Polarization Deficiency and Excess Free Energy of Ion Hydration in Electric Fields

Parameter-Fitting-Free Continuum Modeling of Electric Double Layer in Aqueous Electrolyte

Electric double layers (EDLs) play fundamental roles in various electrochemical processes. Despite the extensive history of EDL modeling, there remain challenges in the accurate prediction of its structure without expensive computation. Herein, we propose a predictive multiscale continuum model of EDL that eliminates the need for parameter fitting. This model computes the distribution of the electrostatic potential, electron density, and species' concentrations by taking the extremum of the total grand potential of the system. The grand potential includes the microscopic interactions that are newly introduced in this work: polarization of solvation shells, electrostatic interaction in parallel plane toward the electrode, and ion-size-dependent entropy. The parameters that identify the electrode and electrolyte materials are obtained from independent experiments in the literature. The model reproduces the trends in the experimental differential capacitance with multiple electrode and nonadsorbing electrolyte materials (Ag(110) in NaF, Ag(110) in NaClO4, and Hg in NaF), which verifies the accuracy and predictiveness of the model and rationalizes the observed values to be due to changes in electron stability. However, our calculation on Pt(111) in KClO4 suggests the need for the incorporation of electrode/ion-specific interactions. Sensitivity analyses confirmed that effective ion radius, ion valence, the electrode's Wigner-Seitz radius, and the bulk modulus of the electrode are significant material properties that control the EDL structure. Overall, the model framework and findings provide insights into EDL structures and predictive capability at low computational cost.

Electrostatic free energies carry structural information on nucleic acid molecules in solution

Over the last several decades, a range of experimental techniques from x-ray crystallography and atomic force microscopy to nuclear magnetic resonance and small angle x-ray scattering have probed nucleic acid structure and conformation with high resolution both in the condensed state and in solution. We present a computational study that examines the prospect of using electrostatic free energy measurements to detect 3D conformational properties of nucleic acid molecules in solution. As an example, we consider the conformational difference between A- and B-form double helices whose structures differ in the values of two key parameters—the helical radius and rise per basepair. Mapping the double helix onto a smooth charged cylinder reveals that electrostatic free energies for molecular helices can, indeed, be described by two parameters: the axial charge spacing and the radius of a corresponding equivalent cylinder. We show that electrostatic free energies are also sensitive to the local structure of the molecular interface with the surrounding electrolyte. A free energy measurement accuracy of 1%, achievable using the escape time electrometry (ET e) technique, could be expected to offer a measurement precision on the radius of the double helix of approximately 1 Å. Electrostatic free energy measurements may, therefore, not only provide information on the structure and conformation of biomolecules but could also shed light on the interfacial hydration layer and the size and arrangement of counterions at the molecular interface in solution.

Carbon-Nanotube-Electrolyte Interface: Quantum and Electric Double Layer Capacitance

We present a comprehensive study of the electrochemical capacitance between a one-dimensional electronic material and an electrolyte. In contrast to a conventional, planar electrode, the nanoscale dimension of the electrode (with diameter smaller than the Debye length and approaching the size of the ions in solution) qualitatively changes the capacitance, which we measure and model herein. Furthermore, the finite density of states in these low dimensional electronic systems results in a quantum capacitance, which is comparable to the electrochemical capacitance. Using electrochemical impedance spectroscopy (EIS), we measure the ensemble average, complex, frequency dependent impedance (from 0.1 Hz to 1 MHz) between a purified (99.9%) semiconducting nanotube network and an aqueous electrolyte (KCl) at different concentrations between 10 mM and 1 M. The potential dependence of the capacitance is convoluted with the potential dependence of the in-plane conductance of the nanotube network, which we model using a transmission-line model to account for the frequency dependent in-plane impedance as well as the total interfacial impedance between the network and the electrolyte. The ionic strength dependence of the capacitance is expected to have a root cause from the double layer capacitance, which we model using a modified Poisson-Boltzmann equation. The relative contributions from those two capacitances can be quantitatively decoupled. We find a total capacitance per tube of 0.67-1.13 fF/μm according to liquid gate potential varying from -0.5 to -0.7 V.

