Depletion of ideal polymer chains near a spherical colloid particle beyond the Dirichlet boundary conditions

We reconsider the depletion interaction of an ideal polymer chain, characterized by the gyration radius R(G) and bond length a , and an impenetrable spherical colloid particle of radius R . Forbidding the polymer-colloid penetration explicitly (by the use of Mayer functions) without any other requirement we derive and solve analytically an integral equation for the chain partition function of a long ideal polymer chain for the spherical geometry. We find that the correction to the solution of the Dirichlet problem depends on the ratios R/R (G) and R/a . The correction vanishes for the continuous chain model (i.e. in the limit R/R (G) --> 0 and R/a --> infinity but stays finite (even for an infinite chain) for the discrete chain model. The correction can become substantial in the case of nano-colloids (the so-called protein limit).