Depletion attraction free energy

The magnitude of the depletion attraction free energy, is proportional to the osmotic pressure of the polymer solution, which in turn is determined by

molecular weight M. The range of depletion attraction is proportional to the thickness of the depletion zone. A, which is roughly equal to the radius of gyration, Rq, of the free polymer. A simple expression for Gdep is [7],... 

Our model predicts destabilization of colloidal dispersions at low polymer concentration and restabilisation in (very) concentrated polymer solutions. This restabilisation is not a kinetic effect, but is governed by equilibrium thermodynamics, the dispersed phase being the situation of lowest free energy at high polymer concentration. Restabilisation is a consequence of the fact that the depletion thickness is, in concentrated polymer solutions, (much) lower than the radius of gyration, leading to a weaker attraction. 

Afp free energy of attraction per unit area, due to depletion, between two plates... 

The consequences for suspended particles can be understood from either a mechanical or a thermodynamic standpoint. A particle immersed in a polymer solution experiences an osmotic pressure acting normal to its surface. For an isolated particle, the integral of the pressure over the entire surface nets zero force. But when the depletion layers of two particles overlap, polymer will be excluded from a portion of the gap (Fig. 30). Consequently, the pressure due to the polymer solution becomes unbalanced, resulting in an attraction. The same conclusion follows from consideration of the Helmholtz free-energy. Overlap of the depletion layers reduces the total volume depleted of polymer, thereby diluting the bulk solution and decreasing the free energy. 

The origin of the phenomenon that is responsible for depletion flocculation is somewhat different from the gas/solid situation in that the solvent molecules are squeezed out to a lower potential energy in the bulk rather than a lower potential energy in the adsorbed state. The attraction arises from a free energy of mixing of essentially pure solvent with bulk polymer solution rather than from a simple internal energy change. 

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