Replica Ornstein Zernike Research Articles

Applicability of a central force water model to study adsorption in disordered hydrophobic matrices—replica Ornstein–Zernike theory

A simple central force water model to study adsorption in random Lennard-Jones-like matrices has been studied using the replica Ornstein–Zernike integral equation theory in hypernetted-chain (HNC) approximation and in HNC+bridge approximation. The structure of water in obstacle matrices of different sizes was studied, showing that the model appropriately accounts for the hydrophobic hydration. By calculating the chemical potential of water in the model adsorbent, we have constructed the adsorption isotherm. Except for the cases of highly dispersed matrices, water gets excluded from the crowded hydrophobic environment, as expected experimentally.

Rose water in random porous media: Associative replica Ornstein-Zernike theory study

The properties of water are vastly affected by its local environment or in other words the system in which water is present. There are many systems in which water is confined in pores of different sizes and shapes. We studied the system in which porous media consisted of quenched Lennard-Jones disks and water modelled as rose water which was allowed to move inside pores. Associative replica Ornstein–Zernike theory was used to calculate the properties of the system. The accuracy of the theory under different conditions was tested against Monte Carlo simulations. The advantage of the theory is that it is magnitudes faster than computer simulations. From pair distribution functions calculated with the theory, the effects of different conditions on the structure of the system was investigated. We also studied how different conditions such as fluid temperature, fluid density, matrix density and matrix particle size affect a fraction of bonded molecules, excess internal energy and isothermal compressibility.

Replica Ornstein-Zernike Theory Applied for Studying the Equilibrium Distribution of Electrolytes across Model Membranes.

By means of replica Ornstein-Zernike theory (supplemented in a few cases by Monte Carlo simulations) we examined the distribution of an annealed primitive model +1:-1 electrolyte in a mixture with uncharged hard spheres, or another model +1:-1 or +2:-1 electrolyte inside and outside the quenched vesicles, decorated by a model membrane, and across the membrane phase. We explored the influence of the size and charge of the annealed fluid on the partition equilibrium, as well as the effect of the vesicle size and membrane interaction parameters (repulsive barrier height, attractive depth, and membrane width). A hydrophobic cation, present in the mixture with NaCl, slightly enhanced the concentration of sodium ions inside the model vesicle, compared to pure NaCl solution. The replica theory was in good agreement with computer simulations and as such adequate for studying partitioning of small and hydrophobic ions or hydrophobic solutes across model membranes.

On thermodynamics and mobility of ions enclosed within charged nanoporous system

New simulations and integral equation results are presented for a model partly quenched system composed of monovalent ions. Static and dynamic properties of the system are explored using the replica Ornstein–Zernike theory in the hypernetted chain approximation and Brownian dynamic simulations. The model system consists of two subsystems: one is a collection of charged obstacles (matrix), and the other is an invading electrolyte. The overall system is electroneutral, while the subsystems are not. Charged species are represented by Lennard–Jones spheres of equal size, with either positive or negative charge in the center. The solvent is treated as a continuous dielectric. The purpose of this study is to correlate the mobility of ions (self-diffusion coefficients) with their individual activity coefficients. In addition, the effects of the matrix preparation and of the conditions of observation (dielectric constant of solvent, temperature) are investigated. For the first time, the effect of the charged obstacles on the excess internal energy of the electrolyte solution is also examined.

