No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
In memory of Lesser Blum
Doug Henderson brought his profound knowledge of ionic solutions to biology in his study of ion channels. Ion channels are proteins that conduct ions and electric current across otherwise insulating membranes. The ions are so crowded in these protein channels that the competition between charge and space dominates their properties. Here is how that work started from an unjustified claim (by me), a rather rude question by Doug Henderson, a fortunate reply and a memorable drive, all resolved by a calculation by Dezsö Boda.
The lattice fluid model of the system with short range and long range Coulomb interactions is suggested. In the framework of the collective variables method, the screening of the Coulomb interactions in the bulk is considered. It is shown that the Debye length includes additional concentration dependence inversely proportional to the square root of the mean concentration of vacant sites like what was known at the plane boundary. The Coulomb interaction contribution to the free energy of the system is calculated in the approach close to the mean spherical approximation and is given in an analytical form.
The influence of the variation of the crystal field near the system boundary on the structure and characteristics of the electric double layer is investigated. As compared to the system with equal crystal potentials at the lattice sites throughout the system the pronounced difference for the electrical capacitance appears at low absolute values of the surface potential and it is more pronounced for negative electric potentials. The capacitance diverges as the potential values at which the electric field tends to zero and attains negative values in regions of the surface potentials depending on their polarity and values of the surface crystal potential. Negative values of the capacitance may indicate the thermodynamic instability of the system that can result from neglecting the short range interaction contribution.
By considering the solution of the Mean Spherical Approximation (MSA) given by Lesser Blum, we addressed the problem of specificity in aqueous electrolyte solutions. The reference diameter of the cations is defined as the biggest possible diameter of the cation (obtained with the less associating anion). Then the specificity is taken into account by an association term similar to Bjerrum theory. The resulting activity coefficients can be used to describe pure electrolyte and electrolyte mixtures up to molar concentrations. Hydration appear to be relatively stable with small cations but it strongly depends on the anion for big cations. The validity of Zdanovskii-Stokes-Robinson mixing rule has also been tested and it appears to be valid with typically a 1% accuracy for molar concentrations.
The critical region of the hierarchical reference theory (HRT) is investigated further. This extends an earlier work by us where the critical properties of the HRT were concluded indirectly via another accurate but somewhat different theory, the self-consistent Ornstein-Zernike approximation (SCOZA), and numerical work. In the present work we perform our analysis directly upon the HRT partial differential equation to establish ordinary differential equations for the subleading scaling contributions. Again we find that the HRT critical indices in three dimensions are simple rational numbers.
We study the vapour-liquid critical parameters of an ionic fluid confined in a disordered porous medium by using the theory which combines the collective variables approach with an extension of the scaled particle theory. The ionic fluid is described as a two-component charge- and size-asymmetric primitive model, and a porous medium is modelled as a disordered matrix formed by hard-spheres obstacles. In the particular case of the fixed valencies 2:1, the coexistence curves and the corresponding critical parameters are calculated for different matrix porosities as well as for different diameters of matrix and fluid particles. The obtained results show that the general trends of the reduced critical temperature and the reduced critical density with the microscopic characteristics are similar to the trends obtained in the monovalent case. At the same time, it is noticed that an ion charge asymmetry significantly weakens the effect of the matrix presence.
Virial coefficients B 2 to B 4 for the non-polarizable TIP4P/2005 model of water and the polarizable BK3 model were computed. An analysis and assessment of available experimental and pseudoexperimental data is carried out. Various forms of the virial expansion are examined with respect to their potential use for the description of steam (working agent in turbines). At higher temperatures (higher densities) the expansion starts exhibiting an irregular behavior indicating that at these conditions the vapor can likely not be viewed as a system made up only of individual molecules, and the occurrence of clusters of different size must be accounted for.