Conversion of an instantaneous activating K+ channel into a slow activating inward rectifier

The miniature channel, Kcv, is a structural equivalent of the pore of all K⁺ channels. Here, we follow up on a previous observation that a largely voltage-insensitive channel can be converted into a slow activating inward rectifier after extending the outer transmembrane domain by one Ala. This gain of rectification can be rationalized by dynamic salt bridges at the cytosolic entrance to the channel; opening is favored by voltage-sensitive formation of salt bridges and counteracted by their disruption. Such latent voltage sensitivity in the pore could be relevant for the understanding of voltage gating in complex Kv channels.

Chromatography and the hundred year mystery of inorganic ions at aqueous interfaces: adsorption of inorganic ions at the Porous Graphitic Carbon Aqueous Interface follows the Hofmeister series

Many physical phenomena are affected by the structure of water interfaces, yet it remains an active and controversial subject. A great deal of recent theoretical endeavour and computer simulations question the validity of the Onsager Samaras theory of the ion-free interface between an electrolyte solution and an hydrophobic surface. Experimental results play a crucial role in assessing the legitimacy of the theories. Experimental data are scarce, while simulation results suggest an increasing surface affinity of ions with increasing chaotropic character, in dramatic contradiction to the classical view. Chromatography is a powerful separative technique, but we originally used it as a tool to detect the adsorption of chloride electrolytes and sodium electrolytes, strongly expected to shun any dielectric boundary, onto an hydrophobic surface, and to rank ions according to their adsorbophilicities. Frontal analysis gave unequivocal experimental evidence to this unexpected phenomenon and it was used to quantify it. The infinite dilution equilibrium constants for adsorption of kosmotropes and chaotropes onto the interface were obtained and contrasted to the Jones-Dole B viscosity coefficients, that is a common quantifier of the Hofmeister effect. It is clear that (i) the more chaotropic the ion is, the more it contributes to the global adsorbophilicity of the electrolyte; (ii) the influence of the variable anion is more than twofold that of the variable cation, thereby confirming a robust observation in many other physical systems. Standard free energy of adsorption for each electrolyte was calculated and its reliability was commented upon. The central issue in this paper is the effective and ascertained adsorption of electrolytes onto an hydrophobic surface and the fact that the adsorbophilicity of an electrolyte may be inferred from its position in the Hofmeister series.

Dependence of interaction free energy between solutes on an external electrostatic field

To explore the athermal effect of an external electrostatic field on the stabilities of protein conformations and the binding affinities of protein-protein/ligand interactions, the dependences of the polar and hydrophobic interactions on the external electrostatic field, -Eext, were studied using molecular dynamics (MD) simulations. By decomposing Eext into, along, and perpendicular to the direction formed by the two solutes, the effect of Eext on the interactions between these two solutes can be estimated based on the effects from these two components. Eext was applied along the direction of the electric dipole formed by two solutes with opposite charges. The attractive interaction free energy between these two solutes decreased for solutes treated as point charges. In contrast, the attractive interaction free energy between these two solutes increased, as observed by MD simulations, for Eext = 40 or 60 MV/cm. Eext was applied perpendicular to the direction of the electric dipole formed by these two solutes. The attractive interaction free energy was increased for Eext = 100 MV/cm as a result of dielectric saturation. The force on the solutes along the direction of Eext computed from MD simulations was greater than that estimated from a continuum solvent in which the solutes were treated as point charges. To explore the hydrophobic interactions, Eext was applied to a water cluster containing two neutral solutes. The repulsive force between these solutes was decreased/increased for Eext along/perpendicular to the direction of the electric dipole formed by these two solutes.

