Electrolytes in a nanometer slab-confinement: Ion-specific structure and solvation forces

Adsorbing DNA to Mica by Cations: Influence of Valency and Ion Type

Ion-mediated attraction between DNA and mica plays a crucial role in biotechnological applications and molecular imaging. Here, we combine molecular dynamics simulations and single-molecule atomic force microscopy experiments to characterize the detachment forces of single-stranded DNA at mica surfaces mediated by the metal cations Li+, Na+, K+, Cs+, Mg2+, and Ca2+. Ion-specific adsorption at the mica/water interface compensates (Li+ and Na+) or overcompensates (K+, Cs+, Mg2+, and Ca2+) the bare negative surface charge of mica. In addition, direct and water-mediated contacts are formed between the ions, the phosphate oxygens of DNA, and mica. The different contact types give rise to low- and high-force pathways and a broad distribution of detachment forces. Weakly hydrated ions, such as Cs+ and water-mediated contacts, lead to low detachment forces and high mobility of the DNA on the surface. Direct ion-DNA or ion-surface contacts lead to significantly higher forces. The comprehensive view gained from our combined approach allows us to highlight the most promising cations for imaging in physiological conditions: K+, which overcompensates the negative mica charge and induces long-ranged attractions. Mg2+ and Ca2+, which form a few specific and long-lived contacts to bind DNA with high affinity.

Dendritic polyelectrolytes with monovalent and divalent counterions: the charge regulation effect and counterion release

The charge regulation and the release of counterions are extremely important and substantial in determining the charge state of polyelectrolytes and the interaction between polyelectrolytes and proteins. Going beyond monovalent to multivalent cations, it is well-known that the effects of ions are qualitatively different. Therefore, the well-accepted descriptions of the charge regulation and the counterion release based on monovalent ions do not immediately apply to systems with multivalent ions. Here, we study the key structural and electrostatic features of charged dendrimers at hand of the pharmaceutically important dendritic polyglycerol sulfate (dPGS) macromolecule equilibrated with monovalent and divalent salts by molecular dynamics (MD) simulations. Following a simple but accurate scheme to determine its effective radius, the counterion condensed layer of the dPGS is determined with high accuracy and we observe the sequential replacement of condensed monovalent cations (MCs) to divalent cations (DCs) rendering a smaller dPGS effective charge versus the DC concentration. We resolve and track the release of counterions on the dPGS along its binding pathway with the plasma protein Human Serum Albumin (HSA). We find that the release of MCs remains favorable for the complexation leading to a considerable amount of release entropy as the driving force for complexation. The release of DCs only occurs above a certain DC concentration with a comparably smaller number of released ions than MCs. Its contribution to the binding free energy is small indicating a subtle cancellation between the entropy gain in releasing DCs and the enthalpy penalty from dissociating DCs from the dendrimer.

Correlation function approach for diffusion in confined geometries

This paper describes a formalism for extracting spatially varying transport coefficients from simulations of a molecular fluid in a nanochannel. This approach is applied to self-diffusion of a Lennard-Jones fluid confined between two parallel surfaces. A numerical grid is laid over the domain confining the fluid, and fluid properties are projected onto the grid cells. The time correlation functions between properties in different grid cells are calculated and can be used as the basis for a fitting procedure for extracting spatially varying diffusion coefficients from the simulation. Results for the Lennard-Jones system show that transport behavior varies sharply near the liquid-solid boundary and that the changes depend on the details of the liquid-solid interaction. A quantitative difference between the reduced and detailed models is discussed. It is found that the difference could be associated with assumptions about the form of the transport equations at molecular scales in lieu of problems with the method itself. The study suggests that this approach to fitting molecular simulations to continuum equations may guide the development of appropriate coarse-grained equations to model transport phenomena at nanometer scales.

Specific ion effects on electrocapillarity in aqueous electrolytes confined within nanochannels

A nanoslit is a long, extremely narrow (nanometers apart) opening between two parallel plates. An overlapped electric double layer is formed when an electrolyte is present inside the slit and there exist distributions of the osmotic pressure and the Maxwell stress across the nanoslit, which lead to the electrocapillarity effect. This feature can be incorporated with the specific ion effects by considering the nonelectrostatic interactions between ions and confining walls, as they significantly influence the potential, electric field, and ion distributions across the nanoslit. In the present work, the electromechanical approach is integrated with the concept of specific ion effects to analyze the behavior of an electrolyte confined in a one-dimensional nanochannel. For a nanochannel, the average outward normal stress exerted on the cross section of a channel (P_{zz}[over ¯]) can be regarded as a measure of electrocapillarity and it is the driving force of the flow. This electrocapillarity measure is analyzed by using the solution of the modified Poisson-Boltzmann equation as a function of the bulk concentration of the electrolyte, the boundary potential, and most importantly, the ion-specific interfacial interactions. The significance of the present work can be manifested by the increasing usage of extremely narrow channels in nanoscaled systems, which will require proper consideration of specific ion effects in determining the behavior of the confined electrolyte.

