilute limit, both δ and δ_i reduce to depletion thickness δ₀ of ideal chains. The pair potential for flat plates can be described by a modified Asakura-Oosawa equation, in which δ_i takes the place of the original δ₀; this replacement accounts for the concentration and solvency dependence. For the interaction between two spheres of radius a the contact potential is of order aφb and nearly insensitive to solvency; again, the range of attraction is smaller for better solvents. For two spheres we calculate the second virial coefficient as a function of concentration and solvent quality and its consequences for the stability of a colloidal dispersion at low colloid concentrations. For relatively short polymer chains the solvent quality hardly matters, For intermediate and large polymer-to-colloid size ratios, increasing the solvent quality leads to an increased miscibility. This implies that the increase in the osmotic pressure for polymers in a good solvent is overcompensated by a decrease of the depletion thickness, leading to weaker interactions.