Lattice Gas Approach Research Articles

Large Fluctuations in Nonideal Coarse-Grained Systems.

Using the recently introduced molecular dynamics lattice gas approach, we test fluctuations of coarse-grained quantities. We show that as soon as the system can no longer be considered an ideal gas fluctuations fail to diminish upon coarse graining as is usually expected. These results suggest that current approaches to simulating fluctuating hydrodynamics may have to be augmented to achieve quantitative results for systems with a nonideal equation of state. The molecular dynamics lattice gas method gives a guidance to the exact nature of the fluctuation in such systems.

Reproducing micro X-ray computed tomography (microXCT) observations of air–water distribution in porous media using revised pore-morphology method

This study presents a novel and simple morphology approach to generate two-dimensional air–water distribution in porous media considering Or and Tuller’s cavitation mechanism (published in 2002). The connectedness condition for the nonwetting phase is replaced by the Laplace equation. An algorithm is developed to detect the ruptured water spaces that are incorrectly formed in the throat by the morphology approach, but cannot exist in a real thermodynamic equilibrium system. The distributions of soil moisture, water retention curve, and air–liquid interface area at different saturations predicted by this method are in a good quantitative agreement with the experimental observations on glass beads and Ottawa sand from micro X-raycomputed tomography (microXCT). Compared to Lu et al.’s Monte Carlo lattice-gas approach (published in 2010), another computational method to generate the soil moisture distribution, the proposed approach provides better results with significantly less computational power.

Surface tension of molecular liquids: Lattice gas approach

The approach of global isomorphism between the fluid and the Ising model is applied to obtain an expression for the surface tension of the Lennard-Jones fluid on the basis of the information about the Ising model. This is done in a broad interval of temperatures along the phase coexistence, and is valid both in a 2D and a 3D. The relation between the critical amplitudes of the surface tension of the fluid and the Ising model is derived in the vicinity of the critical point. The obtained theoretical estimates agree well with the literature results for the surface tension. The methodology is demonstrated for the 2D LJ fluid on the basis of the exact solution of the 2D Ising model and is tested for the 3D LJ fluid. As a result, an expression for the surface tension without any fitting parameter is derived.

Effects of smooth random surface on fluid monolayer thermodynamics

We consider the lattice gas approach to statistical mechanics of fluid adsorbed on random surfaces with fluid-fluid and fluid-surface potentials. It was shown that effective Hamiltonian contains quenched random interactions and random site fields. Their statistical features combine the properties of random geometry and fluid-fluid pair interaction potential. The high-temperature expansion leads to infinite-ranged random field model and Sherrington–Kirkpatrick spin-glass model. Thermodynamic properties are evaluated using replica theory procedure widely used to analyze quenched disorder systems. On the other hand we consider the random field model in random graph with finite connectivity instead of previous “infinite-ranged” approximations. This model has been investigated using finite connectivity technique. The replica symmetry ansatz for the order function is expressed in terms of an effective-field distribution. Analysis of random geometry effects on thermodynamic properties in such approach was done for the first time.

Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons

On a large class of lattices (such as the sawtooth chain, the kagome and the pyrochlore lattices), the quantum Heisenberg and the repulsive Hubbard models may host a completely dispersionless (flat) energy band in the single-particle spectrum. The flat-band states can be viewed as completely localized within a finite volume (trap) of the lattice and allow for construction of many-particle states, roughly speaking, by occupying the traps with particles. If the flat-band happens to be the lowest-energy one, the manifold of such many-body states will often determine the ground-state and low-temperature physics of the models at hand even in the presence of strong interactions. The localized nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system. As a result, the ground-state and low-temperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems. In this review, we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. The main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems, we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat-band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki–Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.

