Thermodynamic and structural properties of repulsive hard-core Yukawa fluid: integral equation theory, perturbation theory and Monte Carlo simulations

The thermodynamic and structural properties of purely repulsive hard-core Yukawa particles in the fluid state are determined through Monte Carlo simulation and modeled using perturbation theory and integral equation theory in the mean spherical approximation (MSA). Systems of particles with Yukawa screening lengths of 1.8, 3.0, and 5.0 are examined with results compared to variations of MSA and perturbation theory. Thermodynamic properties were predicted well by both theories in the fluid region up to the fluid-solid phase boundary. Further, we found that a simplified exponential version of the MSA is the most accurate at predicting radial distribution function at contact. Radial distribution function of repulsive hard-core Yukawa particles are also reported. The results show that methods based on MSA and perturbation theory that are typically applied to the attractive hard-core Yukawa potential can also be extended to the purely repulsive hard-core Yukawa potential.     

Charge reversal in real colloids: Experiments, theory and simulations

In the last years, the inclusion of ionic short-range correlations in the study of colloidal stability has led to significant disagreements with the predictions obtained from classical treatments. An example of these discrepancies is the occurrence of charge reversal of charged particles. In order to shed light on this issue, the charge reversal of latex particles in the presence of asymmetric electrolytes has been investigated through Monte Carlo (MC) simulations. In particular, experimental results concerning electrophoretic mobility reversals and the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) predictions have been compared with simulations in which two alternative methods for evaluating energies have been applied. A realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, the existence of a reversal in the electrophoretic mobility due to ion size correlations and without requiring specific counterion adsorption is probed. Moreover, the simulations appears as a useful tool for explaining those results in which the HNC/MSA does not reproduce the experimental trends.     

On attractive interaction of a colloid pair of like charge at infinite dilution

Numerical data on the potential of mean force W(r) at infinite dilution of a highly charged colloid pair embedded in a 1:1 electrolyte are reported. The authors obtain attractive minima (W<0) at short interparticle distance in these potential functions in hypernetted chain (HNC) approximation, as salt concentration is increased. These minima, however, disappear in all system sets studied when a self-consistent Zerah-Hansen (ZH) closure is used. The authors infer that the attractive minima obtained in a HNC closure are spurious and result from the neglect of bridge diagrams in HNC approximation. An expression of bridge function, which the ZH closure in effect incorporates in W(r) to remove attractive minima, is derived in terms of modification of correlation functions. Features of repulsive pair potentials obtained using the ZH closure, their dependence on particle charge and salt concentration, and their agreement with those of the Derajguin-Landau-Verwey-Overbeek theory are investigated.     

Cluster formation in two-Yukawa fluids

We present a different and efficient method for implementing the analytical solution of Ornstein-Zernike equation for two-Yukawa fluids in the mean spherical approximation. We investigate, in particular, the conditions for the formation of an extra low-Q peak in the structure factor, which we interpret as due to cluster formation in the two-Yukawa fluid when the interparticle potential is composed of a short-range attraction and a long-range repulsion. We then apply this model to interpret the small angle neutron scattering data for protein solutions at moderate concentrations and find out that the presence of a peak centered at Q=0 (zero-Q peak) besides the regular interaction peak due to charged proteins implies an existence of long-range attractive interactions besides the charge repulsion.     

The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: an integral equation study

The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation for a totally asymmetric primitive model electrolyte around a spherical macroparticle is obtained and solved numerically in the case of size-asymmetric systems. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular-dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential versus charge relationship, radial distribution functions, mean electrostatic potential, and cumulative reduced charge for representative examples of 1:1 and 2:2 salts with a size-asymmetry ratio of 2. Our results are collated with those of the modified Gouy-Chapman (MGC) and unequal radius modified Gouy-Chapman (URMGC) theories and with those of HNC/MSA in the restricted primitive model (RPM) to assess the importance of size-asymmetry effects. One of the most striking characteristics found is that, contrary to the general belief, away from the point of zero charge the properties of an asymmetric electrical double layer (EDL) are not those corresponding to a symmetric electrolyte with the size and charge of the counterion, i.e., counterions do not always dominate. This behavior suggests the existence of a new phenomenology in the EDL that genuinely belongs to a more realistic size-asymmetric model where steric correlations are taken into account consistently. Such novel features cannot be described by traditional mean-field theories such as MGC, URMGC, or even by enhanced formalisms, such as HNC/MSA, if they are based on the RPM.     

