 Solution

In the Asakura-Oosawa model, nonadsorbing polymers are treated as ideal, mutually penetrable particles, but their centers cannot enter a layer around a hard colloid. The polymer osmotic pressure is $\Pi =\rho k_{\mathrm{B}}T$ in the ideal dilute limit, with the appropriate number density in the space dimension considered.

For fixed polymer number, reducing the inaccessible volume increases the available volume and lowers the polymer Helmholtz free energy. Equivalently, at fixed polymer chemical potential, the polymer contribution to the effective colloid potential isWhen the excluded layers overlap, their union occupies less space than two separate layers. More polymer configurations become available, so the resulting depletion force attracts the colloids. It is an entropy-driven effective interaction, even though each microscopic colloid–polymer interaction is purely repulsive.