The Influence of Dielectric Decrement on Electrokinetics

We treat the dielectric decrement induced by excess ion polarization as a source of ion specificity and explore its impact on electrokinetics. We employ a modified Poisson-Nernst-Planck (PNP) equations accounting for the dielectric decrement. The dielectric decrement is determined by the excess ion polarization parameter α and when α = 0 the standard PNP model is recovered. Our model shows that ions saturate at large zeta potentials (ζ). Because of ion saturation, a condensed counterion layer forms adjacent to the charged surface, introducing a new length scale, the thickness of the condensed layer (l_c ). For the electro-osmotic mobility, the dielectric decrement weakens the electro-osmotic flow owing to the decrease of the dielectric permittivity. At large ζ, when α ≠ 0, the electro-osmotic mobility is found to be proportional to ζ/2, in contrast to ζ predicted by the standard PNP model. This is attributed to ion saturation at large ζ. In terms of the electrophoretic mobility M_e , we carry out both an asymptotic analysis in the thin-double-layer limit and solve the full modified PNP model to compute M_e . Our analysis reveals that the impact of the dielectric decrement is intriguing. At small and moderate ζ, the dielectric decrement decreases M_e with an increasing α. At large ζ, it is well known that the surface conduction becomes significant and plays an important role in determining M_e . It is observed that the dielectric decrement effectively reduces the surface conduction. Hence in stark contrast, M_e increases as α increases. Our predictions of the contrast dependence of the mobility on α at different zeta potentials qualitatively agree with experimental results on the dependence of the mobility among ions and provide a possible explanation for such ion specificity. Finally, the comparisons between the thin-double-layer asymptotic analysis and the full simulations of the modified PNP model suggest that at large ζ the validity of the thin-double-layer approximation is determined by l_c rather than the traditional Debye length.

A method for treating the passage of a charged hard sphere ion as it passes through a sharp dielectric boundary

In the implicit solvent models of electrolytes (such as the primitive model (PM)), the ions are modeled as point charges in the centers of spheres (hard spheres in the case of the PM). The surfaces of the spheres are not polarizable which makes these models appropriate to use in computer simulations of electrolyte systems where these ions do not leave their host dielectrics. The same assumption makes them inappropriate in simulations where these ions cross dielectric boundaries because the interaction energy of the point charge with the polarization charge induced on the dielectric boundary diverges. In this paper, we propose a procedure to treat the passage of such ions through dielectric interfaces with an interpolation method. Inspired by the "bubble ion" model (in which the ion's surface is polarizable), we define a space-dependent effective dielectric coefficient, ε(eff)(r), for the ion that overlaps with the dielectric boundary. Then, we replace the "bubble ion" with a point charge that has an effective charge q/ε(eff)(r) and remove the portion of the dielectric boundary where the ion overlaps with it. We implement the interpolation procedure using the induced charge computation method [D. Boda, D. Gillespie, W. Nonner, D. Henderson, and B. Eisenberg, Phys. Rev. E 69, 046702 (2004)]. We analyze the various energy terms using a spherical ion passing through an infinite flat dielectric boundary as an example.

Mediating role of multivalent cations in DNA electrostatics: an epsilon-modified Poisson-Boltzmann study of B-DNA-B-DNA interactions in mixture of NaCl and MgCl2 solutions

