Equilibrium characteristics of semiflexible polymer solutions near probe particles

We present a numerical analysis of the mean-field theory for the structure of semiflexible polymer solutions near spherical surfaces, and use the framework to study the depletion characteristics of semiflexible polymers near colloids and nanoparticles. Our results suggest that the depletion characteristics depend sensitively on the polymer concentrations, the persistence lengths, and the radius of the particles. Broadly, two categories of features are identified based on the relative ratios of the persistence lengths to the correlation length of the polymer solution. For the limit where the correlation length is larger than the persistence length, the correlation length proves to be the critical length scale governing both the depletion thickness and the curvature effects. In contrast, for the opposite limit, the depletion thickness and the curvature effects are dependent on a length scale determined by an interplay between the persistence length and the correlation length. This leads to nontrivial (numerical) scaling laws governing the concentration and radii dependence of the depletion thicknesses. Our study also highlights the manner by which the preceding features rationalize the parametric dependencies of insertion free energies of small probes in semiflexible polymer solutions.