Modeling of a predator prey dynamic system with harvesting using the lattice gas approach

This paper uses the lattice gas model to incorporate spatial and stochastic elements in a prey-predator dynamic system. In this system, the habitat is partitioned in two adjacent patches, one of them being a prey reserve. The habitat is populated by two competing prey and a common predator. In the reserve, prey harvesting is prohibited. In the other patch, harvesting of one of the prey is allowed at a constant quota rate. The evolution of the system is investigated using local species interactions. The effect of different levels of constant quota harvesting are investigated using the lattice gas approach, first by the mean field approximation method and then by simulation. The system attains a stable equilibrium below a threshold constant harvest value on condition that the survival rate of the non-harvested prey exceeds that of the harvested prey. Furthermore, the predator biomass conversion rate for the non-harvested prey should be more than that for the harvested prey. If the aforementioned conditions are not met, the population of the harvested prey outside the reserve declines to extinction in finite time. This paper concludes that the maximum constant harvest level for stable species populations can be significantly increased by introducing harvesting for the non harvested prey. Key words: Prey, predator, constant quota harvest, lattice gas model.

Lattice Gas Model for H2 Adsorption in Nanoporous Zinc Hexacyanometallates

Zinc hexacyanometallates Zn3A2[M(CN)6]2 with different exchangeable alkaline cations A+ and framework transition metals M constitute an excellent model system to study H2 adsorption in nanoporous solids. A lattice gas approach, based on experimental data and simple considerations on the position and energies of adsorption sites, is proposed. Coverage and adsorption enthalpies are calculated and compared with experimental results. The interplay of three necessary conditions for H2 storage in porous solids—free volume to accommodate guest molecules, charge centers to bind them, and fast diffusion during adsorption or desorption—is discussed.

The importance of boundary effects in diffusion of hydrocarbon molecules in aone-dimensional zeolite channel

Single-file diffusion of propane and toluene molecules inside a narrow, effectivelyone-dimensional zeolite pore was experimentally studied by Czaplewski et al. Using astochastic lattice gas approach, we obtain an analytical description of this process for thecase of single-component loading. We show that a good quantitative agreement with theexperimental data for the desorption temperature of the hydrocarbon molecules can beobtained if the process of desorption from the boundary is associated with a higheractivation energy than the diffusion process in the bulk. We also present dynamical MonteCarlo simulation results for two-component loading which demonstrate in agreement withthe experimental findings the effects of mutual blockage of the molecules due to single-filediffusion.

Coarse-grained lattice models for drying-mediated self-assembly of nanoparticles

We present a coarse-grained lattice gas approach applicable for modelling the drying-mediated self-assembly of nanoparticles. The approach is exemplified for self-assembly of binary superlattices and for the hierarchical self-assembly of nanoparticles over patterned templates. The theory predicts many observed superstructures along with novel morphologies yet to be explored. The role of solvent evaporation, nanoparticle diffusion mechanisms, surface patterning, and the relevant time and length scales are discussed.

Quantum lattice gas approach for the Maxwell equations

We show that a quantum lattice gas approach can provide a viable means for numerically solving the classical Maxwell equations. By casting the Maxwell equations in Dirac form, the propagator may be discretized, and we describe how the accuracy relative to the time step may be systematically increased. The quantum lattice gas form of the discretization is suitable for implementation on hybrid classical-quantum computers. We discuss a number of extensions, including application to inhomogeneous media.

Connector model for describing many-body interactions at surfaces

First-principles calculations based on density-functional theory indicate that high-order many-body interactions are significant in Al clusters on Al(110) and Al(100). The large number of many-body interactions renders a full-lattice-gas approach ineffective for such systems. To simplify the description of adsorbate interactions, we utilize two different schemes. First, we find effective parameters for Al adatom interactions using the leave-one-out cross-validation method. Second, we propose the connector model, which is based on additive single-atom connector units. The central idea of the connector model is to combine groups of many-body interactions into important structural units (e.g., step edges) that have a single interaction energy. We find that the connector model is more accurate and efficient in representing high-order many-body interactions than the traditional lattice-gas approach and it may be suitable for describing a variety of surface phenomena such as thin-film and crystal growth, adsorption, phase transitions, and catalysis at surfaces.

