Asymptotic decay of pair correlations in a Yukawa fluid

Sound speed in Yukawa one-component plasmas across coupling regimes

A many-body system of charged particles interacting via a pairwise Yukawa potential, the so-called Yukawa one-component plasma (YOCP), is a good approximation for a variety of physical systems. Such systems are completely characterized by two parameters: the screening parameter, κ, and the nominal coupling strength, Γ. It is well known that the collective spectrum of the YOCP is governed by a longitudinal acoustic mode, both in the weakly and strongly coupled regimes. In the long-wavelength limit, the linear term in the dispersion (i.e., ω=sk) defines the sound speed s. We study the evolution of this latter quantity from the weak- through the strong-coupling regimes by analyzing the dynamic structure function S(k,ω) in the low-frequency domain. Depending on the values of Γ and κ and w=s/v_{th} (i.e., the ratio between the phase velocity of the wave and the thermal speed of the particles), we identify five domains in the (κ,Γ) parameter space in which the physical behavior of the YOCP exhibits different features. The competing physical processes are the collective Coulomb-like versus binary-collision-dominated behavior and the individual particle motion versus quasilocalization. Our principal tool of investigation is molecular dynamics (MD) computer simulation from which we obtain S(k,ω). Recent improvements in the simulation technique have allowed us to obtain a large body of high-quality data in the range Γ={0.1-10000} and κ={0.5-5}. The theoretical results based on various models are compared in order to see which one provides the most cogent physical description and the best agreement with MD data in the different domains.

Theoretical analysis of screened many-body electrostatic interactions between charged polarizable particles

This paper builds on two previous studies [Lindgren et al., J. Comput. Phys. 371, 712 (2018) and Quan et al., "A domain decomposition method for the Poisson-Boltzmann solvation models," SIAM J. Sci. Comput. (to be published); e-print arXiv:1807.05384] to devise a new method to solve the problem of calculating electrostatic interactions in a system composed by many dielectric particles, embedded in a homogeneous dielectric medium, which in turn can also be permeated by charge carriers. The system is defined by the charge, size, position, and dielectric constant of each particle, as well as the dielectric constant and the Debye length of the medium. The effects of taking into account the dielectric nature of the particles are explored in selected scenarios where the presence of electrolytes in the medium can significantly influence the total undergoing interactions. The description of the mutual interactions between all particles in the system as being truly of many-body nature reveals how such effects can effectively influence the magnitudes and even directions of the resulting forces, especially those acting on particles that have a null net charge. Particular attention is given to a situation that can be related to colloidal particles in an electrolyte solution, where it is shown that polarization effects alone can substantially raise or lower-depending on the dielectric contrast between the particles and the medium-the energy barrier that divides particle coagulation and flocculation regions, when an interplay between electrostatic and additional van der Waals forces is considered. Overall, the results suggest that for an accurate description of the type of system in question, it is essential to consider particle polarization if the separation between the interacting particles are comparable to or smaller than the Debye length of the medium.

Representation of the direct correlation function of the hard-sphere fluid

An accurate representation of the structural pair correlation functions of the hard sphere (HS) fluid up to the freezing density is proposed which combines the pole expression for the total correlation function h(r), the Ornstein-Zernike equation, and molecular dynamics (MD) computer simulation data. In the scheme, h(r) is expressed in terms of a set of pole parameters, which reveals how the tail of the Fourier transform of h(r) contains information on the discontinuities in the derivatives of the direct correlation function (DCF). This formulation leads to a DCF expressed as the sum of a numerically obtainable part and an analytic part which consists of elementary integral terms, some of which are found to give rise to the discontinuities. An exact formula for the magnitude of these discontinuities is derived, which indicates that there is a particular density (ρ≅0.133) below which the magnitude of the discontinuities decreases with increasing order of the derivative. With the accurate MD simulation data the set of parameters that specifies h(r) was determined. These can be used to obtain the different structural functions of the HS fluid, and following the calculation stages of the pole structure scheme the DCF is obtained. From this route to the DCF the second pole of the HS fluid can be determined and the non-negligible role of the "out of core" part of the DCF at high densities is revealed. The density-dependent separation range where the two pole approximation represents well the h(r) has been determined.

