Influence of ion properties on the equilibrium and transport properties of electrolyte solutions

Strong electrolytes are described in the framework of the primitive model in which the solvent is regarded as a dielectric continuum, using the mean spherical approximation. The analytical solution of the equilibrium and transport properties is dependent on the ions' diameters and valencies. For hydrated or nonspherical ions, an effective diameter must be fitted. A sensitivity study of the osmotic coefficient and the transport coefficients is performed on theoretical 1-1, 2-1, and 3-1 electrolytes, up to a total ion concentration of 2 mol/L.     

Activity coefficients of single electrolytes in concentrated solutions derived from a quasi-lattice model

This paper describes a new model to calculate the mean activity coefficients of dissociated electrolytes in concentrated solutions. It is based on three assumptions: (i) a quasi-lattice arrangements of ions in solution; (ii) a contribution from ion-water interactions to the mean activity coefficients; (iii) a concentration dependence of the dielectric constant. The mean activity coefficients of thirteen strong electrolytes from moderately dilute solutions to saturated solutions are found to correlate well by this model. For dilute solutions, a limiting equation in which only ion-specific parameters are required is proposed. It is suggested that specific ionwater interactions might be the major source of the nonideality of strong electrolyte solutions at high concentrations.     

FTIR study of ion dissociation in PMMA based gel electrolytes containing ammonium triflate: Role of dielectric constant of solvent

The effect of dielectric constant of solvent on the presence of ion aggregates/undissociated salt and their dissociation with the addition of polymer has been studied by FTIR for polymethylmethacrylate (PMMA) based gel electrolytes containing ammonium triflate (NH₄CF₃SO₃). Salt is fully dissociated in electrolytes containing dimethylacetamide (DMA)—a high dielectric constant solvent and some ion aggregates are also present whereas in electrolytes containing diethylcarbonate (DEC)—a low dielectric constant solvent, some undissociated salt is present. The conductivity behaviour of polymer gel electrolytes has been found to depend upon the dielectric constant of the solvent used. PMMA plays the role of a stiffener in electrolytes containing DMA and results in a small decrease in conductivity whereas in electrolytes containing DEC, the addition of PMMA results in an increase in conductivity which has been explained to be due to an increase in free ion concentration by the dissociation of undissociated salt and ion aggregates. The presence of free ions, ion aggregates, undissociated salt has also been examined by FTIR spectroscopy.     

Liquid-structure forces and electrostatic modulation of biomolecular interactions in solution

Molecular interactions in solution are controlled by the bulk medium and by the forces originating in the structured region of the solvent close to the solutes. In this paper, a model of electrostatic and liquid-structure forces for dynamics simulations of biomolecules is presented. The model introduces information on the microscopic nature of the liquid in the vicinity of polar and charged groups and the associated non-pairwise character of the forces, thus improving upon conventional continuum representations. The solvent is treated as a polar and polarizable medium, with dielectric properties described by an inhomogeneous version of the Onsager theory. This treatment leads to an effective position-dependent dielectric permittivity that incorporates saturation effects of the electric field and the spatial variation of the liquid density. The non-pairwise additivity of the liquid-structure forces is represented by centers of force located at specific points in the liquid phase. These out-of-the-solute centers are positioned at the peaks of liquid density and exert local, external forces on the atoms of the solute. The density is calculated from a barometric law, using a Lennard-Jones-type solute-liquid effective interaction potential. The conceptual aspects of the model and its exact numerical solutions are discussed for single alkali and halide ions and for ion-pair interactions. The practical aspects of the model and the simplifications introduced for efficient computation of forces in molecular solutes are discussed in the context of polar and charged amino acid dimers. The model reproduces the contact and solvent-separated minima and the desolvation barriers of intermolecular potentials of mean force of amino acid dimers, as observed in atomistic dynamics simulations. Possible refinements based on an improved treatment of molecular correlations are discussed.     

