Cluster kinetics for glassforming materials

We propose that cluster kinetics based on monomer-cluster, addition-dissociation and cluster fission-fusion provide a way to understand glassforming behavior. The four rate coefficients for the transformations are Arrhenius functions of temperature. Local equilibrium relations for the reversible rates provide expressions for monomer and amorphous cluster concentrations that are related to the Kauzmann temperature and supercooled liquid viscosity. Cluster dynamics are related to observable vitrification kinetics through free volume theory. With a single fitting parameter representing phase transformation energies, the double exponential (nonArrhenius) temperature dependence for viscosity and dielectric relaxation time compares well with experimental data. The one energy parameter alone provides an interpretation for strong and fragile glass materials.     

Tracer diffusion in concentrated lattice gas models. Rectangular lattices with anisotropic jump rates

An approximate theory is developed for tracer diffusion in rectangular lattice gas models with anisotropic jump rates to neighboring unoccupied sites in different directions. Comparison with Monte Carlo simulations on quadratic lattices with several ratios for the jump rates in orthogonal directions shows a satisfactory agreement in all cases investigated.     

Ionic diffusion and local hopping in copper chalcohalide glasses measured using Cu tracer and I-Mössbauer spectroscopy

For the first time, ⁶⁴Cu tracer measurements of ionic diffusion were performed for several copper-rich glass compositions in the CuI---As₂Se₃, CuI---SbI₃---As₂Se₃, CuI---PbI₂---As₂Se₃, CuI---PbI₂---SbI₃---As₂Se₃ and Cu₂Se---As₂Se₃ systems. In accordance with previous a.c. impedance results and Wagner d.c. polarization measurements, it was found that pure Cu⁺ ion-conducting glasses (50CuI---17PbI₂---33As₂Se₃ and 50CuI---20PbI₂---10SbI₃---20As₂Se₃) exhibit the highest copper tracer diffusion coefficients, D_Cu, and the lowest diffusion activation energies. The values of D_Cu at room temperature are higher by 4.5–5.5 orders of magnitude than those in an As₂Se₃ glass. The Haven ratio, H_R, is found to be 0.52–0.61 (ternary glass) and 0.93–1.00 (quaternary glass). Short-range diffusional displacements of the iodide ions induced by the hopping Cu⁺ ions are also detected in the CuI---PbI₂---SbI₃---As₂Se₃ glassy system using ¹²⁹I-Mössbauer spectroscopy in the temperature range of 4.2 to 305 K. The activation energy of local hopping, E_h ≈ 0.31 eV, is very similar to that of bulk ionic conductivity (0.37 eV) and copper diffusion (≈ 0.33 eV). In contrast to CuI-based vitreous alloys, 50Cu₂Se---50As₂Se₃ glass exhibits D_Cu that are two to five orders of magnitude lower, and the copper ion transport number, t_Cu⁺, is between 10⁻³ and 10⁻⁴ in the temperature range 140–170 °C.     

Anomalous behaviour of the diffusion coefficient in interacting adsorbates

Langevin simulations provide an effective way to study collective effects of Brownian particles immersed in a two-dimensional periodic potential. In this paper, we concentrate essentially on the behaviour of the tracer (D_Tr) and collective diffusion coefficients (D_C) as function of friction (Γ). Our simulations show that in the high friction limit, the two physical quantities D_Tr and D_C present qualitatively the same behaviour, for both coupled and decoupled substrate potentials. However, for the low friction regime, and especially for the coupled potential case, an anomalous diffusion behaviour is found where D_Tr∼Γ^-σ_Tr and D_C∼Γ^-σ_C, with σ_Tr<σ_C<1. We also found that in the case of weak dynamical coupling between the adparticles and the substrate, the exponents are not universal and rather depend on the potentials. Moreover, changes in the inter-particle potentials may reverse the behaviour to a normal one.     

