Electrolyte Theory Research Articles

The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration.

According to classical electrolyte theories interactions in dilute (low ion density) electrolytes decay exponentially with distance, with the Debye screening length the characteristic length scale. This decay length decreases monotonically with increasing ion concentration due to effective screening of charges over short distances. Thus, within the Debye model no long-range forces are expected in concentrated electrolytes. Here we reveal, using experimental detection of the interaction between two planar charged surfaces across a wide range of electrolytes, that beyond the dilute (Debye-Hückel) regime the screening length increases with increasing concentration. The screening lengths for all electrolytes studied-including aqueous NaCl solutions, ionic liquids diluted with propylene carbonate, and pure ionic liquids-collapse onto a single curve when scaled by the dielectric constant. This nonmonotonic variation of the screening length with concentration, and its generality across ionic liquids and aqueous salt solutions, demonstrates an important characteristic of concentrated electrolytes of substantial relevance from biology to energy storage.

Unified Thermodynamics for All Concentrations of Electrolytes Based on Hydration and Partial Dissociation (Without Activity Coefficients, 1995-)

Twenty years ago in the ECS meeting at Reno, May 1995, the author presented her breakthrough paper on the partial dissociation and hydration of NaCl from ‘zero to saturation’. This totally replaced the idea of complete dissociation and the activity coefficient corrections in thermodynamics and confirmed the theory of electrolytic dissociation founded over a century ago by Svante Arrhenius for which he was awarded the Nobel Prize in 1903. According to his original theory (1884 - ), a fraction (α ) mole of an electrolyte like NaCl dissociates in water into 2α moles of ions, the rest (1-α)being in the undissociated form: NaCl (1- α ) ↔ Na+( α ) + Cl- ( α ) (1) Thus every mole of salt increased to (1-α) + 2α = (1+α) = i ( >1) moles of solute on dissolving in water. With the ratio of the equivalent conductivity at any concentration (L) to that at infinite dilution (Lo) as a measure of the degree of dissociation (α),this factor, i, called van't Hoff factor, explained the increase in osmotic pressure as observed by van't Hoff. This theory was greatly successful in explaining many other properties of dilute electrolyte solutions. While attempts were in progress to extend the theory to concentrated solutions, the thermodynamics of solutions was replaced (Lewis and Randall, 1921) by that of the empirical concepts of activity and activity coefficients. Since the Debye-Huckel theory of interionic interaction for completely dissociated electrolytes, as shown: NaCl → Na+ + Cl- (2) was able to nearly explain the concentration dependence of activity coefficients for very dilute solutions, the latter equations based on complete dissociation were gradually extended to higher concentrations until they resulted in extremely elaborate equations (Pitzer, 1973) without physical significance. The author became aware of the complexity of the theory of simple electrolytes like NaCl (aq) during her doctoral work on strong electrolytes. In the following years, she abandoned this theory and started reinvestigating the available experimental data on the properties of electrolytes (Heyrovska, 1979, 1980). Gradually it became clear that, with the degrees of dissociation (α)and the hydration numbers evaluated by the author from the vapor pressure (or osmotic coefficient) data (instead of from the conductivity ratio), the original idea of partial dissociation due to Arrhenius, as per equation (1), and of 'free water' (Bousfield, 1917), could explain quantitatively the non-ideal properties of electrolytes over a large range of concentrations (Heyrovska, 1987, 1988). Further advance was made by the author in 1995 on realizing that the molalities of ‘free’ water in the "surface and bulk of solution" are different. This made a breakthrough in the theory of electrolytes, which could then be extended to the whole range of concentrations from "zero to saturation" (Heyrovska, 1995, 1996) for the first time. Many thermodynamic properties of solutions could thus be explained quantitatively in terms of simple mathematical relations involving the degrees of dissociation, hydration numbers and volumes of ions and ion pairs, without any empirical parameters. For review papers on the subject, see Heyrovska, 1998, 2003, 2006, 2011 and 2013. For a complete list of references and Table of equations, see Refs. 11,12 below and the literature therein. Full list of all publications are in: www.jh-inst.cas.cz/~rheyrovs. Some selected references pertaining to the ‘whole concentration range’ are given below.