Potential of mean force of water–proton bath and molecular dynamic simulation of proteins at constant pH

An advanced implicit solvent model of water–proton bath for protein simulations at constant pH is presented. The implicit water–proton bath model approximates the potential of mean force of a protein in water solvent in a presence of hydrogen ions. Accurate and fast computational implementation of the implicit water–proton bath model is developed using the continuum electrostatic Poisson equation model for calculation of ionization equilibrium and the corrected MSR6 generalized Born model for calculation of the electrostatic atom–atom interactions and forces. Molecular dynamics (MD) method for protein simulation in the potential of mean force of water–proton bath is developed and tested on three proteins. The model allows to run MD simulations of proteins at constant pH, to calculate pH‐dependent properties and free energies of protein conformations. The obtained results indicate that the developed implicit model of water–proton bath provides an efficient way to study thermodynamics of biomolecular systems as a function of pH, pH‐dependent ionization‐conformation coupling, and proton transfer events. © 2012 Wiley Periodicals, Inc.     

LiTFSI structure and transport in ethylene carbonate from molecular dynamics simulations

Molecular dynamics (MD) simulations using a many-body polarizable force field were performed on ethylene carbonate (EC) doped with lithium bistrifluoromethanesulfonamide (LiTFSI) salt as a function of temperature and salt concentration. At 313 K Li+ was coordinated by 2.7-3.2 EC carbonyl oxygen atoms and 0.67-1.05 TFSI- oxygen atoms at EC:Li = 10 and 20 salt concentrations. In completely dissociated electrolytes, however, Li+ was solvated by approximately 3.8 carbonyl oxygen atoms from EC on average. The probability of ions to participate ion aggregates decreased exponentially with an increase in the size of the aggregate. Ion and solvent self-diffusion coefficients and conductivity predicted by MD simulations were in good agreement with experiments. Approximately half of the charge was transported by charged ion aggregates with the other half carried by free (uncomplexed by counterion) ions. Investigation of the Li+ transport mechanism revealed that contribution from the Li+ diffusion together with its coordination shell to the total Li+ transport is similar to the contribution arising from Li+ exchanging solvent molecules in its first coordination shell with solvents from the outer shells.     

Mean Ionic Activity Coefficients of Alkali Metals Dissolved in High Dielectric Constant Solvents: A Comparison Between Experimental Data and Fuoss Theoretical Data

Abstract

Ionic association of strong univalent symmetrical electrolytes dissolved in Hydrogen Bonded Solvents (HBS) having high dielectric constants, has been studied in terms of mean ionic activity coefficient. This parameter has been analysed with the Fuoss's Paired Ion Model in the concentration range 0.5-500m0lm^-3. The experimental data are consistent with this model. It has been shown that fits to the experimental data could be obtained with fixed values of fraction of contact pain α and Gurney radius corresponding to the Contact Pair (CP). The results of fractions of free ions γ and conducting ions (p) as a function of concentration are also discussed. Conductimetric pairing constants K Lanbad; and Gibbs free energy δG are deduced to explain this ionic association. The iduence of the dielectric constant of the solvent on the ionic association has been also investigated in this work.     

Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: comparison between experiments, analytical calculations and numerical simulations

We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.     

Potentials of mean force between ionizable amino acid side chains in water

Potentials of mean force (PMF) between all possible ionizable amino acid side chain pairs in various protonation states were calculated using explicit solvent molecular dynamics simulations with umbrella sampling and the weighted histogram analysis method. The side chains were constrained in various orientations inside a spherical cluster of 200 water molecules. Beglov and Roux's Spherical Solvent Boundary Potential was used to account for the solvent outside this sphere. This approach was first validated by calculating PMFs between monatomic ions (K(+), Na(+), Cl(-)) and comparing them to results from the literature and results obtained using Ewald summation. The strongest interaction (-4.5 kcal/mol) was found for the coaxial Arg(+).Glu(-) pair. Many like-charged side chains display a remarkable lack of repulsion, and occasionally a weak attraction. The PMFs are compared to effective energy curves obtained with common implicit solvation models, namely Generalized Born (GB), EEF1, and uniform dielectric of 80. Overall, the EEF1 curves are too attractive, whereas the GB curves in most cases match the minima of the PMF curves quite well. The uniform dielectric model, despite some fortuitous successes, is grossly inadequate.     

