Stochastic simulation of catalytic surface reactions in the fast diffusion limit

The master equation of a lattice gas reaction tracks the probability of visiting all spatial configurations. The large number of unique spatial configurations on a lattice renders master equation simulations infeasible for even small lattices. In this work, a reduced master equation is derived for the probability distribution of the coverages in the infinite diffusion limit. This derivation justifies the widely used assumption that the adlayer is in equilibrium for the current coverages and temperature when all reactants are highly mobile. Given the reduced master equation, two novel and efficient simulation methods of lattice gas reactions in the infinite diffusion limit are derived. The first method involves solving the reduced master equation directly for small lattices, which is intractable in configuration space. The second method involves reducing the master equation further in the large lattice limit to a set of differential equations that tracks only the species coverages. Solution of the reduced master equation and differential equations requires information that can be obtained through short, diffusion-only kinetic Monte Carlo simulation runs at each coverage. These simulations need to be run only once because the data can be stored and used for simulations with any set of kinetic parameters, gas-phase concentrations, and initial conditions. An idealized CO oxidation reaction mechanism with strong lateral interactions is used as an example system for demonstrating the reduced master equation and deterministic simulation techniques.     

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.     

Incorporation of inhomogeneous ion diffusion coefficients into kinetic lattice grand canonical monte carlo simulations and application to ion current calculations in a simple model ion channel

To deal with inhomogeneous diffusion coefficients of ions without altering the lattice spacing in the kinetic lattice grand canonical Monte Carlo (KLGCMC) simulation, an algorithm that incorporates diffusion coefficient variation into move probabilities is proposed and implemented into KLGCMC calculations. Using this algorithm, the KLGCMC simulation method is applied to the calculation of ion currents in a simple model ion channel system. Comparisons of ion currents and ion concentrations from these simulations with Poisson-Nernst-Planck (PNP) results show good agreement between the two methods for parameters where the latter method is expected to be accurate.     

On the coupling between slow diffusion transport and barrier crossing in nucleation

We model the coupling between slow diffusion transport and nucleation using the diffusion equation, an Ostwald-Freundlich boundary condition, and a mass balance linking nucleus size to flux across the nucleus-solution interface. The model retains some characteristics of the classical nucleation theory because of the common theoretical foundations behind classical nucleation theory and the Ostwald-Freundlich equation. For example, the classically critical-sized nucleus in the uniform supersaturated concentration field is an unstable equilibrium point. However, the model also shows that certain types of concentration profiles can drive a classically pre-critical nucleus over the nucleation barrier. We identify the separatrix as a function of both nucleus size and characteristics of the local concentration field. Our analysis may be useful for understanding the effects of local concentration fluctuations and especially for understanding the role of dense precursor particles in driving two-step nucleation processes. Our analysis may also provide a starting point for further statistical field theory analyses of local concentration fluctuations and their effects on nucleation rates.     

Determination of the diffusion coefficients from sintering data of ultrafine oxide particles

Many kinetic equations derived from a simple geometrical model can account for the shrinkage rate of pellets of particles. Nevertheless, even when a kinetic equation is followed the calculation of the apparent diffusion coefficient may not be meaningful if the system under study and the theoretical model does not fit closely. This is shown by the experimental results on sintering of fine particles of anatase and alumina. When the system closely fits the model, the predicted sintering equation is observed and the calculated diffusion coefficients are close to the cation diffusion coefficients. But when the system (polyhedral particles) does not fit the model, an apparent agreement is found between the experimental results and the theoretical law corresponding to an unrelated model so that the calculated diffusion coefficient is meaningless.     

Molecular-dynamics analysis of the diffusion of molecular hydrogen in all-silica sodalite

In order to investigate the technical feasibility of crystalline porous silicates as hydrogen storage materials, the self-diffusion of molecular hydrogen in all-silica sodalite is modeled using large-scale classical molecular-dynamics simulations employing full lattice flexibility. In the temperature range of 700-1200 K, the diffusion coefficient is found to range from 1.610(-10) to 1.810(-9) m(2)/s. The energy barrier for hydrogen diffusion is determined from the simulations allowing the application of transition state theory, which, together with the finding that the pre-exponential factor in the Arrhenius-type equation for the hopping rate is temperature-independent, enables extrapolation of our results to lower temperatures. Estimates based on mass penetration theory calculations indicate a promising hydrogen uptake rate at 573 K.     