Improving charge-sensitive biomolecule sensors with the right choice of electrolyte

Biomolecule detectors are crucial to many fields, from medicine to environmental conservation. One type of sensor detects charged biomolecules in solution by flowing an electrolyte over a receptor-functionalized surface (e.g., a transistor) before and after the analyte binds to the surface. This changes the surface charge, and a change in a device property like a conductance is measured. The change in the device property correlates with the concentration of analyte in the solution. While many groups have tested this method, most studies have only used electrolytes with small cations like potassium and calcium. Here, we use density functional theory of electrolytes to calculate how different electrolytes affect the output of these detectors. We determined that the signal of these devices could be improved by using electrolytes with a minimal concentration of large, monovalent cations. Likewise, the sensitivity of these devices can be improved with a moderate-to-low concentration of large, monovalent cations. Therefore, using electrolytes with large (∼0.9nm diameter), monovalent ions may increase the sensitivity of currently-used sensors.

Continuum Theory of Calcium Channels: Fundamental Insights from Simplified Models

While molecular dynamics is a very powerful tool for understanding ion permeation and selectivity in ion channels, not all systems lend themselves to analysis with MD. Calcium channels are one example because they are selective for Ca2+ in the micro- to millimolar concentration range, concentrations far too low for MD simulations. Sophisticated modern continuum theories of electrolytes (e.g., Density Functional Theory, DFT, and the Mean Spherical Approximation, MSA) provide a way to analyze the physics of calcium channels using simplified channel structures based on the “important” amino acids, as determined by experiments. The advantage of these theories over older ones like Poisson-Boltzmann is that they include the size of the ions, which turns out to be of fundamental importance to calcium channel selectivity. In the case of ryanodine receptor, the Ca2+ release channel in muscle, these theories can quantitatively reproduce existing current/voltage experimental data, as well as predicting new nonlinear effects that were later confirmed by experiments. In general, DFT, MSA, and other continuum theories can be powerful tools to understand ion/protein interactions. Their continuing improvement to include more physical interactions as well as their fast computational speed make them an ideal complement to particle simulations.

Decay behavior of screened electrostatic surface forces in ionic liquids: the vital role of non-local electrostatics.

Screened electrostatic surface forces, also called double layer forces, between surfaces in ionic liquids can, depending on the circumstances, decay in an exponentially damped, oscillatory manner or in a plain exponential way (the latter as in dilute electrolyte solutions where ion-ion correlations are very weak). The occurrence of both of these behaviors in dense ionic liquids, where ion-ion correlations are very strong, is analyzed in the current work using exact statistical mechanics formulated in a manner that is physically transparent. A vital ingredient in understanding the decay behaviors is the fact that electrostatics in dense electrolytes have a non-local nature caused by the strong correlations. It is shown that the effects of non-locality can be elucidated by a remarkably simple, general expression for the decay parameter κ that replaces the classical expression for the inverse Debye length κDH of the Debye-Hückel (DH) and non-linear Poisson-Boltzmann approximations. This exact expression is valid for both the plain exponential and the oscillatory cases. It shows how strong correlations can give rise to plain exponential decay with a long decay length. Such a decay can arise from anion-cation associations of various kinds, for instance transient ion pairing or association caused by many-body correlations; ion pairing is a possibility but not a necessity for this to occur. Theoretical analysis is done for systems consisting of ions with an arbitrary shape and internal charge density and immersed planar walls with arbitrary internal charge distribution and any short-range ion-surface interaction. The screened electrostatic surface force between two walls is at large separations proportional to the product of effective surface charge densities of each wall. For the oscillatory case, each wall contributes with a phase shift to the oscillations of the interaction.

