The replica Ornstein-Zernike equations for an electrolyte adsorbed in a charged, disordered matrix were applied to a model, where both subsystems consisted of points carrying a single (positive or negative) charge. While the system as a whole was electroneutral, each of the subsytems had a net charge. The results of this study are compared with the ones previously obtained, where the interactions in such a system were considered to be the same as in the case of electroneutral subsystems.
In this paper we propose and explore a method of analysis of the scattering experimental data for uniform liquid-like systems. In our pragmatic approach we are not trying to introduce by hands an artificial small parameter to work out a perturbation theory with respect to the known results e.g., for hard spheres or sticky-hard spheres (all the more that in the agreement with the notorious Landau statement, there is no any physical small parameter for liquids). Instead of it guided by the experimental data we are solving the the Ornstein-Zernike equation with a trial (variational) form of the i…
Analytic solution of the multidensity Ornstein-Zernike equation for hard-sphere fluid with tetrahedral quadrupolar-like surface adhesion
University of Ljubljana, Faculty of Chemistry and Chemical Technology（卢布尔雅那大学化学与化学技术学院）；Yukhnovskii Institute for Condensed Matter Physics（尤赫诺夫斯基凝聚态物理研究所）；Heriot-Watt University（赫瑞-瓦特大学）
We derive a dynamic Ornstein-Zernike equation for classical fluids undergoing overdamped Brownian motion and driven out of equilibrium. Inhomogeneous two-time correlation functions are obtained from functional differentiation of the one-body density and current with respect to an appropriately chosen external field. Functional calculus leads naturally to non-Markovian equations of motion for the two-time correlators. Memory functions are identified as functional derivatives of a space- and time-nonlocal power dissipation functional. We propose an excess (over ideal gas) dissipation functional …
The properties of a classical simple liquid can be strongly affected by application of an external potential that supports inhomogeneity. To understand the nature of these property changes the equilibrium particle distribution functions of the liquid have, typically, been evaluated individually as functions of system control parameters, such as the packing fraction of a hard sphere liquid. In this study we focus attention on two distribution functions that characterize the inhomogeneous liquid: the pair direct correlation function $c(\mathbf{r}_1,\mathbf{r}_2)$ and the pair correlation functio…
A key challenge for soft materials design and coarse-graining simulations is determining interaction potentials between components that give rise to desired condensed-phase structures. In theory, the Ornstein-Zernike equation provides an elegant framework for solving this inverse problem. Pioneering work in liquid state theory derived analytical closures for the framework. However, these analytical closures are approximations, valid only for specific classes of interaction potentials. In this work, we combine the physics of liquid state theory with machine learning to infer a closure directly …
The main goal of this thesis is to provide an exploration of the use of computational intelligence techniques to study the numerical solution of the Ornstein-Zernike equation for simple liquids. In particular, a continuous model of the hard sphere fluid is studied. There are two main proposals in this contribution. First, the use of neural networks as a way to parametrize closure relation when solving the Ornstein-Zernike equation. It is explicitly shown that in the case of the hard sphere fluid, the neural network approach seems to reduce to the so-called Hypernetted Chain closure. For the se…
An iterative Monte Carlo inversion method for the calculation of particle pair potentials from given particle pair correlations is proposed in this paper. The new method, which is best referred to as Iterative Ornstein-Zernike Inversion, represents a generalization and an improvement of the established Iterative Boltzmann Inversion technique [Reith, Pütz \& Müller-Plathe, J. Comput. Chem. 24, 1624 (2003)]. Our modification of Iterative Boltzmann Inversion consists of replacing the potential of mean force as an approximant for the pair potential with another, generally more accurate approximant…
Spatial distribution of reduced density of hard spheres near a hard-sphere dimer: Results from three-dimensional Ornstein-Zernike equations coupled with several different closures and from grand canonical Monte Carlo simulation
本研究使用三维 OZ 方程耦合多种闭合计算硬球二聚体附近溶剂硬球的约化密度及分布函数，发现引入桥函数使结果更接近 MC 模拟，但在三重分布函数上未必改善。
We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation to this system. The one-particle orientational distribution function has a nontrivial dependence on the orientation and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids. We solve both equations for hard ellipsoids on a sc lattice. Compared to molecular liquids, the tensorial orientational correlators exhibit less structure. However, depending on the lengths a and b of t…
A recent version of statistical associating fluid theory (SAFT), namely SAFT2, is coupled with the van der Waals and Platteeuw theory to study the alkane hydrate phase equilibrium conditions. The model is found to provide an accurate representation of the alkane hydrate dissociation conditions with and without inhibitors, such as salts, alcohols, as well as mixed salts and alcohol. Based on SAFT2, a heterosegmented SAFT equation of state is developed to model the thermodynamic properties of aqueous ionic liquid (IL) solutions, which is recently discovered as dual function gas hydrate inhibitor…
We investigate the spatial structure of dense square-shoulder fluids. To this end we derive analytical perturbative solutions of the Ornstein-Zernike equation in the low- and high-temperature limits as expansions around the known hard sphere solutions. We then discuss the suitability of perturbative approaches in relation to the Ornstein-Zernike equation.
