Charge fluctuations from molecular simulations in the constant-potential ensemble.

We revisit the statistical mechanics of charge fluctuations in capacitors. In constant-potential classical molecular simulations, the atomic charges of electrode atoms are treated as additional degrees of freedom which evolve in time so as to satisfy the constraint of fixed electrostatic potential for each configuration of the electrolyte. The present work clarifies the role of the overall electroneutrality constraint, as well as the link between the averages computed within the Born-Oppenheimer approximation and that of the full constant-potential ensemble. This allows us in particular to derive a complete fluctuation-dissipation relation for the differential capacitance, that includes a contribution from the charge fluctuations (around the charges satisfying the constant-potential and electroneutrality constraints) also present in the absence of an electrolyte. We provide a simple expression for this contribution from the elements of the inverse of the matrix defining the quadratic form of the fluctuating charges in the energy. We then illustrate numerically the validity of our results, and recover the expected continuum result for an empty capacitor with structureless electrodes at large inter-electrode distances. By considering a variety of liquids between graphite electrodes, we confirm that this contribution to the total differential capacitance is small compared to that induced by the thermal fluctuations of the electrolyte.

Coordination numbers and physical properties in molten salts and their mixtures.

Mixtures of trivalent metal halides with alkali halides are involved in many technologies but, from a more fundamental and general perspective, are worthy of study as interesting systems in which to examine the relationship between atomic-scale structure and physical properties. Here we examine the relationship between the viscosity and local and longer range structural measures in such mixtures where the trivalent metal cations span a significant size range and exhibit different behaviours in the dependence of their viscosity on the mixture composition. We characterise the structure and dynamics of the first coordination shell and the relationship between its structural relaxation time and the shear relaxation time of the mixture (the Maxwell relaxation time). We are then led to an examination of the structure of the networks which progressively form between the trivalent metal cations as their concentration increases in the mixtures. Here we find significant differences between small and larger cations, sufficient to explain the different behaviour of their viscosities. We draw attention to the similarities and differences of these networks with those which form in highly viscous, glass-forming materials like BeF2:LiF.

Relationships between atomic diffusion mechanisms and ensemble transport coefficients in crystalline polymorphs.

Ionic transport in conventional ionic solids is generally considered to proceed via independent diffusion events or "hops." This assumption leads to well-known Arrhenius expressions for transport coefficients, and is equivalent to assuming diffusion is a Poisson process. Using molecular dynamics simulations of the low-temperature B1, B3, and B4 AgI polymorphs, we have compared rates of ion hopping with corresponding Poisson distributions to test the assumption of independent hopping in these common structure types. In all cases diffusion is a non-Poisson process, and hopping is strongly correlated in time. In B1 the diffusion coefficient can be approximated by an Arrhenius expression, though the physical significance of the parameters differs from that commonly assumed. In low temperature B3 and B4, diffusion is characterized by concerted motion of multiple ions in short closed loops. Diffusion coefficients cannot be expressed in a simple Arrhenius form dependent on single-ion free energies, and intrinsic diffusion must be considered a many-body process.

Thermal conductivity of simple liquids: origin of temperature and packing fraction dependences.

The origin of both weak temperature dependence and packing fraction dependence of T(1/4)η(3/2) in the thermal conductivity of the simple Lennard-Jones (LJ) liquid is explored. In order to discuss the relative contributions from attractive or repulsive part of the interaction potential separately, the thermal conductivity of a series of Weeks-Chandler-Anderson (WCA) fluids is calculated by molecular dynamics simulations. The results show that the repulsive part plays the main role in the heat conduction, while the attractive part has no direct effect on the thermal conductivity for a given packing fraction. By investigating WCA fluids with potentials of varying softness, we explain the difference observed between the LJ liquids such as argon and Coulombic liquids such as NaCl.

On the molecular origin of supercapacitance in nanoporous carbon electrodes.

