The depletion thickness in solutions of semi-flexible polymers near colloidal surfaces: analytical approximations

We derive a simple, yet accurate approximate mean-field expression for the depletion thickness δ_sf of a solution of dilute semi-flexible polymers next to a hard surface. In the case of a hard wall this equation has the simple form δ_sf = δ₀[1 - tanh(p_sf/δ₀)], where p_sf accounts for the degree of flexibility and δ₀ is the depletion thickness in the case of fully flexible polymers. For fixed polymer coil size, increasing the chain stiffness leads to a decrease in the depletion thickness. The approach is also extended to include higher polymer concentrations in the semidilute regime. The analytical expressions are in quantitative agreement with numerical self-consistent field computations. A remarkable finding is that there is a maximum in the depletion thickness as a function of the chain stiffness in the semidilute concentration regime. This also means that depletion attractions between colloidal particles reach a maximum for a certain chain stiffness, which may have important implications for the phase stability of colloid-polymer mixtures. The derived equations could be useful for the description of interactions in- and phase stability of mixtures of colloids and semi-flexible polymers.