Self-diffusion and activity coefficients of ions in charged disordered media

Self-diffusion and single ion activity coefficients of ions of size symmetric electrolytes were studied in the presence of a collection of charged obstacles (called matrix) within a "soft" version of the primitive model of electrolyte solutions. The matrix subsystem possesses a net charge, depending on the concentration and charge of obstacles. The brownian dynamics method was used to calculate the self-diffusion coefficients of mobile species. The replica Ornstein-Zernike theory for the partly quenched systems was used to calculate the individual activity coefficients of mobile ionic species. The results reflect the competition between attractive (obstacle-counterion, co-ion-counterion), and repulsive (obstacle-co-ion) interactions in these model systems. For the simplest possible system of symmetric monovalent ions the latter effect wins: Co-ions are excluded from the area around obstacles, and this slows down their diffusion compared to that of counterions. Introduction of divalent charges into the system changes this result when the concentration of obstacles is low. We compare these results to those obtained for the corresponding fully annealed systems, i.e., where all the species are mobile. In most cases the self-diffusion and activity coefficients of counterions and co-ions in the presence of charged obstacles follow the trends of the fully annealed solution, which are dictated by the composition of the mixture. In few situations, however, the presence of charged obstacles modifies these trends. Our study allows us to clearly identify the effects due to obstacles, and to separate them from those arising from the composition of the solution. In the case of charge and size symmetric systems, the results for the individual activity coefficients fully support the hypothesis of the "electrostatic excluded volume". Thermodynamic and dynamic results are consistent in explaining the behavior of the systems studied.

Solvent primitive model for electrolyte solutions in disordered porous matrices of charged species. Replica Ornstein-Zernike theory and grand canonical Monte Carlo simulations

We present a theoretical study of a quenched–annealed system in which an annealed component is the restricted primitive model electrolyte in a mixture with an uncharged hard sphere species, i.e. the solvent primitive model (SPM), whereas a disordered quenched medium is modelled as the restricted primitive model (RPM) electrolyte. The annealed mixture is in thermal and chemical equilibrium with an external reservoir containing the same SPM. The system is studied by using the replica Ornstein–Zernike (ROZ) integral equation theory complemented with the hypernetted chain (HNC) approximation and via the grand canonical Monte Carlo simulations. We are primarily interested in collecting computer simulation data and comparing them with theoretical predictions at room temperature (298.15 K). In terms of physical observables, our focus is in the selectivity effects of adsorption of the mixture described by the adsorption isotherms as well as by the composition isotherms. The influence of the ionic matrix density and of the bulk state of the SPM mixture on adsorption and selectivity are examined in detail. Besides, we analyse the dependence of the internal energy and the constant volume heat capacity on the conditions of adsorption. Finally, we explore briefly the effects of quenching conditions of the RPM matrix on the pair distribution functions of fluid ions in the mixture. In general, the theory is in a very good agreement with computer simulations.

Self-diffusion of ions in charged nanoporous media

Self-diffusion coefficients of ions of a charge and size symmetric +1 : −1 electrolyte were studied in the presence of ionic obstacles carrying ten negative elementary charges within a “soft” version of the primitive model of electrolytes. The Brownian dynamics method was used to calculate the diffusion coefficients of mobile species. Simulations were complemented with the replica Ornstein–Zernike theory for partly-quenched systems to calculate the activity coefficients of individual ions and the Donnan exclusion coefficient. We study the influence of (i) the size of the pores, which varies with the concentration of quenched charged nanoparticles, and (ii) the presence of added salt on the mobility and thermodynamics of small ions. We show that for dilute matrices (low concentration of charged obstacles) the diffusion coefficient of counterions is smaller or equal to that of co-ions. The opposite is true for concentrated matrices: here counterions are considerably faster than co-ions. In dilute matrices, where obstacles are distributed at larger distances, the counterions are strongly attracted by fixed obstacles. As a consequence, they are slowed down in comparison with the co-ions. In concentrated matrices, where the average size of the pores is small, the counterions can take advantage of hopping from one obstacle to another, whereas the co-ions, repelled by the obstacles, need to diffuse in the space between the layers of counterions surrounding the obstacles. Thermodynamic calculations are consistent with the Brownian dynamics results.

A computational study of electrolyte adsorption in a simple model for intercalated clays

A pillared interlayered clay is represented by a two-dimensional quenched charged disordered medium, in which the pillar configuration is produced by the quench of a two-dimensional electrolyte and the subsequent removal of the anions (that act as a template). The cation charge is counterbalanced by a neutralizing background that is an ideal representation of the layer's negative charge in the experimental system. In this paper we investigate the adsorption of electrolyte particles in this charged disordered medium resorting both to the use of the replica Ornstein-Zernike equation in the hypernetted chain approximation and grand canonical Monte Carlo simulations. The theoretical approach qualitatively reproduces the simulated behavior of the adsorbed fluids. Theoretical estimates of the material porosities obtained for various types of pillar distributions are in good agreement with the simulation. We investigate the influence of the matrix on correlation functions and adsorption isotherms.