Phase behavior of attractive and repulsive ramp fluids: integral equation and computer simulation studies

Using computer simulations and a thermodynamically self-consistent integral equation we investigate the phase behavior and thermodynamic anomalies of a fluid composed of spherical particles interacting via a two-scale ramp potential (a hard core plus a repulsive and an attractive ramp) and the corresponding purely repulsive model. Both simulation and integral equation results predict a liquid-liquid demixing when attractive forces are present, in addition to a gas-liquid transition. Furthermore, a fluid-solid transition emerges in the neighborhood of the liquid-liquid transition region, leading to a phase diagram with a somewhat complicated topology. This solidification at moderate densities is also present in the repulsive ramp fluid, but in this case inhibits the fluid-fluid separation.     

Electrokinetic properties of monovalent electrolytes confined in charged nanopores: Effect of geometry and ionic short-range correlations

The electrokinetic properties (such as capillary conductance, electroviscosity, and the streaming potential) are obtained for a restricted primitive model electrolyte confined in a slitlike nanopore made up of two infinite parallel plates and in a cylindrical cavity of infinite extension. The hypernetted chain/mean spherical approximation (HNC/MSA) is used to obtain the equilibrium ionic concentration profiles inside the pores, which in turn are used to calculate the electrokinetic properties via linear hydrodynamic equations. Our results are compared with those obtained via the classical Poisson–Boltzmann (PB) theory. Important quantitative and qualitative effects, attributed to geometry and to the proper consideration of short-range correlations by HNC/MSA, are discussed.     

Structure of inhomogeneous attractive and repulsive hard-core yukawa fluid: grand canonical Monte Carlo simulation and density functional theory study

A density functional theory is proposed for an inhomogeneous hard-core Yukawa (HCY) fluid based on Rosenfeld's perturbative method. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-core repulsion and a quadratic functional Taylor expansion for the long-ranged attractive or repulsive interactions. To test the established theory, grand canonical ensemble Monte Carlo simulations are carried out to simulate the density profiles of attractive and repulsive HCY fluid near a wall. Comparison with the results from the Monte Carlo simulations shows that the present density functional theory gives accurate density profiles for both attractive and repulsive HCY fluid near a wall. Both the present theory and simulations suggest that there is depletion for attractive HCY fluid at low temperature, but no depletion is found for repulsive HCY fluid. The calculated results indicate that the present density functional theory is better than those of the modified version of the Lovett-Mou-Buff-Wertheim and other density functional theories. The present theory is simple in form and computationally efficient. It predicts accurate radial distribution functions of both attractive and repulsive HCY fluid except for the repulsive case at high density, where the theory overestimates the radial distribution function in the vicinity of contact.     

Application of Lagrangian theorem-based density-functional approximation free of adjustable parameters to nonhard-sphere fluid

A recently proposed parameter free version of a Lagrangian theorem-based density functional approximation (LTDFA) [S. Zhou, Phys. Lett. A 319, 279 (2003)] for hard-sphere fluid is applied to hard-core attractive Yukawa model fluid by dividing bulk second-order direct correlation function (DCF) of fluid under consideration into hard-core part and tail part. The former is treated by the parameter free version of the LTDFA, while the tail part is treated by second-order functional perturbation expansion approximation as done in a recent partitioned DFA [S. Zhou, Phys. Rev. E 68, 061201 (2003)]. Two versions of mean spherical approximation (MSA) for the bulk second-order DCF are employed as input, one is the less accurate plain MSA whose tail part of the second-order DCF is strictly independent of a density argument, the other is the more accurate inverse temperature expansion version of the MSA whose tail part is not strictly independent of the density argument. Calculational results indicate that prediction based on the plain MSA is far more accurate than that based on the inverse temperature expansion version of the MSA. The reason is considered to be that the partitioned DFA requires that the tail part is highly or completely independent of the density argument, the plain MSA, by assuming that the tail part is exactly the potential itself, embodies all of the nonlinearities into the hard-core part which can be treated satisfactorily by the parameter free version of the LTDFA. The present investigation results in a universal method for constructing DFA for nonuniform any nonhard-sphere interaction potential fluids.     