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of silicon

We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.

Swelling of ionic microgel particles in the presence of excluded-volume interactions: a density functional approach

In this work a new density functional theory framework is developed to predict the salt-concentration dependent swelling state of charged microgels and the local concentration of monovalent ions inside and outside the microgel.

Multiscale modeling of lithium ion batteries: thermal aspects

The thermal behavior of lithium ion batteries has a huge impact on their lifetime and the initiation of degradation processes. The development of hot spots or large local overpotentials leading, e.g., to lithium metal deposition depends on material properties as well as on the nano- und microstructure of the electrodes. In recent years a theoretical structure emerges, which opens the possibility to establish a systematic modeling strategy from atomistic to continuum scale to capture and couple the relevant phenomena on each scale. We outline the building blocks for such a systematic approach and discuss in detail a rigorous approach for the continuum scale based on rational thermodynamics and homogenization theories. Our focus is on the development of a systematic thermodynamically consistent theory for thermal phenomena in batteries at the microstructure scale and at the cell scale. We discuss the importance of carefully defining the continuum fields for being able to compare seemingly different phenomenological theories and for obtaining rules to determine unknown parameters of the theory by experiments or lower-scale theories. The resulting continuum models for the microscopic and the cell scale are numerically solved in full 3D resolution. The complex very localized distributions of heat sources in a microstructure of a battery and the problems of mapping these localized sources on an averaged porous electrode model are discussed by comparing the detailed 3D microstructure-resolved simulations of the heat distribution with the result of the upscaled porous electrode model. It is shown, that not all heat sources that exist on the microstructure scale are represented in the averaged theory due to subtle cancellation effects of interface and bulk heat sources. Nevertheless, we find that in special cases the averaged thermal behavior can be captured very well by porous electrode theory.

Electroneutrality breakdown and specific ion effects in nanoconfined aqueous electrolytes observed by NMR

Ion distribution in aqueous electrolytes near the interface plays a critical role in electrochemical, biological and colloidal systems, and is expected to be particularly significant inside nanoconfined regions. Electroneutrality of the total charge inside nanoconfined regions is commonly assumed a priori in solving ion distribution of aqueous electrolytes nanoconfined by uncharged hydrophobic surfaces with no direct experimental validation. Here, we use a quantitative nuclear magnetic resonance approach to investigate the properties of aqueous electrolytes nanoconfined in graphitic-like nanoporous carbon. Substantial electroneutrality breakdown in nanoconfined regions and very asymmetric responses of cations and anions to the charging of nanoconfining surfaces are observed. The electroneutrality breakdown is shown to depend strongly on the propensity of anions towards the water-carbon interface and such ion-specific response follows, generally, the anion ranking of the Hofmeister series. The experimental observations are further supported by numerical evaluation using the generalized Poisson-Boltzmann equation.

Ion-specific adsorption and electroosmosis in charged amorphous porous silica

Aqueous electrolyte solutions (NaCl, KCl, CsCl, and SrCl₂) confined in a negatively charged amorphous silica slit pore.

Variational Implicit Solvation with Poisson-Boltzmann Theory

We incorporate the Poisson-Boltzmann (PB) theory of electrostatics into our variational implicit-solvent model (VISM) for the solvation of charged molecules in an aqueous solvent. In order to numerically relax the VISM free-energy functional by our level-set method, we develop highly accurate methods for solving the dielectric PB equation and for computing the dielectric boundary force. We also apply our VISM-PB theory to analyze the solvent potentials of mean force and the effect of charges on the hydrophobic hydration for some selected molecular systems. These include some single ions, two charged particles, two charged plates, and the host-guest system Cucurbit[7]uril and Bicyclo[2.2.2]octane. Our computational results show that VISM with PB theory can capture well the sensitive response of capillary evaporation to the charge in hydrophobic confinement and the polymodal hydration behavior and can provide accurate estimates of binding affinity of the host-guest system. We finally discuss several issues for further improvement of VISM.

