Overlap integral thermodynamics

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. 

This approach may yield a result for that is superior to the simple test particle result if the overlap in the two distribution functions is significant. Contrarily, if the distributions do not overlap significantly, it is difficult to extract a reliable result from either the test particle or overlapping distribution formulae, and an alternative approach like thermodynamic integration or the staged insertion method is favored. 

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