Ionic self-diffusion in concentrated aqueous electrolyte solutions

Diffusiophoretic Transport of Charged Colloids in Ionic Surfactant Gradients Entirely below versus Entirely above the Critical Micelle Concentration

When placed in an ionic surfactant gradient, charged colloids will undergo diffusiophoresis at a velocity, uDP = MDP∇ ln S, where MDP is the diffusiophoretic mobility and S is the surfactant concentration. The diffusiophoretic mobility depends in part on the charges and diffusivities of the surfactants and their counterions. Since micellization decreases surfactant diffusivity and alters charge distributions in a surfactant solution, MDP of charged colloids in ionic surfactant gradients may differ significantly when surfactant concentrations are above or below the critical micelle concentration (CMC). The role of micelles in driving diffusiophoresis is unclear, and a previously published model that accounts for micellization suggests the possibility of a change in the sign of MDP above the CMC [Warren, P. B.; . Soft Matter 2019, 15, 278-288]. In the current study, microfluidic channels were used to measure the transport of negatively charged polystyrene colloids in sodium dodecyl sulfate (SDS) surfactant gradients established at SDS concentrations that are either fully above or fully below the CMC. Interpretation of diffusiophoresis was aided by measurements of the colloid electrophoretic mobility as a function of SDS concentration. A numerical transport model incorporating the prior diffusiophoretic mobility model for ionic surfactant gradients was implemented to elucidate signatures of positive and negative diffusiophoretic mobilities and compare with experiments. The theoretically predicted sign of the diffusiophoretic mobility below the CMC was determined to be particularly sensitive to uncertainty in colloid and surfactant properties, while above the CMC, the mobility was consistently predicted to be positive in the SDS concentration range considered in the experiments conducted here. In contrast, experiments only showed signatures of a negative diffusiophoretic mobility for these negatively charged colloids with no change of sign. Colloid diffusiophoretic transport measured in micellar solutions was more extensive than that below the CMC with the same ∇ ln S.

Range and sensitivity of 17O nuclear spin-lattice relaxation as a probe of aqueous electrolyte dynamics

The study of electrolytic solutions is of relevance in many research fields, ranging from biophysics, materials, and colloid science to catalysis and electrochemistry. The dependence of solution dynamics on the nature of electrolytes and their concentrations has been the subject of many experimental and computational studies, yet it remains challenging to obtain a full understanding of the factors that govern solution behavior. Here, we provide additional insights into the behavior of aqueous solutions of alkali chlorides by combining 17O relaxation data with diffusion and viscosity data and contrast their behavior with 1H nuclear magnetic resonance relaxation data. The main findings are that 17O relaxation correlates well with viscosity data but not with diffusion data, while 1H relaxation correlates with neither. Certain ionic trends match known ion-specific series behavior, especially at high concentrations. Notably, we also examine the ranges of the interactions and conclude that the majority of the effects are tied to local water reorientation dynamics.

Anomalous Concentration Dependence of Viscosity: Hidden Role of Cross-Correlations in Aqueous Electrolyte Solutions

The viscosity of aqueous electrolyte solutions exhibits well-known composition-dependent anomalies that show certain definitive trends and universal features. The viscosity of LiCl and NaCl solutions increases with concentration in a monotonic fashion, while solutions of KCl, RbCl, and CsCl exhibit a more complex behavior. Here, the viscosity first decreases and then increases with increasing concentration, with a rather broad minimum at intermediate concentrations (ca. 1-3 m). To unearth the origin of such puzzling behavior, we carried out detailed molecular-level analyses by interrogating the exact Green-Kubo expression of viscosity in terms of the stress-stress time correlation function (SS-TCF). The total SS-TCF can be decomposed into a collection of three self- and three cross-SS-TCFs arising from the three constituent components (water, cations, and anions). Mode coupling theory (MCT) analysis for the friction on ions and the viscosity of the solution suggests the possible importance of two-particle static and time-dependent cross-correlations between water and the ions. We calculate the viscosity and other dynamical properties for all five electrolyte (LiCl, NaCl, KCl, RbCl, and CsCl) solutions over a range of concentrations, using two models of water (SPC/E and TIP4P/2005). The total viscosity derives non-negligible contributions from all of the terms. The cross-correlations are found to be surprisingly large and seen to play a hidden role in the concentration dependence. However, the importance of cross-correlations is often not discussed. Our study leads to a theoretical understanding of the microscopic origin of the observed anomalies in the composition dependence of viscosity across all five electrolytes.