NaCl crystallization in apolar nanometer-sized confinement studied by atomistic simulations

The structure and growth of molecular NaCl crystals in bulk and in a narrow, nanometer-sized apolar confinement are examined by explicit-water molecular dynamics computer simulations. It is demonstrated that fast crystallization and subsequent diffusion-controlled cluster growth in bulk is triggered by supersaturations that exceed a certain threshold value. In confinement, simulated in a pseudo grand canonical setup, salt is shown to be expelled from the narrow apolar slab region, and the effective ion concentration inside the nanoconfinement is always considerably lower than the reservoir salt concentration so that no fast crystallization takes place. For very small slab widths (d<1.5 nm) salt is almost entirely expelled while water remains in the slab, indicating a capillary evaporation phenomenon for the polar ions. If forced into the apolar confinement by simulating in a strictly canonical setup, we find stable crystals only if at least three crystalline planes fit into the slab, which happens above a 2-nm slab width. In this case the (100) plane of the bulk crystal is oriented parallel to the apolar surface delimited by a subnanometer thin hydration layer. This work presents molecular-level insight of salt crystallization in apolar confinements of a nanometer scale with possible implications in double-layer supercapacitor physics and geological salt weathering.

A proposed voltage dependence of the ionic strength of a confined electrolyte based on a grand canonical ensemble model

Electrodes with highly porous morphologies are of great technological interest, as their exceptionally high specific surface areas make them ideal for use in capacitors, battery electrodes and electrochemical sensors. There is a large body of research focusing on the structure of confined electrolytes in these systems, but the majority of these studies focus on cases where the length scale of the porous domain is equal to or less than the Debye screening length of the electrolyte. In this work, we use a thermodynamic model to consider the structure of electrolytes in mesoscale domains, where the pore dimensions are significantly larger than the Debye screening length. In this limit, the interface is screened by the electrochemical double layer and the enclosed volume primarily consists of an electroneutral 'bulk liquid' domain. Despite the absence of direct interactions between ions in the bulk domain and the charged interface, we show that minimization of the free energy of the system leads to a reduction in the ionic strength of the electrolyte within the bulk liquid domain of the pore. Based on our model studies, we anticipate that this depletion will apply for porous domains with widths of the order of 50-200 nm even under mild experimental conditions and low applied voltages. The results imply relationships between electrolyte strength, surface morphology and applied voltage that may be important in device design.

Anionic and cationic Hofmeister effects on hydrophobic and hydrophilic surfaces

Using a two-step modeling approach, we address the full spectrum of direct, reversed, and altered ionic sequences as the charge of the ion, the charge of the surface, and the surface polarity are varied. From solvent-explicit molecular dynamics simulations, we extract single-ion surface interaction potentials for halide and alkali ions at hydrophilic and hydrophobic surfaces. These are used within Poisson-Boltzmann theory to calculate ion density and electrostatic potential distributions at mixed polar/unpolar surfaces for varying surface charge. The resulting interfacial tension increments agree quantitatively with experimental data and capture the Hofmeister series, especially the anomaly of lithium, which is difficult to obtain using continuum theory. Phase diagrams that feature different Hofmeister series as a function of surface charge, salt concentration, and surface polarity are constructed from the long-range force between two surfaces interacting across electrolyte solutions. Large anions such as iodide have a high hydrophobic surface affinity and increase the effective charge magnitude on negatively charged unpolar surfaces. Large cations such as cesium also have a large hydrophobic surface affinity and thereby compensate an external negative charge surface charge most efficiently, which explains the well-known asymmetry between cations and anions. On the hydrophilic surface, the size-dependence of the ion surface affinity is reversed, explaining the Hofmeister series reversal when comparing hydrophobic with hydrophilic surfaces.