Lightweight, low-cost supercapacitors with the capability of rapidly storing a large amount of electrical energy can contribute to meeting continuous energy demands and effectively levelling the cyclic nature of renewable energy sources. The excellent electrochemical performance of supercapacitors is due to a reversible ion adsorption in porous carbon electrodes. Recently, it was demonstrated that ions from the electrolyte could enter sub nanometre pores, greatly increasing the capacitance. However, the molecular mechanism of this enhancement remains poorly understood. Here we provide the first quantitative picture of the structure of an ionic liquid adsorbed inside realistically modelled microporous carbon electrodes. We show how the separation of the positive and negative ions occurs inside the porous disordered carbons, yielding much higher capacitance values (125 F g(-1)) than with simpler electrode geometries. The proposed mechanism opens the door for the design of materials with improved energy storage capabilities. It also sheds new light on situations where ion adsorption in porous structures or membranes plays a role.

Charge fluctuations in nanoscale capacitors.

The fluctuations of the charge on an electrode contain information on the microscopic correlations within the adjacent fluid and their effect on the electronic properties of the interface. We investigate these fluctuations using molecular dynamics simulations in a constant-potential ensemble with histogram reweighting techniques. This approach offers, in particular, an efficient, accurate, and physically insightful route to the differential capacitance that is broadly applicable. We demonstrate these methods with three different capacitors: pure water between platinum electrodes and a pure as well as a solvent-based organic electrolyte each between graphite electrodes. The total charge distributions with the pure solvent and solvent-based electrolytes are remarkably Gaussian, while in the pure ionic liquid the total charge distribution displays distinct non-Gaussian features, suggesting significant potential-driven changes in the organization of the interfacial fluid.

Computer simulations of ionic liquids at electrochemical interfaces.

Ionic liquids are widely used as electrolytes in electrochemical devices. In this context, many experimental and theoretical approaches have been recently developed for characterizing their interface with electrodes. In this perspective article, we review the most recent advances in the field of computer simulations (mainly molecular dynamics). A methodology for simulating electrodes at constant electrical potential is presented. Several types of electrode geometries have been investigated by many groups in order to model planar, corrugated and porous materials and we summarize the results obtained in terms of the structure of the liquids. This structure governs the quantity of charge which can be stored at the surface of the electrode for a given applied potential, which is the relevant quantity for the highly topical use of ionic liquids in supercapacitors (also known as electrochemical double-layer capacitors). A key feature, which was also shown by atomic force microscopy and surface force apparatus experiments, is the formation of a layered structure for all ionic liquids at the surface of planar electrodes. This organization cannot take place inside nanoporous electrodes, which results in a much better performance for the latter in supercapacitors. The agreement between simulations and electrochemical experiments remains qualitative only though, and we outline future directions which should enhance the predictive power of computer simulations. In the longer term, atomistic simulations will also be applied to the case of electron transfer reactions at the interface, enabling the application to a broader area of problems in electrochemistry, and the few recent works in this field are also commented upon.

Characterizing heterogeneous dynamics at hydrated electrode surfaces.

In models of Pt 111 and Pt 100 surfaces in water, motions of molecules in the first hydration layer are spatially and temporally correlated. To interpret these collective motions, we apply quantitative measures of dynamic heterogeneity that are standard tools for considering glassy systems. Specifically, we carry out an analysis in terms of mobility fields and distributions of persistence times and exchange times. In so doing, we show that dynamics in these systems is facilitated by transient disorder in frustrated two-dimensional hydrogen bonding networks. The frustration is the result of unfavorable geometry imposed by strong metal-water bonding. The geometry depends upon the structure of the underlying metal surface. Dynamic heterogeneity of water on the Pt 111 surface is therefore qualitatively different than that for water on the Pt 100 surface. In both cases, statistics of this ad-layer dynamic heterogeneity responds asymmetrically to applied voltage.

Structure and dynamics in yttrium-based molten rare earth alkali fluorides.

