Colloid-Polymer Mixtures in the Protein Limit

We computed the phase-separation behavior and effective interactions of colloid-polymer mixtures in the “protein limit,” where the polymer radius of gyration is much larger than the colloid radius. For ideal polymers, the critical colloidal packing fraction tends to zero, whereas for interacting polymers in a good solvent the behavior is governed by a universal binodal, implying a constant critical colloid packing fraction. In both systems the depletion interaction is not well described by effective pair potentials but requires the incorporation of many-body contributions.

Figure 1

Fluid-fluid binodals for a mixture of noninteracting polymers and HS colloids with different size-ratios $q$, in the (${\phi }_c,{\phi }_p$) plane. The polymer volume fraction is defined as ${\phi }_p={\rho }_p\frac{4}{3}\pi R_g^3$, and can thus be higher than 1. Crosses indicate the estimated critical point, obtained by extrapolating the calculated phase boundaries. The full lines are a guide to the eye. Dashed lines denote the simple theory described in the text, with stars marking the critical points.

Figure 2

Fluid-fluid binodals for a mixture of interacting polymers and HS colloids at different size-ratios $q$. Filled symbols are direct simulation data. The open symbols are the colloid limit ($q\lesssim 1$) results from Ref. 21. Solid lines are a guide to the eye. Inset: The same binodals plotted in a reduced polymer density representation. The dotted curve corresponds to a simple theory for the universal binodal when polymers are in a good solvent while the dashed line is for polymers in a poorer solvent. Crosses and stars as in Fig. 1.

Figure 3

Effective colloid-colloid pair potentials induced by interacting polymers for $q=7.78$. Theoretical lines from Ref. 30. Inset: Reduced second osmotic virial coefficient $B_2^{*}=B_2/[(16/3)\pi R_c^3]$ as a function polymer densities for several size ratios.