Potentials of mean force acting between two ions in SPC/E water have been determined via molecular dynamics simulations using the spherical cavity approach ( J. Phys. Chem. B 2006 , 110 , 10878 ). The potentials were obtained for Me(2+)-Me(+) pairs, where Me(2+) means cations Mg(2+) and Ca(2+) and Me(+) denotes monovalent ions Li(+), Na(+), and K(+). The hard-core interaction distance for effective Me(2+)-Me(+) potentials appears to be of about 5 A that looks like a sum of the effective radii of a Me(2+) ion (3 A) and of an alkali metal ion Me(+) (about 2 A). These ion-ion interaction parameters were used in the epsilon-Modified Poisson-Boltzmann (epsilon-MPB) calculations ( J. Phys. Chem. B 2007 , 111 , 5264 ) of ionic distributions around DNA generalized for the arbitrary mixture of different ion species. Ionic distributions around an all-atom geometry model of B-DNA in solution of a mixture of NaCl and MgCl(2) were obtained. It was found that even a small fraction of ions Mg(2+) led to sharp condensation of Mg(2+) near the phosphate groups of DNA due to polarization deficiency of cluster [Mg(H(2)O)(6)](2+) in an external field. The epsilon-MPB calculations of the B-DNA-B-DNA interaction energies suggest that adding 1 mM of Mg(2+) to 50 mM solution of NaCl notably affects the force acting between the two macromolecules. Being compared to Poisson-Boltzmann results and to MPB calculations for the primitive model of ions, the epsilon-MPB results also indicate an important contribution of dielectric saturation effects to the mediating role of divalent cations in the DNA-DNA interaction energies.

Electrostatics of B-DNA in NaCl and CaCl2 solutions: ion size, interionic correlation, and solvent dielectric saturation effects

The epsilon-modified Poisson-Boltzmann (-MPB) equations ( J. Phys. Chem. B, 2007, 111, 5264) have been solved on a three-dimensional grid for an all-atom geometry model of B-DNA. The approach is based on the implicit solvent model including finite sizes of hydrated ions and a dielectric approximation of the ion hydration shell. Results were obtained for the detailed geometry model of B-DNA in dilute and moderately concentrated solutions of NaCl and CaCl(2). All -MPB parameters of ions and dielectric medium were extracted from published results of all-atom molecular dynamics simulations. The study allows evaluations of the ion size, interionic correlation, and the solvent dielectric saturation effects on the ion distributions around DNA. It unambiguously suggests that the difference between the -MPB and Poisson-Boltzmann distributions of ions is low for Na(+) counterions. Such a difference in the case of divalent counterions Ca(2+) is dramatic: the dielectric saturation of the ion hydration shell leads to point-like adsorption of Ca(2+) on the phosphate groups of DNA. The -MPB equations were also applied to calculate the energy of interaction between two B-DNA molecules. Results agree with previously published simulations and experimental data. Some aspects of ion specificity of polyelectrolyte properties are discussed.

Effective interaction potentials for alkali and alkaline earth metal ions in SPC/E water and prediction of mean ion activity coefficients

The potential of mean force (PMF) acting between two simple ions surrounded by SPC/E water have been determined by molecular dynamics (MD) simulations using a spherical cavity approach. Such effective ion-ion potentials were obtained for Me-Me, Me-Cl-, and Cl(-)-Cl- pairs, where Me is a Li+, Na+, K+, Mg2+, Ca2+, Sr2+, and Ba2+ cation. The ionic sizes estimated from the effective potentials are not pairwise additive, a feature in the frequently used primitive model for electrolytes. The effective potentials were used in Monte Carlo (MC) simulations with implicit water to calculate mean ion activity coefficients of LiCl, NaCl, KCl, MgCl2, CaCl2, SrCl2, and BaCl2. Predicted activities were compared with experimental ones in the electrolyte concentration range 0.1-1 M. A qualitative agreement for LiCl and a satisfactory agreement for NaCl were found, whereas the predictions for KCl by two K+ models were less coherent. In the case of alkaline earth metal ions, all experimental activities were successfully reproduced at c = 0.1 M. However, at higher concentrations, similar deviations occurred for all divalent cations, suggesting that the dependence of the permittivity on the salt concentration and the polarization deficiency arising from the ordering of water molecules in the ion hydration shells are important in such systems.

