Fluid-fluid and fluid-solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory

Abstract

We study the Kern-Frenkel model for patchy colloids using Barker-Henderson second-order thermodynamic perturbation theory. The model describes a fluid where hard sphere particles are decorated with one patch, so that they interact via a square-well potential if they are sufficiently close one another, and if patches on each particle are properly aligned. Both the gas-liquid and fluid-solid phase coexistences are computed and contrasted against corresponding Monte Carlo simulations results. We find that the perturbation theory describes rather accurately numerical simulations all the way from a fully covered square-well potential down to the Janus limit (half coverage). In the region where numerical data are not available (from Janus to hard-spheres), the method provides estimates of the location of the critical lines that could serve as a guideline for further efficient numerical work at these low coverages. A comparison with other techniques, such as integral equation theory, highlights the important aspect of this methodology in the present context.

Effect of glycerol and dimethyl sulfoxide on the phase behavior of lysozyme: Theory and experiments

“…For example, theoretical calculations based on anisotropic attractive interactions successfully describe both the width of the binodal and the gap between the binodal, and the fluid-solid transition for aqueous protein solutions without additives. 60,79,80 Anisotropic attractive interactions are indeed induced by hydrophobic patches on the lysozyme surface, and have been taken into account in a patchy sphere model by Curtis et al 81 Anisotropic attractions as well as repulsions, e.g., as due to an anisotropic charge distribution or van der Waals interaction, are not taken into account in our DLVO model. Our model furthermore neglects nonelectrostatic contributions to the lysozyme pair potential that originate from dispersion forces between the micro-ions and proteins.…”

Self-assembly mechanism in colloids: perspectives from statistical physics

“…In the case of isotropic potential, the original method is due to Zwanzig [23], but the most useful version was given by Barker and Henderson few years later [24]. The method was recently extended to the Kern-Frenkel potential [25,26], and it is based on a second-order cumulant expansion of the excess free energy. In order to illustrate the method, let us derive the first order term.…”

“…In the present context, this means that we are starting from a fluid of hardspheres and perturbatively decorating the hard-sphere surface with a attractive patches. We now discuss how a classic perturbation theory due to Barker and Henderson [24,37,38] can be adapted to the Kern-Frenkel model to infer thermodynamical properties [25,26]. In the case of isotropic potential, the original method is due to Zwanzig [23], but the most useful version was given by Barker and Henderson few years later [24].…”

“…This will be discussed in Section 4.1. The second is a thermodynamic perturbation theory, again originally devised for isotropic potentials [23,24], and more recently applied to the Kern-Frenkel potential [25,26] (see Section 4.2). Finally, Section 5 will draw some conclusions and open perspectives.…”

How to model the interaction of charged Janus particles

“…The most straightforward approach is to model the particles as hard spheres and to use a square-well potential that is sensitive to the orientation of the patches, as introduced by Kern and Frenkel [17] . This potential can easily be implemented and is used quite often [10,11,[18][19][20][21][22][23][24] . Also variants with distance-dependent potentials, such as Lennard-Jones or Yukawa, have been employed for the simulation of hard [25] and soft spheres [9,15,[26][27][28][29][30][31] .…”