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.

The effect of dispersion interactions on the properties of LiF in condensed phases.

Classical molecular dynamics simulations are performed on LiF in the framework of the polarizable ion model. The overlap repulsion and polarization terms of the interaction potential are derived on a purely non-empirical, first-principles basis. For the dispersion, three cases are considered: a first one in which the dispersion parameters are set to zero and two others in which they are included, with different parametrizations. Various thermodynamic, structural and dynamic properties are calculated for the solid and liquid phases. The melting temperature is also obtained from direct coexistence simulations of the liquid and solid phases. Dispersion interactions appear to have an important effect on the densities of both phases and on the melting point, although the liquid properties are not affected when simulations are performed in the NVT ensemble at the experimental density.

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.

Thermal conductivity of molten alkali metal fluorides (LiF, NaF, KF) and their mixtures.

The thermal conductivities of molten alkali fluorides (LiF, NaF, and KF) and their mixtures (LiF-NaF, LiF-KF, and NaF-KF binaries and LiF-NaF-KF ternary) are predicted using molecular dynamics simulation with the Green-Kubo method. A polarizable ion model is used to describe the interionic interactions. All the systems except LiF-KF and LiF-NaF-KF mixtures follow a scaling law: it is proportionnal to mA (-1/2)(N/V)(2/3), where mA is the arithmetic average of the ionic species masses in a given melt and N is the total number of ions included in the system volume V. In LiF-KF and LiF-NaF-KF mixtures a significant departure from the scaling law is observed. By examining separately the effects of the cation mass and size asymmetry in LiF-KF mixtures, we show that both of them account for half of the deviation. Finally, we observe that the temperature dependence of the thermal conductivity is very small in these molten fluorides.

Structure and Raman spectra in cryolitic melts: simulations with an ab initio interaction potential.

The Raman spectra of cryolitic melts have been calculated from molecular dynamics computer simulations using a polarizable ionic potential obtained by force-fitting to ab initio electronic structure calculations. Simulations which made use of this ab initio derived polarizable interaction potential reproduced the structure and dynamical properties of crystalline cryolite, Na3AlF6, rather well. The transferability of the potential model from solid state to the molten state is tested by comparing results for the Raman spectra of melts of various compositions with those previously obtained with empirically developed potentials and with experimental data. The shapes of the spectra and their evolution with composition in the mixtures conform quite well to those seen experimentally, and we discuss the relationship between the bands seen in the spectra and the vibrational modes of the AlFn((3­n)) coordination complexes which are found in the NaF/AlF3 mixtures. The simulations thus enable a link between the structure of the melt as derived through Raman spectroscopy and through diffraction experiments. We report results for quantities which relate to the degree of cross-linking between these coordination complexes and the diffusive properties of ions.

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.

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.

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.

Simulating Supercapacitors: Can We Model Electrodes As Constant Charge Surfaces?

Supercapacitors based on an ionic liquid electrolyte and graphite or nanoporous carbon electrodes are simulated using molecular dynamics. We compare a simplified electrode model in which a constant, uniform charge is assigned to each carbon atom with a realistic model in which a constant potential is applied between the electrodes (the carbon charges are allowed to fluctuate). We show that the simulations performed with the simplified model do not provide a correct description of the properties of the system. First, the structure of the adsorbed electrolyte is partly modified. Second, dramatic differences are observed for the dynamics of the system during transient regimes. In particular, upon application of a constant applied potential difference, the increase in the temperature, due to the Joule effect, associated with the creation of an electric current across the cell follows Ohm's law, while unphysically high temperatures are rapidly observed when constant charges are assigned to each carbon atom.

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.

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.

From molten salts to room temperature ionic liquids: simulation studies on chloroaluminate systems.

An interaction potential including chloride anion polarization effects, constructed from first-principles calculations, is used to examine the structure and transport properties of a series of chloroaluminate melts. A particular emphasis was given to the study of the equimolar mixture of aluminium chloride with 1-ethyl-3-methylimidazolium chloride, which forms a room temperature ionic liquid EMI+ -AlCl4-. The structure yielded by the classical simulations performed within the framework of the polarizable ion model is compared to the results obtained from entirely electronic structure-based simulations: An excellent agreement between the two flavors of molecular dynamics is observed. When changing the organic cation EMI+ by an inorganic cation with a smaller ionic radius (Li+, Na+, K+), the chloroaluminate speciation becomes more complex, with the formation of Al2Cl7-, in small amounts. The calculated transport properties (diffusion coefficients, electrical conductivity and viscosity) of EMI+ -AlCl4- are in good agreement with experimental data.

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.

A dipole polarizable potential for reduced and doped CeO(2) obtained from first principles.

In this paper we present the parameterization of a new interionic potential for stoichiometric, reduced and doped CeO(2). We use a dipole polarizable potential (DIPPIM: the dipole polarizable ion model) and optimize its parameters by fitting them to a series of density functional theory calculations. The resulting potential was tested by calculating a series of fundamental properties for CeO(2) and by comparing them against experimental values. The values for all the calculated properties (thermal and chemical expansion coefficients, lattice parameters, oxygen migration energies, local crystalline structure and elastic constants) are within 10-15% of the experimental ones, an accuracy comparable to that of ab initio calculations. This result suggests the use of this new potential for reliably predicting atomic scale properties of CeO(2) in problems where ab initio calculations are not feasible due to their size limitations.

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.

Thermal conductivity of ionic systems from equilibrium molecular dynamics.

Thermal conductivities of ionic compounds (NaCl, MgO, Mg(2)SiO(4)) are calculated from equilibrium molecular dynamics simulations using the Green-Kubo method. Transferable interaction potentials including many-body polarization effects are employed. Various physical conditions (solid and liquid states, high temperatures, high pressures) relevant to the study of the heat transport in the Earth's mantle are investigated, for which experimental measures are very challenging. By introducing a frequency-dependent thermal conductivity, we show that important coupled thermoelectric effects occur in the energy conduction mechanism in the case of liquid systems.

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.