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We revisit the statistical mechanics of charge fluctuations in capacitors. In constant-potential classical molecular simulations, the atomic charge 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 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.

We use molecular dynamics simulations to study the exchange kinetics of water molecules at a model metal electrode surface -- exchange between water molecules in the bulk liquid and water molecules bound to the metal. This process is a rare event, with a mean residence time of a bound water of about 40 ns for the model we consider. With analysis borrowed from the techniques of rare-event sampling, we show how this exchange or desorption is controlled by (1) reorganization of the hydrogen bond network within the adlayer of bound water molecules, and by (2) interfacial density fluctuations of the bulk liquid adjacent to the adlayer. We define collective coordinates that describe the desorption mechanism. Spatial and temporal correlations associated with a single event extend over nanometers and tens of picoseconds., Comment: 10 pages, 9 figures

Ionic solids and melts are compounds in which the interactions are dominated by electrostatic effects. However, the polarization of the ions also plays an important role in many respects as has been clarified in recent years thanks to the development of realistic polarizable interaction potentials. After detailing these models, we illustrate the importance of polarization effects on a series of examples concerning the structural properties, such as the stabilization of particular crystal structures or the formation of highly-coordinated multivalent ions in the melts, as well as the dynamic properties such as the diffusion of ionic species. The effects on the structure of molten salts interfaces (with vacuum and electrified metal) is also described. Although most of the results described here concern inorganic compounds (molten fluorides and chlorides, ionic oxides...), the particular case of the room-temperature ionic liquids, a special class of molten salts in which at least one species is organic, will also be briefly discussed to indicate how the ideas gained from the study of "simple" molten salts are being transferred to these more complex systems., Comment: 16 pages, 9 figures

Many scientific-software projects test their codes inadequately, or not at all. Despite its well-known benefits, adopting routine testing is often not easy. Development teams may have doubts about establishing effective test procedures, writing test software, or handling the ever-growing complexity of test cases. They may need to run (and test) on restrictive HPC platforms. They almost certainly face time and budget pressures that can keep testing languishing near the bottom of their to-do lists. This paper presents DDTS, a framework for building test suite applications, designed to fit scientific-software projects' requirements. DDTS aims to simplify introduction of rigorous testing, and to ease growing pains as needs mature. It decomposes the testing problem into practical, intuitive phases; makes configuration and extension easy; is portable and suitable to HPC platforms; and exploits parallelism. DDTS is currently used for automated regression and developer pre-commit testing for several scientific-software projects with disparate testing requirements., Comment: Fixed bad formatting on last page

The origin of both weak temperature dependence and packing fraction dependence of $T^{1/4}\eta^{3/2}$ 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., Comment: 4 pages, 4 figures

Using molecular dynamics simulations with recently developed importance sampling methods, we show that the differential capacitance of a model ionic liquid based double-layer capacitor exhibits an anomalous dependence on the applied electrical potential. Such behavior is qualitatively incompatible with standard mean-field theories of the electrical double layer, but is consistent with observations made in experiment. The anomalous response results from structural changes induced in the interfacial region of the ionic liquid as it develops a charge density to screen the charge induced on the electrode surface. These structural changes are strongly influenced by the out-of-plane layering of the electrolyte and are multifaceted, including an abrupt local ordering of the ions adsorbed in the plane of the electrode surface, reorientation of molecular ions, and the spontaneous exchange of ions between different layers of the electrolyte close to the electrode surface. The local ordering exhibits signatures of a first-order phase transition, which would indicate a singular charge-density transition in a macroscopic limit.

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 parameterizations. Various thermodynamic, structural and dynamic properties are calculated for the solid and liquid phases. The melting temperature is also obtained by direct coexistence simulations of the liquid and solid phases. Dispersion interactions appear to have an important effect on the density 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., Comment: 8 pages, 5 figures

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 characterised by concerted motion of multiple ions in short closed loops. Diffusion coefficients can not be expressed in a simple Arrhenius form dependent on single-ion free-energies, and intrinsic diffusion must be considered a many-body process.

