Thermodynamic properties of short-range attractive Yukawa fluid: Simulation and theory

Parameters of the Liquid-Gas-State Triangle for Hard-Core Attractive Yukawa Fluids

We discuss the triangle of the liquid-gas concept within the fluid-lattice gas isomorphism approach and the Zeno-element, taking the hard-core Yukawa fluid (HCAYF) as an example. The applicability of such an isomorphism is demonstrated by the symmetrization of binodals with mapping onto the Ising model coexistence curve. We show that the parameters of the isomorphism transformation reflect the liquid-phase instability for hard-core Yukawa potential and its generalization. We also provide a simple mean-field estimate for the parameter z of the fluid-lattice gas transformation and use it to obtain the locus of the critical point.

Phase separation and dynamical arrest of protein solutions dominated by short-range attractions

The interplay of liquid-liquid phase separation (LLPS) and dynamical arrest can lead to the formation of gels and glasses, which is relevant for such diverse fields as condensed matter physics, materials science, food engineering, and the pharmaceutical industry. In this context, protein solutions exhibit remarkable equilibrium and non-equilibrium behaviors. In the regime where attractive and repulsive forces compete, it has been demonstrated, for example, that the location of the dynamical arrest line seems to be independent of ionic strength, so that the arrest lines at different ionic screening lengths overlap, in contrast to the LLPS coexistence curves, which strongly depend on the salt concentration. In this work, we show that the same phenomenology can also be observed when the electrostatic repulsions are largely screened, and the range and strength of the attractions are varied. In particular, using lysozyme in brine as a model system, the metastable gas-liquid binodal and the dynamical arrest line as well as the second virial coefficient have been determined for various solution conditions by cloud-point measurements, optical microscopy, centrifugation experiments, and light scattering. With the aim of understanding this new experimental phenomenology, we apply the non-equilibrium self-consistent generalized Langevin equation theory to a simple model system with only excluded volume plus short-range attractions, to study the dependence of the predicted arrest lines on the range of the attractive interaction. The theoretical predictions find a good qualitative agreement with experiments when the range of the attraction is not too small compared with the size of the protein.

Hard-core attractive Yukawa fluid global isomorphism with the lattice gas model

In this work, we study the global isomorphism between the liquid–vapor equilibrium of the hardcore attractive Yukawa fluid (HCAYF) and that of the Lattice Gas (LG) model of the Ising-like type. The applicability of the global isomorphism transformation and the dependence of its parameters on the screening length of the Yukawa potential are discussed. These parameters determine both the slope of the rectilinear diameter of the liquid–vapor binodal and the Zeno-element, which are the core ingredients of the fluid–LG isomorphism. We compare the Zeno-element parameters with the virial Zeno-line parameters, which are commonly used in the literature for the formulation of generalized law of the correspondent states. It is demonstrated that the Zeno-element parameters appear to be sensitive to the liquid state instability when the interaction potential becomes too short-ranged, while the virial ones do not show any peculiarities connected with this specific of the HCAYF.

Perturbation theories for fluids with short-ranged attractive forces: A case study of the Lennard-Jones spline fluid

It is generally not straightforward to apply molecular-thermodynamic theories to fluids with short-ranged attractive forces between their constituent molecules (or particles). This especially applies to perturbation theories, which, for short-ranged attractive fluids, typically must be extended to high order or may not converge at all. Here, we show that a recent first-order perturbation theory, the uv-theory, holds promise for describing such fluids. As a case study, we apply the uv-theory to a fluid with pair interactions defined by the Lennard-Jones spline potential, which is a short-ranged version of the LJ potential that is known to provide a challenge for equation-of-state development. The results of the uv-theory are compared to those of third-order Barker–Henderson and fourth-order Weeks–Chandler–Andersen perturbation theories, which are implemented using Monte Carlo simulation results for the respective perturbation terms. Theoretical predictions are compared to an extensive dataset of molecular simulation results from this (and previous) work, including vapor–liquid equilibria, first- and second-order derivative properties, the critical region, and metastable states. The uv-theory proves superior for all properties examined. An especially accurate description of metastable vapor and liquid states is obtained, which might prove valuable for future applications of the equation-of-state model to inhomogeneous phases or nucleation processes. Although the uv-theory is analytic, it accurately describes molecular simulation results for both the critical point and the binodal up to at least 99% of the critical temperature. This suggests that the difficulties typically encountered in describing the vapor–liquid critical region are only to a small extent caused by non-analyticity.

