Free Volume Theory for Big Plus Small Hard Spheres

1 Free Volume Theory for Big Plus Small Hard Spheres 

In 1964 Lebowitz and Rowlinson [6] showed that, within the Percus-Yevick treatment of hard sphere fluids [7], binary hard sphere mixtures are completely miscible for aU concentrations and size ratios. This proof was later extended by Vrij [8] to hard sphere mixtures with an arbitrary number of components. Up till 1990, it was indeed generally beUeved that hard sphere mixtures do not phase 

Lekkerkerker and R. Tuinier, Colloids and the Depletion Interaction, Lecture Notes in Physics, 833, DOI 10.1007/978-94-007-1223-2 5, 

5 Phase Transitions of Hard Spheres Plus Colloids 

The free volume treatment given for hard spheres + penetrable hard spheres can be extended to the case of asymmetric hard sphere mixtures as follows. The osmotic equilibrium system considered is depicted in a schematic way in Fig. 5.2. We assume the depletion layers are equal to the radii of the small hard spheres. Following the same steps as in Chap. 3 we obtain for the semi-grand potential of the asymmetric hard sphere mixture. 

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