Anomalous ionic transport in glassy electrolytes

Summary We discuss the dynamic structure model recently introduced by Bunde, Maass and Ingram to account for the anomalies of ionic transport in glassy ionic conductors. The model is based on the experimental evidence that ions in glass maintain their distinct local environments. Key features include a site memory effect that introduces vacancies appropriate to each kind of mobile ion, and a mismatch energy that emerges whenever an ion attempts to enter a different kind of site, the combination of both leads to the formation of fluctuating percolation pathways. The connectivity of these pathways determines the ion mobility in the glassy network. The exploration of this model by numerical methods leads i) to a power law relationship between ionic conductivity and cation content (now confirmed in the literature) and ii) to the elucidation of many facets of the mixed alkali effect. It is suggested that the model could form the basis for a comprehensive theory of vitreous electrolytes. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Fast interfacial ionic conduction in nanostructured glass ceramics

The hopping movements of mobile ions in a nanostructured LiAlSiO4 glass ceramic are characterized by time-domain electrostatic force spectroscopy (TDEFS). While the macroscopic conductivity spectra are governed by a single activation energy, the nanoscopic TDEFS measurements reveal three different dynamic processes with distinct activation energies. Apart from the ion transport processes in the glassy and crystalline phases, we identify a third process with a very low activation energy, which is assigned to ionic movements at the interfaces between the crystallites and glassy phase. Such interfacial processes are believed to play a key role for obtaining high ionic conductivities in nanostructured solid electrolytes.     

Preparation and characterization of superionic materials in a new mixed system (Cu(1−x)AgxI)–(Ag2O)–(P2O5), (0.05≤x≤0.25)

In this paper attempts have been made to prepare superionic glassy electrolytes in the mixed system 30(Cu_(1−x)Ag_xI)–46.66(Ag₂O)–23.33(P₂O₅), where x=0.05, 0.1, 0.15, 0.2 and 0.25, respectively, using the melt quenching process. The solid samples were characterized by X-ray diffraction (XRD), differential scanning calorimetry (DSC), Fourier transform infrared (FT-IR) spectroscopy and silver ionic transport number studies. XRD analysis and FT-IR spectroscopic results have provided details regarding the various phases present in the new system and also indicated the formation of composite materials consisting of glassy and crystalline phases. The transport number measurements have indicated the formation of superionic solids having Ag⁺ ions as the mobile species in the present system.     

A nonlinear macroscopic multi-phasic model for describing interactions between solid,fluid and ionic species in biological tissue materials

A nonlinear, macroscopic multi-phasic model for describing the interactions between solid, fluid, and ionic species in porous materials is presented. Governing equations are derived based on the nonlinear theories of solid mechanics, linear flow theory of Newtonian fluids, and theory of irreversible thermodynamics for the transport of ions and ionic solutions. The model shows that the transport coupling between ions and ionic solution exists only when the porous material has a membrane-like feature, which could be inside the material or on the material boundaries. Otherwise, the coupling occurs only between the solid and fluid phases and the transport of ionic species will have no effect on the macroscopic stresses, strains and displacements of the porous material. As an application of the present multi-phasic model, a numerical example of the human cornea under the shock of NaCl hypertonic solution applied to its endothelial surface is presented. This is a typical example of how ionic transport induces swelling in biological tissues. The results obtained from the present multi-phasic model demonstrate that the mechanical properties of the tissue have an important influence on the swelling of the cornea. Without taking into account this influence, the predicted swelling may be exaggerated.     

The role of disorder in superionic conductors

This paper illustrates from a phenomenological point of view why the study of superionic conductors is essentially a study of disorders. Crystals that are good ionic conductors lack a long-range order in their mobile-ion sublattice. Moreover, low-temperature anomalies typical of amorphous materials appear to be rather common in superionic crystals. In several solid electrolytes the coupling between “disorder modes” typical of glasses and translational degrees of freedom of the ions can be shown to enhance ionic diffusion. The observed, or expected, properties of these superionic conductors are briefly discussed. The hypothesis that disorder may often play a dynamic role in ion transport in solids suggests ways to synthesize materials of technological interest.     

Investigation of the free volume and ionic conducting mechanism of poly（ethylene oxide）-LiClO_4 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.     

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.     

Ionic conductivity and tracer diffusion in a lattice containing random traps

A model where the lattice contained a number of randomly distributed traps equal to the number of diffusing particles was investigated rigorously. Monte Carlo methods were used to determine the relevant correlation factors in the tracer diffusion and ionic conductivity. It was found that the temperature dependence of the correlation factors contributed a relatively small component to the activation energy of the overall transport process. The relevance of the findings to atomic transport in fluorite-related oxides containing divalent dopant ions is commented on.     