Direct visualization of single ions in the Stern layer of calcite

Calcite is among the most abundant minerals on earth and plays a central role in many environmental and geochemical processes. Here we used amplitude modulation atomic force microscopy (AFM) operated in a particular regime to visualize single ions close to the (1014) surface of calcite in solution. The results were acquired at equilibrium, in aqueous solution containing different concentrations of NaCl, RbCl, and CaCl(2). The AFM images provide a direct and atomic-level picture of the different cations adsorbed preferentially at certain locations of the calcite-water interface. Highly ordered water layers at the calcite surface prevent the hydrated ions from directly interacting with calcite due to the energy penalty incurred by the necessary restructuring of the ions' solvation shells. Controlled removal of the adsorbed ions from the interface by the AFM tip provides indications about the stability of the adsorption site. The AFM results show the familiar "row pairing" of the carbonate oxygen atoms, with the adsorbed monovalent cations located adjacent to the most prominent oxygen atoms. The location of adsorbed cations near the surface appears better defined for monovalent ions than for Ca(2+), consistent with the idea that Ca(2+) ions remain further away from the surface of calcite due to their larger hydration shell. The precise distance between the different hydrated ions and the surface of calcite is quantified using MD simulation. The preferential adsorption sites found by MD as well as the ion residence times close to the surface support the AFM findings, with Na(+) ions dwelling substantially longer and closer to the calcite surface than Ca(2+). The results also bring new insights into the problem of the Stern and electrostatic double layer at the surface of calcite, showing that parameters such as the thickness of the Stern layer can be highly ion dependent.

Competitive adsorption and ordered packing of counterions near highly charged surfaces: From mean-field theory to Monte Carlo simulations

Competitive adsorption of counterions of multiple species to charged surfaces is studied by a size-effect-included mean-field theory and Monte Carlo (MC) simulations. The mean-field electrostatic free-energy functional of ionic concentrations, constrained by Poisson's equation, is numerically minimized by an augmented Lagrangian multiplier method. Unrestricted primitive models and canonical ensemble MC simulations with the Metropolis criterion are used to predict the ionic distributions around a charged surface. It is found that, for a low surface charge density, the adsorption of ions with a higher valence is preferable, agreeing with existing studies. For a highly charged surface, both the mean-field theory and the MC simulations demonstrate that the counterions bind tightly around the charged surface, resulting in a stratification of counterions of different species. The competition between mixed entropy and electrostatic energetics leads to a compromise that the ionic species with a higher valence-to-volume ratio has a larger probability to form the first layer of stratification. In particular, the MC simulations confirm the crucial role of ionic valence-to-volume ratios in the competitive adsorption to charged surfaces that had been previously predicted by the mean-field theory. The charge inversion for ionic systems with salt is predicted by the MC simulations but not by the mean-field theory. This work provides a better understanding of competitive adsorption of counterions to charged surfaces and calls for further studies on the ionic size effect with application to large-scale biomolecular modeling.

Effective interaction between two ion-adsorbing plates: Hofmeister series and salting-in/salting-out phase diagrams from a global mean-field analysis

Interactions between ions and solutes are key to ion-specificity. A generic model in which ions interact via square well potentials of finite range with charged plates is solved analytically on the Poisson-Boltzmann level and analyzed globally for varying surface charge, salt concentration, and ion-surface affinity. Ion adsorption as well as depletion can lead to stably bound plates at finite separation, relevant for the equilibrium salting-out of small solutes such as proteins. The interplate pressure at large plate separation, relevant for aggregation kinetics of large solutes, exhibits direct as well as indirect Hofmeister ordering, depending on surface charge and salt concentration. A simple method for mapping explicit ion-surface potentials of mean force as obtained from solvent-explicit molecular dynamics simulations onto square-well potential parameters is demonstrated.

Density functional for ternary non-additive hard sphere mixtures

Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data.

Radial distribution functions of non-additive hard sphere mixtures via Percus' test particle route

Using fundamental density functional theory we calculate the partial radial distribution functions, g(ij)(r), of a binary non-additive hard sphere mixture using either Percus' test particle approach or inversion of the analytic structure factor obtained via the Ornstein-Zernike route. We find good agreement between the theoretical results and Monte Carlo simulation data for both positive and moderate negative non-additivities. We investigate the asymptotic, [Formula: see text], decay of the g(ij)(r) and show that this agrees with the analytic analysis of the contributions to the partial structure factors in the plane of complex wavevectors. We find the test particle density profiles to be free of unphysical artefacts, contrary to earlier reports.

Translocation of DNA molecules through nanopores with salt gradients: the role of osmotic flow

Recent experiments of translocation of double-stranded DNA through nanopores [M. Wanunu et al., Nature Nanotech. 5, 160 (2009)] reveal that the DNA capture rate can be significantly influenced by a salt gradient across the pore. We show that osmotic flow combined with electrophoretic effects can quantitatively explain the experimental data on the salt-gradient dependence of the capture rate.