Lateral diffusion of proteins in the plasma membrane: spatial tessellation and percolation theory

The obstructed diffusion of proteins in the plasma membrane is studied using computer simulation and an analysis using spatial tessellation and percolation theory. The membrane is modeled as a two-dimensional space with fixed hard disc obstacles, and the proteins are modeled as hard discs. The simulations show a transition from normal to anomalous diffusion as the area fraction, phim, of obstacles is increased and to confined diffusion for area fractions above the pecolation threshold, which occurs for phim=0.22. A Voronoi tessellation procedure is used to map the continuous space system onto an effective lattice model, with the connectivity of bonds determined from a geometric criterion. The estimate of the percolation threshold obtained from this lattice model is in excellent agreement with the simulation results, although the nature of the dynamics in the continuous space model is different from lattice models. At high obstacle area fractions (but below the percolation threshold), the primary mode of transport is a hopping motion between voids, consistent with experiment. The simulations and analysis emphasize the importance of structural correlations between obstacles.     

Sorption and diffusion of oxygen in plasticized ethyl cellulose films of varying degrees of substitution

Plasticized films cast from ethyl cellulose were examined to evaluate the effect of the degree of substitution, DS, and the plasticizer content on the sorption and diffusion of oxygen. Sorption and permeation measurements were performed over a temperature range of 25–65°C on three different types of ethyl cellulose in the DS range 1.7–2.5 that had been plasticized with organic esters of comparatively low molecular weight. Sorption coefficients were determined by the pressure decay method, and permeability coefficients were measured independently according to ASTM D-1434-66. The diffusion coefficients were calculated assuming Fickian transport, and were compared to the values directly obtained from the evaluation of the sorption kinetics. The permeability coefficient indicates that there is a significant improvement of the barrier properties of the materials when the DS is reduced and when the plasticizer content is at the absolute minimum required. It was found that the variation in the magnitude of the permeability coefficient is related to the value of the diffusion coefficient, which is governed by the chemical composition of the mixtures. In contrast, the solubility of oxygen was determined by the physical state of the polymer matrix and increased rapidly at temperatures significantly below the glass transition temperature. Using an ergodic model, the diffusion coefficients obtained were related to the size distribution of microvoids in the materials and relative values for the diffusion coefficient were computed as a function of DS and temperature. The model calculates the concentration (number per volume) of voids that are large enough to be occupied by a penetrant molecule. It was assumed that the unoccupied volume fraction as a function of the cohesive energy density follows a Boltzmann distribution. The cohesive energy density and the unoccupied volume fraction of the polymer-plasticizer mixtures were calculated by fitting the Simha-Somcynsky equation of state to pressure-volume-temperature data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 639–653, 1997     

The effect of matrix structure on the diffusion of fluids in porous media

The effect of matrix structure on the transport properties of adsorbed fluids is studied using computer simulations and percolation theory. The model system consists of a fluid of hard spheres diffusing in a matrix of hard spheres fixed in space. Three different arrangements of the fixed spheres, random, templated, and polymeric, are investigated. For a given matrix volume fraction the diffusion coefficient of the fluid, D, is sensitive to the manner in which the matrix is constructed, with large differences between the three types of matrices. The matrix is mapped onto an effective lattice composed of vertices and bonds using a Voronoi tessellation method where the connectivity of bonds is determined using a geometric criterion, i.e., a bond is connected if a fluid particle can pass directly between the two pores the bond connects, and disconnected otherwise. The percolation threshold is then determined from the connectivity of the bonds. D displays universal scaling behavior in the reduced volume fraction, i.e., D approximately (1-phi(m)phi(c))(gamma), where phi(m) is the matrix volume fraction and phi(c) is the matrix volume fraction at the percolation threshold. We find that gamma approximately 2.2, independent of matrix type, which is different from the result gamma approximately 1.53 for diffusion in lattice models, but similar to that for conduction in Swiss cheese models. Lattice simulations with biased hopping probabilities are consistent with the continuous-space simulations, and this shows that the universal behavior of diffusion is sensitive to details of local dynamics.     

