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- Percolation of colloids with distinct interaction sitesPublication . Tavares, Jose; Teixeira, Paulo; Gama, MargaridaWe generalize the Flory-Stockmayer theory of percolation to a model of associating (patchy) colloids, which consists of hard spherical particles, having on their surfaces f short-ranged-attractive sites of m different types. These sites can form bonds between particles and thus promote self-assembly. It is shown that the percolation threshold is given in terms of the eigenvalues of a m x m matrix, which describes the recursive relations for the number of bonded particles on the ith level of a cluster with no loops; percolation occurs when the largest of these eigenvalues equals unity. Expressions for the probability that a particle is not bonded to the giant cluster, for the average cluster size and the average size of a cluster to which a randomly chosen particle belongs, are also derived. Explicit results for these quantities are computed for the case f = 3 and m = 2. We show how these structural properties are related to the thermodynamics of the associating system by regarding bond formation as a (equilibrium) chemical reaction. This solution of the percolation problem, combined with Wertheim's thermodynamic first-order perturbation theory, allows the investigation of the interplay between phase behavior and cluster formation for general models of patchy colloids.
- Re-entrant phase behaviour of network fluids: A patchy particle model with temperature-dependent valencePublication . Russo, J.; Tavares, Jose; Teixeira, Paulo; Gama, Margarida; SCIORTINO, FrancescoWe study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost epsilon(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for epsilon(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3605703]
- Reentrant Phase Diagram of Network FluidsPublication . Russo, J.; Tavares, Jose; Teixeira, Paulo; Gama, Margarida; SCIORTINO, FrancescoWe introduce a microscopic model for particles with dissimilar patches which displays an unconventional "pinched'' phase diagram, similar to the one predicted by Tlusty and Safran in the context of dipolar fluids [Science 290, 1328 (2000)]. The model-based on two types of patch interactions, which account, respectively, for chaining and branching of the self-assembled networks-is studied both numerically via Monte Carlo simulations and theoretically via first-order perturbation theory. The dense phase is rich in junctions, while the less-dense phase is rich in chain ends. The model provides a reference system for a deep understanding of the competition between condensation and self-assembly into equilibrium-polymer chains.