An alternative explanation of the change in T-dependence of the effective Debye-Waller factor at T(c) or T(B).

The cusp-like temperature dependence of the Debye-Waller factor or non-ergodicity parameter f(Q)(T) at some temperature T(c) above T(g) found by experiments in several fragile glassformers has been considered as critical evidence for validity of the ideal Mode Coupling Theory (MCT). A comprehensive review of experimental data of f(Q)(T) and beyond brings out various problems of the MCT predictions. For example, the molten salt, 0.4Ca(NO3)2-0.6KNO3 (CKN), was the first glassformer measured by neutron scattering to verify the cusp-like behavior of f(Q)(T) at T(c) predicted by ideal MCT. While the fits of the other scaling laws of MCT to viscosity, light scattering, and dielectric relaxation data all give T(c) in the range from 368 to 375 K, there is no evidence of cusp-like behavior of f(Q)(T) at T(c) from more accurate neutron scattering data obtained later on by Mezei and Russina [J. Phys.: Condens. Matter 11, A341 (1999)] at temperatures below 400 K. In several molecular glass-formers, experiments have found at temperatures below T(c) that [1-f(Q)(T)] is manifested as nearly constant loss (NCL) in the frequency dependent susceptibility. The NCL persists down to below T(g) and is not predicted by the ideal MCT. No clear evidence of the change of T-dependence of f(Q)(T) at any T(c) was found in intermediate and strong glassformers, although ideal MCT does not distinguish fragile and strong glassformers in predicting the critical behavior of f(Q)(T) a priori. Experiments found f(Q)(T) changes T-dependence not only at T(c) but also at the glass transition temperature T(g). The changes of T-dependence of f(Q)(T) at T(c) and T(g) are accompanied by corresponding changes of dynamic variables and thermodynamic quantities at T(B) ≈ T(c) and at T(g). The dynamic variables include the relaxation time τ(α)(T), the non-exponentiality parameter n(T), and the generalized fragility m(T) of the structural α-relaxation. The thermodynamic quantities are the free volume deduced from positron annihilation spectroscopy, and the configurational entropy obtained from adiabatic calorimetry measurements. These changes of dynamic variables and thermodynamic quantities in temperature dependence at T(B) ≈ T(c) occur concurrently with the change of f(Q)(T) and suggest the effects are related, and have to be explained altogether. Since this task cannot be carried out by the ideal MCT, we have provided a different interpretation of f(Q)(T) and an alternative explanation of the change in its T-dependence of f(Q)(T) at T(B) ≈ T(c) as well as the other dynamic variables. We show f(Q)(T) originates from the dissipation of the molecules while caged by the anharmonic intermolecular potential, and manifested as the NCL at lower temperatures. The cusp-like change of T-dependence of f(Q)(T) at T(c) originates from the corresponding change of free volume and configurational entropy at T(B) ≈ T(c), which also explains the simultaneous changes of the T-dependencies of the other dynamic variables. The alternative explanation is able to resolve the conundrum in CKN because T(B) is ≥400 K, and hence the change of T-dependence of f(Q)(T) at T(c) ≈ T(B) was not observed in data taken at temperatures lower than 400 K by Mezei and Russina. The alternative explanation also can rationalize the difference between fragile and non-fragile glassformers in the strength of the observed changes of f(Q)(T) at T(c) and T(g) as well as the other dynamic quantities at T(B) ≈ T(c) and T(g).

Molecular dynamics study of network statistics in lithium disilicate: Q(n) distribution and the pressure-volume diagram.

Molecular dynamics simulations have been performed to study the structures along the pressure-volume diagram of network-glasses and melts exemplified by the lithium disilicate system. Experimentally, densification of the disilicate glass by elevated pressure is known and this feature is reasonably reproduced by the simulations. During the process of densification or decompression of the system, the statistics of Q(n) (i.e., SiO4 tetrahedron unit with n bridging oxygen linked to the silicon atom where n = 0, 1, 2, 3, or 4) change, and the percentage of the Q3 structures show the maximum value near atmospheric pressure at around T(g). Changes of Q(n) distribution are driven by the changes of volume (or pressure) and are explained by the different volumes of structural units. Furthermore, some pairs of network structures with equi-volume, but having different distributions of Q(n) (or different heterogeneity), are found. Therefore, for molecular dynamics simulations of the Q(n) distributions, it is important to take into account the complex phase behavior including poly-structures with different heterogeneities as well as the position of the system in the P-V-T diagram.