Prediction of the Standard State Partial Molar Volume of Aqueous Electrolytes to High Temperatures and High Pressures

The unified theory of electrolytes (J. Phys. Chem. B 2009, 113, 2398–2403) is used for the prediction of the standard state partial molar volumes of aqueous chlorides and hydroxides of the alkali metals, alkali earth metals, and the first row transition metals to high temperatures and pressures. The only required input to the model is the thermodynamic properties from reference tables at 298.15 K and 0.1 MPa. Comparison of the predicted values for the standard state partial molar volumes of aqueous electrolytes from this study with the available experimental data indicates good agreements to well within the combined uncertainties of the experimental data and the present model up to 623.15 K and 400 MPa. The present model is also compared with the correlations of Sedlbauer–O’Connell–Wood (SOCW) and the revised equation of Helgeson, Kirkham, and Flowers (HKF), which has been incorporated in the SUPCRT92 software.

THE DIFFERENTIAL CAPACITANCE OF THE ELECTRIC DOUBLE LAYER IN THE DIFFUSION BOUNDARY LAYER OF ION-EXCHANGE MEMBRANE SYSTEMS

The effect of the membrane diffuse layer on the differential capacitance of the diffuse layer in the diffusion boundary layer of an ion-exchange membrane system, as well as on the meaning of this capacitance in the interpretation of the electrochemical impedance, have been investigated. On the one hand, the effect of the diffuse layer in the membrane phase on the electric double layer capacitance is analysed on the basis of the Poisson-Boltzmann equation in the Gouy-Chapman theory for a symmetric binary electrolyte. The results are compared with the analytical expressions obtained by using the Debye-Hückel approximation and by considering ideal membranes with an infinitely thin diffuse layer. On the other hand, the electrochemical impedance of a diffusion layer adjacent to an ideal membrane for a uni-univalent electrolyte has been numerically studied on the basis of the Nernst-Planck and Poisson equations, including a charge transfer resistance between solution and membrane described by a Chang-Jaffé equation, in order to establish the role played by the differential capacitance of the electric double layer. The impedance has been studied by using the network simulation method and the results obtained from the characteristic frequency of the interfacial charge transfer process are compared with the theoretical expressions for the electric double layer capacitance of an ideal system, not only under equilibrium conditions but also by considering the polarization concentration phenomenon.

Atomistic and Molecular Effects in Electric Double Layers at High Surface Charges.

The Poisson-Boltzmann theory for electrolytes near a charged surface is known to be invalid due to unaccounted physics associated with high ion concentration regimes. To investigate this regime, fluids density functional theory (f-DFT) and molecular dynamics (MD) simulations were used to determine electric surface potential as a function of surface charge. Based on these detailed computations, for electrolytes with nonpolar solvent, the surface potential is shown to depend quadratically on the surface charge in the high charge limit. We demonstrate that modified Poisson-Boltzmann theories can model this limit if they are augmented with atomic packing densities provided by MD. However, when the solvent is a highly polar molecule, water in this case, an intermediate regime is identified in which a constant capacitance is realized. Simulation results demonstrate the mechanism underlying this regime, and for the salt water system studied here, it persists throughout the range of physically realistic surface charge densities so the potential's quadratic surface charge dependence is not obtained.

Joule heating induced interfacial instabilities in free-surface electro-osmotic flows

Application of an external electrostatic field across a conducting electrolyte results in the development of a thermal gradient within the fluid domain as a consequence of the heat generated due to Joule heating. The generalized Gouy–Chapman theory for symmetric electrolytes is used to explain the explicit dependence of the electrical potential and velocity distribution on this differential temperature distribution within the fluid. Subsequently the highly coupled system of Orr–Sommerfeld equations is solved using a Chebyshev collocation algorithm to perform a linear stability analysis of the free-surface electro-osmotic flow system of a conducting electrolyte. An extensive parametric study, consisted with the electrokinetic and thermal properties of the electrolyte as well as the applied field strength characteristics, is performed. In particular, the role of the two important dimensionless parameters representing the applied field strength and the electrical conductivity of the fluid in regulating the length and time scales of instability occurring at the free liquid–air interface is summarized in this study, as well as their combined influence on the inception and growth of the interfacial mode of instability.