Dynamics of supercooled liquids and understanding the glass transition

The self-consistent mode coupling theory of glass transition is briefly reviewed. The existance of a temperature T_c, higher than the usual calorimetric glass transition temperature, across which the dynamics of the fluid becomes quite different are indicated through different experimental results. Above T_c the viscosity tends to diverge with a power law while for lower temperature this sharp transition is cutoff. Such changes in the transport properties can be understood from the self-consistent mode coupling theory. The relaxation functions predicted by the mode-coupling theory over different time scales are indicated. The models with proper wave-vector dependence are also discussed.     

Tracer impurity diffusion in single-crystal rutile (TiO2−x)

By means of the radioactive-tracer sectioning technique, the tracer diffusion of the impurity ions, ⁴⁶Sc, ⁵¹Cr, ⁵⁴Mn, ⁵⁹Fe, ⁶⁰Co, ⁶³Ni and ⁹⁵Zr, in rutile single crystals was measured as functions of crystal orientation, temperature, oxygen partial pressure and Al impurity content. The diffusion coefficients are very sensitive to the electric charge of the impurity ions. Divalent impurities (e.g., Co and Ni) diffuse extremely rapidly in TiO₂, compared to cation self-diffusion, and exhibit an extreme anisotropy in diffusion behavior, divalent-impurity diffusion parallel to the c-axis is much larger than it is perpendicular to the c-axis. Trivalent impurity ions (Sc and Cr) and tetravalent impurity ions (Zr) diffuse similar to cation self-diffusion, both as functions of temperature and oxygen partial pressure. The divalent impurity ions Co and Ni apparently diffuse as interstitial ions along open channels parallel to the c-axis. The results suggest that Sc, Cr and Zr ions diffuse by an interstitialcy mechanism involving the simultaneous and cooperative migration of tetravalent interstitial titanium ions and the tracer-impurity ions. Iron ions diffuse both as divalent and as trivalent ions. The impurity diffusion as functions of oxygen partial pressure and Al-impurity content are consistent with calculations of point-defect concentrations in rutile.     

A statistical-mechanical theory of self-diffusion in glass-forming liquids

A statistical-mechanical theory of self-diffusion in glass-forming liquids is presented. A non-Markov linear Langevin equation is derived from a Newton equation by employing the Tokuyama-Mori projection operator method. The memory function is explicitly written in terms of the force-force correlation functions. The equations for the mean-square displacement, the mean-fourth displacement, and the non-Gaussian parameter are then formally derived. The present theory is applied to the glass transitions in the glass-forming liquids to discuss the crossover phenomena in the dynamics of a single particle from a short-time ballistic motion to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of analyses of the simulation results by the mean-field theory proposed recently by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that for times longer than the β-relaxation time the dynamics of a single particle is identical to that discussed in the suspensions.     

An existence of universality in the dynamics of two types of glass-forming liquids - fragile liquids and strong liquids

By employing a simplified nonlinear memory function proposed recently by the present author, a universal equation for a collective-intermediate scattering function derived based on the time-convolutionless mode-coupling theory is numerically solved to study the dynamics of glass-forming liquids. The numerical calculation is done based on the simulation results performed on two types of liquids, fragile liquids and strong liquids. Those are then shown to be uniquely determined by the long-time collective diffusion coefficient $D(q_m)$, where $q_m$ is a first peak position of a static structure factor for a whole system. Thus, there exists such a universality that there is only one solution for different liquids of a same type at a given value of D. This may be consistent with the fact that strong liquids are structurally quite different from fragile liquids. Finally, it is emphasized that such a universality must be helpful to predict $q_m$ from experimental data.     

Tracer diffusion of dimers on correlated heterogeneous surfaces

The diffusion of a single dimer adsorbed on highly correlated heterogeneous substrates is studied through Monte Carlo simulations. The topography has been characterized by patches of weak and strong adsorbing sites, arranged in a chessboard-like ordered structure. The time behavior of the mean-square displacement of the dimer is analyzed for different temperatures and patch size. Based on this analysis, a possible method for the characterization of the correlated heterogeneous topography from dimer diffusion measurements is discussed.     