Chemical short-range order and lattice deformations inMgyTi1−yHxthin films probed by hydrogenography

A multisite lattice gas approach is used to model pressure--optical-transmission isotherms (PTIs) recorded by hydrogenography on ${\mathrm{Mg}}_{y}{\mathrm{Ti}}_{1\ensuremath{-}y}{\mathrm{H}}_{x}$ sputtered thin films. The model reproduces the measured PTIs well and allows us to determine the chemical short-range order parameter $s$. The $s$ values are in good agreement with those determined from extended x-ray absorption fine structure measurements. Additionally, the PTI multisite modeling yields a parameter $L$ that accounts for the local lattice deformations with respect to the average ${\mathrm{Mg}}_{y}{\mathrm{Ti}}_{1\ensuremath{-}y}$ lattice given by Vegard's law. It is thus possible to extract two essential characteristics of a metastable alloy from hydrogenographic data.

A Computational Study of the Reconstruction of Amorphous Mesoporous Materials from Gas Adsorption Isotherms and Structure Factors via Evolutionary Optimization

A general method for the three-dimensional reconstruction of mesoporous materials by evolutionary optimization against target data is developed. The method is applied specifically in reconstruction of amorphous material models using gas adsorption data, structure factor data, or a combination of both. A recently introduced lattice-gas approach is used to model adsorption in these calculations, and a high-pass limited Fourier representation is used to facilitate evolution of large-scale structures during the optimization. Reconstructions are made of several material models which mimic real materials obtained either by phase separation and etching or by sol-gel processing. Analysis of the reconstructions provides considerable insight into the type and quantity of structural information probed by gas adsorption and small-angle scattering experiments. We find that reconstructions based only on structure factors tend to underestimate the mean pore size. We also find that in many cases excellent reconstructions can be obtained using only adsorption-branch data, and that in all cases reconstructions based jointly on both types of data are superior to those based only on one, suggesting that these measures contain "complementary" information. It is also found that in most cases the use of desorption data is not warranted, and that the use of adsorption data taken at many temperatures will not improve reconstructions. The reproducibility of the method is shown to be satisfactory. The method can be computationally expensive if gas adsorption data are used, but it is easily parallelized, and therefore results can still be obtained in reasonable time. Finally, the possible application of this approach to real systems, including templated porous materials, is discussed.

Theoretical description of the adsorption and the wetting behavior of alkanes on water

The wetting behavior of alkanes of medium chain length (e.g., pentane, hexane, and heptane) on water is more complex than the usually observed first-order wetting transition from partial to complete wetting by showing a sequence of two transitions. In this sequential-wetting scenario, a first-order transition from a microscopically thin to a mesoscopically thick layer of liquid on the substrate surface is followed by a continuous divergence of the film thickness upon increase of the temperature. This critical transition to complete wetting at T(w,c) is solely determined by long-range interactions between substrate and adsorbate, which are well-described by Dzyaloshinskii-Lifshitz-Pitaevskii [Adv. Phys. 10, 165 (1961)] theory in terms of the static dielectric constants and the refractive indices of the media involved. The first-order thin-thick transition, however, which occurs at a lower temperature T(w,1), results from an interplay of short-range and long-range forces and is notoriously more difficult to describe because a satisfactory theory of the short-range interactions between substrate and adsorbate is still missing. The approach presented in this paper attempts to account for the short-range interactions in an effective way: Within a Cahn-type [J. Chem. Phys. 66, 3667 (1977)] theory that has been augmented for long-range interactions and modified to treat the first layer of adsorbed molecules in a lattice-gas approach, the contact energy is deduced from the surface pressure, which in turn is calculated using a two-dimensional van der Waals equation of state and an expression for the Henry's law constant that was derived by Hirasaki [J. Adhes. Sci. Technol. 7, 285 (1993)]. The method uses only the dielectric properties of the isolated bulk media and simple assumptions on the size and the shape of the adsorbed alkane molecules and leads to satisfactory results for the transition temperatures T(w,1) and T(w,c).

Adsorption in Controlled-Pore Glasses: Comparison of Molecular Simulations with a Mean-Field Lattice Gas Model

We consider the possible quantitative application of a lattice-gas model approach to the calculation of adsorption isotherms. In order to validate such application, we use the lattice-gas approach to solve for the adsorption and desorption isotherms in model controlled-pore glasses that have previously been the subject of an extensive series of Grand Canonical Monte Carlo simulations. We find that the lattice-gas model augmented with longer-ranged interactions provides a quite good account of adsorption in some of these systems for appropriate choice of several system parameters, but that the quality of agreement depends on the pore size of the material.