Isothermal titration calorimetry was used to determine the temperature and salt concentration dependence of the enthalpy of mixing, δmix H, of bovine serum albumin (BSA) in aqueous buffer solutions with several low molecular weight salts. Three buffers were used: acetate (pH=4.0), MOPS (7.2), and borate (9.2). Since the isoionic point of BSA is at pI ≈ 4.7, the net charge of BSA in acetate buffer was positive (≈ +20), while in the other two buffer solutions it was negative (≈-15 in MOPS and ≈-25 in borate). The majority of the recorded heat effects were exothermic, while only at pH=9.2 a weak endothermic effect upon mixing BSA with LiCl, NaCl, and KCl was observed. For all buffer solutions the absolute values of δmix H of sodium salts followed the order: NaCl < NaBr < NaNO3 < NaI < NaSCN, which is the reverse Hofmeister series for anions. The magnitude of the effects was the largest in acetate buffer and decreased with an increasing pH value of the solution. While the effect of varying the anion of the added salts was strongly pronounced at all pH values, the effect of the cation (LiCl, NaCl, KCl, RbCl and CsCl salts) was weak. The most interesting feature of the results obtained for pH >pI was the fact that δmix H were considerably more sensitive to the anion (co-ion to the net BSA charge) than to the cation species. This indicated that anions interacted quite strongly with the BSA even at pH values where the net charge of the protein was negative. We showed that δmix H at high addition of salts correlated well with the enthalpy of hydration of the corresponding salt anion. This finding suggested, consistently with some previous studies, that a part of the exothermic contribution to δmix H originated from the hydration changes upon the protein-salt interaction. Theoretical analysis, based on the primitive model of highly asymmetric electrolyte solutions solved within the mean spherical approximation, was used to estimate Coulomb effects upon mixing.
The mesoscopic field theory for ionic systems [A. Ciach and G. Stell, J. Mol. Liq. 87, 255 (2000)] is extended to the system with charged boundaries. A very simple expression for the excess grand potential functional of the charge density is developed. The size of hard-cores of ions is taken into account in the expression for the internal energy. The functional is suitable for a description of a distribution of ions in ionic liquids and ionic liquid mixtures with neutral components near a weakly charged wall. The Euler-Lagrange equation is obtained, and solved for a flat confining surface. An exponentially damped oscillatory charge density profile is obtained. The electrostatic potential for the restricted primitive model agrees with the simulation results on a semiquantitative level.
We examine the adsorption of the primitive-model “ionic” mixtures modeled in terms of the screened Debye potentials on a hard structureless wall. It is well-known that the screened Debye potentials are of the Yukawa form. They could approach the Coulomb potentials when the screen parameter λ vanishes. Thus the study of the mixtures of repulsive and attractive Yukawa molecules can mimic the ionic fluid behavior at small λ. One of the advantages of using this Yukawa potential is that it avoids the long-range interactions and mitigates the complications inherent in the Coulomb potential.
We have previously developed a third-order Ornstein-Zernike relation (OZ3) and have adapted it to the adsorption of many types of fluids on hard walls. Specifically, a new generation of closures was developed for use in the Euler-Lagrange equations of the density functional theory (DFT) for determining the non-uniform densities of various fluid types: such as the Lennard-Jones fluid, as well as the regular Yukawa fluids (with finite λ values) on an inhomogeneous substrate. In this work, we examine the applicability of the OZ3-inspired bridge functions to the adsorption of the “small-λ” Yukawa fluids. The mixtures of these Yukawa fluids are, for simplicity, called the Yukawa ions, in contrast to the Coulomb ions. The results shall mimic the electrical double layers in electrochemistry.
The Euler-Lagrange equations for the binary mixtures are solved with new OZ3 closures. Two types of closures are investigated: one derived from the Jackson-Feenberg approximation, and the other derived from the linear cavity approximation. The results are compared with the Monte-Carlo results on primitive-model symmetric ions and asymmetric ions on a neutral hard structureless wall. Satisfactory agreements are obtained. It is noted that the contact value theorems (i.e. the hard-wall sum rules) play an instrumental role in obtaining the accurate results.
The solution of the associative mean spherical approximation for the ion-dipole model of an electrolyte solution is simplified and analyzed. It is shown that the description of this model can be reduced to a system of three coupled non-linear algebraic equations for ion-ion, ion-dipole and dipole-dipole energy parameters J0, b1⁰ and b2. A possibility of introducing ionic and dipolar scaling parameters ΓB and λ is discussed. Analytical expressions for the thermodynamic functions and solvent static dielectric permittivity are presented.
We consider the solvent-solvent interaction energy change associated with the solvent restructuring in response to a progressive change in the interaction between the solute and the solvent molecules. We derive expressions for this solvent restructuring energy using a new solvent scaling scheme in which the solvent-solvent potential energy is scaled relative to its reference value. We find that we can naturally extend the familiar single-coupling parameter methodology with a second coupling parameter that controls the solvent-solvent interactions. In doing so we can not only access information about the solvent restructuring energy, but also quantify the statistical correlations between the fluctuations of the solute-solvent and the solvent-solvent interaction energies. Based on these findings we implement a molecular dynamics simulation strategy to evaluate the solvent restructuring energetics associated with turning on the electrostatic interactions between one initially uncharged water molecule dissolved in liquid water, using both the TIP4P-2005 and OPC water models. We also use the theory to explore the dependence of the solvent restructuring energy on solute-solvent coupling, both in general and in the special case in which the solute-solvent coupling is accurately described by the linear response approximation.
