How patchy can one get and still condense? The role of dissimilar patches in the interactions of colloidal particles
Résumé
We investigate the influence of strong directional, or bonding, interactions on the phase diagram of complex fluids, and in particular on the liquid-vapour critical point. To this end we revisit a simple model and theory for associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type $A$ and one is of type $B$; the interactions between each pair of spots have strengths $\epsilon_{AA}$, $\epsilon_{BB}$ and $\epsilon_{AB}$. The theory is applied over the whole range of bonding strengths and results are interpreted in terms of the equilibrium cluster structures of the coexisting phases. In systems where unlike sites do not interact (i.e., where $\epsilon_{AB}=0$), the critical point exists all the way to $\epsilon_{BB}/\epsilon_{AA}=0$. By contrast, when $\epsilon_{BB}=0$, there is no critical point below a certain finite value of $\epsilon_{AB}/\epsilon_{AA}$. These somewhat surprising results are rationalised in terms of the different network structures of the two systems: two long $AA$ chains are linked by one $BB$ bond (X-junction) in the former case, and by one $AB$ bond (Y-junction) in the latter. The vapour-liquid transition may then be viewed as the condensation of these junctions and, we find that X-junctions condense for any attractive $\epsilon_{BB}$ (i.e., for any fraction of $BB$ bonds), whereas condensation of the Y-junctions requires that $\epsilon_{AB}$ be above a finite threshold (i.e., there must be a finite fraction of $AB$ bonds).
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