Phase diagrams of binary mixtures of patchy colloids with distinct numbers of patches: The network fluid regime (original) (raw)
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Phase diagrams of binary mixtures of patchy colloids with distinct numbers of patches
2010
We calculate the network fluid regime and phase diagrams of binary mixtures of patchy colloids, using Wertheim's first order perturbation theory and a generalization of Flory-Stockmayer's theory of polymerization. The colloids are modelled as hard spheres with the same diameter and surface patches of the same type, AAA. The only difference between species is the number of their patches -or functionality-, fA(1)f_A^{(1)}fA(1) and fA(2)f_A^{(2)}fA(2) (with fA(2)>fA(1)f_A^{(2)}>f_A^{(1)}fA(2)>fA(1)). We have found that the difference in functionality is the key factor controlling the behaviour of the mixture in the network (percolated) fluid regime. In particular, when fA(2)ge2fA(1)f_A^{(2)}\ge2f_A^{(1)}fA(2)ge2fA(1) the entropy of bonding drives the phase separation of two network fluids which is absent in other mixtures. This changes drastically the critical properties of the system and drives a change in the topology of the phase diagram (from type I to type V) when fA(1)>2f_A^{(1)}>2fA(1)>2. The difference in functionality also determines the miscibility at high (osmotic) pressures. If fA(2)−fA(1)=1f_A^{(2)}-f_A^{(1)}=1fA(2)−fA(1)=1 the mixture is completely miscible at high pressures, while closed miscibility gaps at pressures above the highest critical pressure of the pure fluids are present if fA(2)−fA(1)>1f_A^{(2)}-f_A^{(1)}>1fA(2)−fA(1)>1. We argue that this phase behaviour is driven by a competition between the entropy of mixing and the entropy of bonding, as the latter dominates in the network fluid regime.
Phase behaviour of pure and mixed patchy colloids — Theory and simulation
Current Opinion in Colloid & Interface Science, 2017
We review the phase behaviour of pure and mixed patchy colloids, as revealed (mostly) by theory and computer simulation. These experimentally-realisable systems are excellent models for investigating the general problem of the interplay between (equilibrium) phase transitions and self-assembly in soft condensed matter. We focus on how liquid-vapour condensation can be preempted by the formation of different types of aggregates, in particular rings, which we argue is relevant to the criticality of empty fluids and network fluids, and possibly also of dipolar fluids. In this connection we also discuss percolation and gelation in pure and mixed patchy colloids. Finally, we describe the rich phase behaviour of (mostly binary) patchy colloid mixtures.
The Journal of chemical physics, 2008
We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically, we study hard spheres whose surface is decorated by a small number f of identical sites ("sticky spots") interacting via a short-ranged square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to the results of Gibbs and grand canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.
Molecular Physics, 2009
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 hardcore 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 ǫ AA , ǫ BB and ǫ 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 ǫ AB = 0), the critical point exists all the way to ǫ BB /ǫ AA = 0. By contrast, when ǫ BB = 0, there is no critical point below a certain finite value of ǫ AB /ǫ 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 ǫ BB (i.e., for any fraction of BB bonds), whereas condensation of the Y-junctions requires that ǫ AB be above a finite threshold (i.e., there must be a finite fraction of AB bonds).
Bicontinuous and mixed gels in binary mixtures of patchy colloidal particles
Soft Matter, 2012
We investigate the thermodynamics and percolation regimes of model binary mixtures of patchy colloidal particles. The particles of each species have three sites of two types, one of which promotes bonding of particles of the same species while the other promotes bonding of different species. We find up to four percolated structures at low temperatures and densities: two gels where only one species percolates, a mixed gel where particles of both species percolate but neither species percolates separately, and a bicontinuous gel where particles of both species percolate separately forming two interconnected networks. The competition between the entropy and the energy of bonding drives the stability of the different percolating structures. Appropriate mixtures exhibit one or more connectivity transitions between the mixed and bicontinuous gels, as the temperature and/or the composition changes.
Phase Diagram of Patchy Colloids: Towards Empty Liquids
Physical Review Letters, 2006
We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbors offers the possibility of generating liquid states (i.e., states with temperature T lower than the liquid-gas critical temperature) with a vanishing occupied packing fraction (), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the (T-) plane, possibly favoring the establishment of homogeneous disordered materials at small , i.e., stable equilibrium gels.
Effects of patch size and number within a simple model of patchy colloids
The Journal of Chemical Physics, 2010
We report on a computer simulation and integral equation study of a simple model of patchy spheres, each of whose surfaces is decorated with two opposite attractive caps, as a function of the fraction χ of covered attractive surface. The simple model explored -the two-patch Kern-Frenkel model -interpolates between a square-well and a hard-sphere potential on changing the coverage χ. We show that integral equation theory provides quantitative predictions in the entire explored region of temperatures and densities from the square-well limit χ = 1.0 down to χ ≈ 0.6. For smaller χ, good numerical convergence of the equations is achieved only at temperatures larger than the gasliquid critical point, where however integral equation theory provides a complete description of the angular dependence. These results are contrasted with those for the one-patch case. We investigate the remaining region of coverage via numerical simulation and show how the gas-liquid critical point moves to smaller densities and temperatures on decreasing χ. Below χ ≈ 0.3, crystallization prevents the possibility of observing the evolution of the line of critical points, providing the angular analog of the disappearance of the liquid as an equilibrium phase on decreasing the range for spherical potentials. Finally, we show that the stable ordered phase evolves on decreasing χ from a threedimensional crystal of interconnected planes to a two-dimensional independent-planes structure to a one-dimensional fluid of chains when the one-bond-per-patch limit is eventually reached.