Generalization of the friction theory for viscosity modeling

The friction theory (FT) approach relates the viscosity of a fluid to its equation of state (EoS), and it is known to give good results for a large number of compounds over wide ranges of temperature and pressure. Previous FT versions were restricted to use EoS of the van der Waals type, i.e., EoS explicitly consisting of a repulsive and an attractive term, which limited the number of usable EoS as well as the accuracy of the viscosity predictions. In this work, the restriction is removed by means of a pragmatic generalized definition of repulsive and attractive terms based on the internal pressure concept. As a result, the FT theory can be extended to practically all types of EoS, from theoretical ones (e.g., EoS based on thermostatistical or renormalization theories) to the highly accurate empirical reference EoS. In combination with the later, the FT is shown to represent experimental viscosity data for several fluids, including water, with an accuracy as high as that required for reference models. Additionally, some relevant phenomena, such as the critical anomaly, appear to follow naturally from the physics already built into the EoS.     

Electric double layers with electrolyte mixtures: integral equations theories and simulations

A study of a planar electric double layer (EDL) in the presence of mixtures of electrolyte is presented. In particular, results from the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) theory are compared with Monte Carlo (MC) simulations. In this way, the charge inversion induced by mixtures of multivalent and monovalent counterions is probed. Since overcharging phenomena in nature emerge under such conditions, the role of ion-ion correlations in the EDL appears as a crucial point in this kind of study. Unlike previous related works, a realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, a qualitative agreement between the results obtained from the theory and MC simulations is found. However, some discrepancies arise when the charge inversion is expected to be more noticeable, namely at high surface charges and/or elevated concentrations of multivalent electrolytes. Such differences are explained in terms of an overestimation of the charge inversion by the integral equation (IE) formalism.     

Further test of third order + second-order perturbation DFT approach: hard core repulsive Yukawa fluid subjected to diverse external fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.     

Hydration of ionic species studied by the reference interaction site model with a repulsive bridge correction

We have tested the reference interaction site model (RISM) for the case of the hypernetted chain (HNC) and the partially linearized hypernetted chain (PLHNC) closures improved by a repulsive bridge correction (RBC) for ionic hydrated species. We have analyzed the efficiency of the RISM/HNC+RBC and RISM/PLHNC+RBC techniques for decomposition of the electrostatic and the nonpolar hydration energies on the energetic and the enthalpic parts for polyatomic ions when the repulsive bridge correction is treated as a thermodynamic perturbation, and investigate the repulsive bridge effect on the electrostatic potential induced by solvent on solute atoms. For a number of univalent and bivalent atomic ions, molecular cations, and anions, the method provides hydration energies deviating only by several percents from the experimental data. In most cases, the enthalpic contributions to the free energies are also close to the experimental results. The above models are able to satisfactory predict the hydration energies as well as the electrostatic potential around the ionic species. For univalent atomic ions, they also provide qualitative estimates of the Samoilov activation energies.     

Toward the description of electrostatic interactions between globular proteins: potential of mean force in the primitive model

Monte Carlo simulations are used to calculate the exact potential of mean force between charged globular proteins in aqueous solution. The aim of the present paper is to study the influence of the ions of the added salt on the effective interaction between these nanoparticles. The charges of the model proteins, either identical or opposite, are either central or distributed on a discrete pattern. Contrarily to Poisson-Boltzmann predictions, attractive, and repulsive direct forces between proteins are not screened similarly. Moreover, it has been shown that the relative orientations of the charge patterns strongly influence salt-mediated interactions. More precisely, for short distances between the proteins, ions enhance the difference of the effective forces between (i) like-charged and oppositely charged proteins, (ii) attractive and repulsive relative orientations of the proteins, which may affect the selectivity of protein/protein recognition. Finally, such results observed with the simplest models are applied to a more elaborate one to demonstrate their generality.     

Negative electron affinities from conventional electronic structure methods

If the potential V describing the interaction between an excess electron and a ground-state neutral or anionic parent is sufficiently attractive at short range, electron-attached states having positive electron affinities (EAs) can arise. Even if the potential is not attractive enough to produce a bound state, metastable electron-attached states may still occur and have lifetimes long enough to give rise to experimentally detectable signatures. Low-energy metastable states arise when the attractive components of V combine with a longer-range repulsive contribution to produce a barrier behind which the excess electron can be temporarily trapped. These repulsive contributions arise from either the centrifugal potential in the excess electron’s angular kinetic energy or long-range Coulomb repulsion in the case of an anionic parent. When there is no barrier, this kind of low-energy metastable state does not arise, but improper theoretical calculations can lead to erroneous predictions of their existence. Conventional electronic structure methods with, at most, minor modifications are described for properly characterizing metastable states and for avoiding incorrectly predicting the existence of metastable states with negative EAs where no barrier is present.     

