= Asakura-Oosawa model
{c}
{title2=$U_{\mathrm{dep}}(R)=-\Pi_p\pi(4R_e+R)(2R_e-R)^2/12$}
The <Asakura-Oosawa model> treats dilute nonadsorbing <polymer> coils as mutually interpenetrable ideal particles excluded from a layer around each <colloid>. For colloid radius $a$ and polymer exclusion thickness $R_g$, two exclusion spheres of radius $R_e=a+R_g$ overlap when $2a\leq R<2R_e$. Adding their two <spherical cap> volumes gives $V_{\mathrm{ov}}=\pi(4R_e+R)(2R_e-R)^2/12$. Multiplication by $-\Pi_p$ gives the displayed pair <free energy>, with zero depletion interaction beyond $2R_e$. The range is controlled by polymer size and the depth by reservoir polymer concentration. At larger polymer concentration, polymer interactions and many-body overlap effects require care.
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