The standard model of enhanced ionic conductivities in solid electrolyte heterostructures follows from a continuum mean-field description of defect distributions that makes no reference to crystalline structure. To examine ionic transport and defect distributions while explicitly accounting for ion-ion correlations and lattice effects, we have performed molecular dynamics simulations of a model coherent fluorite heterostructure without any extrinsic defects, with a difference in standard chemical potentials of mobile fluoride ions between phases induced by an external potential. Increasing the offset in fluoride ion standard chemical potentials across the internal interfaces decreases the activation energies for ionic conductivity and diffusion and strongly enhances fluoride ion mobilities and defect concentrations near the heterostructure interfaces. Non-charge-neutral "space-charge" regions, however, extend only a few atomic spacings from the interface, suggesting a continuum model may be inappropriate. Defect distributions are qualitatively inconsistent with the predictions of the continuum mean-field model, and indicate strong lattice-mediated defect-defect interactions. We identify an atomic-scale "Frenkel polarisation" mechanism for the interfacial enhancement in ionic mobility, where preferentially oriented associated Frenkel pairs form at the interface and promote local ion mobility via concerted diffusion processes.

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., Comment: 12 pages, 10 figures, perspective article

We use molecular dynamics simulations to explore the impact of a non-ionic solvent on the structural and capacitive properties of supercapacitors based on an ionic liquid electrolyte and carbon electrodes. The study is focused on two pure ionic liquids, namely 1-butyl-3-methylimidazolium hexafluorophosphate and 1-butyl-3-methylimidazolium tetrafluoroborate, and their 1.5 M solutions in acetonitrile. The electrolytes, represented by coarse-grained models, are enclosed between graphite electrodes. We employ a constant potential methodology which allows us to gain insight into the influence of solvation on the polarization of the electrodes as well as the structural and capacitive properties of the electrolytes at the interface. We show that the interfacial characteristics, different for two distinct pure ionic liquids, become very similar upon mixing with acetonitrile.

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.

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-AlCl 4. 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 Al2Cl 7- in small amounts. The calculated transport properties (diffusion coefficients, electrical conductivity and viscosity) of EMI-AlCl4 are in good agreement with experimental data.

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 adlayer dynamic heterogeneity responds asymmetrically to applied voltage., Comment: 6 page, 4 figures

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 accross 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 (Y3+ 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 the one of yttrium cation when the content in YF3 increases. Implications on the validity of the Nernst-Einstein relation for estimating the electrical conductivity are discussed., Comment: 7 pages, 6 figures, 1 supplementary material

We present a study of the solvation properties of model aqueous electrode interfaces. The exposed electrodes we study strongly bind water and have closed packed crystalline surfaces, which template an ordered water adlayer adjacent to the interface. We find that these ordered water structures facilitate collective responses in the presence of solutes that are correlated over large lengthscales and across long timescales. Specifically, we show that the liquid water adjacent to the ordered adlayers forms a soft, liquid-vapor-like interface with concomitant manifestations of hydrophobicity. Temporal defects in the adlayer configurations create a dynamic heterogeneity in the degree to which different regions of the interface attract hydrophobic species. The structure and heterogeneous dynamics of the adlayer defects depend upon the geometry of the underlying ordered metal surface. For both 100 and 111 surfaces, the dynamical heterogeneity relaxes on times longer than nanoseconds. Along with analyzing time scales associated with these effects, we highlight implications for electrolysis and the particular catalytic efficiency of platinum., Comment: 9 pages, 8 figures

Realistic modeling of ionic systems necessitates taking explicitly account of many-body effects. In molecular dynamics simulations, it is possible to introduce explicitly these effects through the use of additional degrees of freedom. Here we present two models: The first one only includes dipole polarization effect, while the second also accounts for quadrupole polarization as well as the effects of compression and deformation of an ion by its immediate coordination environment. All the parameters involved in these models are extracted from first-principles density functional theory calculations. This step is routinely done through an extended force-matching procedure, which has proven to be very succesfull for molten oxides and molten fluorides. Recent developments based on the use of localized orbitals can be used to complement the force-matching procedure by allowing for the direct calculations of several parameters such as the individual polarizabilities., Comment: 19 pages, 7 figures

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) and optimize its parameters by fitting them to a series of DFT calculations. The resulting potential was tested by calculating a series of fundamental properties for CeO$_2$ and by comparing them to experimental values. The agreement for all the calculated properties (thermal and chemical expansion coefficients, lattice parameters, oxygen migration energies, local crystalline structure and elastic constants) is within 10-15% of the experimental one, 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., Comment: 12 pages, 6 figures and 5 tables. Accepted on Journal of Physics: Condensed Matter

Polarizable interaction potentials, parametrized using ab initio electronic structure calculations, have been used in molecular dynamics simulations to study the conduction mechanism in Y2 O3 - and Sc2 O3 -doped zirconias. The influence of vacancy-vacancy and vacancy-cation interactions on the conductivity of these materials has been characterised. While the latter can be avoided by using dopant cations with radii which match those of Zr4+ (as is the case of Sc3+), the former is an intrinsic characteristic of the fluorite lattice which cannot be avoided and which is shown to be responsible for the occurrence of a maximum in the conductivity at dopant concentrations between 8 and 13 %. The weakness of the Sc-vacancy interactions in Sc2 O3 -doped zirconia suggests that this material is likely to present the highest conductivity achievable in zirconias., Comment: 17 pages, 6 figure

