Phase Behaviour of Colloid Ideal Polymer Mixtures

2 Phase Behaviour of Colloid -i- Ideal Polymer Mixtures 

The first step in taking into account more appropriate polymer physics compared to the simple description of penetrable hard spheres is by considering the polymers as ideal chains. Then one needs to ineorporate the correct depletion thickness of non-adsorbing ideal chains near a eoUoidal hard sphere into free volume theory. 

In Chap. 2 we saw that an analytical expression (2.62) can be derived for the depletion thickness around a sphere due to ideal polymer chains  

In Fig. 2.16 we plotted (4.2). It follows that the depletion thickness, normalised as Ss/R, drops with increasing q. For q 1 the depletion thickness is larger than Rg but not much the maximum is 2/01 1.13 times Rg in the limit q 0. For qr 1 the depletion thickness is smaller than Rg. In Fig. 4.5, 5 as normalized with the sphere radius R is plotted as a function of q. 

We now incorporate the correct depletion thickness into free volume theory presented in Sect. 3.3. We consider the osmotic equilibrium between a polymer solution (reservoir) and the colloid-polymer mixture (system) of interest, see Fig. 4.6. The general expression for the semi-grand potential for Nc hard spheres plus interacting polymers as depletants, see (3.18), is 

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Phase Behaviour of Colloid + Ideal Polymer Mixtures... 

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