Thermodynamic scaling of α-relaxation time and viscosity stems from the Johari-Goldstein ß-relaxation or the primitive relaxation of the coupling model.

By now it is well established that the structural α-relaxation time, τ(α), of non-associated small molecular and polymeric glass-formers obey thermodynamic scaling. In other words, τ(α) is a function Φ of the product variable, ρ(γ)/T, where ρ is the density and T the temperature. The constant γ as well as the function, τ(α) = Φ(ρ(γ)/T), is material dependent. Actually this dependence of τ(α) on ρ(γ)/T originates from the dependence on the same product variable of the Johari-Goldstein ß-relaxation time, τ(ß), or the primitive relaxation time, τ(0), of the coupling model. To support this assertion, we give evidences from various sources itemized as follows. (1) The invariance of the relation between τ(α) and τ(ß) or τ(0) to widely different combinations of pressure and temperature. (2) Experimental dielectric and viscosity data of glass-forming van der Waals liquids and polymer. (3) Molecular dynamics simulations of binary Lennard-Jones (LJ) models, the Lewis-Wahnström model of ortho-terphenyl, 1,4 polybutadiene, a room temperature ionic liquid, 1-ethyl-3-methylimidazolium nitrate, and a molten salt 2Ca(NO(3))(2)·3KNO(3) (CKN). (4) Both diffusivity and structural relaxation time, as well as the breakdown of Stokes-Einstein relation in CKN obey thermodynamic scaling by ρ(γ)/T with the same γ. (5) In polymers, the chain normal mode relaxation time, τ(N), is another function of ρ(γ)/T with the same γ as segmental relaxation time τ(α). (6) While the data of τ(α) from simulations for the full LJ binary mixture obey very well the thermodynamic scaling, it is strongly violated when the LJ interaction potential is truncated beyond typical inter-particle distance, although in both cases the repulsive pair potentials coincide for some distances.

Molecular dynamics studies of ionically conducting glasses and ionic liquids: wave number dependence of intermediate scattering function.

Dynamical heterogeneity is a key feature to characterize both acceleration and slowing down of the dynamics in interacting disordered materials. In the present work, the heterogeneous ion dynamics in both ionically conducting glass and in room temperature ionic liquids are characterized by the combination of the concepts of Lévy distribution and multifractality. Molecular dynamics simulation data of both systems are analyzed to obtain the fractional power law of the k-dependence of the dynamics, which implies the Lévy distribution of length scale. The multifractality of the motion and structures makes the system more complex. Both contributions in the dynamics become separable by using g(k,t) derived from the intermediate scattering function, F(s)(k,t). When the Lévy index obtained from F(s)(k,t) is combined with fractal dimension analysis of random walks and multifractal analysis, all the spatial exponent controlling both fast and slow dynamics are clarified. This analysis is generally applicable to other complex interacting systems and is deemed beneficial for understanding their dynamics.

Molecular dynamics study of thermodynamic scaling of the glass-transition dynamics in ionic liquids over wide temperature and pressure ranges.

