Kinetic Lattice Gas Model Research Articles

Dynamical density functional approach to supercooled liquid and glass transition

Slow dynamics which shows up in supercooled liquid near the glass transition is discussed on the basis of the discretized version of the dynamical density functional equation which is the mesoscopic kinetic equation put forth recently in an attempt to go beyond the current mode-coupling theories. The discretization was realized through an appropriate mapping of the equation onto the kinetic lattice gas model in such a way that the master equation for the latter could approximately lead to the former upon coarse-graining of the spatio-temporal scales. The kinetic lattice gas model, which contains no ad hoc parameters except the direct correlation function of the reference liquid, is then solved for a hard-sphere liquid by using the ordinary Monte Carlo method to give successfully the thermally activated hopping process which is dominant at later times. Aspect of the free-energy landscape is also discussed.

Hopping Processes from Dynamical Density Functional Theory for a Deeply Supercooled Hard-Sphere Liquid

Through the mapping onto the kinetic lattice gas model the dynamical density functional equation is solved by the Monte Carlo method in a deeply supercooled hard-sphere liquid, while focusing on how the system explores the free-energy landscape during a relaxation process. A variety of metastable states appear as the supercooling proceeds beyond the equilibrium crystallization point. Our approach is the first to reproduce the hopping transitions among these states as a solution of a mesoscopic kinetic equation.

Early Stage of Slow Dynamics in Dynamical Density Functional Theory of a Hard-Sphere Liquid near the Glass Transition

The dynamical density functional equation put forth recently in an attempt to go beyond the current mode coupling theories of supercooled liquid and glass transitions is solved by mapping to the kinetic lattice gas model. Analyses of the dynamic structure factor in the initial stage of freezing reveal that the equation correctly captures the mode coupling mechanism of density fluctuations.

Kinetic model for a spontaneous islanding during ultra-high vacuum deposition

A self-consistent kinetic lattice gas model for surface morphological transformation during ultra-high vacuum deposition (UHVD) at submonolayer coverage is studied. The possibility for the formation of stable arrays of self-assembled nanostructures is shown. Within a range of parameters, islands have very narrow size distribution and are arranged in a periodic lattice.

Non-equilibrium effects on thermal desorption spectra

Using dynamical Monte Carlo simulations, we explore a kinetic lattice-gas model to investigate unimolecular thermal desorption of non-equilibrated adsorbates. We compare our simulation results under non-equilibrium conditions (either finite or zero hopping rate) with those under quasi-equilibrium conditions. The differences between the observed kinetic behavior in the non-equilibrium and quasi-equilibrium cases are elucidated quantitatively by considering correlations with various configurational distributions of adsorbates.

Sticking and thermal desorption of O2 on Ag(001)

The coverage dependence of the sticking coefficient and temperature programmed desorption kinetics for molecular adsorption of oxygen on Ag(001) are investigated both experimentally and theoretically. The nearly exponential decrease of the sticking coefficient as a function of coverage by about five orders of magnitude is explained within a kinetic lattice gas model to be the result of strong nearest- and next-nearest-neighbor repulsions. The latter also shape the desorption spectra which are calculated within the same model under the assumption that fast surface diffusion maintains the adsorbate in quasiequilibrium during desorption. Because the desorption rate is proportional to the sticking coefficient under these conditions, we find a massive decrease of the pre-exponential factor in the Arrhenius parametrization of the rate as a function of coverage which explains the peculiar shape of the desorption spectra.

Theory of sticking: The effect of lateral interactions

A generalization of the kinetic lattice gas model is used to study the coverage and temperature dependence of the sticking coefficient due to intrinsic and extrinsic precursors and in the presence of lateral interactions.

Slow dynamics in condensed matter: spinodal decomposition and glass transition

A brief review is presented about our recent work on computer studies of a continuum model describing spinodal decomposition of binary fluid, which quantitatively accounts for corresponding experimental results. We then switch over to discussing problems of glass transitions. First we consider the ultraslow mode observed in fragile glass-formers, where the diffusive behavior of this mode is explained in terms of phase dynamics describing slow relaxation of spatial heterogeneous structure resulting from spontaneous break-down of continuous translational symmetry. Next we present a stochastic model for density fluctuation in supercooled liquids, which is mapped onto a certain kinetic lattice gas model which is convenient for Monte Carlo simulation studies.

Temperature programmed desorption from the Si(100):Br and Si(100):D/Br surfaces: theory and experiment