The transport properties of molten LiF-YF3 mixtures have been studied by pulsed field gradient nuclear magnetic resonance spectroscopy, potentiometric experiments, and molecular dynamics simulations. The calculated diffusion coefficients and electric conductivities compare very well with the measurements across a wide composition range. We then extract static (radial distribution functions, coordination numbers distributions) and dynamic (cage correlation functions) quantities from the simulations. Then, we discuss the interplay between the microscopic structure of the molten salts and their dynamic properties. It is often considered that variations in the diffusion coefficient of the anions are mainly driven by the evolution of its coordination with the metallic ion (Y(3+) here). We compare this system with fluorozirconate melts and demonstrate that the coordination number is a poor indicator of the evolution of the diffusion coefficient. Instead, we propose to use the ionic bonds lifetime. We show that the weak Y-F ionic bonds in LiF-YF3 do not induce the expected tendency of the fluoride diffusion coefficient to converge toward one of the yttrium cation when the content in YF3 increases. Implications on the validity of the Nernst-Einstein relation for estimating the electrical conductivity are discussed.

Effects of lattice polarity on interfacial space charges and defect disorder in ionically conducting AgI heterostructures.

Heterostructured (ß/γ)-AgI exhibits a spontaneous lattice polarization not accounted for in standard space-charge models. This polarization field dominates the positional variation of energies of isolated defects, and Ag(+) vacancies and interstitials are stabilized at alternate [ß/γ] interfaces. This suggests enhanced Frenkel pair separation, analogous to electronic charge separation in polar semiconductor heterostructures. Stoichiometric systems are, however, characterized by associated Frenkel pairs due to strong V(Ag)-Ag(i) interactions and show no enhancement of defect numbers. In nonstoichiometric systems, lattice polarization does direct the distribution of the excess defect species, and defect-defect interactions enhance local Frenkel pair concentrations at interfaces, suggesting that nonstoichiometry is critical to the extreme room-temperature ionic conductivities observed in heterostructured AgI nanoplates.

Optical basicity scales in protic solvents: water, hydrogen fluoride, ammonia and their mixtures.

In an inorganic material, a measure of the Lewis basicity of a solvent is commonly provided by the optical basicity, i.e. the ability of the solvent molecules to donate their electrons to an acidic species. This quantity is known to vary with the polarizability of the Lewis base. In protic solvents, the Lewis definition of basicity is barely used; it is replaced by the more purpose-built Brønsted-Lowry scale, and its generalized variant proposed by Hammett. In this study, individual molecular polarizabilities were computed from first-principles for a series of protic solvents: pure water, hydrogen fluoride, ammonia and their mixtures. From these calculations optical basicity scales were set up for each Lewis base. It was shown that these scales correlate with the Hammett acidity. It is therefore possible to build a common optical basicity scale, in which any material (protic solvents, inorganic materials) can unambiguously be classified.

Ions in solutions: Determining their polarizabilities from first-principles.

Dipole polarizabilities of a series of ions in aqueous solutions are computed from first-principles. The procedure is based on the study of the linear response of the maximally localized Wannier functions to an applied external field, within density functional theory. For most monoatomic cations (Li(+), Na(+), K(+), Rb(+), Mg(2+), Ca(2+) and Sr(2+)) the computed polarizabilities are the same as in the gas phase. For Cs(+) and a series of anions (F(-), Cl(-), Br(-) and I(-)), environmental effects are observed, which reduce the polarizabilities in aqueous solutions with respect to their gas phase values. The polarizabilities of H((aq)) (+), OH((aq)) (-) have also been determined along an ab initio molecular dynamics simulation. We observe that the polarizability of a molecule instantaneously switches upon proton transfer events. Finally, we also computed the polarizability tensor in the case of a strongly anisotropic molecular ion, UO(2) (2+). The results of these calculations will be useful in building interaction potentials that include polarization effects.

Internal mobilities and diffusion in an ionic liquid mixture.