Influence of a uniform driving force on tracer diffusion in a one-dimensional hard-core lattice gas

The influence of a uniform driving force on tracer diffusion is investigated for a one-dimensional lattice gas where particles jump stochastically to unoccupied neighboring sites. A new, simple calculation is presented for the diffusion coefficient of a tracer particle with respect to its average drift, obtained recently by rigorous methods by De Masi and Ferrari. A theoretical expression describing the tracer particle mean square displacement approximately for all times is derived and found to be in excellent agreement with the results of Monte Carlo simulations.     

Ionic liquids in external electric and electromagnetic fields: a molecular dynamics study

The non-thermal effects of external electric and electromagnetic fields in the microwave to far-infrared frequency range and at (r.m.s.) electric field intensities of 10^?3 to 0.25?V/Å_r.m.s. on neat salts of 1,3-dimethyl-imidazolium hexafluorophosphate ([dmim][PF₆]) and 1-butyl-3-methyl-imidazolium hexafluorophosphate ([bmim][PF₆]) have been investigated by means of non-equilibrium molecular dynamics simulation. Significant alterations in molecular mobility were found vis-à-vis zero-field conditions. Using Green–Kubo and transient time correlation function analysis, the electrical conductivity of these ionic liquids has been estimated. The results indicate that ionic liquids respond most significantly to frequencies much lower than those of smaller polar solvents such as water, although the mechanism of the field response is almost exclusively translational.     

Tracer diffusion in lattice gases

It has been proved that a tracer particle in a reversible lattice gas converges to Brownian motion. However, only in a few particular cases has a strictly positive self-diffusion coefficientD been established. Here we supply the missing piece and show thatD>0 in general. The exceptions are one-dimensional lattice gases with nearest neighbor jumps only, for whichD=0. The proof establishes a variational formula forD which could be used to obtain realistic bounds.     

Excluded volume effect on entropy and clustering behaviors in supercooled liquids and glasses

We study the significant entropy changes in supercooling and glass transition by developing a two (H and L) state cluster model, where the H-state represents the clusters with the coordination number z being larger than the reference size z_R and the L-state those with z<z_R, respectively. We exploit the excluded volume effect on the clustering behaviors of various glass-formers and the temperature dependence (at fixed pressure of 1 atmosphere) of the entropy difference between the two cluster states on the basis of , where as taken universally for all the glass-formers investigated. The temperature dependence of the average size 〈z_c^∗〉 of clusters with z≥z_R is then determined for some representative glass-formers, such as GeO₂, 1-propanol, glycerol, propylene carbonate, o-terphenyl, and so forth, covering the entire fragility spectrum studied experimentally. As a result, the temperature dependence of 〈z_c^∗〉 is found to highly depend on the fragility index ? associated with the temperature dependence of the excluded volume B^∗(?,T) of which statistical mechanical representation is given by the generic van der Waals equation of state. With decreasing T toward the glass transition temperature T_g, 〈z_c^∗〉 increases to attain universally about 13 at T_g regardless of the fragility and molecular details of the glass-formers. We specifically analyze in depth the theoretical predictions for the cluster sizes and the experimental estimations for the length scales associated with temporary clusters of slow segments in supercooled glycerol as about 1.4±0.5 nm for glycerol at 10 K above T_g. Given the large uncertainties associated with the experiment, the present theory appears to be in good agreement with the experiment.     