On analytical theories for conductivity and self-diffusion in concentrated electrolytes

Describing analytically the transport properties of electrolytes, such as their conductivity or the self-diffusion of the ions, has been a central challenge of chemical physics for almost a century. In recent years, this question has regained some interest in light of Stochastic Density Field Theory (SDFT) - an analytical framework that allows the approximate determination of density correlations in fluctuating systems. In spite of the success of this theory to describe dilute electrolytes, its extension to concentrated solutions raises a number of technical difficulties, and requires simplified descriptions of the short-range repulsion between the ions. In this article, we discuss recent approximations that were proposed to compute the conductivity of electrolytes, in particular truncations of Coulomb interactions at short distances. We extend them to another observable (the self-diffusion coefficient of the ions) and compare them to earlier analytical approaches, such as the mean spherical approximation and mode-coupling theory. We show how the treatment of hydrodynamic effects in SDFT can be improved, that the choice of the modified Coulomb interactions significantly affects the determination of the properties of the electrolytes, and that comparison with other theories provides a guide to extend SDFT approaches in this context.

Ionic fluctuations in finite volumes: fractional noise and hyperuniformity

Observing finite regions of a bigger system is a common aim, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite observation volumes. However, kinetic properties have received little attention, especially not in ionic solutions, where electrostatic interactions play a decisive role. Here, we probe ionic fluctuations in finite volumes with Brownian dynamics and build an analytical framework that reproduces our simulation results and is broadly applicable to other systems with pairwise interactions. Particle number and charge correlations exhibit a rich phenomenology with time, characterized by a diversity of timescales. The noise spectrum of both quantities decays as 1/f3/2, where f is the frequency. This signature of fractional noise shows the universality of 1/f3/2 scalings when observing diffusing particles in finite domains. The hyperuniform behaviour of charge fluctuations, namely that correlations scale with the area of the observation volume, is preserved in time. Correlations even become proportional to the box perimeter at sufficiently long times. Our results pave the way to understand fluctuations in more complex systems, from nanopores to single-particle electrochemistry.

Quantitative imaging and modeling of colloidal gelation in the coagulant dipping process

Many common elastomeric products, including nitrile gloves, are manufactured by coagulant dipping. This process involves the destabilization and gelation of a latex dispersion by an ionic coagulant. Despite widespread application, the physical chemistry governing coagulant dipping is poorly understood. It is unclear which properties of an electrolyte determine its efficacy as a coagulant and which phenomena control the growth of the gel. Here, a novel experimental protocol is developed to directly observe coagulant gelation by light microscopy. Gel growth is imaged and quantified for a variety of coagulants and compared to macroscopic dipping experiments mimicking the industrial process. When the coagulant is abundant, gels grow with a t1/2 time dependence, suggesting that this phenomenon is diffusion-dominated. When there is a finite amount of coagulant, gels grow to a limiting thickness. Both these situations are modeled as one-dimensional diffusion problems, reproducing the qualitative features of the experiments including which electrolytes cause rapid growth of thick gels. We propose that the gel thickness is limited by the amount of coagulant available, and the growth is, therefore, unbounded when the coagulant is abundant. The rate of the gel growth is controlled by a combination of a diffusion coefficient and the ratio of the critical coagulation concentration to the amount of coagulant present, which in many situations is set by the coagulant solubility. Other phenomena, including diffusiophoresis, may make a more minor contribution to the rate of gel growth.

Systematic Evaluation of Ion Diffusion and Water Exchange

As a fundamental property of all fluids, diffusion plays myriad roles in both science and our daily lives. Diffusive properties of many liquids including water have been extensively studied both experimentally and theoretically, while for transition metal ions, there exist significant experimental data that have not been extensively studied theoretically. Hence, high-confidence predictions for challenging systems like radioactive ions that are biohazardous cannot be reliably generated. In this work, a workflow named ISAIAH (Ion Simulation using AMBER for dIffusion Action when Hydrated) was designed to accurately simulate the diffusion coefficients of 15 monoatomic ions with charges varying from -1 to +3 in four water models. As the results indicate, good agreement with experimental values was achieved, leading us to select ²³⁹Pu⁴⁺ (for which no experimental data are available) as a candidate ion to make a theoretical prediction of its diffusion coefficient in water. Among all the force field parameter sets, the ones parametrized using an augmented 12-6-4 Lennard-Jones (LJ) potential showed lower average unsigned errors (AUE) for ions of various radii and electron configurations relative to some 12-6 LJ parameters. This observation agrees well with the fact that diffusion is affected by both the hydration free energy (HFE) and the ion-oxygen distance (IOD) between solute and solvent molecules, both of which are handled well by the 12-6-4 model.