The internal mobility gives the rate at which one ionic species moves relative to the other species present in an ionic mixture, it mirrors the differential strength of the interactions between different ionic species. In this work we examine the dependence of the internal mobilities of the Li(+) and K(+) ions on the composition in molten mixtures of LiF and KF. We compare them to the behaviour of the individual diffusion coefficients and the self-exchange velocities, which measure the rate at which an ion separates from its nearest-neighbour coordination shell. The examination is made using molecular dynamics simulations with polarizable, first-principles parameterised interaction potentials which are shown to reproduce the limited available experimental data on the transport properties of these mixtures extremely well. The results confirm that the composition-dependence of the internal mobilities in LiF/KF follows the unusual type-II behaviour, which is not reflected in that of the diffusion coefficients or the self-exchange velocities.

Local coordination about La(3+) in molten LaCl3 and its mixtures with alkali chlorides.

The local structure around the La(3+) ions in molten LaCl(3) and its mixtures with alkali and alkaline earth chlorides has been investigated by using extended X-ray absorption fine structure (XAFS) and molecular dynamics (MD) techniques. Such mixtures, which are of current technological interest, are known to be thermodynamically nonideal, and there has been a good deal of work to understand the structural effects factors that contribute to the nonideality. New experimental methods allow observations at the La K-absorption edge at the high temperatures of interest, and the ability of the technique to obtain reliable information even at very low La(3+) concentrations in multicomponent mixtures is demonstrated. Both the mean La(3+)-Cl(-) interionic separation and the mean La(3+) coordination number are found to decrease as the concentration of La(3+) in the mixture decreases. The rate of decrease depends on the identity of the alkali and alkaline earth cations present in the mixtures in a way that parallels the degree of nonideality of the different systems; it is greatest for those alkali cations that coordinate Cl(-) weakly. In dilute mixtures with such cations La(3+) is able to adopt a very stable octahedral coordination geometry but this is inhibited by the presence of more strongly coordinating cations like Li(+) and Mg(2+).

Diffusion coefficients and local structure in basic molten fluorides: in situ NMR measurements and molecular dynamics simulations.

The local structure and the dynamics of molten LiF-KF mixtures have been studied by nuclear magnetic resonance (NMR) and molecular dynamics simulations. We have measured and calculated the self-diffusion coefficients of fluorine, lithium and potassium across the full composition range around the liquidus temperature and at 1123 K. Close to the liquidus temperature, D(F), D(Li) and D(K) change with composition in a way that mimics the phase diagram shape. At 1123 K D(F), D(Li) and D(K) depend linearly on the LiF molar fraction. These results show that the composition affects the self-diffusion of anions and cations more weakly than the temperature. The activation energy for diffusion was also determined and its value can be correlated with the strength of the anion-cation interaction in molten fluoride salts.

Calculations of the thermal conductivities of ionic materials by simulation with polarizable interaction potentials.

Expressions for the energy current of a system of charged, polarizable ions in periodic boundary conditions are developed in order to allow the thermal conductivity in such a system to be calculated by computer simulation using the Green-Kubo method. Dipole polarizable potentials for LiCl, NaCl, and KCl are obtained on a first-principles basis by "force matching" to the results of ab initio calculations on suitable condensed-phase ionic configurations. Simulation results for the thermal conductivity, and also other transport coefficients, for the melts are compared with experimental data and with results obtained with other interaction potentials. The agreement with experiment is almost quantitative, especially for NaCl and KCl, indicating that these methodologies, perhaps with more sophisticated forms for the potential, can be used to predict thermal conductivities for melts for which experimental determination is very difficult. It is demonstrated that the polarization effects have an important effect on the energy current and are crucial to a predictive scheme for the thermal conductivity.

Local structure and ionic conductivity in the Zr(2)Y(2)O(7)-Y(3)NbO(7) system.