Experimentally, superpositioning of dynamic properties such as viscosity, relaxation times, or diffusion coefficients under different conditions of temperature T, pressure P, and volume V by the scaling variable TV(gamma) (where gamma is a material constant) has been reported as a general feature of many kinds of glass-forming materials. In the present work, molecular dynamics (MD) simulations have been performed to study the scaling of dynamics near the glass-transition regime of ionic liquids. Scaling in the simulated 1-ethyl-3-methylimidazolium nitrate (EMIM-NO(3)) system has been tested over wide ranges of temperatures and pressures. TV(gamma) scaling of the dynamics is well described by master curves with gamma = 4.0 +/- 0.2 and 3.8 +/- 0.2 for cation and anion, respectively. Structures and Coulombic terms of the corresponding states are found to be quite similar. The temperature and pressure dependence of the pair correlation function show similar trends and therefore can be superpositioned onto the master curve. Although the behaviors with gamma = 4 might be expected from the relation, gamma = n/3, for the dynamics with the soft-core-type potential U = epsilon(sigma/r)(n), with n = 12, pair potentials used in the MD simulation have a more complex form, and not all the repulsive terms can play their roles in the heterogeneous structures determined by ion-ion interactions. Scaling is related to the common part of effective potentials related to the pair correlation functions, including the many-body effect in real space.

Mixing effects in glass-forming Lennard-Jones mixtures.

Mixing effects have been investigated from molecular dynamics simulations at constant number of particles, volume, and temperature on the Kob-Andersen glass-forming Lennard-Jones atomic mixture A(x)B(1-x) for 0 < or = x < or = 1 compositions. Upon cooling, crystallization is observed for x < or = 0.5 and x > or = 0.9 compositions. The crystalline states can be described by a quite complex coexistence of voids (x < or = 0.5), point defects, and one or two crystal structures which were characterized and found identical to those reported by Fernandez and Harrowell [Phys. Rev. E 67, 011403 (2003)] from energy minimization. Amorphization is also seen at 0.6 < or = x < or = 0.8 compositions and it is suggested that both crystal structures, CsCl and fcc-hcp, do not compete at these compositions since only one type of crystalline seed is found in the liquid, either fcc/hcp or CsCl. A significant decrease in the diffusion constants for both A and B particles is also seen above x(A) approximately = 0.5. The problem of the extraordinary stability of the model against crystallization is discussed.

Heterogeneous dynamics of ionic liquids from molecular dynamics simulations.

Molecular dynamics simulations have been performed to study the complex and heterogeneous dynamics of ions in ionic liquids. The dynamics of cations and anions in 1-ethyl-3-methyl imidazolium nitrate (EMIM-NO(3)) are characterized by van Hove functions and the corresponding intermediate scattering functions F(s)(k,t) and elucidated by the trajectories augmented by the use of singular spectrum analysis (SSA). Several time regions are found in the mean squared displacement of the ions. Change in the slope in a plot of the diffusion coefficient against temperature is found at around 410 K in the simulation. Heterogeneous dynamics with the presence of both localized ions and fast ions capable of successive jumps were observed at long time scales in the self-part of the van Hove functions and in the trajectories. Non-Gaussian dynamics are evidenced by the self-part of the van Hove functions and wave number dependence of F(s)(k,t) and characterized as Levy flights. Successive motion of some ions can continue even after several nanoseconds at 370 K, which is longer than the onset time of diffusive motion, t(dif). Structure of the long time dynamics of fast ions is clarified by the phase space plot of the successive motion using the denoised data by SSA. The continual dynamics are shown to have a long term memory, and therefore local structure is not enough to explain the heterogeneity. The motion connecting localized regions at about 370 K is jumplike, but there is no typical one due to local structural changes during jump motion. With the local motion, mutual diffusion between cation and anion occurs. On decreasing temperature, mutual diffusion is suppressed, which results in slowing down of the dynamics. This "mixing effect of cation and anion" is compared with the "mixed alkali effect" found in the ionics in the ionically conducting glasses, where the interception of paths by different alkali metal ions causes the large reduction in the dynamics [J. Habasaki and K. L. Ngai, Phys. Chem. Chem. Phys. 9, 4673 (2007), and references herein]. Although a similar mechanism of the slowing down is observed, strong coupling of the motion of cation and anion prevents complete interception unless deeply supercooled, and this explains the wide temperature region of the existence of the liquid and supercooled liquid states in the ionic liquid.

Molecular dynamics study of the dynamics near the glass transition in ionic liquids.

