Electrolytes at charged interfaces: Ion–ion–interface three-body correlation functions

The structure and thermodynamics for model 2–2 electrolytes at a charged interface have been determined by the so-called “pair” approximation of integral equation theory. In addition to Coulombic interactions, the potential models for the ion–ion and ion–wall interactions employ “soft” continuous potentials rather than “hard”-sphere or “hard”-wall potentials. The solvent is modeled as a structureless dielectric continuum at 25 °C. The structure is calculated using the inhomogeneous Ornstein–Zernike relation, together with the hypernetted chain closure and two choices for the functional relationship between the singlet and pair correlation functions. Both the interfacial density profile and the inhomogeneous pair correlation functions are calculated. Some thermodynamic properties of these systems are also evaluated. The results of the pair approximation are compared with the so-called “singlet” approximation, selected computer simulation results, Gouy–Chapman–Stern predictions, and experimental data. While qualitative agreement is generally found between the two levels of integral equation approximation, measurable quantitative improvements exist for both structural and thermodynamic predictions in the pair approximation.

Theory of the interface between a classical plasma and a hard wall

In the primitive model of the electric double layer an electrolyte near a charged surface is modeled by an assembly of charged hard spheres in a medium of dielectric constant ε. We solve numerically the inhomogeneous Ornstein–Zernike equation for the pair correlation functions in the hypernetted chain and mean spherical approximations together with the Lovett–Mou–Buff–Wertheim equation for the density of the ions near a charged surface. For highly charged surfaces the profiles display layering and charge reversal. The density profiles and diffuse layer potential are generally in excellent agreement with Monte Carlo data. The pair correlation functions at small separation are significantly different from correlation functions in the bulk and at larger separation have the well-known power law decay (r−3) as function of separation when both hard spheres are kept at constant distance from the surface.

The adsorption of associating hard spheres on a hard wall by using the nonuniform Percus–Yevick equation for the local density and the pair correlation functions is studied. A comparison of the density profiles with computer simulation data indicates that this approximation predicts the fluid structure significantly better than the singlet Percus–Yevick and hypernetted chain approximations.

Capillary waves of a vapor-liquid interface in a gravitational field very close to the critical temperature

We report results for the electronic, structural and dynamical properties of liquid GaAs simulated by using ab initio molecular dynamics. Results for the total and partial structure factors, self-diffusion properties, pair correlation and angular distribution functions, and the electronic density of states are presented. Our calculated structure factor and pair correlation functions are in good agreement with available experimental data. A “common neighbor” cluster analysis is used to examine the structure of the liquid.

We have investigated the liquid‐like 3D Yukawa system of microparticles confined in a cubic box with the hard walls. The general reconstruction technique (see E. M. Apfelbaum, Phys. Plasmas 14, 123703 (2007)) has been applied to reconstruct the interparticle interaction potential from the obtained pair correlation function at different values of the coupling parameter Γ. It has been shown that for the cases Γ>1 when the pair correlation functions are nonmonotonic, the techniques can not be used to reconstruct the potential, while it is possible to do for the small Γ values (Γ>>1).

ABSTRACTA field-theoretical approach is applied to study the structure of an oscillating Yukawa fluid in contact with a hard wall. The system is described beyond the mean field approximation with the Gaussian fluctuations taken into account. Analytical expressions for the pair correlation function, the density profiles, and the adsorption coefficient are derived. These results are analysed for different values of the temperature and the bulk density as well as the parameters of the pair potential. In order to estimate the validity of the applied approximations, the theoretical results are compared with the original computer simulations data. We show that the Gaussian approximation provides a much better description of the fluid density profile as compared to the mean field approximation.

ABSTRACTWe formulate an approach to the A + A → products reaction based on a reaction-diffusion model. We construct the first equations in a moment hierarchy whose first two members are the global density of A particles and the pair correlation function. We terminate the hierarchy by relating the three-particle correlation function to two-particle correlation functions and thereby obtain a set of coupled equations that turns out to be linear and hence analytically tractable.This approach leads naturally to the proportionality of the rate of the reaction to the pair correlation function evaluated at r=a, where a is the diameter of the reacting particles. It also confirms the relation between anomalous kinetics and the deviation of the pair correlation function from that associated with a random distribution of particles.Numerical simulations in one and two dimensions that support our theory are presented in a companion paper in this session.

The Percus-Yevick integral equation has been solved for hard spherocylinders, using an algorithm introduced in a previous paper. The pair correlation function (PCF) and the direct correlation function have been obtained and the dependence of these functions on the elongation as well on the numerical density is presented. Some of the spherical harmonic coefficients corresponding to the PCF are also shown and compared with Monte Carlo simulations. The best agreement is obtained for intermediate elongations, corresponding to molecules such as Cl2 and for the first harmonic coefficient. The variation of the PCF of selected orientations with density is similar to that of hard spheres. Nevertheless, the variation for each orientation with elongation is more complicated trending to the hard sphere limit in different ways.