Testing predictions of macroscopic binary diffusion coefficients using lattice models with site heterogeneity

Quantitatively predicting mass transport rates for chemical mixtures in porous materials is important in applications of materials such as adsorbents, membranes, and catalysts. Because directly assessing mixture transport experimentally is challenging, theoretical models that can predict mixture diffusion coefficients using only single-component information would have many uses. One such model was proposed by Skoulidas, Sholl, and Krishna (Langmuir, 2003, 19, 7977), and applications of this model to a variety of chemical mixtures in nanoporous materials have yielded promising results. In this paper, the accuracy of this model for predicting mixture diffusion coefficients in materials that exhibit a heterogeneous distribution of local binding energies is examined. To examine this issue, single-component and binary mixture diffusion coefficients are computed using kinetic Monte Carlo for a two-dimensional lattice model over a wide range of lattice occupancies and compositions. The approach suggested by Skoulidas, Sholl, and Krishna is found to be accurate in situations where the spatial distribution of binding site energies is relatively homogeneous, but is considerably less accurate for strongly heterogeneous energy distributions.     

Diffusion of chain molecules and mixtures in carbon nanotubes: the effect of host lattice flexibility and theory of diffusion in the Knudsen regime

A novel algorithm for modeling the influence of the host lattice flexibility in molecular dynamics simulations is extended to chain-like molecules and mixtures. This technique, based on a Lowe-Andersen thermostat, maintains the advantages of both simplicity and efficiency. The same diffusivities and other properties of the flexible framework system are reproduced. Advantageously, the computationally demanding flexible host lattice simulations can be avoided. Using this methodology we study the influence of flexibility on diffusion of n-alkanes inside single-walled carbon nanotubes. Furthermore, results are shown for diffusion of two mixtures (methane-helium and ethane-butane). Using these results we investigate the accuracy of theories describing diffusion in the Knudsen regime. For the dynamics in carbon nanotubes the Knudsen diffusivities are much too low. The Smoluchowski model gives better results. Interestingly, the extended Smoluchowski model can reproduce our simulation results obtained with a rigid host lattice. We modify this model to also treat collisions with a flexible interface correctly. As the tangential momentum accommodation coefficient is needed for the theoretical models, we introduce a simple concept to calculate it.     

环己烷在聚乙烯和聚异丁烯中无限稀释扩散系数 的测定

采用填充柱的反相气相色谱方法,基于Hadj-Romdhane-Danner色谱过程的数学模型,在323.2～363.2K温度范围内测定了环己烷在聚异丁烯和聚乙烯膜中的无限稀释扩散系数。从实验数据可以看出,环己烷更容易在PIB中发生扩散。对实测扩散数据进行了自由体积理论关联,结果表明,采用空穴自由体积替代Vrentas-Duda自由体积理论方程中自由体积项的修正方程能很好地描述溶剂分子扩散系数随温度的变化关系。     

Sorption/diffusion behaviour of anionic surfactants in polyacrylamide hydrogels: from experiment to modelling

The sorption and diffusion processes of anionic surfactants with different chain length through polyacrylamide hydrogels with low swelling degree have been studied by electrical conductivity measurements. The multicomponent equilibrium equation has been used to model the sorption isotherms of different anionic surfactant in the hydrogels. Such isotherms show that initial rapid sorption of unimer surfactant into the membranes occurs, suggesting that non-freezing water can be involved in these interactions. In aqueous solution, at concentrations near and above the critical micelle concentration an anti-co-operative region is found. The diffusion coefficients of the anionic surfactants inside the hydrogel matrix show that the mobility of diffusing surfactant entities is dependent on cross-linker concentration and chain length. The Cukier hydrodynamic model and the free volume theory as modified by Peppas and Reinhart were applied to explain the dependence of the diffusion coefficients of surfactant on surfactant concentration inside the hydrogel. The hydrodynamic model was applied with success to the more hydrophilic surfactant, sodium 1-octanesulfonate, showing that the diffusion coefficients, D, increase when the resistance to hydrodynamic medium decreases; when the surfactant chain length increases (sodium dodecyl sulfate and sodium 1-hexadecane sulphonate) the variation of D with the free volume can only be understood considering the sieving effect produced by the surfactant inside gel.     

