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) = δ(0)[1 − tanh(p(sf)/δ(0))], where p(sf) accounts for the degree of flexibility and δ(0) 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.