On the molecular correlations that result in field-dependent conductivities in electrolyte solutions

Employing recent advances in response theory and nonequilibrium ensemble reweighting, we study the dynamic and static correlations that give rise to an electric field-dependent ionic conductivity in electrolyte solutions. We consider solutions modeled with both implicit and explicit solvents, with different dielectric properties, and at multiple concentrations. Implicit solvent models at low concentrations and small dielectric constants exhibit strongly field-dependent conductivities. We compare these results to Onsager-Wilson theory of the Wien effect, which provides a qualitatively consistent prediction at low concentrations and high static dielectric constants but is inconsistent away from these regimes. The origin of the discrepancy is found to be increased ion correlations under these conditions. Explicit solvent effects act to suppress nonlinear responses, yielding a weakly field-dependent conductivity over the range of physically realizable field strengths. By decomposing the relevant time correlation functions, we find that the insensitivity of the conductivity to the field results from the persistent frictional forces on the ions from the solvent. Our findings illustrate the utility of nonequilibrium response theory in rationalizing nonlinear transport behavior.

Assessment of the Wolf method using the Stillinger-Lovett sum rules: From strong electrolytes to weakly charged colloidal dispersions

The Ewald method has been the cornerstone in molecular simulations for modeling electrostatic interactions of charge-stabilized many-body systems. In the late 1990s, Wolf and collaborators developed an alternative route to describe the long-range nature of electrostatic interactions; from a computational perspective, this method provides a more efficient and straightforward way to implement long-range electrostatic interactions than the Ewald method. Despite these advantages, the validity of the Wolf potential to account for the electrostatic contribution in charged fluids remains controversial. To alleviate this situation, in this contribution, we implement the Wolf summation method to both electrolyte solutions and charged colloids with moderate size and charge asymmetries in order to assess the accuracy and validity of the method. To this end, we verify that the proper selection of parameters within the Wolf method leads to results that are in good agreement with those obtained through the standard Ewald method and the theory of integral equations of simple liquids within the so-called hypernetted chain approximation. Furthermore, we show that the results obtained with the original Wolf method do satisfy the moment conditions described by the Stillinger-Lovett sum rules, which are directly related to the local electroneutrality condition and the electrostatic screening in the Debye-Hückel regime. Hence, the fact that the solution provided by the Wolf method satisfies the first and second moments of Stillinger-Lovett proves, for the first time, the reliability of the method to correctly incorporate the electrostatic contribution in charge-stabilized fluids. This makes the Wolf method a powerful alternative compared to more demanding computational approaches.

Thermodynamics and diffusion in size-symmetric and asymmetric dense electrolytes

MD simulation results for model size-symmetric and asymmetric electrolytes at high densities and temperatures (well outside the liquid-gas coexistence region) are generated and analyzed focusing on thermodynamic and diffusion properties. An extension of the mean spherical approximation for electrolytes originally derived for charged hard sphere fluids is adapted to these systems by exploiting the separation of short range and Coulomb interaction contributions intrinsic to these theoretical models and is found to perform well for predicting equation of state quantities. The diffusion coefficients of these electrolytes can also be reasonably well predicted using entropy scaling ideas suitably adapted to charged systems and mixtures. Thus, this approach may provide an avenue for studying dense electrolytes or complex molecular systems containing charged species at high pressures and temperatures.

Multiple Scales in the Simulation of Ion Channels and Proteins

Computation of living processes creates great promise for the everyday life of mankind and great challenges for physical scientists. Simulations molecular dynamics have great appeal to biologists as a natural extension of structural biology. Once a biologist sees a structure, she/he wants to see it move. Molecular biology has shown that a small number of atoms, sometimes even one messenger ion, like Ca(2+), can control biological function on the scale of cells, organs, tissues, and organisms. Enormously concentrated ions-at number densities of ~20 M-in protein channels and enzymes are responsible for many of the characteristics of living systems, just as highly concentrated ions near electrodes are responsible for many of the characteristics of electrochemical systems. Here we confront the reality of the scale differences of ions. We show that the scale differences needed to simulate all the atoms of biological cells are 10(7) in linear dimension, 10(21) in three dimensions, 10(9) in resolution, 10(11) in time, and 10(13) in particle number (to deal with concentrations of Ca(2+)). These scales must be dealt with simultaneously if the simulation is to deal with most biological functions. Biological function extends across all of them, all at once in most cases. We suggest a computational approach using explicit multiscale analysis instead of implicit simulation of all scales. The approach is based on an energy variational principle EnVarA introduced by Chun Liu to deal with complex fluids. Variational methods deal automatically with multiple interacting components and scales. When an additional component is added to the system, the resulting Euler Lagrange field equations change form automatically-by algebra alone-without additional unknown parameters. Multifaceted interactions are solutions of the resulting equations. We suggest that ionic solutions should be viewed as complex fluids with simple components. Highly concentrated solutions-dominated by interactions of components-are easily computed by EnVarA. Successful computation of ions concentrated in special places may be a significant step to understanding the defining characteristics of biological and electrochemical systems. Indeed, computing ions near proteins and nucleic acids may prove as important to molecular biology and chemical technology as computing holes and electrons has been to our semiconductor and digital technology.

Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton's least action and Rayleigh's dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an "extra layer" of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler-Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler-Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler-Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson-Nernst-Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary "binding" in the channel, and the eventual accumulation of salts in "unstirred layers" near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions.

How the excluded volume architecture influences ion-mediated forces between proteins

The effective interactions between model proteins of various shapes are computed by means of Monte Carlo simulations. In particular, we determine how the modification of the excluded volume architecture influences both entropic and purely electrostatic ion-mediated forces between proteins. We find that interprotein interactions are strongly affected by protein shape, which results in a high decrease of electrostatic screening for typical active site geometries. Effective interactions are then closer to the direct Coulombic interactions, and both affinity and selectivity are enhanced by several orders of magnitude.

Long-time self-diffusion of charged colloidal particles: electrokinetic and hydrodynamic interaction effects

The authors analyze the long-time self-diffusion of charge-stabilized colloidal macroions in nondilute suspensions using a mode-coupling scheme developed for multicomponent suspensions of interacting Brownian spheres. In this scheme, all ionic species, including counterions and electrolyte ions, are treated on an equal footing as charged hard spheres undergoing overdamped Brownian motion. Hydrodynamic interactions between all ions are accounted for on the far-field level. We show that the influence on the colloidal long-time self-diffusion coefficient arising from the relaxation of the microionic atmosphere surrounding the colloids, the so-called electrolyte friction effect, is usually insignificant in comparison with the friction contributions arising from direct and hydrodynamic interactions between the colloidal particles. This finding is true even for small colloid concentrations unless the mobility difference between colloidal particles and microions is not large. Furthermore, we observe an interesting nonmonotonic density dependence of the colloidal long-time self-diffusion coefficient in suspensions with low amount of added salt. We show that this unusual density dependence is due to colloid-colloid hydrodynamic interactions.

A general treatment for the conductivity of electrolytes in the whole concentration range in aqueous and nonaqueous solutions

Despite the great importance of ion transport, most of the widely accepted models and theories are valid only in the not very practical limit of low concentrations. Aiming to extend the range of applicability to moderate concentrations, a number of modified models and equations (some approximate, some fundamented on different assumptions, and some just empirical) have been reported. In this work, a general treatment for the electrical conductivity of ionic solutions has been developed, considering the electrical conductivity as a transport phenomenon governed by dissipation and feedback. A general expression for the dependence of the specific conductivity on the solution viscosity (and indirectly on concentration), from which the whole conductivity curve can be obtained, has been derived. The validity of this general approach is demonstrated with experimental results taken from the literature for aqueous and nonaqueous solutions of electrolytes.

Analytical theories of transport in concentrated electrolyte solutions from the MSA

Ion transport coefficients in electrolyte solutions (e.g., diffusion coefficients or electric conductivity) have been a subject of extensive studies for a long time. Whereas in the pioneering works of Debye, Hückel, and Onsager the ions were entirely characterized by their charge, recent theories allow specific effects of the ions (such as the ion size dependence or the pair association) to be obtained, both from simulation and from analytical theories. Such an approach, based on a combination of dynamic theories (Smoluchowski equation and mode-coupling theory) and of the mean spherical approximation (MSA) for the equilibrium pair correlation, is presented here. The various predicted equilibrium (osmotic pressure and activity coefficients) and transport coefficients (mutual diffusion, electric conductivity, self-diffusion, and transport numbers) are in good agreement with the experimental values up to high concentrations (1-2 mol L(-1)). Simple analytical expressions are obtained, and for practical use, the formula are given explicitly. We discuss the validity of such an approach which is nothing but a coarse-graining procedure.

Simple model for ac ionic conduction in solids

We present a model for the ac conduction in ionically conducting solids that takes into account, in a simple way, the interaction between carriers. The Coulomb force forms an "ionic atmosphere" that exerts a restoring force on a central ion, whose motion corresponds to an overdamped oscillator. We consider the effect of the relaxation of the ionic atmosphere by introducing an additional equation for the displacement of the potential toward the particle position. The general behavior of the ac conductivity can be understood in terms of two types of motions: motion of the bound ion at high frequencies determined by microscopic friction, and a much slower motion coupled to the surrounding carriers relaxation at low frequencies.