Water and other tetrahedral liquids: order, anomalies and solvation

In order to understand the common features of tetrahedral liquids with water-like anomalies, the relationship between local order and anomalies has been studied using molecular dynamics simulations for three categories of such liquids: (a)?atomistic rigid-body models for water (TIP4P, TIP4P/2005, mTIP3P, SPC/E), (b)?ionic melts, BeF(2) (TRIM model) and SiO(2) (BKS potential) and (c)?Stillinger-Weber liquids parametrized to model water (mW) and silicon. Rigid-body, atomistic models for water and the Stillinger-Weber liquids show a strong correlation between tetrahedral and pair correlation order and the temperature for the onset of the density anomaly is close to the melting temperature. In contrast, the ionic melts show weaker and more variable degrees of correlation between tetrahedral and pair correlation metrics, and the onset temperature for the density anomaly is more than twice the melting temperature. In the case of water, the relationship between water-like anomalies and solvation is studied by examining the hydration of spherical solutes (Na(+), Cl(-), Ar) in water models with different temperature regimes of anomalies (SPC/E, TIP4P and mTIP3P). For both ionic and nonpolar solutes, the local structure and energy of water molecules is essentially the same as in bulk water beyond the second-neighbour shell. The local order and binding energy of water molecules are not perturbed by the presence of a hydrophobic solute. In the case of ionic solutes, the perturbation is largely localized within the first hydration shell. The binding energies for the ions are strongly dependent on the water models and clearly indicate that the geometry of the partial charge distributions, and the associated multipole moments, play an important role. However the anomalous behaviour of the water network has been found to be unimportant for polar solvation.     

Anomalous electrical conductivity behavior at elevated pressure in the protic ionic liquid procainamide hydrochloride

Using broadband dielectric spectroscopy, we investigated the effect of hydrostatic pressure on the conductivity relaxation time τ{σ} of the supercooled protic ionic liquid, procainamide hydrochloride, a common pharmaceutical. The pressure dependence of τ{σ} exhibited anomalous behavior in the vicinity of the glass transition T{g}, manifested by abrupt changes in activation volume. This peculiar behavior, paralleling the change in temperature dependence of τ{σ} near T{g}, is a manifestation of the decoupling between electrical conductivity and structural relaxation. Although the latter effectively ceases in the glassy state, free ions retain their mobility but with a reduced sensitivity to thermodynamic changes. This is the first observation of decoupling of ion migration from structural relaxation in a glassy conductor by isothermal densification.     

Dynamical screening and ionic conductivity in water from ab initio simulations

We present a method to calculate ionic conductivities of complex fluids from ab initio simulations. This is achieved by combining density functional theory molecular dynamics simulations with polarization theory. Conductivities are then obtained via a Green-Kubo formula using time-dependent effective charges of electronically screened ions. The method is applied to two different phases of warm dense water. We observe large fluctuations in the effective charges; protons can transport effective charges greater than +e for ultrashort time scales. Furthermore, we compare our results with a simpler model of ionic conductivity in water that is based on diffusion coefficients. Our approach can be directly applied to study ionic conductivities of electronically insulating materials of arbitrary composition, e.g., complex molecular mixtures under such extreme conditions that occur deep inside giant planets.     

Predictability of ion transport properties from the structure of solid electrolytes

The concept of bond valence (BV) is widely used in crystal chemical considerations, e.g. to assess equilibrium positions of atoms in crystal structures from an empirical relationship between bond lengthR _M−X and bond valenceS _A−X =exp [(R ₀ −R _M−X ) /b] as sites where the BV sumV(A)=∑ s _M−X equals the formal valenceV _id of the cationM ⁺ . Our modified BV approach that systematically accounts for the softness of the bond may then be effectively used to study the interplay between structure and properties of solid electrolytes. This is exemplified for correlations to experimental data from IR, NMR, and impedance spectroscopy. Combining the bond valence approach with reverse Monte Carlo (RMC) modeling or molecular dynamics (MD) simulations provides a deeper understanding of ion transport mechanisms, especially in highly disordered or amorphous solids. Local structure models for crystalline electrolytes are derived by combining crystallographic structure information with simulations. A method for the prediction of the activation energy of the ionic conductivity from the bond valence analysis of the crystal structure is proposed. Taking into account the mass dependence of the conversion factor from bond valence mismatch into an activation energy scale, we could establish a correlation that holds for different types of mobile ions. The strong coupling of the H⁺ transfer to the anion motion in proton conductors requires a special treatment. For glassy solid electrolytes RMC structure models are BV-analyzed to assess the total number of equilibrium sites and to identify transport pathways for the mobile ions. Recently, we have reported a correlation between the pathway volume fraction and the transport properties that permits to predict both absolute value and activation energy of the dc ionic conductivities of disordered solids (including mixed alkali glasses) directly from their structural models. Here we discuss a corresponding BV analysis of molecular dynamics simulation trajectories that allows quantifying the evolution of pathways in time and the influence of temperature on the transport pathways. Paper presented at the Patras Conference on Solid State Ionics — Transport Properties, Patras, Greece, Sept. 14 — 18, 2004.     

