  We investigate effective interactions between a colloidal particle, immersed
in a binary mixture of smaller spheres, and a semipermeable membrane. The
colloid is modeled as a big hard sphere and the membrane is represented as an
infinitely thin surface which is fully permeable to one of the smaller spheres
and impermeable to the other one. Within the framework of the density
functional theory we evaluate the depletion potentials, and we consider two
different approximate theories - the simple Asakura-Oosawa approximation and
the accurate White-Bear version of the fundamental measure theory. The
effective potentials are compared with the corresponding potentials for a hard,
nonpermeable wall. Using statistical-mechanical sum rules we argue that the
contact value of the depletion potential between a colloid and a semipermeable
membrane is smaller in magnitude than the potential between a colloid and a
hard wall. Explicit calculations confirm that the colloid-semipermeable
membrane effective interactions are generally weaker than these near a hard
nonpermeable wall. This effect is more pronounced for smaller osmotic
pressures. The depletion potential for a colloidal particle inside a
semipermeable vesicle is stronger than the potential for the colloidal particle
located outside of a vesicle. We find that the asymptotic decay of the
depletion potential for the semipermeable membrane is similar to that for the
nonpermeable wall and reflects the asymptotics of the total correlation
function of the corresponding binary mixture of smaller spheres. Our results
demonstrate that the ability of the membrane to change its shape constitutes an
important factor in determining the effective interactions between the
semipermeable membrane and the colloidal macroparticle.