Invited: Applications of DFT Calculations to Platinum Surface Electrochemistry

The current status of electronic structure calculations on electrocatalysis will be discussed in this presentation. After a quick review of atomistic modellings of electrified solid / liquid interfaces, a method combining density functional theory and a continuum electrolyte theory will be presented. It will be shown that this theory can give thermodynamic properties of electrochemical reactions, such as electro-oxidation, specific anion adsorptions, underpotential deposition of Cu and oxygen reduction reaction, on closed packed single crystal platinum surfaces within practically useful accuracies. When the method is applied to structures other than the closed packed surfaces, such as stepped platinum surfaces, difficulties arise in modellings and accuracies. Some prescriptions to overcome those problems also will be discussed.[1] R. Jinnouchi and A. B. Anderson, Phys. Rev. B, 77, 245417 (2008).[2] R. Jinnouchi and A. B. Anderson, J. Phys. Chem. C, 112, 8747 (2008).[3] R. Jinnouchi, E. Toyoda, T. Hatanaka and Y. Morimoto, J. Phys. Chem. C, 114, 17557 (2010).[4] R. Jinnouchi, T. Hatanaka, Y. Morimoto and M. Osawa, Phys. Chem. Chem. Phys., 14, 3208 (2012).[5] R. Jinnouchi, T. Hatanaka, Y. Morimoto and M. Osawa, Electrochim. Acta, 101, 254 (2013).[6] K. Kodama, A. Shinohara, N. Hasegawa, K. Shinozaki, R. Jinnouchi, T. Suzuki, T. Hatanaka and Y. Morimoto, ECS Trans., 58, 363 (2013).[7] R. Jinnouchi, K. Kodama, T. Hatanaka and Y. Morimoto, Phys. Chem. Chem. Phys., 13, 21070 (2011).[8] E. Toyoda, R. Jinnouchi, T. Ohsuna, T. Hatanaka, T. Aizawa, S. Otani, Y. Kido and Y. Morimoto, Angew. Chem. Int. Ed., 52, 4137 (2013).[9] R. Jinnouchi, K. Kodama and Y. Morimoto, J. Electroanal. Chem.,716, 31 (2013).

Studies on the Conductivity of Cationic Latexes and Its Adsorption on Cotton Fabrics by Conductometric Titration

The electrostatic interaction,and adsorption of cationic latex on the surface of cotton fibers have been extensively studied because of their practical and theoretical importance. In this paper,conductometric titration was used to determine the chloride ion content at the surface of cationic latex and to analyze the conductivity of cationic latex. Moreover,the adsorption isotherm of cationic latex on cotton fabrics was explored deeply. Within the range of 0. 05 ~ 0. 3 × 10-8mol / L,a good linear relationship between the concentration( cp) of latex and the conductivity( Λ) was obtained( Λ = 8. 0913cp+ 1. 8093,R2= 0. 9986). The limiting molar conductivity of cationic colloidal nucleus,calculated according to the electrolyte theory, was not a constant at 25 ℃. The limiting molar conductivity decreased with the increase of the latex' s concentration. Finally,the adsorption isotherm of cationic latex on cotton fabrics was fitted to the Langmuir adsorption isotherm model.

Effect of Ionic Ordering in Conductivity Experiments of DNA Aqueous Solutions

The effects of ionic ordering in DNA water solutions are studied by conductivity experiments. The conductivity measurements are performed for the solutions of DNA with KCl salt in the temperature interval from 28 to 70 ∘C. The salt concentration varied from 0 to 2 M. The measurements of the conductivity of solutions without DNA but with the same concentration of KCl salt are also performed. The results show that, in the case of a salt-free solution of DNA, the melting process of the double helix is observed, while, in the case of the DNA solution with added salt, the macromolecule denaturation is not featured. For salt concentrations lower than some critical one (0.4 M), the DNA solution conductivity is higher than the conductivity of a KCl water solution without DNA. Starting from the critical concentration, the conductivity of a KCl solution is higher than the conductivity of a DNA solution with added salt. For the description of the experimental data, a phenomenological model is elaborated basing on electrolyte theory. In the framework of the developed model, a mechanism of counterion ordering is introduced. According to this mechanism the electrical conductivity of the system at low salt concentrations is caused by counterions of the DNA ion-hydrate shell. At an increasing the amount of salt to the critical concentration, counterions condense on the DNA polyanion. A further increase of the salt concentration leads to the formation of DNA-salt complexes, which decreases the conductivity of the system.