From a general expression for the closure condition, a condition which is necessary within the formalism of integral equations used to study the thermodynamic and structural properties of a classical fluid, the direct correlation function can be expressed as a series of Yukawa-type terms, for r ij > σ ij, and as the hard-sphere approximation, for lower distances. With this closure condition, it is possible to solve the Ornstein-Zernike equation. The symmetry properties of the Baxter functions allow inferring the existence of a characteristic scaling matrix for each system. The structural and thermodynamic properties may then be written in terms of the elements of this scaling matrix. In this work, the solution of the problem is presented in general form, and it is explicitly developed for particular systems.
An increasing number of industrial applications rely on controlling solutes in water above and below its critical point. Processes such as hydrothermal synthesis, steam power generation and ultra-high enthalpy geothermal power are all influenced by factors such as mineral precipitation, pH and solute speciation. The supercritical point of water is remarkable in that slight changes in temperature and pressure can cause dramatic changes in some solute properties. Here, it was found that our approach reliant on molecular statistical thermodynamic expressions for hard sphere (HS), ion-dipole and dipole-dipole interactions via mean spherical approximation (MSA) provided excellent agreement to available experimental data. In addition to model parameters having some physical meaning, this approach used less adjustable parameters than the well-known Helgeson-Kirkham-Flowers (HKF) model. Furthermore, the model was used to obtain standard thermodynamic values for HCl⁰(aq), KCl⁰(aq) and NaOH⁰(aq) ion pairs. In total, modeling parameters for 10 different aqueous species were obtained to demonstrate the capabilities of the approach.
A variety of models and hypothesis have been proposed to interpret the temperature dependence of the mean square displacement (MSD) of protein, that is obtained from the inelastic neutron scattering (INS) measurement, but a consensus seems yet to be achieved. The most controversial point is concerned with the physics behind the abrupt change of gradient of MSD plotted against temperature. The phenomenon is attributed to different physics by different authors, such as glass transition, alpha to beta transition, harmonic to anharmonic transition, coupling of protein and hydrated-water dynamics, and so forth. In the present paper, we propose a theory to analyse the elastic incoherent neutron scattering (EINS) data of aqueous solutions of protein, based on the generalized Langevin theory combined with the 3D-RISM/RISM equation [B. Kim and F. Hirata, J. Chem. Phys., 138, 054108 (2012)]. The theory gives closed equations for the elastic incoherent structure factor (EISF) and MSD as a function of temperature. Based on the theory, the abrupt change of the gradient of MSD in the temperature dependence is interpreted as an onset of ". solvent-induced elasticity," or "free energy elasticity," with increasing temperature.
We propose several versions of primitive models of room temperature ionic liquids (RTILs) and develop a mean spherical approximation (MSA)-type theory for their description. RTIL is modeled as a two-component mixture of hard-sphere anions and flexible linear chain cations, represented by tangentially bonded hard spheres with the charge located on one of the terminal beads. The theoretical description of the model is carried out using the solution of the appropriately modified associative MSA (AMSA). Our solution reduces to solving one nonlinear algebraic equation for the Blum's screening parameter Γ, which in turn is used to express all thermodynamic properties of the models of interest. We calculate liquid-gas phase diagrams using theoretical and computer simulation methods for two versions of the model, represented by the dimer (D) and chain (C) models. Theoretical predictions for the phase diagrams appear to be in reasonably good agreement with computer simulation results. It is demonstrated that the models and theory are able to qualitatively reproduce experimentally observed phase behavior of RTILs, in particular the decrease of the critical temperature and critical density with increasing asymmetry of the model in its shape and position of the charge.
We present a model for polyelectrolyte solutions within the binding mean spherical approximation. An approach developed previously, to describe polyelectrolytic chain solutions and on the other hand to describe the association of counterions on spherical polyions is generalized, considering both the polyelectrolytic chain formation and the association of counterions on the chains. Thermodynamic properties deduced from this model are presented. The associative part of the Helmholtz energy is deduced from the thermodynamic perturbation theory. Analytic expressions for the electrostatic contributions to the internal and Helmholtz energies are established.