Unified description of linear screening in dense plasmas

Electron screening of ions is among the most fundamental properties of plasmas, determining the effective ionic interactions that impact all properties of a plasma. With the development of new experimental facilities that probe high-energy-density physics regimes ranging from warm dense matter to hot dense matter, a unified framework for describing dense plasma screening has become essential. Such a unified framework is presented here based on finite-temperature orbital-free density functional theory, including gradient corrections and exchange-correlation effects. We find a new analytic pair potential for the ion-ion interaction that incorporates moderate electronic coupling, quantum degeneracy, gradient corrections to the free energy, and finite temperatures. This potential can be used in large-scale "classical" molecular dynamics simulations, as well as in simpler theoretical models (e.g., integral equations and Monte Carlo), with no additional computational complexity. The new potential theoretically connects limits of Debye-Hückel-Yukawa, Lindhard, Thomas-Fermi, and Bohmian quantum hydrodynamics descriptions. Based on this new potential, we predict ionic static structure factors that can be validated using x-ray Thomson scattering data.

Exponential approximation for one-component Yukawa plasma

A theory based on the exponential approximation of the liquid-state theory is applied to study properties of several models of one-component Yukawa plasma characterized by different values of the screening parameter z. The results of the new theory are compared to the results of a conventional theory, which is based on the first-order mean spherical approximation, and to the results of a Monte Carlo simulation. The new theory shows improvements in the predictions for the thermodynamic and structural properties of Yukawa plasmas with high and intermediate values of the screening parameter, z, and coupling parameter, Γ. For low values of z and Γ, the new theory is comparable in accuracy to the conventional theory, which in turn agrees well with the results of the Monte Carlo simulation.

Binary non-additive hard sphere mixtures: fluid demixing, asymptotic decay of correlations and free fluid interfaces

Using a fundamental measure density functional theory we investigate both bulk and inhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large (positive) non-additivity the mixture phase separates into two fluid phases with different compositions. We calculate bulk fluid-fluid coexistence curves for a range of size ratios and non-additivity parameters and find that they compare well to simulation results from the literature. Using the Ornstein-Zernike equation, we investigate the asymptotic, [Formula: see text], decay of the partial pair correlation functions, g(ij)(r). At low densities a structural crossover occurs in the asymptotic decay between two different damped oscillatory modes with different wavelengths corresponding to the two intra-species hard-core diameters. On approaching the fluid-fluid critical point there is a Fisher-Widom crossover from exponentially damped oscillatory to monotonic asymptotic decay. Using the density functional we calculate the density profiles for the planar free fluid-fluid interface between coexisting fluid phases. We show that the type of asymptotic decay of g(ij)(r) not only determines the asymptotic decay of the interface profiles, but is also relevant for intermediate and even short-ranged behaviour. We also determine the surface tension of the free fluid interface, finding that it increases with non-additivity, and that on approaching the critical point mean-field scaling holds.

X-ray Thomson scattering in warm dense matter at low frequencies

The low-frequency portion of the x-ray Thomson scattering spectrum is determined by electrons that follow the slow ion motion. This ion motion is characterized by the ion-ion dynamic structure factor, which contains a wealth of information about the ions, including structure and collective modes. The frequency-integrated (diffraction) contribution is considered first. An effective dressed-particle description of warm dense matter is derived from the quantum Ornstein-Zernike equations, and this is used to identify a Yukawa model for warm dense matter. The efficacy of this approach is validated by comparing a predicted structure with data from the extreme case of a liquid metal; good agreement is found. A Thomas-Fermi model is then introduced to allow the separation of bound and free states at finite temperatures, and issues with the definition of the ionization state in warm dense matter are discussed. For applications, analytic structure factors are given on either side of the Kirkwood line. Finally, several models are constructed for describing the slow dynamics of warm dense matter. Two classes of models are introduced that both satisfy the basic sum rules. One class of models is the "plasmon-pole"-like class, which yields the dispersion of ion-acoustic waves. Damping is then included via generalized hydrodynamics models that incorporate viscous contributions.

Surviving structure in colloidal suspensions squeezed from 3D to 2D

Combining colloidal-probe experiments and computer simulations, we analyze the solvation forces F of charged silica colloids confined in films of various thicknesses h. We show that the oscillations characterizing F(h), for sufficiently large h, are determined by the dominant wavelength of the bulk radial distribution function. As a consequence, both quantities display the same power-law density dependence. This is the first direct evidence, in a system treatable both by experiment and by simulation, that the structural wavelength in bulk and confinement coincide, in agreement with predictions from density functional theory. Moreover, theoretical and experimental data are in excellent quantitative agreement.