Phase coexistence in polydisperse multi-Yukawa hard-sphere fluid: high temperature approximation

High temperature approximation (HTA) is used to describe the phase behavior of polydisperse multi-Yukawa hard-sphere fluid mixtures. It is demonstrated that in the frames of the HTA the model belongs to the class of "truncatable free energy models," i.e., the models with thermodynamical properties (Helmholtz free energy, chemical potential, and pressure) defined by the finite number of generalized moments. Using this property we were able to calculate the complete phase diagram (i.e., cloud and shadow curves as well as binodals) and size distribution functions of the coexisting phases of several different models of polydisperse fluids. In particular, we consider polydisperse one-Yukawa hard-sphere mixture with factorizable Yukawa coefficients and polydisperse Lennard-Jones (LJ) mixture with interaction energy parameter and/or size polydispersity. To validate the accuracy of the HTA we compare theoretical results with previously published results of more advanced mean spherical approximation (MSA) for the one-Yukawa model and with the Monte Carlo (MC) computer simulation results of [Wilding et al. J. Chem. Phys. 121, 6887 (2004); Phys. Rev. Lett. 95, 155701 (2005)] for the LJ model. We find that overall predictions of the HTA are in reasonable agreement with predictions of the MSA and MC, with the accuracy range from semiquantitative (for the phase diagram) to quantitative (for the size distribution functions).     

Protein interactions studied by SAXS: effect of ionic strength and protein concentration for BSA in aqueous solutions

We have studied a series of samples of bovine serum albumin (BSA) solutions with protein concentration, c, ranging from 2 to 500 mg/mL and ionic strength, I, from 0 to 2 M by small-angle X-ray scattering (SAXS). The scattering intensity distribution was compared to simulations using an oblate ellipsoid form factor with radii of 17 x 42 x 42 A, combined with either a screened Coulomb, repulsive structure factor, SSC(q), or an attractive square-well structure factor, SSW(q). At pH = 7, BSA is negatively charged. At low ionic strength, I < 0.3 M, the total interaction exhibits a decrease of the repulsive interaction when compared to the salt-free solution, as the net surface charge is screened, and the data can be fitted by assuming an ellipsoid form factor and screened Coulomb interaction. At moderate ionic strength (0.3-0.5 M), the interaction is rather weak, and a hard-sphere structure factor has been used to simulate the data with a higher volume fraction. Upon further increase of the ionic strength (I >or= 1.0 M), the overall interaction potential was dominated by an additional attractive potential, and the data could be successfully fitted by an ellipsoid form factor and a square-well potential model. The fit parameters, well depth and well width, indicate that the attractive potential caused by a high salt concentration is weak and long-ranged. Although the long-range, attractive potential dominated the protein interaction, no gelation or precipitation was observed in any of the samples. This is explained by the increase of a short-range, repulsive interaction between protein molecules by forming a hydration layer with increasing salt concentration. The competition between long-range, attractive and short-range, repulsive interactions accounted for the stability of concentrated BSA solution at high ionic strength.     

A new cubic simplified perturbed hard-body equation of state

A new cubic equation of state (EOS) was developed in this study for vapor-liquid equilibrium (VLE) calculations of nonpolar fluids. The repulsive term of this EOS reexpressed the results of Walsh and Gubbins (1990) from their modified thermodynamic perturbation theory of polymerization into a simple form in which a non-spherical parameter was employed to account for the different shapes of molecules. The repulsive compressibility factors calculated from this EOS agree well with the molecular simulation data for various kinds of hard bodies ranging from a single hard sphere to tangent or fused long chain molecules. A simple attractive term was then coupled with the repulsive to complete the EOS in a cubic form. Equation parameters were determined for a diversity of nonpolar real fluids. These parameters were expressed in generalized forms for engineering computations. Satisfactory results from this EOS on the saturated properties of pure nonpolar fluids were obtained. This EOS was also extended to calculate the VLE of nonpolar fluid mixtures. The results are again satisfactory over wide ranges of temperature and pressure.