An electric interfacial layer is created when the mobile ions or charged nanoparticles of an electrolyte interact with a surface of an extended charged object. The competition between electrostatic attraction and translational entropy loss of the mobile nanoparticles results in a diffuse interfacial layer of nanoparticles close to the charged surface. Due to its simplicity and transparency first wide spread theoretical description of the electric interfacial layer was the Poisson-Boltzmann theory. Numerous improvements were applied that account for charge-charge correlations, steric effects and solvent properties. The present article focuses on spherical mobile nanoparticles which have charge distributed over the surface and have finite size. The nanoparticles are sandwiched between two parallel like-charged walls. We perform the minimization of an appropriate free energy functional, which leads to a non-linear integro-differential equation for the electrostatic potential that is solved numerically. Our model predicts condensation of nanoparticles to oppositely charged surface. For highly charged surfaces and nanoparticles of finite size we observed big differences in the volume charge density profiles between soft and hard spheres. The theoretical predictions are in a good agreement with Monte Carlo simulations.
Life occurs in concentrated `Ringer Solutions' derived from seawater that Lesser Blum studied for most of his life. As we worked together, Lesser and I realized that the questions asked of those solutions were quite different in biology from those in the physical chemistry he knew. Biology is inherited. Information is passed by handfuls of atoms in the genetic code. A few atoms in the proteins built from the code change macroscopic function. Indeed, a few atoms often control biological function in the same sense that a gas pedal controls the speed of a car. Biological questions then are most productive when they are asked in the context of evolution. What function does a system perform? How is the system built to perform that function? What forces are used to perform that function? How are the modules that perform functions connected to make the machinery of life. Physiologists have shown that much of life is a nested hierarchy of devices, one on top of another, linking atomic ions in concentrated solutions to current flow through proteins, current flow to voltage signals, voltage signals to changes in current flow, all connected to make a regenerative system that allows electrical action potentials to move meters, under the control of a few atoms. The hierarchy of devices allows macroscopic properties to emerge from atomic scale interactions. The structures of biology create these devices. The concentration and electrical fields of biology power these devices, more than anything else. The resulting organisms reproduce. Evolution selects the organisms that reproduce more and thereby selects the devices that allow macroscopic control to emerge from the atomic structures of genes and proteins and their motions.
The effect of multivalent counterions on the spherical electric double layers containing asymmetric electrolytes with size and charge asymmetry is studied using density functional theory and Monte Carlo simulations, in a systematic manner. A primitive model representation of the system is followed, where the macroion and small ions are represented as uniformly charged hard spheres of different size within a dielectric continuum as solvent. The theory approximates the hard-sphere contribution through a weighted density approach, whereas a functional expansion around the uniform fluid is used for the ionic part. The theory reproduces the simulation data quantitatively for a wide range of system parameters. The present study reflects the importance of size and charge correlations with inclusion of multivalent counterions as observed in spherical double layers.
A new analytical expression was derived for the chemical potential of a hard sphere dipole in hard sphere dipole fluid at infinite dilution of the solute using the mean spherical approximation (MSA). A set of Monte Carlo (MC) simulations has been carried out to investigate the scope of applicability of the derived equation. The mean reaction field (MRF) approach was used in our MC computations. Two different MC methods (Widom particle insertion and thermodynamic integration) were applied for obtaining the chemical potential change associated with the dipole creation at the solute particle to provide adequate accuracy of the MC simulations. Also, corresponding changes in the mean potential energy were calculated by direct method and by thermodynamic integration. The solvation energies have been obtained for the systems of dipolar hard spheres with reduced dipole moment 1.0 at the reduced densities 0.2, 0.5, and 0.8. Computations have been made for solute particles with the reduced dipole moment varied from 0.0 to 1.5 and the hard sphere diameter varied from 0.5 to 2.0. The variation of those quantities with the molecular parameters was analyzed and compared with the MSA equation and Kirkwood classical expressions. It was found that the MSA calculations agree relatively well with MC simulations at densities less than 0.5 and solute dipole moment less than 1.0.
Our previous simulations found that permeation of Na⁺ and K⁺, in contrast with Cl⁻, causes significant membrane deformation and formation of a water wire in the membrane hydrophobic domain. Clearly, positive charges have a propensity to interact more strongly with lipids and thus induce serious defects to membrane. Since calcium is one of the most common and important metals in biology, we take it as template of a +2 charge and made the unprecedented effort to bring it across the membrane in molecular simulations. It is observed that under the ion/lipid ratio of 1:126 permeation of a +2 charge would badly disturb the bilayer structure, even lipid "flip-flop" is quite common, and cause leakage of water molecules by a widely-reported "All or None" manner, suggesting unassisted permeation of small molecules with 2 or more positive charges to be severe threats to cell membranes. More importantly, we found "All or None" leakage may be closely related to the "game" of hydrophilic and hydrophobic forces caused by positive charges. Our findings may be enlightening for the exploration of underlying mechanisms of the antimicrobial peptides and similar positively charged molecules acting on membranes.
