Polymer depletion interaction between a particle and a wall

The attractive depletion interaction between a spherical particle and a planar wall in a dilute solution of long flexible nonadsorbing free polymer chains is found to depend crucially on the particle to polymer size ratio rho. While the polymer-induced force between particle and wall decreases monotonically with increasing distance for large rho, for small rho it has a maximum at a distance of the order of the polymer size. For ideal chains we study the crossover from large to small rho behavior in full quantitative detail. Besides the free energy of interaction and the force, we also discuss the spatial variations of the densities of chain-ends and chain-monomers near the wall and particle. Two independent procedures, (1) solving directly the diffusion equation for the density of ends in terms of planar and spherical waves and (2) minimizing the Ginzburg-Landau functional of the "magnetic analog" of the polymer problem, are used to obtain results numerically for a broad range of ratios of the three lengths particle size, polymer size and distance of particle from the wall. Besides previously known cases, we find two more interesting limiting regions of the length ratios for which analytical results can be obtained.