Improvements in Li Air Batteries through Electrocatalysts, Electrode Structure Design and Modelling

Rechargeable Li-air batteries allow Li+ and e- in the cell to react with O2 from the air and enable an increase in storage capacities up to 10 times cf. with Li ion. The air cathode is a new challenge for the battery. New nanostructured air cathode materials were fabricated, characterised by using XRD, TEM and SEM and tested as cathodes in rechargeable Li-air batteries. Such 3D nanomaterials displayed high capacity (up to 3000 mAhg-1). The superior performance of the nanomaterials was attributed to their structures which acted as transport pores The relationship between composition, especially ratios of catalyst to carbon, structure, properties and performance shall be discussed. Measures to tackle technical barriers in battery design and engineering will also be addressed. We have investigated the use of bifunctional MnO2/Au catalysts. This has provided significant improvement in its stability (stable cycling > 100) as well as a great improvement in the lithium air cell capacity (10,000mAh/g). Battery performance is still affected by loss in capacity after repeated cycling due to instability of certain solvents and cathode carbon supports and ingress of CO2. A micro-macro homogeneous mathematical model was developed for the cycling operation of a porous Li-air cathode using concentrated binary electrolyte theory. The model includes mechanism for solvent degradation and production of Li carbonates. The physical and chemical property data is carefully applied in this model to predict the time dependance of electrolyte concentration, non-uniform porosity and reaction rate and loss of capacity after cycling. Alternative modes of battery operation are explored to improve power and energy density performance

A mixture theory of electrolytes containing solvation effects

In this work we present a new mixture theory of a liquid solvent containing completely dissociated ions to study the space charge layer of electrolytes in contact with some inert metals. We incorporate solvation shell effects (i) in our derivation of the mixing entropy and (ii) in the pressure model. Chemical potentials of ions and solvent molecules in the incompressible limit are then derived from a free energy function. For the thermodynamic equilibrium the coupled equation system of mass and momentum balance, the incompressibility constraint and the Poisson equation are summarized. With that we study the space charge layer of the electrolytic solution for an applied half cell potential and compare our results to historic and recent interpretations of the double layer in liquid electrolytes. The novelties of the model are: (i) the potential and pressure dependence of the free charge density in equilibrium (ii) the calculation of entropic contributions due to solvated ions, and (iii) the natural prediction of a solvated anion saturation layer which we finally reinterpret as Stern layer.

Theory of dipolaron solutions

A fundamental task of statistical physics is to predict the system’s statistical properties and compare them with observable data. We formulate the theory of dipolaron solutions and analyze the screening effects for permanent and field-induced dipolarons. The mathematical treatment of the collective behavior and microscopical morphology of dipolaron solutions are discussed. The presented computations show that the electric field shielding of dipolarons in dielectric nanosolutions is quite different from that of counterionic nano-complexes of Debye–Hückel theory of electrolytes. The limiting case of screening length λ=0 in dipolaron solutions corresponds to Coulomb’s law for the potential and field of uniformly charged sphere.

Observation of separate cation and anion electrophoretic mobilities in pure ionic liquids