In this paper we propose a model for the two dimensional fluid with one site-site associating point. We studied its structural and thermodynamic properties by the Monte Carlo computer simulations, the site-site integral equation theory (RISM), the Wertheim's thermodynamic perturbation theory (TPT) and the Wertheim's integral equation theory (WIET) for associative liquids. The model can have arbitrary position of the associating point from the center of particles. All particles have Lennard-Jones core while interactions between associating points are modeled as Gaussian like potential where the interaction depends only on the distance between sites. The methods were used to study the thermodynamic and structural properties as a function of the position of associating point, temperature and density. The accuracy of the analytic theories were checked by comparing the theoretical results with the corresponding Monte Carlo ones. The theories are quite accurate for cases when the associating point is on the surface and only dimers can be formed. In this case, the theories correctly predict the pair correlation functions of the model, internal energy, ratios of free and bonded particles and chemical potential. This is no longer true when associating point is away from the surface of particles and the higher clusters are formed.
The zeta potential and the structure of a model cylindrical double layer obtained through the Poisson-Boltzmann theory, the hypernetted chain/mean spherical approximation integral equation theory, the modified Poisson-Boltzmann theory, and the density functional theory are compared with the corresponding Monte Carlo simulation results. The cylindrical double layer consists of an infinitely long cylinder with a uniform surface charge immersed in a restricted primitive model electrolyte (equi-sized, rigid spherical ions in a continuum dielectric). Calculations have been performed at room temperature and in a water-like solvent for 1:1, 2:2, 2:1/1:2 valency electrolytes for different electrolyte concentrations, axial charge parameters (surface charge densities), and ionic diameters. The results for the zeta potential, the mean electrostatic potential, and the electrode-ion singlet distributions predicted by the formal statistical mechanical theories reproduce the simulation data to a high level of accuracy overall for the range of physical parameters studied. The theoretical predictions, except that due to the classical mean field theory, also reveal a remarkable consistency among themselves. The results also (a) explore the relationship between the occurrence of charge reversal and the negative derivative of the mean electrostatic potential,(b) provide insight into the connection between reversed and extremal values of the zeta potential versus surfaced charge density curves and some aspects of electrokinetics, viz., inverted electrophoretic velocities and the possible existence of differently charged colloids with the same mobility, and (c) suggest a plausible identification of the integrated surface charge density at a point near the cylindrical polyion surface with the electrokinetic charge.
We study models of hairy nanoparticles in contact with a hard wall. According to the first model the ligands are grafted to a spherical core, while in the second model they can slide over the core surface. Using Molecular Dynamics simulations we investigate the differences in the structure of both system close to the wall. In order to characterize the distribution of the ligands around the core we have calculated the end-to-end distances of the ligands and the lengths and orientation of the mass dipoles. Moreover, for the model with mobile ligands we also employed a density functional approach to obtain the density profiles. We have found that the proposed version of the theory is capable to predict the structure of the system with a reasonable accuracy.
An explicit water molecular dynamics simulations were used to probe (6,6) and (9,9) single-walled carbon nanotubes, functionalized with three carboxylate ion groups at each of the two openings, as potential nanocarriers in aqueous solutions. Three tetraalkylammonium cations (i.e., tetraethyl-, tetrapropyl-, and tetrabuthylammonium) were tested as corks to cap the nanotube openings. The variation of the sizes of the nanotubes (diameter) and of the cork cations (bulkiness) allowed us to select the proper corks that fit the nanotube openings best. Smaller tetraalkylammonium ions could easily fit the openings, but since they are less hydrophobic compared to their larger analogues they showed less affinity for the interior of the nanotubes. On the other hand, the hydrophobicity (and thus the affinity for the nanotubes) can be adjusted through the increase of tetraalkylammonium cation size, providing that the cork still fits the opening. Additionally, an external electric field was tested as a means of nanotube uncorking. The field is capable of disjoining corked ions from the functionalized nanotube openings, triggering in this way a potential cargo release stored inside the nanotubes.