Two separate Li ionic motions observed by Li and B NMR in xLi2S + (1 − x)B2S3 glassy fast ionic conductors

Studies of ion dynamics in the highly conductive glassy fast ionic conductor (FIC) xLi₂S + (1 − x)B₂S₃ (x = 0.65 and 0.70) were made with NMR nuclear spin lattice relaxation (NSLR) R₁(ω, T) of both mobile ⁷Li and immobile ¹¹B ions, and ⁷Li NMR line narrowing δν(T). The possible dependence of ion dynamics on the short range order structures (SRO) and the distribution of activation energies (DAE) in this highly conductive FIC was investigated. Two Gaussian DAE were employed to fit ⁷Li NSLR data, where each Gaussian DAE was correlated to a separate ¹¹B NSLR in a BS₃ and in a BS₄ group. The long range diffusion of Li ions among BS₃ groups and a seemingly localized ionic hopping motion around BS₄ group is suggested as a microscopic model for the ion dynamics in thioborate glasses, namely a ‘two channel relaxation’.     

The transport of slow ions in gases: Experiment, theory, and applications

This review is concerned with the two most important transport phenomena in involving slow ions in gases, namely their drift and diffusion in an externally applied electric field. The energy range of interest extends from thermal values at low temperatures up to about 10 eV. The transport phenomena are first discussed in physical terms, and experimental techniques for measuring ionic drift velocities and diffusion coefficients are then described. Brief coverage is given to ionic transport theory up to the time of Wannier's landmark contributions in 1951–1952; later theoretical developments are treated in more detail. Special emphasis is placed on aspects of modern theory that permit the determination of interaction potentials and collision frequencies for momentum transfer from experimental transport data. The review ends with a discussion of several applications of transport data to ionospheric problems.     

Using pressure,temperature and frequency as variables to study the dynamics of mobile ions in materials with disordered structures

Complementary ways for studying the motion of mobile ions in materials with disordered structures are obtained by varying pressure, tempe- rature and frequency. New results are presented based on a combination of experimental work and modelling. Pressure-dependent measurements on alkali borate glasses show there is a remarkable difference between the activation volumes for conduction and diffusion, with ΔV_σ< ΔV_D, implying that the Haven ratio decreases with increasing pressure. We propose a mechanism that is characterised by a directionally positive correlation between successive hops of different ions into a moving vacant site. The effect of increasing pressure is to increase the degree of directional correlation and thus to make the conduction pathways increasingly linear in aspect. In sodium borate glasses with much lower sodium content, a maximum has been observed when ionic conductivity is plotted versus temperature at fixed frequency. This feature is identified as being of the nearly constant loss (NCL) type, caused by localised flip-flop movements of interacting charges in the B₂O₃ network. In crystalline γ-RbAg₄I₅, a related localised effect has also been found, in this case caused by activated hops of silver ions confined within structural “pockets”. Finally, the frequency dependence of the ionic conductivity is reviewed in fragile ionic melts. Fragility is interpreted here as a consequence of the shape of the local ionic potentials, which unlike in glass do not reflect the pre-existence of empty cation sites for successive ions to hop into. This difference in short-range, short-time behaviour leads directly to the emergence of non-Arrhenius dc conductivity and fluidity behaviours in molten salts. We are thus able to establish a common phenomenological and theoretical approach to ion transport in a wide range of systems, largely based on broadband conductivity spectroscopy.     

