Van ’t Hoff’s Law, Donnan Equilibria, and the Depletion Force

This chapter examines osmotic phenomena in colloidal systems by introducing osmosis, osmotic pressure, and Van ‘t Hoff’s law, and by establishing their biological, technological, and thermodynamic significance. It derives Van ‘t Hoff’s law through osmotic equilibrium, particle kinetics, and membrane-based force arguments, extends the result with virial corrections, and shows how osmotic measurements determine molecular mass under defined ideality assumptions. The chapter analyses charged colloids through the Donnan equilibrium, explaining ionic contributions to osmotic pressure, the Donnan potential, salt partitioning, and the limiting low- and high-salt regimes. It describes salt depletion as a direct consequence of electrochemical equilibrium and links osmotic pressure differences to measurable forces in dispersed soft-matter systems. Finally, the chapter develops depletion forces in colloid–polymer mixtures, introduces the Asakura–Oosawa–Vrij potential, and demonstrates how polymer-induced osmotic pressure gradients generate reversible and tunable attractions between colloids.