For biotechnological drugs, it is desirable to formulate antibody solutions with low viscosities. We go beyond previous colloid theories in treating protein-protein self-association of molecules that are antibody-shaped and flexible and have spatially specific binding sites. We consider interactions either through fragment antigen (Fab-Fab) or fragment crystallizable (Fab-Fc) binding. Wertheim's theory is adapted to compute the cluster-size distributions, viscosities, second virial coefficients, and Huggins coefficients, as functions of antibody concentration. We find that the aggregation properties of concentrated solutions can be anticipated from simpler-to-measure dilute solutions. A principal finding is that aggregation is controllable, in principle, through modifying the antibody itself, and not just the solution it is dissolved in. In particular: (i) monospecific antibodies having two identical Fab arms can form linear chains with intermediate viscosities. (ii) Bispecific antibodies having different Fab arms can, in some cases, only dimerize, having low viscosities. (iii) Arm-to-Fc binding allows for three binding partners, leading to networks and high viscosities.
The energy density of an electric double layer (EDL) capacitor, a type of supercapacitor, depends on the ion distribution within the micropores of electrodes that are typically made of amorphous carbon. By using coarse-grained models and the classical density functional theory, we investigate the distributions of ionic species among different idealized nanopores in contact with an asymmetric ionic liquid mixture and the effects of the bulk electrolyte composition on capacitive energy storage. We find that a charged pore is always small-ion selective, provided all ions have the same valence and similar non-electrostatic interactions. While small ions enhance both the EDL capacitance and the accessibility of micropores, an ionic mixture containing ions of different sizes may yield a capacitance higher than those corresponding to pure ionic liquids. The increased capacitance may be attributed to more efficient ion packing near the charged surface. At certain conditions, the improvement is on a par with the anomalous capacitance rise for pure ionic liquids in electrodes with ultranarrow pores.
In this article, dedicated to the memory of Lesser Blum, we develop a theory for the physical clusters which were introduced some time ago in our group (J. Chem Phys. 116, 1097-1108, 2002). The physical cluster definition establishes that a system particle belongs to the cluster if it is (nonspecifically) bonded to other particles of the cluster along a finite time period τ (the residence time). Our theory has as main ingredients the Stillinger criterion of instantaneous connectivity, that involves a connectivity distance d, the generalized time-dependent pair distribution function of Oppenheim and Bloom that acts as a classical propagator and also the cluster pair correlation function for a weaker version of the physical clusters that requires connectivity just at the extremes of the time period no matter what happens in between. With these tools we express the time dependent pair connectedness function for the physical clusters in the strong sense as a path integral. The path integral is solved by means of a perturbation expansion where the nonperturbed connectedness function coincides with the generalized pair distribution function of Oppenheim and Bloom. We apply the theory to Lennard-Jones fluids at low densities and perform molecular dynamics simulations to check the goodness of diverse functions that appear in the theory.
A primitive model electrolyte in mixture with uncharged hard spheres was used to model the concentration dependence of the mean activity coefficient of sodium chloride in aqueous solutions of poly(ethylene glycol) (PEG) of different degree of polymerization and concentration. Ornstein-Zernike integral equation was numerically solved using the hypernetted chain (HNC) closure and the results were compared with the results of an analytical solution valid within the mean spherical approximation (MSA) closure. Good agreement between the HNC and MSA activity coefficients was obtained. However, at higher NaCl concentrations the convergence of the numerical solution was not satisfied for large model PEG molecules. The presence of the neutral component in the solution increases the mean activity coefficients in the whole concentration range due to the confinement. For a given NaCl and PEG concentration, decreasing the dielectric constant of the solution diminishes the activity coefficient due to stringer interaction between the ions. Mean activity coefficients of NaCl in two aqueous solutions differing in the concentrations of PEG (molecular weight of 12,000gmol⁻¹) were determined also experimentally and compared with MSA results. The agreement was semi-qualitative, mainly due to difficulties in estimating good model parameters for the PEG molecules and the potential decrease of the dielectric constant of the solvent.
Molecular dynamics simulations of the dissolution of aspirin in water are reported. Crystals initially cubic and cylindrical in shape are considered, and the influence of temperature is examined. All simulations are carried out in a manner designed to prevent the build up of any significant concentration of aspirin in solution, physically corresponding to sink conditions. It is found that aspirin dissolution follows a three stage mechanism similar in most respects to earlier observations for nanocrystals of NaCl and urea. In the initial stage, molecules are first lost from corners and edges of the crystal, the crystal is solution annealed into a particular limiting shape, that then persists throughout a large fraction of the dissolution process. For aspirin, initially cubic crystals anneal into a cylindrical shape, in contrast with the near spherical shapes attained by cubic NaCl and urea crystals. In an intermediate stage, during which most of the crystal dissolves, the dissolution rate is well described by a simple classical model which assumes that the rate is proportional to the active surface area of the crystal. For aspirin, the active surface area is identified as the curved surface of a cylinder for both crystal shapes. In the final stage, the small remaining crystal looses its structure and rapidly dissolves. Given that a similar three stage mechanism applies to crystals as varied as NaCl, urea, and aspirin, we conjecture that this mechanism is possibly quite general, and might apply to many ionic and molecular crystals. As for NaCl and urea, an analysis of the activation energy associated with aspirin dissolution strongly suggests that detachment of molecules from the crystal is the rate determining step, at least under the sink conditions.