A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein–Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.

Application of Replica Ornstein-Zernike equations in studies of the adsorption of electrolyte mixtures in disordered matrices of charged particles

The Replica Ornstein-Zernike (ROZ) equations were used to study the adsorption of ions from electrolyte mixtures. The adsorbent was represented as a quenched primitive model +1: 1 size symmetric electrolyte, while the mobile particles were ions differing in charge and/or size. The ROZ equations in hypernetted-chain (HNC) approximation were tested against new Monte Carlo results in the grand canonical ensemble; good agreement between the two methods was obtained. The ROZ/HNC theory was then used to study the exclusion coefcients as a function of size and/or charge asymmetry of the annealed ions.

Colloid–polymer mixtures in the presence of quenched disorder: a theoretical and computersimulation study

We use theory and computer simulation to study the structure and phase behavior ofcolloid–polymer mixtures in the presence of quenched disorder. The Asakura–Oosawamodel (AO) (Asakura and Oosawa 1954 J. Chem. Phys. 22 1255) is used to describe thecolloid–colloid, colloid–polymer, and polymer–polymer pair interactions. We theninvestigate the behavior of this model in the presence of frozen-in (quenched) obstacles.The obstacles will be placed according to two different scenarios, both of which areexperimentally feasible. In the first scenario, polymers are distributed at positions drawnfrom an ideal gas configuration. In the second scenario, colloidal particles aredistributed at positions drawn from an equilibrium hard sphere configuration. Weinvestigate how the unmixing transition of the AO model is affected by the type ofquenched disorder. The theoretical formalism is based on the replica methodof Given and Stell (1994 Physica A 209 495). Our foremost aim is to test theaccuracy of three common closures to the replica Ornstein–Zernike equations,namely the hypernetted chain, the Percus–Yevick, and the Martinov–Sarkisovequations. The accuracy is determined by comparison with grand canonical MonteCarlo simulations. We find that, for quenched polymer disorder, all three closuresperform remarkably well. However, when quenched colloid disorder is considered,i.e. the second mentioned scenario, the predictions of all three closures worsendramatically.

Integral Equation Theory of Adsorption in Templated Materials: Influence of Molecular Attraction

Understanding the fundamental properties of fluids under confinement in templated porous media is important for the rational design of materials with tailored functions. However, theoretical descriptions remain elusive. Although a number of approaches have been developed within the replica Ornstein−Zernike (ROZ) formalism, they have thus far been limited mainly to simple species. Another challenge is associated with the general applicability of integral equation theories, originally developed for bulk liquids, to confined systems in general and, in particular, to molecular systems confined in templated structures. In this work, we extend our previous theory of molecular species adsorbed in a templated porous material (a ROZ solution to a reference interaction site model) to systems with attractive interactions. We explore the scope and applicability of direct routes toward the chemical potential in combination with several well-established closures, such as Percus−Yevick, mean spherical approximation, hypernetted chain closure (HNC), partially linearized HNC (PLHNC), and Martynov−Sarkisov. The relative accuracy, thermodynamic consistency, and ease of convergence are explored. Although only semiquantitative agreement can be expected from these approximate closure relations, we demonstrate that the proposed theory predicts templated molecular recognition with reasonable accuracy.