New experimental temperature programmed desorption (TPD) data have been obtained under carefully controlled UHV conditions following the adsorption of bromine and the co-adsorption of bromine and atomic deuterium on the single crystal Si(100): 2 × 1 surface. Coverages ranged from maxima of θ = 1.5 ML (atomic deuterium alone) and 1.0 ML (atomic bromine alone) and included a wide combination of the two co-adsorbed species down to a lower limit of 0.05 ML atomic deuterium and 0.2 ML atomic bromine. When bromine alone was absorbed at surface temperatures of 380 ± 10 K, the only observed TPD product was silicon dibromide. When the total coverage of bromine and deuterium atoms was high (≳ 1 ML), the TPD data were much more complex and as well as showing the usual ß 1 and ß 2 desorption peaks of deuterium, analogous peaks for DBr were also observed together with the above-mentioned SiBr 2 peak. The data have been interpreted using a kinetic lattice-gas model which describes the atomic bromine and deuterium co-adsorbed on the surface in terms of nine basic units: dideuteride (SiD 2), doubly occupied dimers (DSiSiD), singly occupied dimers (SiSiD), unoccupied dimers (SiSi) together with the analogous bromine substituted and mixed deuterium-bromine species. Using a quasi-equilibrium approximation and including up to five competing desorption pathways corresponding to the product peaks observed, the TPD spectra for deuterium, deuterium bromide and silicon dibromide are determined and compared with the observed experimental data. By fitting the simulated data to the experimental curves it was shown that both ß 1 desorption processes and desorption of SiBr 2 were consistent with first order kinetic behaviour. On the other hand both ß 2 processes were found to obey second order kinetics. The frequency factors for the first-order processes were determined as 1 × 10 15s −1 (D 2 and DBr) and 2 × 10 15s −1 (SiBr 2) with the corresponding activation energies being 57.5 kcal mol −1 (D 2), 61 kcal mol −1 (DBr) and 61 kcal mol −1 (SiBr 2). For the second-order processes, the frequency factors (expressed in first-order units) were found to be 2 × 10 15s −1 (for both D 2 and DBr) with the activation energies being 45 kcal mol −1 (D 2) and 49 kcal mol −1 (DBr).

Theoretical and simulation studies of recombinative temperature programmed desorption

Using Monte Carlo simulations and both quasichemical (for nearest neighbors) and mean field (for next-nearest neighbors) approximations, we explore a kinetic lattice gas model to investigate recombinative thermal desorption. A previously introduced Monte Carlo algorithm, which correctly relates Monte Carlo simulation time and real time, is extended in order to quantify the kinetics and energetics of recombinative thermal desorption spectra. We consider the effects of lateral interactions between adsorbates, lattice geometry, and limited mobility of the adsorbate (nonequilibrium) on the temperature programmed desorption spectra. Furthermore, we analyze the apparent coverage dependence of both the activation energy and the preexponential factor of the desorption rate coefficient for both repulsive and attractive nearest-neighbor interactions on a square lattice. For a repulsive nearest-neighbor interaction, we find that kinetic compensation occurs for a surface coverage less than 0.6. However, for surface coverages greater than 0.6, we find that the activation energy and preexponential factor do not vary sympathetically. For an attractive nearest-neighbor interaction, kinetic compensation is only observed at high coverage. We elucidate the compensation effect quantitatively by considering the configurational distribution of adsorbates.

Oscillating hydrogen-water reactions on a platinum field emitter

The spatial and temporal behavior of surface reaction-diffusion-fronts has been examined during oscillating H 2 H 2O reactions on a Pt field ion emitter. Mass and energy resolved measurements, discriminating between different reaction pathways, have been made of local yields of ions such as H 3O + and H 3O + · H 2O. Periodic out-bursts of ion yields correlate with the passage of wave fronts across the emitter apex imaged by field ion microscopy. The experimental observations together with the predictions of a kinetic lattice gas model suggest that the supply of hydrogen, primarily by surface diffusion from the emitter shank plays a vital role.

A kinetic lattice-gas model for the triangular lattice with strong dynamic correlations. I. Self-diffusion

Self-diffusion in a lattice-gas model with two-vacancy assisted hopping on the triangular lattice is investigated, by both Monte Carlo simulation and analytical calculation. A very rapid decrease of the tracer-correlation factor and marked size effects in finite lattices give evidence for strong dynamic correlations in both space and time at high particle concentration. Although the decrease of the self-diffusion coefficient over 3.5 decades for concentrations up to c=0.77 is best fitted by a power law (0.835-c)3.54, it is argued that the model does not have a sharp dynamical phase transition with a critical concentration lower than one. The argument is based on a proof of absence of permanently blocked particles in infinite lattices at all concentrations below one. The self-diffusion coefficient is calculated analytically within a pair approximation which gives good results for lower concentrations, but fails at the higher concentrations. The approximation is in qualitative agreement with the Monte Carlo data for the tracer-correlation factor at all concentrations for a variant of the model with one-vacancy assisted hopping, in which the dynamic correlations are less pronounced.

A kinetic lattice-gas model for the triangular lattice with strong dynamic correlations. II. Collective diffusion

The density-density correlation function and the site-occupation autocorrelation function are calculated for the lattice-gas model with two-vacancy assisted hopping on the triangular lattice, by both Monte Carlo simulation and analytical approximations. The non-exponential time dependence of the density-density correlation function for short wavelengths and high concentrations is explained by the strong spatial inhomogeneity of the collective diffusion process. The coefficient of collective diffusion decreases very rapidly at the highest concentrations, similarly to the self-diffusion coefficient. The analytical calculations for a two-variable approximation and a mode-coupling approximation give good results for lower concentrations. At higher concentrations the mode-coupling approximation is unstable, leading to a diverging rather than decaying correlation function for concentrations higher than 0.34.