The Zr(0.5-0.5x)Y(0.5+0.25x)Nb(0.25x)O(1.75) solid solution possesses an anion-deficient fluorite structure across the entire 0≤x≤1 range. The relationship between the disorder within the crystalline lattice and the preferred anion diffusion mechanism has been studied as a function of x, using impedance spectroscopy measurements of the ionic conductivity (σ), powder neutron diffraction studies, including analysis of the 'total' scattering to probe the nature of the short-range correlations between ions using reverse Monte Carlo (RMC) modelling, and molecular dynamics (MD) simulations using potentials derived with a strong ab initio basis. The highest total ionic conductivity (σ = 2.66 × 10(-2) Ω(-1) cm(-1) at 1473 K) is measured for the Zr(2)Y(2)O(7) (x = 0) end member, with a decrease in σ with increasing x, whilst the neutron diffraction studies show an increase in lattice disorder with x. This apparent contradiction can be understood by considering the local structural distortions around the various cation species, as determined from the RMC modelling and MD simulations. The addition of Nb(5+) and its stronger Coulomb interaction generates a more disordered local structure and enhances the mobility of some anions. However, the influence of these pentavalent cations is outweighed by the effect of the additional Y(3+) cations introduced as x increases, which effectively trap many anions and reduce the overall concentration of the mobile O(2-) species.

Calculation of activities of ions in molten salts with potential application to the pyroprocessing of nuclear waste.

The ability to separate fission products by electrodeposition from molten salts depends, in part, on differences between the interactions of the different fission product cations with the ions present in the molten salt "solvent". These differences may be expressed as ratios of activity coefficients, which depend on the identity of the solvent and other factors. Here, we demonstrate the ability to calculate these activity coefficient ratios using molecular dynamics simulations with sufficient precision to guide the choice of suitable solvent systems in practical applications. We use polarizable ion interaction potentials which have previously been shown to give excellent agreement with structural, transport, and spectroscopic information of the molten salts, and the activity coefficients calculated in this work agree well with experimental data. The activity coefficients are shown to vary systematically with cation size for a set of trivalent cations.

Conductivity-viscosity-structure: unpicking the relationship in an ionic liquid.

The relationships between the ionic mobility, the viscosity, and the atomic-scale structure are investigated in computer simulations of mixtures of LiF and the network glass-forming material BeF(2). The simulations span a wide range of compositions, across which the fluidity of the system changes greatly due to the break-up of the Be-F network by the addition of the LiF. The relationship between the conductivity and viscosity passes from that expected for independently diffusing ions in the dilute mixtures to strongly decoupled Li+ migration through a viscous network at higher concentrations. The transition between these régimes is linked to the changing local and intermediate-scale structure in the melts. The decoupling phenomenon is associated with the appearance of migration channels in the network which leads to cooperative effects in the Li+ migration.

Ionic motion in crystalline cryolite.

The character of the ion dynamics in crystalline cryolite, Na(3)AlF(6), a model double perovskite-structured mineral, has been examined in computer simulations using a polarizable ionic potential obtained by force-fitting to ab initio electronic structure calculations. NMR studies, and conductivity measurements, have indicated a high degree of mobility, in both Na(+) ion diffusion and reorientation of the AlF(6) octahedral units. The simulations reproduce the low-temperature (tilted) crystal structure and the existence of a transition to a cubic structure at elevated temperatures, in agreement with diffraction measurements, though the calculated transition temperature is too low. The reorientational dynamics of the AlF(6) octahedra is shown to consist of a hopping motion between the various tilted positions of the low-temperature form, even above the transition temperature. The rate of reorientation estimated by extrapolation to the temperature régime of the NMR measurements is consistent with the experimental data. In addition, we report a novel cooperative "tilt-swapping" motion of the differently tilted sublattices, just below the transition temperature. The perfect crystals show no Na(+) diffusion, in apparent disagreement with observation. We argue, following previous analyses of the cryolite phase diagram, that the diffusion observed in the experimental studies is a consequence of defects that are intrinsic to the thermodynamically stable form of cryolite. By introducing defects into the simulation cell, we obtain diffusion rates that are consistent with the NMR and conductivity measurements. Finally, we demonstrate a link between diffusion of the Na(+) ions and the reorientation of AlF(6) units, though the correlation between the two is not very strong.