We study the fluid inclusion of both Lennard-Jones particles and particles with competing interaction ranges --short range attractive and long range repulsive (SALR)-- in a disordered porous medium constructed as a controlled pore glass in two dimensions. With the aid of a full two-dimensional Ornstein-Zernike approach, complemented by a Replica Ornstein-Zernike integral equation, we explicitly obtain the spatial density distribution of the fluid adsorbed in the porous matrix and a good approximation for the average fluid-matrix correlations. The results illustrate the remarkable differences b…
Distribution of a two component electrolyte mixture between the model adsorbent and a bulk aqueous electrolyte solution was studied using the replica Ornstein-Zernike theory and the grand canonical Monte Carlo method. The electrolyte components were modelled to mimic the HCl/NaCl and HCl/CaCl_2 mixtures, respectively. The matrix, invaded by the primitive model electrolyte mixture, was formed from monovalent negatively charged spherical obstacles. The solution was treated as a continuous dielectric with the properties of pure water. Comparison of the pair distribution functions (obtained by the…
Using liquid integral equation theory, we calculate the pair correlations of particles that interact via a smooth repulsive pair potential in d = 4 spatial dimensions. We discuss the performance of different closures for the Ornstein-Zernike equation, by comparing the results to computer simulation data. Our results are of relevance to understand crystal and glass formation in high-dimensional systems.
It is necessary for the statistical description of collective effects in liquids to set that or other approximation between direct and pair correlation functions which describe a neighboring order. The analytical solution of the generalized Ornstein-Zernike (OZ) equation was obtained for a system of particles at T=0. It is shown that in this limit case the neighboring order disappears and the direct correlation function describes a distant order which is typical for the ideal crystal. The approximation correctly describing the limit transition liquid-solid at T=0 will have a physical meaning.
We present a study of the self consistent Ornstein-Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width delta. The main purpose of this investigation is to elucidate whether in the limit delta --> 0, the SCOZA predicts a finite value for the second virial coefficient at the critical temperature B2(Tc), and whether this theory can lead to an improvement of the approximate Percus-Yevick solution of the sticky hard-sphere (SHS) model due to Baxter [R. J. Baxter, J. Chem. Phys. 49, 2770 (1968)]. For SW of non vanishing delta, the difficulties due to the influence of the bo…
The renormalized charge of a simple two-dimensional model of colloidal suspension was determined by solving the hypernetted chain approximation and Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic behavior of the correlations functions is used to define the effective interactions between the components of the system and these effective interactions were compared to those derived from the Poisson-Boltzmann theory. The results we obtained show that, in contrast to the mean-field theory, the renormalized charge does not saturate, but exhibits a maximum value and then dec…
We compared the results of the Madden-Glandt (MG) integral equation approximation for partly-quenched systems with the commonly accepted formalism of Given and Stell (GS). The system studied was a +1:-1 restricted primitive model (RPM) electrolyte confined in a quenched +1:-1 RPM matrix. A renormalization scheme was proposed for a set of MG replica Ornstein-Zernike equations. Long-ranged direct and total correlation functions, describing the interactions between the annealed electrolyte species within the same replicas and between the annealed and matrix particles, appeared to be the same for …
A method for calculating pair correlation functions in a crystal is developed. The method is based on separating the one- and two- particle correlation functions into the symmetry conserving and the symmetry broken parts. The conserving parts are calculated using the integral equation theory of homogeneous fluids. The symmetry broken part of the direct pair correlation function is calculated from a series written in powers of order parameters and that of the total pair correlation function from the Ornstein- Zernike equation. The results found for a two-dimensional hexagonal lattice show that …