Liquid-vapor and liquid-liquid interfaces in Ising fluids: An integral equation approach

The microscopic structure and thermodynamic properties of liquid-vapor and liquid-liquid interfaces in Ising fluids are studied using an integral equation approach. The calculations are performed in the absence and presence of an external magnetic field by solving the corresponding set of Lovett-Mou-Buff-Wertheim integrodifferential equations for the one-particle density distribution functions. The two-particle inhomogeneous direct correlation functions are consistently constructed by nonlinear interpolation between the bulk ones. The bulk correlation functions of the coexisting phases are obtained from the Ornstein-Zernike equations with a modified soft mean spherical approximation for the closure relation. As a result, the density and magnetization profiles at liquid-vapor and liquid-liquid interfaces as well as the surface tension and adsorption coefficients are evaluated in a wide temperature range including subcritical regions. The influence of an external magnetic field on the liquid-vapor interfaces is also considered.

Model colloidal fluid with competing interactions: Bulk and interfacial properties

Using a simple mean field density functional theory (DFT), the authors investigate the structure and phase behavior of a model colloidal fluid composed of particles interacting via a pair potential which has a hard core of diameter sigma, is attractive Yukawa at intermediate separations, and is repulsive Yukawa at large separations. The authors analyze the form of the asymptotic decay of the bulk fluid correlation functions, comparing results from DFT with those from the self-consistent Ornstein-Zernike approximation (SCOZA). In both theories the authors find rich crossover behavior, whereby the ultimate decay of correlation functions changes from monotonic to long wavelength damped oscillatory decay on crossing certain lines in the phase diagram or sometimes from oscillatory to oscillatory with a longer wavelength. For some choices of potential parameters the authors find, within the DFT, a lambda line at which the fluid becomes unstable with respect to periodic density fluctuations. SCOZA fails to yield solutions for state points near such a lambda line. The propensity towards clustering of particles, which is reflected by the presence of a long wavelength (>>sigma) slowly decaying oscillatory pair correlation function, and a structure factor that exhibits a very sharp maximum at small but nonzero wave numbers, is enhanced in states near the lambda line. The authors present density profiles for the planar liquid-gas interface and for fluids adsorbed at a planar hard wall. The presence of a nearby lambda transition gives rise to pronounced long wavelength oscillations in the one-body density profiles at both types of interface.

Screening in Yukawa fluid mixtures

The effective pair potential between mesoscopic charged particles in a neutralizing background medium takes a Yukawa form exp(-lambda r)/r with screening length lambda(-1). We consider a dilute suspension of such Yukawa particles dispersed in a solvent with correlation length xi<lambda(-1) and show that the Yukawa interaction is screened if the pair potentials between solvent particles exhibit Yukawa decay with the same screening length lambda(-1). However, if the solvent pair potentials are shorter ranged than the solute Yukawa potentials, then the effective potential between pairs of solute particles is unscreened, i.e., the effective potential between the solute particles is equal to the bare potential at large particle separations.

Pair-correlation functions and phase separation in a two-component point Yukawa fluid

We investigate the structure of a binary mixture of particles interacting via purely repulsive point Yukawa pair potentials with a common inverse screening length lambda. Using the hypernetted chain closure to the Ornstein-Zernike equations, we find that for a system with "ideal" (Berthelot mixing rule) pair-potential parameters for the interaction between unlike species, the asymptotic decay of the total correlation functions crosses over from monotonic to damped oscillatory on increasing the fluid total density at fixed composition. This gives rise to a Kirkwood line in the phase diagram. We also consider a "nonideal" system, in which the Berthelot mixing rule is multiplied by a factor (1+delta). For any delta>0 the system exhibits fluid-fluid phase separation and remarkably the ultimate decay of the correlation functions is now monotonic for all (mixture) state points. Only in the limit of vanishing concentration of either species does one find oscillatory decay extending to r=infinity. In the nonideal case the simple random-phase approximation provides a good description of the phase separation and the accompanying Lifshitz line.

Density functional theory for the freezing of soft-core fluids

We present a simple density functional theory for the solid phases of systems of particles interacting via soft-core potentials. In particular, we apply the theory to particles interacting via repulsive point Yukawa and Gaussian pair potentials. We find qualitative agreement with the established phase diagrams for these systems. The theory is able to account for the bcc-fcc solid transitions of both systems and the re-entrant melting that the Gaussian system exhibits.

Equilibrium properties and phase diagram of two-dimensional Yukawa systems

Properties of two-dimensional strongly coupled Yukawa systems are explored through molecular dynamics simulations. An effective coupling coefficient gamma* for the liquid phase is introduced on the basis of the constancy of the first peak amplitude of the pair-correlation functions. Thermodynamic quantities are calculated from the pair-correlation function. The solid-liquid transition of the system is investigated through the analysis of the bond-angular order parameter. The static structure function satisfies consistency relation, attesting to the reliability of the computational method. The response is shown to be governed by the correlational part of the inverse compressibility. An analysis of the velocity autocorrelation demonstrates that this latter also exhibits a universal behavior.