Molecular dynamics simulation investigation of hexanoic acid adsorption onto calcite ([formula omitted])surface

We study the asymptotic behavior of the position-orientation profile ρ(1) for a dipolar hard sphere fluid in contact with a neutral hard wall. First, by a virial expansion we show that ρ(1) is not totally determined by the classical image potential, i.e., by a dielectric continuum model. The exact expression of ρ(1) far from the wall is derived by using a renormalized cluster expansion. As predicted by the dielectric continuum model, ρ(1) exhibits an orientational structure and a long tail which decreases as the inverse cubic power of the distance to the wall. We first examine the density profile ρ0(1) which corresponds to the isotropic part of ρ(1). We show that ρ0(1) contains a part reminiscent of the image potential but also some contributions which depends on the pair correlation function and the triplet direct correlation function in bulk phase. When this last function is neglected, ρ0(1) can be considered as the result of a force balance in the interface. In the general result, the triplet direct correlation allows us to obtain a very compact expression for ρ0(1). It is shown that the asymptotic behavior of ρ0(1) reveals the same microscopic properties as the classical electrostriction phenomena which is observed in bulk phase and in presence of an external electric field. Thus, ρ0(1) can be considered as the result of a natural electrostriction induced in the interfacial region by the image potential. The term of lowest symmetry in the orientational structure describes the alignment of a molecule relative to the normal to the wall. Far from the wall, the orientational profile is proportional to the dipolar contribution of the Kerr constant. Thus, the asymptotic behavior of the profile and the Kerr effect are determined by the same function characterizing the alignment of dipoles. This alignment is observed via an external field in the case of the usual Kerr effect and it is naturally induced by the image potential in the interfacial region. The triplet direct correlation function gives rise also to some additional orientational structures which are ignored in the dielectric continuum model. The exact results derived in this paper include some bridge diagrams and consequently they are beyond the wall–particle hypernetted chain approximation.

A microscopic theory is developed which can describe many of the structural and thermodynamic properties of infinitely dilute solutions of apolar solutes in liquid water. The theory is based on an integral equation for the pair correlation functions associated with spherical apolar species dissolved in water. It requires as input the experimentally determined oxygen–oxygen correlation function for pure liquid water. The theory is tested by computing thermodynamic properties for aqueous solutions of apolar solute species. The predictions of both the Henry’s Law constant and the entropy of solution are in good agreement with experiment. The calculation of the latter quantity is essentially independent of any adjustable parameters. It is shown how the correlation functions we have calculated can be used to predict the solubility of more complicated, aspherical, and nonrigid solutes in liquid water. For the more complex molecules it is convenient to study the difference between the excess chemical potential of the molecule and the chemical potentials of its separated components (Ben-Naim’s measure of the hydrophobic interaction strength δA(HI)M). A generalized formula for δA(HI)M is presented which reduces to Ben-Naim’s result in the special case of a rigid solute. The calculations of δA(HI)M for normal alkanes through n-decane are independent of unknown and adjustable mean field parameters. For ethane, the theoretical results for δA(HI)M are in good agreement with experimental data. To treat longer alkanes multipoint correlation functions are required. It is shown that the standard superposition approximation for the multipoint correlation functions predicts qualitatively incorrect results. A correction to the superposition approximation is developed. Its use yields theoretical values for δA(HI)M which agree well with experiment. We also calculate free energies of transfer of n-alkane solutes from a hydrocarbon solvent to liquid water. Here, too, our results are in good agreement with experiment. After testing the theory against experiment, several experimentally inaccessible aspects of the hydrophobic effect are discussed. Analysis of pair correlation functions between spherical apolar species indicates that the hydrophobic interaction becomes more attractive as the solute size is increased at constant temperature, or as the temperature is decreased. The solute–solute correlations in liquid water are compared with those in a nonassociated (hard-spherelike) solvent. Plots are presented which indicate that the insertion of an apolar species increases the intermolecular structure of water in the vicinity of the apolar solute. The effects of solvent environments on the conformations of small chain molecules are discussed. It is shown that hydrocarbon solvents as well as water tend to reduce the spatial extension of the chain molecules from what is found in the gas phase. However, calculations which take cognizance of the detailed structure of the solvent liquids reveal that the average conformational structure of some n-alkanes may be more compact in some nonassociated solvents than in water.

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.

With the CHARMM22 (Chemistry at Harvard Macromolecular Mechanics) all-atom nonbonded potential parameters for alanine dipeptide solute and the transferable intermolecular potential model water for the solvent, the reference interaction site model (RISM) integral equations with the hypernetted chain closure are solved to obtain all the atomic solvent–solute radial distribution functions. The solvation structures of alanine dipeptide in its seven conformations: C7eq, C7ax, C5, αR, β, αL and PII, in aqueous solution are analyzed at the atomic level in terms of the atomic solute–solvent radial distribution functions. At a temperature of T=298.15 K and bulk water density ρ=0.9970 g cm−3, the corresponding solvation free energies are calculated by using Singer and Chandler’s analytic solvation free energy formulation [Mol. Phys. 55, 621 (1985)]. Solvation energies, enthalpies, and entropies are also calculated in the RISM theory framework. The conformational dependence of solvation for alanine dipeptide in aqueous solution is analyzed. The solvation thermodynamcs for alanine dipeptide in aqueous solution are mainly controlled by the strong hydrophobic groups: CH3 and CH, which make alanine dipeptide show strong hydrophobicity. But the differences in the solvation thermodynamics for different alanine dipeptide conformers are controlled by the carbonyl groups and amide groups, which make alanine dipeptide show some hydrophilicity and exist in various conformations in aqueous solution. Solvation of alanine dipeptide in aqueous solution is determined by the competition among the molecular packing effects, intramolecular hydrogen bonds, and intermolecular hydrogen bonds. Due to the intramolecular hydrogen bonds in the two folded C7 conformations, the two most favorable conformations in gas phase become the least solvated in aqueous solution. Due to the intermolecular hydrogen bonds, C5, PII, αL, αR, and β become more solvated in aqueous solution.