In recent work a solution of the Ornstein-Zernike equation for a general Yukawa closure for a single component fluid was found. Because of the complexity of the equations a simplifying assumption was made, namely that the main scaling matrix Gamma had to be diagonal. While in principle this is mathematically correct, it is not physical because it will violate symmetry conditions when different Yukawas are assigned to different components. In this work we show that by using the symmetry conditions the off diagonal elements of Gamma can be computed explicitly for the case of two Yukawas solving a quadratic equation: There are two branches of the solution of this equation, and the physical one has the correct behavior at zero density. The non-physical branch corresponds to the solution of the diagonal approximation. Although the solution is different from the diagonal case, the excess entropy is formally the same as in the diagonal case.
The analytical solution of the mean spherical approximation for the case of equal size ions and different size solvent is reexamined using only two parameters: a polarization parameter λ and a screening parameter Γ. We show that the ion dipole cross energy parameter, which in previous work was obtained solving a cubic equation, can be obtained from a linear algebraic equation. Therefore, the inverse problem of calculating the reduced charge parameter d 0 and the reduced dipole parameter d 2 from λ and Γ is reduced to a system of two equations: a cubic for d 0, and a linear for d 2. Simpler expressions for the thermodynamic parameters are also obtained.
We show that for the internal energy in the nonrestricted ion-dipole model of an ionic solution the formal analogy of the mean spherical approximation (MSA) to the Debye-Hückel theory still holds, although with a screening length that depends on the size of each ion.
An exact formula for the contact value of the density of a system of charged hard spheres near a charged hard wall is obtained by means of a general statistical mechanical argument. In addition, a formula for the contact value of the charge profile in the limit of large field is obtained. Comparison with the corresponding expressions in the Poisson-Boltzmann theory of Gouy and Chapman shows that these latter expressions become exact for large fields, independent of the density of the hard spheres.
A model for the underpotential deposition of metals that occurs in stages is introduced. In this model the deposition takes place as a sequence of first order phase transitions of the adsorbate. In this application we study the underpotential deposition of Cu on a Au(111) surface in the presence of sulfate ions. The voltammogram of the deposition shows two sharp spikes which are reproduced by our model.
The integral equations for the ionic and solvent profiles of a model electrolyte consisting of charged hard spheres (the ions) and dipolar hard spheres (the solvent) near a charged hard wall are examined. The mean spherical approximation (MSA), which is based upon a linearization in the strength of the charge density on the wall, leads to a set of coupled integral equations. In the limit of low concentrations, the ionic terms decouple from the solvent terms so that to obtain the ionic profiles it is only necessary to solve the MSA integral equation for a fluid of pure (i.e. without a solvent) charged hard spheres near a charged hard wall. The coupling of the ionic and solvent terms occurs in the integral equation for the solvent profile. In this paper it is assumed that the MSA integral equation for the solvent profile can be used with some more general and non-linear integral equation for the decoupled ionic contribution. This leads to a theory which is linear only in the response of the solvent to the charge on the wall. Some specific results are given for the case where the ionic terms are treated in the Gouy-Chapman theory. Generally good agreement with experiment is obtained without the use of semiempirical parameters. The discrepancies between the theory and experiment are most likely due to the completely symmetric model of the solvent molecule which has been used rather to the approximations used to obtain the integral equation.
An extended mean spherical approximation is formulated and used to calculate the density and charge profiles and the potential difference of a fluid of charged hard spheres near a charged planar wall. The results are nearly identical to those of the hypernetted chain approximation provided that the same correlation functions for the bulk fluid are used.
