Phase diagram and structural properties of a simple model for one-patch particles (original) (raw)
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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.
Gas–liquid phase coexistence in a tetrahedral patchy particle model
2007
We evaluate the location of the gas-liquid coexistence line and of the associated critical point for the primitive model for water (PMW), introduced by Kolafa and Nezbeda (1987 Mol. Phys. 61 161). Besides being a simple model for a molecular network forming liquid, the PMW is representative of patchy proteins and novel colloidal particles interacting with localized directional short-range attractions. We show that the gas-liquid phase separation is metastable, i.e. it takes place in the region of the phase diagram where the crystal phase is thermodynamically favoured, as in the case of particles interacting via shortrange attractive spherical potentials. We do not observe crystallization close to the critical point. The region of gas-liquid instability of this patchy model is significantly reduced as compared to that from equivalent models of spherically interacting particles, confirming the possibility of observing kinetic arrest in a homogeneous sample driven by bonding as opposed to packing.
A numerical study of one-patch colloidal particles: from square-well to Janus
Phys. Chem. Chem. Phys., 2010
We perform numerical simulations of a simple model of one-patch colloidal particles to investigate: (i) the behavior of the gas-liquid phase diagram on moving from a spherical attractive potential to a Janus potential and (ii) the collective structure of a system of Janus particles. We show that, for the case where one of the two hemispheres is attractive and one is repulsive, the system organizes into a dispersion of orientational ordered micelles and vesicles and, at low T , the system can be approximated as a fluid of such clusters, interacting essentially via excluded volume. The stability of this cluster phase generates a very peculiar shape of the gas and liquid coexisting densities, with a gas coexistence density which increases on cooling, approaching the liquid coexistence density at very low T .
A spherical model with directional interactions: II. Dynamics and landscape properties
Journal of physics. Condensed matter : an Institute of Physics journal, 2010
We study a binary non-additive hard-sphere mixture with square well interactions only between dissimilar particles. An appropriate choice of the inter-particle potential parameters favors the formation of equilibrium structures with tetrahedral ordering (Zaccarelli et al 2007 J. Chem. Phys. 127 174501). By performing extensive event-driven molecular dynamics simulations, we monitor the dynamics of the system, locating the iso-diffusivity lines in the phase diagram, and discuss their location with respect to the gas-liquid phase separation. We observe the formation of an ideal gel which continuously crosses towards an attractive glass upon increasing the density. Moreover, we evaluate the statistical properties of the potential energy landscape for this model. We find that the configurational entropy, for densities within the optimal network-forming region, is finite even in the ground state and obeys a logarithmic dependence on the energy.
Interacting hard-sphere fluids in an external field
Physical Review E, 2021
We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary shape and limited range. Our method of analysis is exact in one dimension and provides demonstrably good approximations in higher dimensions. It can cope with homogeneous and heterogeneous environments. We derive an equation for the pair distribution function. The solution, to be evaluated numerically, in general, or analytically for special cases, enters expressions for the entropy and free energy functionals. For some one-dimensional systems, our approach yields analytic solutions, reproducing available exact results from different approaches.
Scaled Particle Theory for Multicomponent Hard Sphere Fluids Confined in Random Porous Media
The journal of physical chemistry. B, 2016
The formulation of scaled particle theory (SPT) is presented for a quite general model of fluids confined in a random porous media, i.e., a multicomponent hard sphere (HS) fluid in a multicomponent hard sphere or a multicomponent overlapping hard sphere (OHS) matrix. The analytical expressions for pressure, Helmholtz free energy, and chemical potential are derived. The thermodynamic consistency of the proposed theory is established. Moreover, we show that there is an isomorphism between the SPT for a multicomponent system and that for a one-component system. Results from grand canonical ensemble Monte Carlo simulations are also presented for a binary HS mixture in a one-component HS or a one-component OHS matrix. The accuracy of various variants derived from the basic SPT formulation is appraised against the simulation results. Scaled particle theory, initially formulated for a bulk HS fluid, has not only provided an analytical tool for calculating thermodynamic properties of HS flu...
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.
Two interacting particles in a spherical pore
The Journal of Chemical Physics, 2011
In this work we analytically evaluate, for the first time, the exact canonical partition function for two interacting spherical particles into a spherical pore. The interaction with the spherical substrate and between particles is described by an attractive square-well and a square-shoulder potential. In addition, we obtain exact expressions for both the one particle and an averaged two particle density distribution. We develop a thermodynamic approach to few-body systems by introducing a method based on thermodynamic measures [I. Urrutia, J. Chem. Phys. 134, 104503 (2010)] for nonhard interaction potentials. This analysis enables us to obtain expressions for the pressure, the surface tension, and the equivalent magnitudes for the total and Gaussian curvatures. As a by-product, we solve systems composed of two particles outside a fixed spherical obstacle. We study the low density limit for a many-body system confined to a spherical cavity and a many-body system surrounding a spherical obstacle. From this analysis we derive the exact first order dependence of the surface tension and Tolman length. Our findings show that the Tolman length goes to zero in the case of a purely hard wall spherical substrate, but contains a zero order term in density for square-well and square-shoulder wall-fluid potentials. This suggests that any nonhard wall-fluid potential should produce a non-null zero order term in the Tolman length.