A lattice gas approach to conduction in organic material

The current–voltage relationship of organic diodes that are used as organic lightemitting devices is reported. Charged molecules are created at the electrodes by anoxidation/reduction reaction. The charge moves across the material by an electron transfermechanism from a charged molecule to a neutral molecule. The charges are described by alattice gas because there is a low concentration of charges. The concentration of chargedmolecules at the electrode is governed by the Nernst equation and is coupled to theequations of transport. The concentration of charge is determined by a competitionbetween charge creation and charge transport. The applied voltage creates the charge atthe electrodes and causes charge transport. The graphical analysis results in thecharge density and current density as a function of the applied voltage and thedependence of the current density on both temperature and device thickness.

Adsorption of Pure Fluids in Activated Carbon with a Modified Lattice Gas Model

In this article we study the effects of adsorbed phase compression, lattice structure, and pore size distribution on the analysis of adsorption in microporous activated carbon. The lattice gas approach of Ono-Kondo is modified to account for the above effects. Data of nitrogen adsorption at 77 K onto a number of activated carbon samples are analyzed to investigate the pore filling pressure versus pore width, the packing effect, and the compression of the adsorbed phase. It is found that the PSDs obtained from this analysis are comparable to those obtained by the DFT method. The “discrete” nature of the PSDs derived from the modified lattice gas theory is due to the inherent assumption of discrete layers of molecules. Nevertheless, it does provide interesting information on the evolution of micropores during the activation process.

From Atomic Scale Ordering to Mesoscale Spatial Patterns in Surface Reactions: A Heterogeneous Coupled Lattice-Gas Simulation Approach

A current challenge in the modeling of surface reaction-diffusion systems is to connect the length scales from a realistic atomistic treatment of local ordering of adsorbed reactants and of reaction kinetics to an "exact" description of mesoscale spatial pattern formation. We discuss a heterogeneous coupled lattice-gas approach which utilizes parallel kinetic Monte Carlo simulations of lattice-gas models to simultaneously determine the local reaction kinetics and diffusive transport properties at various macroscopic "points" distributed across the surface. These simulations are periodically coupled to reflect macroscopic mass transport via surface diffusion. We place particular emphasis on the key issue of correctly describing the associated chemical or collective diffusion flux. This method is general, but it is discussed here only in the context of simple models for the bistable CO oxidation reaction on surfaces, where macroscopic mass transport involves only diffusion of adsorbed CO. Detailed analysis is presented for a canonical model of CO oxidation which incorporates nearest-neighbor exclusion between adsorbed oxygen, leading to superlattice ordering of this reactant. In this model, interactions of adsorbed CO with other adspecies are ignored. This reduces CO surface transport from a many-particle to a single-particle problem, although one with the complexity of "ant-in-the-labyrinth"-type percolative diffusion (the labyrinth being formed by coadsorbed oxygen).

From atomic scale reactant ordering to mesoscale reaction front propagation: CO oxidation on Pd(100)

We utilize a heterogeneous coupled lattice-gas (HCLG) approach to connect the length scales from a realistic atomistic description of surface reactions to the associated mesoscale spatiotemporal behavior. This method is applied to describe reaction front structure in a model for CO oxidation on Pd(100) which incorporates complex ordering of CO and O adlayers, and a precise treatment of the chemical diffusion for interacting CO adlayers in an environment of coadsorbed O.

A (reactive) lattice-gas approach to economic cycles

A microscopic approach to macroeconomic features is intended. A model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed. A birth–death lattice gas model taking into account the influence of an economic environment on the fitness and concentration evolution of economic entities is numerically and analytically examined. The reaction–diffusion model can also be mapped onto a high-order logistic map. The role of the selection pressure along various dynamics with entity diffusion on a square symmetry lattice has been studied by Monte–Carlo simulation. The model leads to a sort of phase transition for the fitness gap as a function of the selection pressure and to cycles. The control parameter is a (scalar) “business plan”. The business plan(s) allows for spin-offs or merging and enterprise survival evolution law(s), whence bifurcations, cycles and chaotic behavior.