Ionic liquids (ILs) continue to show relevance in many fields, from battery electrolytes, to carbon capture, to advanced separations. These highly ion-dense fluids present unique challenges in understanding their electrochemical properties due to deviations in behavior from existing electrolyte theories. Here we present a novel characterization of ILs using electrophoretic NMR (ENMR) to determine separate cation and anion mobilities. This method uses an applied electric field coincident with a pulsed magnetic field gradient to encode the E-field driven flow into NMR signals for cations ((1)H) and anions ((19)F). We describe the detailed design of these experiments, including quantitative analysis of artifact mitigation and necessary control experiments. We then explore mobilities and diffusion coefficients for two representative ILs: 1-ethyl-3-methyl imidazolium tetrafluoroborate ([C2mim][BF4]) and 1-ethyl-3-methyl imidazolium trifluoromethanesulfonate ([C2mim][TfO]). We further use the individual ion mobilities to calculate the bulk net conductivity, which closely agrees with bulk conductivity measurements obtained using impedance spectroscopy. These observations represent the first reliable measurements of cation and anion mobilities in pure ILs, with errors of ±7%. We discuss this advanced experimental methodology in detail, as well as implications of these sensitive measurements for understanding conduction mechanisms in ion-dense electrolytes.

A contact-corrected density functional theory for electrolytes at an interface

We present a contact-corrected density functional theory for ionic distributions at an interface that not only accounts for the steric effects and electrostatic correlations often ignored by conventional electrochemical methods but also conforms to the exact statistical-mechanical sum rule for the contact ionic densities. The theoretical predictions are in excellent agreement with the simulation results for both the interfacial structure and electrochemical properties over a wide variety of electric double layer systems including those containing asymmetric electrolytes with multivalent ions.

Catalyst Poisoning Property of Sulfonimide Acid Ionomer on Pt (111) Surface

The catalyst poisoning property of a novel ionomer, NBC4, which has two sulfonimide acid groups in its side chain ended with a perfluorobutane, instead of sulfonic acid groups as Nafion does, was theoretically and experimentally compared with that of Nafion. A density functional theory combined with a continuum electrolyte theory showed that the adsorption is weaker for sulfonimide anion than for sulfonate anion on Pt (111) surface. Electrochemical measurements using Pt (111) surfaced single crystal electrodes covered with the ionomer films showed the weaker anion adsorption and higher ORR activity by ca. 50% at 0.82 V vs the reversible hydrogen electrode for NBC4 than for Nafion.

Modelling the micro–macro homogeneous cycling behaviour of a lithium–air battery

A micro–macro homogeneous mathematical model is developed for a rechargeable Li–air battery using a concentrated binary electrolyte theory. The dynamic behaviour of the porous cathode is determined by a numerical solution of the combined continuity, transport and kinetics equations. This model considers the time and space dependence of the battery system, including the mass transport along the depth of the cell, the local mass transfer between lithium peroxide (Li2O2) layer inside the cathode and active surface morphology changing with the Li2O2 growth. The model predicts that the battery capacity and discharge potential are sensitive not only to the solubility of oxygen, which is predominantly limited by depletion of the oxygen concentration, as well as to the cathode porosity, the cathode structure and kinetic parameters. In addition, the charging behaviour is simulated by modelling the dissolution of solid Li2O2 product. The model suggests that the charging voltage can be lowered depending on capability of electrolyte to dissolve the Li2O2 discharge products. As a result, a simulation of electrode behaviour is obtained.

Investigation of the free volume and ionic conducting mechanism of poly(ethylene oxide)-LiClO4 polymeric electrolyte by positron annihilating lifetime spectroscopy

The positron annihilation lifetime and ionic conductivity are each measured as a function of organophilic rectorite (OREC) content and temperature in a range from 160 K to 300 K. According to the variation of ortho-positronium (o-Ps) lifetime with temperature, the glassy transition temperature is determined. The continuous maximum entropy lifetime (MELT) analysis clearly shows that the OREC and temperature have important effects on o-Ps lifetime and free volume distribution. The experimental results show that the temperature dependence of ionic conductivity obeys the Vogel—Tammann—Fulcher (VTF) and Williams—Landel—Ferry (WLF) equations, implying a free-volume transport mechanism. A linear least-squares procedure is used to evaluate the apparent activation energy related to the ionic transport in the VTF equation and several important parameters in the WLF equation. It is worthwhile to notice that a direct linear relationship between the ionic conductivity and free volume fraction is established using the WLF equation based on the free volume theory for nanocomposite electrolyte, which indicates that the segmental chain migration and ionic migration and diffusion could be explained by the free volume theory.