Potential of average force between two ions in a solvent of polarizable hard spheres

A method of obtaining the potential of average force between two ions immersed in a polarizable hard sphere fluid is described. The ions and the solvent particles may have different hard sphere diameters. For large values of the reduced polarizability of the solvent particles, ^*, the potential of average force rises near contact much more steeply than the primitive model would permit and also has maxima and minima vanishing at larger distances, in semiquantitative agreement with the similar results of Patey and Valleau. The oscillating character of the potential of average force is due above all to the oscillations of the radial distribution function between the ion and polarizable hard sphere.     

Conformational and energetic effects of truncating nonbonded interactions in an aqueous protein dynamics simulation

In a previous aqueous protein dynamics study, we compared the rms deviation relative to the crystal structure for distance-dependent and constant dielectric models with and without a nonbonded cutoff. The structures obtained from a constant dielectric simulation with a cutoff were substantially different from the structures obtained from a distance-dependent dielectric simulation, with and without cutoff, and a constant dielectric model without a cutoff. In fact, structures from the distance-dependent dielectric simulations were insensitive to the nonbonded cutoff and in good agreement with the structures generated from the constant dielectric simulation without a cutoff. In addition, the solute-solvent temperature differential and solvent evaporation artifacts, characteristic of the constant dielectric simulation with a cutoff, were not present for the distance-dependent dielectric simulations. In this current work, we explore whether this dielectric-dependent cutoff-sensitive behavior for a constant dielectric model arises from the discontinuities in the forces at the nonbonded cutoff or from neglecting the structure-stabilizing interactions beyond the nonbonded cutoff. We also examine the origin of the dielectric-dependent artifacts, and its potential influence on the structural disparity. Several protocols for protein dynamics simulations are compared using both constant and distance-dependent dielectric models, including implementation of a switching function and a nonbonded cutoff and two different temperature coupling algorithms. We show that the distance-dependent dielectric model conserves energy in the SPASMS molecular mechanics and dynamics software for the time steps and nonbonded cutoffs commonly used in macromolecule simulations. Although the switching function simulation also conserved energy over a range of commonly used cutoffs, the constant dielectric model with a switching function yielded conformational results more similar to a constant dielectric simulation without a switching function than to a constant dielectric model without a nonbonded cutoff. Therefore, the conformational disparity between the dielectric models arises from neglecting important structure-stabilizing interactions beyond the cutoff, rather than differences in energy conservation. © 1993 John Wiley & Sons, Inc.     

A Model Electron Transfer Reaction in Confined Aqueous Solution

Liquid water confined within nanometer-sized channels exhibits a strongly reduced local dielectric constant perpendicular to the wall, especially at the interface, and this has been suggested to induce faster electron transfer kinetics at the interface than in the bulk. We study a model electron transfer reaction in aqueous solution confined between graphene sheets with classical molecular dynamics. We show that the solvent reorganization energy is reduced at the interface compared to the bulk, which explains the larger rate constant. However, this facilitated solvent reorganization is due to the partial desolvation by the graphene sheet of the ions involved in the electron transfer and not to a local dielectric constant reduction effect.     

Ab initio molecular dynamics simulation of the aqueous Ru2+/Ru3+ redox reaction: the Marcus perspective

A well-behaved (low spin) transition metal aqua ion, Ru(aq)(2+), is used as a model system in an ab initio molecular dynamics study of a redox half reaction to which the Marcus theory of electron transfer is assumed to apply. Using constraint methods, we show that aqueous Ru(2+) can be reversibly transformed to Ru(3+) under the control of the classical solvent electrostatic potential as order parameter. The mean force is found to vary linearly with the order parameter in accordance with the Marcus theory. As can be expected for a half reaction, the slope in the oxidized and reduced states are asymmetric differing by approximately a factor of two. As a further test, we verify that the corresponding quadratic potential of mean force is in excellent agreement with the free energy profile obtained from the Gaussian distribution of potential fluctuations sampled from free (unconstrained) runs of the reduced and oxidized system. Similar to experimental electrochemical methods, our simulation scheme enables us to manipulate the effective thermodynamic driving force and align the free energy minima of product and reactant state. The activation energy and reaction entropy computed under these conditions are discussed and analyzed from the Marcus perspective.     