For classical Brownian systems driven out of equilibrium we derive inhomogeneous two-time correlation functions from functional differentiation of the one-body density and current with respect to external fields. In order to allow for appropriate freedom upon building the derivatives, we formally supplement the Smoluchowski dynamics by a source term, which vanishes at the physical solution. These techniques are applied to obtain a complete set of dynamic Ornstein-Zernike equations, which serve for the development of approximation schemes. The rules of functional calculus lead naturally to non-…
Effective interactions between like-charged particles immersed in an electrolyte solution were calculated using two integral equation theories, hypernetted-chain (HNC)-Ornstein--Zernike (OZ) and ionic Percus--Yevick 2 (IPY2)-OZ. When the HNC-OZ theory was adopted, the electrolyte concentration dependence of the effective interaction showed a reentrant behavior. By contrast, the IPY2-OZ theory did not indicate the behavior. Monte Carlo simulations were performed for one of the model systems, and the results agreed qualitatively with those calculated using the HNC-OZ theory.
A novel integral equations approach is applied for studying ion pairing in the restricted primitive model (RPM) electrolyte, i. e., the three point extension (TPE) to the Ornstein-Zernike integral equations. In the TPE approach, the three-particle correlation functions $g^{[3]}({\bf r}_{1},{\bf r}_{2},{\bf r}_{3})$ are obtained. The TPE results are compared to molecular dynamics (MD) simulations and other theories. Good agreement between TPE and MD is observed for a wide range of parameters, particularly where standard integral equations theories fail, i. e., low salt concentration and high io…
Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E \textbf{83}, 011201 (2011)]. It is demonstrated here that the RFA technique yields the exact solution of the Percus-Yevick (PY) closure to the Ornstein-Zernike (OZ) equation for binary mixtures at arbitrary odd dimensions. The proof relies mainly on the Fourier transforms $\hat{c}_{ij}(k)$ of the direct correlation functions defined by the OZ relation. From the analysis of the p…
Electrostatic interactions make a large contribution to solvation free energy in ionic fluids such as electrolytes and colloidal dispersions. The electrostatic contribution to solvation free energy has been ascribed to the self-energy of a charged particle. Here we apply a variational field theory based on lower bound inequality to the inhomogeneous fluids of one-component charged hard-spheres, thereby verifying that the self-energy is given by the difference between the total correlation function and direct correlation function. Based on the knowledge of the liquid state theory, the self-ener…
Monte Carlo simulations of a spherical macroion, surrounded by a size-asymmetric electrolyte in the primitive model, were performed. We considered 1:1 and 2:2 salts with a size ratio of 2 (i.e., with coions twice the size of counterions), for several surface charge densities of the macrosphere. The radial distribution functions, electrostatic potential at the Helmholtz surfaces, and integrated charge are reported. We compare these simulational data with original results obtained from the Ornstein-Zernike integral equation, supplemented by the hypernetted chain/hypernetted chain (HNC/HNC) and h…
We consider fluids where the attractive interaction at distances slightly larger than the particle size is dominated at larger distances by a repulsive contribution. A previous investigation of the effects of the competition between attraction and repulsion on the liquid-vapour transition and on the correlations is extended to the study of the stability of liquid-vapour phase separation with respect to freezing. We find that this long-range repulsive part of the interaction expands the region where the fluid-solid transition preempts the liquid-vapour one, so that the critical point becomes me…
We derive from first principles (without resorting to the replica trick) a density functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the average density profile of the fluid as well as the pair correlation of the fluid and matrix particles. For practical reasons it is preferable to use another functional: the disorder-averaged free energy plus the fluid-matrix interaction energy, which, for fixed fluid-matrix interaction potential, is a functional only of the average density profile of the fluid…