Phase separation of model adsorbates in random matrices

The liquid-liquid phase behavior of binary mixtures in random pores is investigated with non-additive hard spheres using both ROZ (Replica Ornstein-Zernike) integral equations and cavity biased grand canonical Monte Carlo simulations. The critical densities of the coexistence phase envelopes are determined as function of the non-additivity parameter Delta, varying from Delta = 0.2, 0.4, 0.6, up to 0.8. The matrix is made of quenched hard spheres. Its porosity is varied to ascertain the effects of confinement, with packing densities rho(0) ranging from 0.1, 0.3, to 0.5. To obtain fiduciary results from ROZ, we use the accurate ZSEP closure relation proposed earlier with and without thermodynamic consistency. The ZSEP closure is known to enforce the zero-separation theorems via special adjustable parameters in the bridge function. Two versions of this closure are used to assess their accuracies (vis-à-vis the Monte Carlo data): first ZSEP-T, namely, the ZSEP closure with added thermodynamic consistency (the Gibbs-Duhem relation); and second purely ZSEP without adding thermodynamic consistency. It is found that both closures give correct qualitative trend, with errors of ZSEP falling within 8-9%, while ZSEP-T, being more accurate, to within 1-2%. As non-additivity is increased, both versions become more accurate. The critical density rho(c) is found to decrease with decreasing porosity. In addition, rho(c) also decreases with increasing Delta, in a non-monotone fashion.

Replica Ornstein-Zernike theory of adsorption in a templated porous material: Interaction site systems

Molecular templating offers the possibility of porous materials whose selectivity rivals the molecular recognition observed in nature. The design of templated materials requires a molecular understanding of the templating effect on the material structure and performance. We present here a theoretical description of adsorption in a model templated porous material. Our model material is a quenched, equilibrated mixture of template and matrix molecular species where the template component has been subsequently removed. We propose a set of site-site [i.e., reference interaction site model (RISM)] replica Ornstein-Zernike equations relating the correlation functions of template, matrix, and adsorbing fluid molecules. To test this approach, we focus here on systems interacting via hard-sphere site-site potentials and employ a Percus-Yevick closure. We consider chain and cluster species composed of up to five spheres and observe a range of effects associated with template structure, including higher affinity toward, and enhanced templating by, compact cluster molecules. We assess these effects by grand canonical Monte Carlo simulation and discuss their implication to the design of templated molecular recognition materials.

Replica Ornstein-Zernike self-consistent theory for mixtures in random pores.

We present a self-consistent integral equation theory for a binary liquid in equilibrium with a disordered medium, based on the formalism of the replica Ornstein-Zernike (ROZ) equations. Specifically, we derive direct formulas for the chemical potentials and the zero-separation theorems (the latter provide a connection between the chemical potentials and the fluid cavity distribution functions). Next we solve a modified-Verlet closure to ROZ equations, which has built-in parameters that can be adjusted to satisfy the zero-separation theorems. The degree of thermodynamic consistency of the theory is also kept under control. We model the binary fluid in random pores as a symmetrical binary mixture of nonadditive hard spheres in a disordered hard-sphere matrix and consider two different values of the nonadditivity parameter and of the quenched matrix packing fraction, at different mixture concentrations. We compare the theoretical structural properties as obtained through the present approach with Percus-Yevick and Martinov-Sarkisov integral equation theories, and assess both structural and thermodynamic properties by performing canonical standard and biased grand canonical Monte Carlo simulations. Our theory appears superior to the other integral equation schemes here examined and provides reliable estimates of the chemical potentials. This feature should be useful in studying the fluid phase behavior of model adsorbates in random pores in general.

Water-like fluid in the presence of Lennard–Jones obstacles: predictions of an associative replica Ornstein–Zernike theory

What are the properties of water in the presence of a ‘sea’ of inert obstacles? This question arises because biological cells are highly crowded media, and it is of interest to know the properties of water inside them. It also arises for understanding water in confined molecular environments and for mixtures of water with non-polar solutes. We study two-dimensional Mercedes–Benz (MB) water that is freely mobile in a disordered, but fixed, matrix of Lennard–Jones disks. We use the associative replica Ornstein–Zernike equations supplemented by the corresponding hypernetted chain approximation, and we tested the theory using Monte Carlo simulations. We find that the structure of model water is perturbed by the presence of the obstacles. When the density of obstacles is small, the obstacles induce an increased ordering and ‘hydrogen bonding’ of the MB model molecules and increased compressibility, relative to pure fluid, in agreement with previous theoretical and experimental studies. However, interestingly, high obstacle densities reduce MB water structuring, ‘hydrogen bonding’, and compressibility, because the obstacles interfere so extensively with all the possible ways that the fluid can form good ‘hydrogen bonding’ networks.