Dielectric exclusion of ions from membranes

Dielectric exclusion is caused by the interactions of ions with the bound electric charges induced by ions at interfaces between media of different dielectric constants. It is considered as one of mechanisms of nanofiltration. The transport properties of capillary model are expressed through ion distribution and diffusion coefficients. Due to local equilibrium the distribution coefficient is directly related to the excess solvation energy of ion. First, this energy is considered for single ions in single neutral pores in terms of pore size, ion charge, dielectric constants of solvent and membrane matrix and pore geometry. The dielectric exclusion from pores with closed geometry like circular cylinders is shown to be essentially stronger than that from pores with relatively open geometry like slits. Furthermore, the role of finite membrane porosity is analysed for the model of infinite slabs with alternating dielectric constants. The presence of other ions is accounted for within the scope of a mean-field approach, and the screening of dielectric exclusion is thus introduced and considered in some detail. A fixed electric charge is shown to cause additional screening. At the same time the dielectric exclusion makes the Donnan exclusion of ions stronger. Therefore the interaction between those two rejection mechanisms turns out to be non-trivial. Finally, the effect of solvent molecular structure is considered within the scope of non-local electrostatics. It is shown that the solvent non-locality typically results in somewhat stronger dielectric exclusion, however, its most important effect is slowing down the decline of dielectric exclusion with increasing bulk electrolyte concentration.     

Series approach to modeling ion size effects for symmetric electrolytes in the diffuse double layer

An analytical model is developed for the potential drop and differential capacity across the diffuse layer which considers the effects of ion size on these properties. For symmetric electrolytes, this potential drop is expressed in terms of a cubic polynomial in the corresponding estimate in the Gouy-Chapman theory. Optimal polynomial coefficients and model validation for 1:1 and 2:2 electrolytes are provided by fits of Monte Carlo data obtained for a restricted electrolyte in a primitive solvent. Simple relationships between these coefficients and parameters commonly associated with the mean spherical approximation are obtained. It is shown that the series approach accurately describes potential drops and differential capacities of the diffuse layer for 1:1 and 2:2 electrolytes for the chosen assumptions.     

Ion selectivity using membranes comprising functionalized carbon nanotubes

In this paper, we use applied mathematical modelling to investigate the transportation of ions inside functionalized carbon nanotubes, and in particular the transport of sodium and chloride ions. This problem is important for future ion transport and detection, and also arises in ion diffusion inside complex biological channels. Some important future applications of the system for a solvent are ultra-sensitive biosensors and electrolytes for alkaline fuel cells. We model the interactions between the ions and the nanotube by the Lennard-Jones potential and the interactions between the ions and the functional group by the Coulomb potential, while the atomic interactions between the ions is modeled by both the Lennard-Jones and Coulomb potentials. We further assume that the carbon atoms, the charge of the functional group, and the ions are all evenly distributed on the surface of the nanotube, the entry of the nanotube and the envisaged ionic surface, respectively, so that we may use the continuous approximation to calculate the corresponding potential energies. For nanotubes located in salt water, the molecular effects arising from the bulk solution can be extracted from MD simulation studies. Assuming that the solvent is absent, we first determine the acceptance radii for the sodium or chloride ion entering the nanotube, both with and without a functional group, and we then determine the equilibrium positions of two identical ions inside the nanotube. Finally, the transportation time of an intruding ion through the nanotube is deduced from the total axial force. In the presence of a solvent, the molecular effects arising from the bulk solution are examined and we establish that the presence of a solvent stabilizes the selectivity of the ions.     

Density functional theory for efficient ab initio molecular dynamics simulations in solution

We present a density functional for first-principles molecular dynamics simulations that includes the electrostatic effects of a continuous dielectric medium. It allows for numerical simulations of molecules in solution in a model polar solvent. We propose a smooth dielectric model function to model solvation into water and demonstrate its good numerical properties for total energy calculations and constant energy molecular dynamics.