We obtain a new sum rule for the density profile of an electrolyte in contact with a charged flat hard (nonconducting) wall. This, in turn, strongly implies that the decay of the pair correlation near the wall is notfaster than (distance)−d−1, where d is the dimension of the system. (AIP)
The partial solution for the mean spherical model of neutral spheres with electrostatic interactions obtained in a previous communication [L. Blum, J. Chem. Phys. 57, 1862 (1972).] is extended to the general case, in which the electrostatic interactions of odd parity, like the dipole-quadrupole interaction, are included. The solution is given in terms of a linear transform of the direct correlation function, which is shown to be a polynomial in r inside the hard core diameter. The coefficients of this polynomial are determined from a sufficient number of boundary conditions. The method of solution employs the so-called second Baxter form of the Ornstein-Zernike equation [Australian J. Phys. 21, 563 (1968).] which is derived for this particular case. Also, alternative forms of the Ornstein-Zernike equation in coordinate space are obtained. The case of molecules with linear dipole and quadrupole moments is summarily illustrated.
The thermodynamic approach for light scattering developed in a previous paper is extended to include the diffusion process. The results for zero angle are the same as stated before [B. J. Berne and H. L. Frisch, J. Chem. Phys. 47, 3675 (1967); L. Blum and Z. W. Salsburg, ibid. 48, 2292 (1968)], that is, the only remaining contribution to the central Rayleigh line is due to the chemical reactions.
The expansion of the exponential of a tensorial expression such as the interaction or pair correlation function between two nonspherical molecules 1, 2 is of the form ∑mnl λmnl&Fgr;mnl(12), where &Fgr;mnl(12) are invariant tensorial expressions that depend only on the orientation of 1 and 2. The generating function e−∑mnl λmnl&Fgr;mnl =∑pqt ipqt(λ) &Fgr;pqt defines a generalized Bessel function (GBF). We discuss integral representations and recurrence relations for the GBF. The first GBFs for dipolar and linear quadrupolar exponents, which are of interest in the theory of ionic solutions are computed explicitly.
The modified Gouy–Chapman theory of the electrical double layer in which ion‐core effects among the ions are neglected, but are taken into account in the ion–electrode interaction, is applied to the case of 1:1, 2:2, 1:2, and 2:1 electrolytes for both equal and unequal ionic diameters. At large charge densities on the electrode, the counterions dominate and the results approach those of a symmetric electrolyte. However, at small charge densities on the electrode, the effects of asymmetry are evident. In particular, for unequal ionic diameters, a nonzero potential can occur at zero charge on the electrode, even in the absence of specific adsorption.
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
The Ornstein–Zernike equation for a mixture of ions and dipoles near a hard charged wall is obtained. It is shown that the same exact contact and monotonicity theorems, previously derived for the primitive (continuum dielectric) case, also are valid for this model. Rather simple expressions for the contact density, potential difference, capacitance, and distribution functions are obtained in the mean spherical approximation (MSA). These expressions reduce to previously known results in the limits of low and high concentrations of ions. It is found that cooperative alignment of the dipoles near the wall results in an increased potential difference and reduced capacitance of the double layer compared to that calculated when the solvent is represented by a continuum dielectric.
We give a proof and an extension of equations previously derived by Wertheim and Lovett, Mou and Buff, relating the gradient of the density to an integral of the external force over the pair correlation function; when the system has boundaries it also involves a surface contribution. These equations are derived and used for systems which may contain free charges, dipoles, and a rigid background (jellium). In particular, we derive an equation for the density profile near a plane electrode and we show that the correlation function has to decay no faster than ‖x‖−N(N=space dimension) parallel to the electode.
A rigorous theory for the light scattered from a solution of an optically active species is presented. The theory is based on the quantum-mechanical time displaced correlation function for the suceptibility tensors. This formalism leads to the correct form of the Kronig–Kramers relations. Otherwise, the procedure follows the usual theory of light scattered from inactive solutions. The result shows that the parameters usually associated with the optical rotatory power and the ellipticity are linear combinations of two rotational invariants of the fourth-rank tensor formed by the direct product of the dielectric polarizability tensor and the pseudotensor that gives the optical activity. Only for isotropic molecules do we recover the classical result. The depolarization of the light (or ellipticity) is due both to the dielectric polarizability and to the optical activity pseudotensor. If the scattering experiment is done at an angle different from zero, then information about the anisotropy of the molecular susceptibility tensor be obtained. Also, when the system is opalescent, it could be more convenient to look at the scattered light instead of the “transmitted” one.
The interface between a solid and a liquid is modelled by a flat surface with an array of sticky sites which could be placed on a regular lattice, or also randomly. It is first shown that the thermodynamics and distribution functions can be expressed entirely in terms of the distribution functions of the system without the sticky sites. Furthermore, the problem of the occupation of the sites (equivalent to the adsorption isotherm), is a lattice problem which exhibits phase transitions and critical points. A simple application to the interface between a solid and a fluid of hard spheres is discussed.