Application of a radioactive tracer method for diffusion study in some liquids

In this paper a radioactive tracer technique based on sliding cell method developed in our laboratory for the study of diffusion in liquids is presented in detail. This method consists of radioactive and non-radioactive liquid columns of equal length and the radiation detector is placed in a vertical geometry over the diffusion column. Some liquid metals and aqueous electrolyte solutions were studied by this method. The data of liquid metals like mercury and gallium have been analyzed from the point of view of hard sphere model and those of electrolyte solutions from phenomenological theories. Onsager’s coefficientsL ₁₁,L ₁₂,L ₂₂ have been calculated from the experimental data and the variation of diffusion with solute concentration has been explained from ion-ion interaction.     

The long time and Brownian limits for tagged particle motion in liquids

Formally exact theories of tagged particle motion in liquids are developed, based upon kinetic theory for hard spheres and mode coupling for smooth potentials. It is shown that the resulting equations are tractable in the long time and Brownian limits. The coefficient of the long time tail of the velocity correlation function is seen to differ from its low-density form by only the replacement of the low-density viscosity and diffusion constant by the true viscosity and diffusion constant. In the Brownian limit, the slip Stokes-Einstein law is obtained, with the true viscosity. The relation to other work is discussed.Supported by NSF Grant No. CHE81-11422 and by a Dreyfus Teacher-Scholar grant to TK.     

Aggregates in mixtures of ionic liquids

Surfactant-like ionic liquids (C₁₆MIMCl, C₁₆MIMBF₄) aggregate in mixtures with another ionic liquid (EAN). Critical aggregate concentrations and estimations of object sizes are given and compared to aqueous systems and other relevant literature data. The investigated mixtures are stable up to more than 200 °C and can probably be used to extend the limited temperature range of water-based colloids.     

The kinetics of diffusive phase transformations in the light of trans-interface diffusion

A variety of models with detailed coupling of thermodynamics and kinetics at a migrating interface has been developed for simulating diffusive phase transformations. A classification of such models is possible by the way the processes associated with the migrating interface are treated. In case of sharp interface models, the interfacial processes are assumed to be fast enough to not influence overall phase transformation kinetics (i.e. local equilibrium holds), or an effective mobility is attributed to the interface, which is also known as mixed-mode approach. In case of models treating an interface with finite thickness, the kinetic processes inside the interface are described in detail. In this work, a quasi-sharp interface model is analysed using the thermodynamic extremal principle. By this procedure, the implicit assumptions behind the modelling approach are revealed, and the evolution equations are derived. By means of a thick interface model, the contact conditions at both sides of a migrating interface are calculated, and the driving forces for interface migration and trans-interface diffusion are obtained. Based on these driving forces, the quasi-sharp interface model is evaluated and an effective interface diffusion coefficient is calculated.     

Sonochemistry in non-aqueous liquids

The chemical effects of high-intensity ultrasound on organic liquids are reported. In order to probe the factors which affect sonochemistry in non-aqueous solvents, two very different chemical dosimeters have been used: radical trapping by diphenylpicrylhydrazyl and decomposition of Fe(CO)₅. In both cases, good correlation is found between the logarithm of the sonochemical rate and the solvent vapour pressure. This result is justifiable in terms of the cavitation ‘hot-spot’ mechanism of sonochemistry. Thus, decreasing solvent vapour pressure increases the intensity of cavitational collapse, the peak temperature reached during such collapse, and, consequently, the rates of sonochemical reactions.     

Tracer diffusion in the presence of segregating obstacles

Tracer diffusion in an alloy in which the trajectories of one of the species is biased is examined as a model of mass transport with attendant segregation to extended defects (e.g., dynamic strain ageing, grain-boundary segregation). More specifically, we employ Monte Carlo simulation to describe the nonequilibrium diffusive behavior of the components of a two-dimensional lattice gas comprising A and B atoms wherein one of the species (B) interacts with randomly distributed line defects to create equilibrium atmospheres at late times. Various kinetic assumptions and defect densities are explored to highlight the role of B-atom mobility and defect interaction strength on the transport behavior of the A atoms. From the calculated instantaneous diffusivity, several diffusive regimes are then identified and related to evolving segregation profiles and, in particular, to the free area available for diffusion.