Generalized phase behavior of cluster formation in colloidal dispersions with competing interactions

Colloidal liquids interacting with short range attraction and long range repulsion, such as proposed for some protein solutions, have been found to exhibit novel states consisting of equilibrium particle clusters. Monte Carlo simulations are performed for two physically meaningful inter-particle potentials across a broad range of interaction parameters, temperatures and volume fractions to locate the conditions where clustered states are found. A corresponding states phase behavior is identified when normalized by the critical point of an appropriately selected reference attractive fluid. Clustered fluid states and cluster percolated states are found exclusively within the two phase region of the state diagram for a reference attractive fluid, confirming the underlying intrinsic relation between clustered states and bulk phase separation. Clustered and cluster percolated states consistently exhibit an intermediate range order peak in their structure factors with a magnitude above 2.7, leading to a semi-empirical rule for identifying clustered fluids in scattering experiments.

Liquid-vapor phase diagram and surface properties in oppositely charged colloids represented by a mixture of attractive and repulsive Yukawa potentials

The liquid-vapor phase diagrams of equal size diameter σ binary mixtures of screened potentials have been reported for several ranges of interaction using Monte Carlo simulation methods [J. B. Caballero, A. M. Puertas, A. Ferńandez-Barbero, F. J. de las Nieves, J. M. Romero-Enrique, and L. F. Rull, J. Chem. Phys. 124, 054909 (2006); A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)]. Both works report controversial results about the stability of the phase diagram with the inverse Debye screening length κ. Caballero found stability for values of κσ up to 20 while Fortini reported stability for κσ up to 20 while Fortini reported stability for κσ ≤ 4. In this work a spinodal decomposition process where the liquid and vapor phases coexist through an interface in a slab geometry is used to obtain the phase equilibrium and surface properties using a discontinuous molecular dynamics simulations for mixtures of equal size particles carrying opposite charge and interacting with a mixture of attractive and repulsive Yukawa potentials at different values of κσ. An crude estimation of the triple point temperatures is also reported. The isothermal-isobaric method was also used to determine the phase stability using one phase simulations. We found that liquid-vapor coexistence is stable for values of κσ > 20 and that the critical temperatures have a maximum value at around κσ = 10, in agreement with Caballero et al. calculations. There also exists a controversy about the liquid-vapor envelope stability of the pure component attractive Yukawa model which is also discussed in the text. In addition, details about the equivalence between continuous and discontinuous molecular dynamics simulations are given, in the Appendix, for Yukawa and Lennard-Jones potentials.

Structure and thermodynamics of hard-core Yukawa fluids: thermodynamic perturbation approaches

The thermodynamic perturbation theories, which are based on the power series of a coupling constant (λ-expansion), have been proposed for studying the structural and thermodynamic properties of a hard-core Yukawa (HCY) fluid: one (A1-approximation) is the perturbation theory based on the hard-sphere repulsion as a reference system. The other (A2-approximation) is the perturbation theory based on the reference system which incorporates both the repulsive and short-range attractive interactions. The first-order mean-spherical approximation (FMSA) provided by Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] has been employed for investigating the thermodynamic properties of a HCY fluid using the alternative method via the direct correlation function. The calculated results show that (i) the A1 and A2 approximations are in excellent agreements with previous computer simulation results in the literature and compare with the semi-empirical works of Shukla including the higher-order free energy terms, (ii) the A1 and A2 approximations are better than the FMSA and the mean-spherical approximation, (iii) the A2-approximation compares with the A1-approximation, even though the perturbation effect of an A2-approximation is much smaller than that of an A1-approximation, and that (iv) the FMSA study is particularly of advantage in providing the structure and thermodynamics in a simple and analytic manner.