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 second proposal, we explore the fact that if more physical information is incorporated into the theoretical formalism, a better estimate can be obtained with the use of evolutionary optimization techniques. When choosing the modified Verlet closure relation, and leaving a couple of free parameters to be adjusted, the results are as good as those obtained from molecular simulations. The thesis is then closed with a brief summary of the main findings and outlooks on different ways to improve the proposals presented here.
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 …
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 …
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…
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…
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…
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 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…
Line optical tweezer and colloidal-probe atomic force microscopy can measure force curves between two large colloidal particles of chemically the same surfaces in a suspension of small colloidal particles. Recently, the authors proposed a transform theory to obtain the number density distribution of the small colloidal particles on the large colloidal particle from the force curve. In this short letter, we propose another method which utilizes Ornstein-Zernike equation coupled with a closure equation instead of Kirkwood superposition approximation. The new transform theory uses a structure fac…
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…
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.
Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, $h_λ({\bf r},{\bf r}')$, where $λ$ determines the interaction strength. To obtain $h_λ({\bf r},{\bf r}')$ we use the Ornstein-Zernike equation, and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. As the two equations do not form a closed set, an approximate closure relation is required and it determines a type of an approximation. In the present work we investigate the random phase approximation (RPA) closure. We determine th…
The Ornstein-Zernike equation is solved for the hard-sphere and square-well fluids using a diverse selection of closure relations; the attraction range of the square-well is chosen to be $λ=1.5.$ In particular, for both fluids we mainly focus on the solution based on a three-parameter version of the Verlet closure relation [Mol. Phys. 42, 1291-1302 (1981)]. To find the free parameters of the latter, an unconstrained optimization problem is defined as a condition of thermodynamic consistency based on the compressibility and solved using Evolutionary Algorithms. For the hard-sphere fluid, the re…