The temperature dependence of nematic liquid crystalline polymer melt diffusion

Polymer chain diffusion in the nematic mesophase was studied using a model main chain liquid crystalline (LC) polyether based on 2,2'-dimethyl-4,4'-dihydroxyazoxybenzene and mixed alkane spacers. A side chain LC polymethacrylate containing an azobenzene mesogenic group was also investigated. Tracer diffusion coefficients were determined as a function of temperature by an ion-beam depth profiling technique, forward recoil spectrometry. The results confirm that main chain LC polymer chain dynamics are dramatically affected by phase transitions and sample geometry. This behaviour is in marked contrast to the side chain LC polymer which exhibited no phase dependence on the part of the tracer diffusion coefficient.     

Lattice density functional theory of molecular diffusion

A density functional theory of diffusion is developed for lattice fluids with molecular flux as a functional of the density distribution. The formalism coincides exactly with the generalized Ono-Kondo density functional theory when there is no gradient of chemical potential, i.e., at equilibrium. Away from equilibrium, it gives Fick's first law in the absence of a potential energy gradient, and it departs from Fickian behavior consistently with the Maxwell-Stefan formulation. The theory is applied to model a nanopore, predicting nonequilibrium phase transitions and the role of surface diffusion in the transport of capillary condensate.     

Study of diffusion of alkali metals and ammonium chlorides through nanofiltration membrane with selective layer

The diffusion of alkali metals and ammonium chlorides through an OPMN-KM3 composite nanofiltration membrane is studied as a function of the electrolyte concentration on both sides of the membrane. A model is proposed for calculating diffusion coefficients that takes into account changes in the electrolyte concentration in selective pores of membrane. The diffusion coefficients are calculated both using the proposed model and by Fick’s equation. The effect of the orientation of the membrane with respect to the diffusion flux on the diffusion coefficients of salts is analyzed.     

The temperature dependence of nematic liquid crystalline polymer melt diffusion

Abstract

Polymer chain diffusion in the nematic mesophase was studied using a model main chain liquid crystalline (LC) polyether based on 2,2′-dimethyl-4,4′-dihydroxyazoxybenzene and mixed alkane spacers. A side chain LC polymethacrylate containing an azobenzene mesogenic group was also investigated. Tracer diffusion coefficients were determined as a function of temperature by an ion-beam depth profiling technique, forward recoil spectrometry. The results confirm that main chain LC polymer chain dynamics are dramatically affected by phase transitions and sample geometry. This behaviour is in marked contrast to the side chain LC polymer which exhibited no phase dependence on the part of the tracer diffusion coefficient.     

Self‐diffusion of small molecules into rubbery polymers: A lattice free‐volume theory

In the framework of the free‐volume (FV) theory, a new equation was derived for the evaluation of self‐diffusion coefficients of small molecules in polymers above the mixture glass transition temperature. The derivation of the equation turned out to be straightforward once the equivalence between the free volume and the unoccupied volume given by thermodynamic lattice theories is assumed. A parameter evaluation scheme is proposed, which is substantially simpler compared with the conventional Vrentas–Duda approach, even without losing generality. The key assumption is discussed, and its consistency is verified from a numerical viewpoint. A comparison with experimental solvent self‐diffusion coefficients for several solvent/polymer binary systems confirmed that the proposed theory presents good correlative ability over wide temperature and composition ranges. Moreover, the introduced thermodynamic foundation allows one to easily include the pressure effect too. In the frame of the proposed lattice free volume theory, the sizes of the polymer jumping units decrease with temperature and increase with pressure. Such behavior converges with theoretical expectations and opens the way for a predictive FV theory. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 529–540, 2010     

Correlation of the mutual diffusion coefficients of binary liquid mixtures

A correlative UNIDIF model for the mutual diffusion coefficients of binary liquid mixtures is developed using statistical thermodynamics and the absolute reaction rate theory. In this model, a mole fraction average of the logarithm of the pure-component limiting diffusion coefficients is taken as a reference term. The model expresses the excess part of the diffusion coefficient relative to this reference term in a form similar to that of a UNIQUAC equation which comprises two parts due to the combinatorial and residual contributions. The combinatorial part depends on the molecular sizes and shapes. The residual part includes two binary interaction parameters, which are obtained from data regression, for each binary mixture. Mutual diffusion coefficients of nonpolar+nonpolar, nonpolar+polar and polar+polar fluid mixtures are correlated in this study. Optimal binary interaction parameters are presented. Correlation results using the UNIDIF model for mutual diffusion coefficient are satisfactory and are superior to those from other methods.