Dielectric saturation of the ion hydration shell and interaction between two double helices of DNA in mono- and multivalent electrolyte solutions: foundations of the epsilon-modified Poisson-Boltzmann theory

Potentials of mean force between single Na+, Ca2+, and Mg2+ cations and a highly charged spherical macroion in SPC/E water have been determined using molecular dynamics simulations. Results are compared to the electrostatic energy calculations for the primitive polarization model (PPM) of hydrated cations describing the ion hydration shell as a dielectric sphere of low permittivity (Gavryushov, S.; Linse, P. J. Phys. Chem. B 2003, 107, 7135). Parameters of the ion dielectric sphere and radius of the macroion/water dielectric boundary were extracted by means of this comparison to approximate the short-range repulsion of ions near the interface. To explore the counterion distributions around a simplified model of DNA, the obtained PPM parameters for Na+ and Ca2+ have been substituted into the modified Poisson-Boltzmann (MPB) equations derived for the PPM and named the epsilon-MPB (epsilon-MPB) theory. epsilon-MPB results for DNA suggest that such polarization effects are important in the case of 2:1 electrolyte and highly charged macromolecules. The three-dimensional implementation of the epsilon-MPB theory was also applied to calculation of the energies of interaction between two parallel macromolecules of DNA in solutions of NaCl and CaCl2. Being compared to results of MPB calculations without the ion polarization effects, it suggests that the ion hydration shell polarization and inhomogeneous solvent permittivity might be essential factors in the experimentally known hydration forces acting between charged macromolecules and bilayers at separations of less than 20 A between their surfaces.

Experimental anion affinities for the air/water interface

Anion affinities, gammaX-, for the aerial interface of aqueous (Br- + NO3- + I- + SCN- + BF4- + ClO4-) solutions are determined by electrospray ionization mass spectrometry. The composition of the ions ejected from the surface of fissioning nanodroplets shows that gammaX- increase (decrease) exponentially with anionic radii, aX-(dehydration free energies, dGX-), and selectively respond to the presence of surfactants. BF4-, the least hydrated and polarizable anion of the set, has one of the largest gammaX- values. Non-ionic surfactants decrease gammaI- and gammaSCN- but increase gammaBF4-. Cetyltrimethyl ammonium markedly enhances the gammaX- of smaller anions. A similar but weaker effect is observed upon lowering the pH of the bulk solutions from 8.2 to 3.0. Dodecyl sulfate has a negligible effect on gammaX-. Considering that (i) universal many-body electrodynamic interactions will progressively stabilize the interfacial layer as its dielectric permittivity falls relative to that of the bulk solution and (ii) water permittivity is uniformly depressed by increasing concentrations of these anions, we infer that the observed Hofmeister correlation, ln gammaX- infinity - dGX-, is consistent with the optimal depression of the permittivity of the drier interfacial layer by the least hydrated ions. Interfacial ion-ion interactions can significantly influence gammaX- in environmental aqueous media.

Effective Interaction Potentials for Alkali and Alkaline Earth Metal Ions in SPC/E Water and Polarization Model of Hydrated Ions

In the first paper (J. Phys. Chem. B, 2006, 110, 10878), effective ion-ion potentials in SPC/E water were obtained for Me-Me, Me-Cl-, and Cl(-)-Cl- pairs, where Me is Li+, Na+, K+, Mg2+, Ca2+, Sr2+, and Ba2+ cations. In this second part of the study of effective interionic potentials, ion-ion distribution functions obtained from implicit-water Monte Carlo simulations of electrolyte solution with these potentials have been explored. This analysis verifies the range of applicability of the primitive model of electrolyte. It is shown that this approximation can be applied to monovalent electrolyte solutions in a wide range of concentrations, whereas the nature of ion-ion interactions is notably different for 2:1 electrolytes. An improved model of ions is discussed. The model includes approximations of the ion hydration shell polarization and specific short-range ion-ion interaction. It allows approximation of the potential of mean force acting on ions in strong electric fields of highly charged macromolecules and bilayers.