Abstract
We derive a simple, yet accurate approximate mean-field expression for the depletion thickness δsf 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 δsf = δ0[1 − tanh(psf/δ0)], where psf 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.
Highlights
Non-adsorbing polymers induce a net attraction between colloidal particles, often termed the depletion interaction
Upon exceeding a particular polymer concentration, the depletion interaction can lead to phase separation of colloid–polymer mixtures into polymer- and colloid-rich phases.[1,2]
The density profiles and depletion thickness for semi-flexible polymers can be computed using numerical self-consistent field theory,[13,31,32] analytical expressions are useful to estimate other physical properties such as the surface tension[17,33] and phase behavior of colloid–polymer mixtures.[2,8]. It may for instance, yield analytical expressions of the depletion attraction between both flat walls and spheres,[8] and the friction coefficient of colloidal particles diffusing through a semi-flexible polymer solution.[34,35]
Summary
Non-adsorbing polymers induce a net attraction between colloidal particles, often termed the depletion interaction. The density profiles and depletion thickness for semi-flexible polymers can be computed using numerical self-consistent field theory,[13,31,32] analytical expressions are useful to estimate other physical properties such as the surface tension[17,33] and phase behavior of colloid–polymer mixtures.[2,8] it may for instance, yield analytical expressions of the depletion attraction between both flat walls and spheres,[8] and the friction coefficient of colloidal particles diffusing through a semi-flexible polymer solution.[34,35].
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