Kinetic lattice-gas model of cage effects in high-density liquids and a test of mode-coupling theory of the ideal-glass transition

We have devised a kinetic lattice-gas model of an atomic liquid that incorporates the physical features associated with the formation of cages around a particle at high density. The model has simple equilibrium statistics, with a maximum of one particle per lattice site, and simple dynamical rules, so that it is feasible to perform dynamical calculations of the fluctuations about equilibrium over very long time scales. The cages inhibit the motion of the particles and cause the self-diffusion coefficient to fall rapidly with increasing density. Simulation results indicate that as the density \ensuremath{\rho}, defined as the number of particles per lattice site, approaches 0.881, the self-diffusion constant behaves in a critical way as (0.881-\ensuremath{\rho}${)}^{3.2}$. The time dependence of density-density correlation functions is calculated from the simulation results, and relaxation times extracted from these functions show a similar critical behavior. These results suggest that the model undergoes a dynamical transition from ergodic to nonergodic behavior. By investigating different system sizes we exclude the possibility that the observed transition is just a finite-size effect related to the bootstrap percolation problem. The mode-coupling theory (MCT) of ergodic-nonergodic transitions in the absence of activated hopping processes is tested for this model by comparing the behavior of the density correlation functions with the predictions of MCT. Surprisingly few of the MCT predictions hold for the system, depsite the fact that the model was devised to incorporate, in a schematic way, the dynamical cage effects that the MCT is usually regarded as describing. Thus the MCT does not provide a correct description of the cage-induced ideal-glass transition of this model.

Temperature programmed desorption of molecular hydrogen from a Si(100)-2×1 surface: Theory and experiment

New experimental temperature programmed desorption (TPD) data have been obtained under carefully controlled conditions for atomic deuterium on the single crystal Si(100)-2×1 surface. A wide range of coverages from Θ=1.5 to 0.05 ML was used. A kinetic lattice-gas model has been developed which describes atomic hydrogen (or deuterium) adsorbed on the Si(100)-2×1 surface in terms of four basic units: dihydride (SiH2), doubly occupied dimers (H–Si–Si–H), singly occupied dimers (Si–SiH), and unoccupied dimers (Si=Si). The equilibria between these species have been determined by considering both the lattice partition functions and the vibrational partition functions associated with the Si–H bonds. By using a quasiequilibrium approximation and two competing desorption routes corresponding to formation of the β1 and β2 peaks, the TPD spectra for hydrogen (deuterium) molecules are determined and compared with the new experimental data. Fitting the experimental curves with the simulated data from the aforementioned model showed that the desorption process which leads to the β1 peak obeys first-order kinetics with an A factor of 2×1015 s−1 and activation energy of 57 kcal mole−1, whereas the process giving the β2 peak follows second-order kinetics with an activation energy of 47 kcal mole−1 and an A factor (expressed in 1st order units) of 3×1015 s−1.

Kinetic lattice gas model in one dimension: I. Canonical approach

A closure approximation for the one-dimensional kinetic lattice gas model is formulated to truncate the hierarchy of equations of motion for correlation functions. Essentially exact results are obtained both for the equilibrium properties and the time evolution of the adsorbate when up to five-site correlation functions are included. Implications for thermal desorption in systems with slow and fast diffusion are studied for nearest-neighbor interactions.

Kinetic lattice gas model in one dimension : I. Canonical approach

Kinetic lattice gas model in one dimension : I. Canonical approach

Dynamics of multilayer adsorption: a Monte Carlo simulation

The growth of an adsorbed film at an initially empty surface which is exposed at time t = 0 to a gas is studied within the framework of a kinetic lattice gas model by Monte Carlo simulation. The model includes an attractive potential V( z) between adsorbed particles at distance z from the surface, V(z) = −A z 3 and a nearest-neighbor attractive interaction between the gas atoms. Several choices of the surface potential depth A, corresponding to different sequence of layering transitions, are considered. The Monte Carlo process assumes random evaporation/condensation events of gas atoms in adsorbed layers close to the surface, while surface diffusion is disregarded. For temperatures T somewhat less than the interfacial roughening temperature T R of the considered lattice gas model, the time-dependent coverage θ( t) exhibits distinct steps, representing the adsorption of the first, second, third, etc. layer. This layerwise adsorption kinetics also shows up in the surface excess energy due to the adsorbed layer. At temperatures far below T R, pronounced metastability of the empty surface as well as hysteresis is observed. On the other hand, for T > T R a smooth increase of coverage with time is observed, corresponding to wetting behavior rather than layering. We relate this behavior to the corresponding phase diagrams of the model and briefly discuss pertinent experimental applications.

Kinetic lattice gas model: a systematic closure approximation

A systematic closure approximation for the kinetic lattice gas model is formulated that allows one to truncate the hierarchy of equations of motion for correlation functions at any level. In equilibrium, the quasi-chemical approximation and an improved version of Hill's approximation are recovered at the two lowest levels. Implications for thermal desorption in systems with slow and fast diffusion are studied for a square lattice with nearest-neighbor repulsive interactions.

Kinetic lattice gas model: a systematic closure approximation

Kinetic lattice gas model: a systematic closure approximation