Molecular dynamics (MD) simulations have been performed to study the dynamics near the glass transition regime of molecular ions in ionic liquids. The glass transition temperature in the simulated 1-ethyl-3-methyl imidazolium nitrate (EMIM-NO(3)) system was determined by plotting density against temperatures. The dynamics at several temperatures in the liquid, supercooled liquid, and glassy states have been characterized by the diffusion coefficients, fractal dimension analysis of the trajectories, and the van-Hove functions. The diffusion coefficient approximately obeys the Vogel-Fulcher-Tammann (VFT) relation. However, two power laws or two exponentials are also good descriptions of the data. The fractal dimension of the random walks is a measure of the complexity of the trajectory, which is attributed to the geometrical correlations among successive motions. Rapid increase of the fractal dimension of the random walks on decreasing temperature is found for both cations and anions. Temperature dependence of the fractal dimension of the random walks for the long range (accelerated) motion is larger than that for short range (localized) motion. This reasonably explains the change in the slopes found in the temperature dependence of the diffusion coefficients. At around the glass transition temperature, long range motion is essentially absent during the observed times, up to several nano seconds. This feature is also confirmed by the van-Hove functions. Such slowing down of the dynamics in the fragile ionic liquids is characterized by the changes from long range motion to short range motion instead of sudden changes at around T(0) in the VFT relation.

Refinements in the characterization of the heterogeneous dynamics of Li ions in lithium metasilicate.

We have performed the molecular dynamics simulations of ionically conducting lithium metasilicate, Li(2)SiO(3), to get a more in depth understanding of the heterogeneous ion dynamics by separating out the partial contributions from localized and diffusive ions to the mean square displacement (MSD) , the non-Gaussian parameter alpha(2)(t), and the van Hove function G(s)(r,t). Several different cage sizes l(c) have been used for the definition of localized ions. Behaviors of fast ions are obtained by the subtraction of the localized component from the r(2)(t) of all ions, and accelerated dynamics is found in the resultant subensemble. The fractional power law of MSD is explained by the geometrical correlation between successive jumps. The waiting time distribution of jumps also plays a role in determining but does not affect the exponent of its fractional power law time dependence. Partial non-Gaussian parameters are found to be instructive to learn how long length-scale motions contribute to various quantities. As a function of time, the partial non-Gaussian parameter for the localized ions exhibits a maximum at around t(x2), the onset time of the fractional power law regime of . The position of the maximum is slightly dependent on the choice of l(c). The power law increases in the non-Gaussian parameter before the maximum are attributed to the Levy distribution of length scales of successive (long) jumps. The decreases with time, after the maximum has been reached, are due to large back correlation of motions of different length scales. The dynamics of fast ions with superlinear dependence in their MSD also start at time around the maximum. Also investigated are the changes of the characteristic times demarcating different regimes of on increasing temperatures from the glassy state to the liquid state. Relation between the activation energies for short time and long time regimes of is in accord with interpretation of ion dynamics by the coupling model.

Time series analysis of ion dynamics in glassy ionic conductors obtained by a molecular dynamics simulation.

We present several characteristics of ionic motion in glassy ionic conductors brought out by time series analysis of molecular dynamics (MD) simulation data. Time series analysis of data obtained by MD simulation can provide crucial information to describe, understand and predict the dynamics in many systems. The data have been treated by the singular spectrum analysis (SSA), which is a method to extract information from noisy short time series and thus provide insight into the unknown or partially unknown dynamics of the underlying system that generated the time series. Phase-space plot reconstructed using the principal components of SSA exhibited complex but clear structures, suggesting the deterministic nature of the dynamics.

Dynamics of caged ions in glassy ionic conductors.

At sufficiently high frequency and low temperature, the dielectric responses of glassy, crystalline, and molten ionic conductors all invariably exhibit nearly constant loss. This ubiquitous characteristic occurs in the short-time regime when the ions are still caged, indicating that it could be a determining factor of the mobility of the ions in conduction at longer times. An improved understanding of its origin should benefit the research of ion conducting materials for portable energy source as well as the resolution of the fundamental problem of the dynamics of ions. We perform molecular dynamics simulations of glassy lithium metasilicate (Li2SiO3) and find that the length scales of the caged Li+ ions motions are distributed according to a Levy distribution that has a long tail. These results suggest that the nearly constant loss originates from "dynamic anharmonicity" experienced by the moving but caged Li+ ions and provided by the surrounding matrix atoms executing correlated movements. The results pave the way for rigorous treatments of caged ion dynamics by nonlinear Hamiltonian dynamics.

