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- Criticality of colloids with three distinct interaction patches: As simple as A, B, C?Publication . Tavares, Jose; Teixeira, PauloWe systematically study the phase behavior of a simple model of associating fluids which consists of hard spherical particles with three short-ranged attractive sites on their surfaces (sticky spots or patches), of types A, B, and C, that can form bonds with energy ij (i,j = A,B,C). We consider realizations of the model with one, two, or three nonzero ij. Using Wertheim’s first order perturbation theory of association, we establish the minimum requirements on the bond energies for the model to exhibit a liquid-vapor critical point, and investigate the nature of criticality in each case. As a preliminary, we rigorously show that, within this theory, particles with M identical sites do not condense if M < 3, a result that was previously conjectured, but never proved.
- Branching points in the low-temperature dipolar hard sphere fluidPublication . Rovigatti, Lorenzo; Kantorovich, Sofia S.; Ivanov, Alexey O.; Tavares, Jose; SCIORTINO, FrancescoIn this contribution, we investigate the low-temperature, low-density behaviour of dipolar hard-sphere (DHS) particles, i.e., hard spheres with dipoles embedded in their centre. We aim at describing the DHS fluid in terms of a network of chains and rings (the fundamental clusters) held together by branching points (defects) of different nature. We first introduce a systematic way of classifying inter-cluster connections according to their topology, and then employ this classification to analyse the geometric and thermodynamic properties of each class of defects, as extracted from state-of-the-art equilibrium Monte Carlo simulations. By computing the average density and energetic cost of each defect class, we find that the relevant contribution to inter-cluster interactions is indeed provided by (rare) three-way junctions and by four-way junctions arising from parallel or anti-parallel locally linear aggregates. All other (numerous) defects are either intra-cluster or associated to low cluster-cluster interaction energies, suggesting that these defects do not play a significant part in the thermodynamic description of the self-assembly processes of dipolar hard spheres. (C) 2013 AIP Publishing LLC.
- Criticality of colloids with distinct interaction patches: The limits of linear chains, hyperbranched polymers, and dimersPublication . Tavares, Jose; Teixeira, Paulo; Gama, MargaridaWe use a simple model of 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 bonding 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 the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA)not equal 0, epsilon(AB)=epsilon(BB)=0), hyperbranched polymers (epsilon(AB)not equal 0, epsilon(AA)=epsilon(BB)=0), and dimers (epsilon(BB)not equal 0, epsilon(AA)=epsilon(AB)=0). These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when epsilon(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.
- Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functionsPublication . Tavares, Jose; Teixeira, Paulo; Gama, Margarida; SCIORTINO, FrancescoWe calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a-state-dependent-functionality (f) over bar and unique bonding probability (p) over bar. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).
- Temperature-induced structural transitions in self-assembling magnetic nanocolloidsPublication . Kantorovich, Sofia S.; Ivanov, Alexey O.; Rovigatti, Lorenzo; Tavares, Jose; SCIORTINO, FrancescoWith the help of a unique combination of density functional theory and computer simulations, we discover two possible scenarios, depending on concentration, for the hierarchical self-assembly of magnetic nanoparticles on cooling. We show that typically considered low temperature clusters, i.e. defect-free chains and rings, merge into more complex branched structures through only three types of defects: four-way X junctions, three-way Y junctions and two-way Z junctions. Our accurate calculations reveal the predominance of weakly magnetically responsive rings cross-linked by X defects at the lowest temperatures. We thus provide a strategy to fine-tune magnetic and thermodynamic responses of magnetic nanocolloids to be used in medical and microfluidics applications.
- 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]