In this work we study the high pressure behaviour of liquid and glassy GeO2 by means of molecular dynamics simulations. The interaction potential, which includes dipole polarization effects, was parameterized from first-principles calculations. Our simulations reproduce the most recent experimental data to a high degree of precision. The proportion of the various GeOn polyhedra is determined as a function of the pressure: a smooth transition from tetrahedral to octahedral network is observed. Finally, the study of high-pressure, liquid germania confirms that this material presents an anomalous behaviour of the diffusivity as observed in analog systems such as silica and water. The importance of penta-coordinated germanium ions for such behaviour is stressed., Comment: 16 pages, 4 figures, accepted as a Fast Track Communication on Journal of Physics: Condensed Matter

Realistic, first-principles-based interatomic potentials have been used in molecular dynamics simulations to study the effect of cation composition on the ionic conductivity in the Zr2Y2O7-Y3NbO7 system and to link the dynamical properties to the degree of lattice disorder. Across the composition range, this system retains a disordered fluorite crystal structure and the vacancy concentration is constant. The observed trends of decreasing conductivity and increasing disorder with increasing Nb5+ content were reproduced in simulations with the cations randomly assigned to positions on the cation sublattice. The trends were traced to the influences of the cation charges and relative sizes and their effect on vacancy ordering by carrying out additional calculations in which, for example, the charges of the cations were equalised. The simulations did not, however, reproduce all the observed properties, particularly for Y3NbO7. Its conductivity was significantly overestimated and prominent diffuse scattering features observed in small area electron diffraction studies were not always reproduced. Consideration of these deficiencies led to a preliminary attempt to characterise the consequence of partially ordering the cations on their lattice, which significantly affects the propensity for vacancy ordering. The extent and consequences of cation ordering seem to be much less pronounced on the Zr2Y2O7 side of the composition range., Comment: 22 pages, 8 figures, submitted to Journal of Physics: Condensed Matter

The results of molecular dynamics simulations of the properties of water in an aqueous ionic solution close to an interface with a model metallic electrode are described. In the simulations the electrode behaves as an ideally polarizable hydrophilic metal, supporting image charge interactions with charged species, and it is maintained at a constant electrical potential with respect to the solution so that the model is a textbook representation of an electrochemical interface through which no current is passing. We show how water is strongly attracted to and ordered at the electrode surface. This ordering is different to the structure that might be imagined from continuum models of electrode interfaces. Further, this ordering significantly affects the probability of ions reaching the surface. We describe the concomitant motion and configurations of the water and ions as functions of the electrode potential, and we analyze the length scales over which ionic atmospheres fluctuate. The statistics of these fluctuations depend upon surface structure and ionic strength. The fluctuations are large, sufficiently so that the mean ionic atmosphere is a poor descriptor of the aqueous environment near a metal surface. The importance of this finding for a description of electrochemical reactions is examined by calculating, directly from the simulation, Marcus free energy profiles for transfer of charge between the electrode and a redox species in the solution and comparing the results with the predictions of continuum theories. Significant departures from the electrochemical textbook descriptions of the phenomenon are found and their physical origins are characterized from the atomistic perspective of the simulations., Comment: 29 pages, 15 figures

This paper presents the preservice teacher portfolio as a multidimensional tool, addressing three dimensions of the portfolio based on data compiled within one university's teacher preparation program. It recommends the preservice teacher portfolio as a viable tool for assessing preservice teachers' capacity (knowledge, skills, dispositions, and sense of self) and ability to make connections among national standards, state goals, and university vision. Data come from anecdotal notes recorded during observations of students as they developed such portfolios; informal questionnaires and faculty and student surveys addressing the portfolio as a multidimensional tool; and informal faculty interviews about stages of development they observe as teacher candidates progress toward the university's goal of preparing learner centered, inquiring professionals prepared to positively impact all students. Examples from the university's early childhood licensure program are presented. Overall, this teacher preparation program uses portfolios in supporting the capacity building process identified in stages and benchmarks. Throughout the stages, the university supports teacher candidates' increasing capacities to meet the needs of all students through attention to the moral dimension of teaching, the power of technology, the complexity of diversity, and the importance of global and international connections. (Contains 16 bibliographic references.) (SM)