Molecular dynamics study of cage decay, near constant loss, and crossover to cooperative ion hopping in lithium metasilicate.

Molecular dynamics (MD) simulations of lithium metasilicate (Li2SiO3) in the glassy and supercooled liquid states have been performed to illustrate the decay with time of the cages that confine individual Li+ ions before they hop out to diffuse cooperatively with each other. The self-part of the van Hove function of Li+ ions, G(s)(r,t), is used as an indicator of the cage decay. At 700 K, in the early time regime t of Li+ ions also increases very slowly with time approximately as t(0.1) and has weak temperature dependence. Such can be identified with the near constant loss (NCL) observed in the dielectric response of ionic conductors. At longer times, when the cage decays more rapidly as indicated by the increasing buildup of the intensity of G(s)(r,t) at the distance between Li+ ion sites, broadly crosses over from the NCL regime to another power law t(beta) with beta approximately 0.64 and eventually it becomes t(1.0), corresponding to long-range diffusion. Both t(beta) and t(1.0) terms have strong temperature dependence and they are the analogs of the ac conductivity [sigma(omega) proportional, variant omega(1-beta)] and dc conductivity of hopping ions. The MD results in conjunction with the coupling model support the following proposed interpretation for conductivity relaxation of ionic conductors: (1) the NCL originates from very slow initial decay of the cage with time caused by few independent hops of the ions because t(x1)< and are about the same for t of the fast ions increases much more rapidly for t>t(x2). The self-part of the van Hove function of Li+ reveals that first jumps for some Li+ ions, which are apparently independent free jumps, have taken place before t(x2). While after t(x2) the angle between the first jump and the next is affected by the other ions, again indicating cooperative jump motion. The dynamic properties are analogous to those found in supercooled colloidal particle suspension by confocal microscopy.

Monte carlo simulation of the mixed alkali effect with cooperative jumps

In our previous works on molecular dynamics (MD) simulations of lithium metasilicate (Li2SiO3), it has been shown that the long time behavior of the lithium ions in Li2SiO3 has been characterized by the component showing the enhanced diffusion (Levy flight) due to cooperative jumps. It has also been confirmed that the contribution of such component decreases by interception of the paths in the mixed alkali silicate (LiKSiO3). Namely, cooperative jumps of like ions are much decreased in number owing to the interception of the path for unlike alkali-metal ions. In the present work, we have performed a Monte Carlo simulation using a cubic lattice in order to establish the role of the cooperative jumps in the transport properties in a mixed alkali glass. Fixed particles (blockage) were introduced instead of the interception of the jump paths for unlike alkali-metal ions. Two types of cooperative motions (a pull type and a push type) were taken into account. Low-dimensionality of the jump path caused by blockage resulted in a decrease of a diffusion coefficient of the particles. The effect of blockage is enhanced when the cooperative motions were introduced.

Characteristics of slow and fast ion dynamics in a lithium metasilicate glass.

Molecular dynamics simulations of lithium metasilicate (Li(2)SiO(3)) glass have been performed. The motion of lithium ions is divided into slow (A) and fast (B) categories in the glassy state. The waiting time distribution of the jump motion of each component shows power law behavior with different exponents. Slow dynamics are caused by localized jump motions and the long waiting time. On the other hand, the fast dynamics of the lithium ions in Li(2)SiO(3) are characterized as Lévy flight caused by cooperative jumps. Short intervals of jump events also occur in the fast dynamics in the short time region. Both the temporal and spatial terms contribute to the dynamics acceleration and the heterogeneity caused by these two kinds of dynamics is illustrated. The slow dynamics characteristics of the "glass transition" and in the "mixed alkali effect" are discussed.