Structure-conductivity relations in ion conducting glasses

The bond valence method has been applied to reverse Monte Carlo (RMC) produced structural models of a wide range of ion conducting glasses in order to elucidate the relation between the microscopic structure and the ionic conductivity. Our approach allows us to predict the ionic conductivity of the glasses directly from the “pathway volume” of the structural models and to investigate the nature of these low-dimensional conduction pathways. The pathways are defined to be the regions in the structural models where the valence mismatch for each mobile ions remains below a given threshold value. The results for the metal-halide doped glasses show the importance of including M⁺ sites with a high oxide coordination for the long range mobility, responsible for the dc conductivity. Thus, there are no long range migration pathways for M⁺ sites in an entire halide environment. Rather, the mobile ions are generally moving between sites with a local environment of both oxygens and halide ions, in contrast to earlier proposed “cluster models” where it has been assumed that cations associated with salt clusters are responsible for the high ionic conductivity. Finally, our bond valence approach provides a direct explanation for why the conductivity is favoured by highly polarizable anions and cations, since the pathway volume is related to the softness of the M⁺-X bond. Paper presented at the 9th EuroConference on Ionics, Ixia, Rhodes, Greece, Sept. 15 – 21, 2002.     

Modeling electrokinetic flows in microchannels using coupled lattice Boltzmann methods

We present a numerical framework to solve the dynamic model for electrokinetic flows in microchannels using coupled lattice Boltzmann methods. The governing equation for each transport process is solved by a lattice Boltzmann model and the entire process is simulated through an iteration procedure. After validation, the present method is used to study the applicability of the Poisson–Boltzmann model for electrokinetic flows in microchannels. Our results show that for homogeneously charged long channels, the Poisson–Boltzmann model is applicable for a wide range of electric double layer thickness. For the electric potential distribution, the Poisson–Boltzmann model can provide good predictions until the electric double layers fully overlap, meaning that the thickness of the double layer equals the channel width. For the electroosmotic velocity, the Poisson–Boltzmann model is valid even when the thickness of the double layer is 10 times of the channel width. For heterogeneously charged microchannels, a higher zeta potential and an enhanced velocity field may cause the Poisson–Boltzmann model to fail to provide accurate predictions. The ionic diffusion coefficients have little effect on the steady flows for either homogeneously or heterogeneously charged channels. However the ionic valence of solvent has remarkable influences on both the electric potential distribution and the flow velocity even in homogeneously charged microchannels. Both theoretical analyses and numerical results indicate that the valence and the concentration of the counter-ions dominate the Debye length, the electrical potential distribution, and the ions transport. The present results may improve the understanding of the electrokinetic transport characteristics in microchannels.     

Experimental and theoretical investigation of oxygen diffusion in stabilised zirconia

Oxygen diffusion in stabilised zirconias is investigated by the simultaneous application of computer modelling and experimental techniques to yttria-stabilised zirconia. Using the Mott-Littleton method, migration pathways for oxygen ions have been calculated in perfect cubic zirconia. The oxygen migration occurs through a straight pathway, but not starting from the ideal lattice positions. The calculated activation energy of migration is about 0.2 v eV. Oxygen transport is investigated experimentally in YSZ containing 8-24 v mol% Y 2 O 3 as a function of stabiliser content by combining the stable isotope ( 18 O 2 ) method with ionic conductivity measurements. It was found that for a given temperature, diffusion and conductivity are highest for YSZ containing 8-10 v mol% yttria, but with differing activation energies which can be compared to the calculated values.     

Electrical properties of unusual ionic melts

The paper reviews the advances that have been made in recent years in the understanding of electrical transport in fully ionized molten salts, partly dissociated molecular liquids and liquid ionic stoichiometric alloys like CsAu. Special emphasis is placed on the recently observed temperature and pressure induced gradual transition between the limiting cases of molecular insulators and ionic melts. At supercritical temperatures salts undergo a continuous transition from an insulating vapour to a highly conducting ionic fluid if the density is increased sufficiently. This transition is due to a shift of the ionization equilibrium between molecules and ions, in favour of the ions, with increasing density. Poorly conducting molten salts and polar substances like water and ammonia also become more ionic, and consequently better conductors, at very high pressures.

Recent thermodynamic, magnetic and electrical measurements on liquid alloys which are composed of two metallic elements and which are non-metallic at definite stoichiometric compositions are discussed. Special emphasis is placed on the liquid Cs-Au system which resembles in many respects the molten alkalimetal halides.     

Scheme for N-Qubit Toffoli Gate by Transport of Trapped Ultracold Ions

We propose a potentially practical scheme for implementing an n-qubit Toffoli gate by elaborately controlling the transport of ultracold ions through stationary laser beams. Conditioned on the uniform ionic transport velocity, the n-qubit Toffoli gate can be realized with high fidelity and high successful probability under current experimental conditions, which depends on a single resonant interaction with n trapped ions and has constant implementation time with the increase of qubits. We show that the increase of the ion number can improve the fidelity and the successful probability of the Toffoli gate.