Water-like fluid in the presence of Lennard–Jones obstacles: predictions of an associative replica Ornstein–Zernike theory

What are the properties of water in the presence of a ‘sea’ of inert obstacles? This question arises because biological cells are highly crowded media, and it is of interest to know the properties of water inside them. It also arises for understanding water in confined molecular environments and for mixtures of water with non-polar solutes. We study two-dimensional Mercedes–Benz (MB) water that is freely mobile in a disordered, but fixed, matrix of Lennard–Jones disks. We use the associative replica Ornstein–Zernike equations supplemented by the corresponding hypernetted chain approximation, and we tested the theory using Monte Carlo simulations. We find that the structure of model water is perturbed by the presence of the obstacles. When the density of obstacles is small, the obstacles induce an increased ordering and ‘hydrogen bonding’ of the MB model molecules and increased compressibility, relative to pure fluid, in agreement with previous theoretical and experimental studies. However, interestingly, high obstacle densities reduce MB water structuring, ‘hydrogen bonding’, and compressibility, because the obstacles interfere so extensively with all the possible ways that the fluid can form good ‘hydrogen bonding’ networks.

Temperature Effects in Adsorption of a Primitive Model Electrolyte in Disordered Quenched Media: Predictions of the Replica OZ/HNC Approximation

A theoretical study of a quenched−annealed system where both components were modeled as charge symmetric +1:−1 primitive model electrolytes is presented. The adsorbed model electrolyte, mimicking lithium chloride solution, was assumed to be in thermodynamic equilibrium with an external reservoir of the same electrolyte. This partly quenched system was studied by applying the replica Ornstein−Zernike (ROZ) integral equation in the hypernetted chain (HNC) approximation and the grand canonical Monte Carlo technique. The effects of the concentration of matrix ions, pre-quenching conditions, and the electrolyte and solvent conditions on the adsorption of electrolyte were examined. The results indicate that the mean activity coefficient of the adsorbed electrolyte may differ substantially from the value of the corresponding quantity in the equilibrium bulk solution. The concentration of the annealed electrolyte in the matrix can be higher (sorption) or lower (rejection) than the corresponding equilibrium bulk c...

Study of dipolar fluid inclusions in charged random matrices

Structural, thermodynamic, and dielectric properties of a dipolar fluid confined in a charged random matrix are studied by means of grand canonical Monte Carlo simulation and replica Ornstein–Zernike integral equations in the hypernetted chain approximation. The fluid is modeled by a system of dipolar hard spheres. Two matrix topologies are considered: a frozen restricted primitive model matrix and a frozen hard sphere fluid with randomly distributed negative and positive charges. Both models lead to similar results in most cases, with significant deviations from the behavior of the corresponding equilibrated mixtures. The dielectric behavior is particularly interesting, since the effect of partial quenching on the equilibrated mixture recovers the electrostatics of the pure dipolar fluid but with the presence of Coulomb tails in the dipole–dipole total correlations. Differences between the two matrix models arise more vividly in the low density regime, in which the matrix with randomly distributed charges tends to enhance dipole association around the matrix particles. The integral equation results are in relatively good agreement with the computer simulation estimates.

Computer simulation and replica Ornstein—Zernike integral equation studies of a hard-sphere dipolar fluid adsorbed into disordered porous media

By means of extensive grand canonical Monte Carlo simulations and replica Ornstein-Zernike integral equation calculations, we explore the thermodynamics and dielectric behaviour of a dipolar fluid confined in disordered matrices. Different matrix topologies are modelled using, on the one hand, quenched hard-sphere configurations and, on the other, randomly positioned spheres. This illustrates the influence of the pore size and shape on the properties of the adsorbed fluid. For the same purpose, various sizes of the matrix particles have been considered. The integral equation calculations in the hypernetted chain approximation agree quantitatively with the simulation results. As in other studies on quenched disorder, one observes that the effect of confinement when considering hard-sphere matrices is rather limited, exhibiting however a tendency to facilitate the transition to ferroelectric states, as well as favouring the gas-liquid transition. Additionally, one observes that the sensitivity of the fluid properties to changes in the size of the matrix particles is considerably larger when these are randomly positioned.