Diffusion and vibrational relaxation of a diatomic molecule in the pore network of a pure silica zeolite: a molecular dynamics study

The vibrational relaxation and the diffusion of diatomic molecules in the zeolite silicalite have been studied through molecular dynamics simulations in the microcanonical statistical ensemble. The adopted model accounts for the vibrations of the framework and sorbed atoms using a harmonic potential for the silicalite and a Morse potential for the diatomic molecule. The results show that the framework favors the relaxation of diatomics oscillating at frequencies near to its characteristic vibrational frequencies, leading in such cases to lower relaxation times and to an increasing in the energy exchanged per collision. The diffusion of a two-site oscillating molecule representing ethane has been also investigated; the diffusion coefficient and the heat of adsorption agree very well with the experimental data. Arrhenius parameters for the diffusion have been calculated, and some insights into the diffusion mechanism have been obtained from log–log plots and by inspection of the distribution of the ethane molecules in the silicalite channels. Therefore the simplified model adopted seems to adequately describe the diffusive motion and the guest–host energy exchanges, and it could be useful in order to study simple bimolecular reactions in zeolites

Molecular dynamics simulation of an activated transfer reaction in zeolites

The activated transfer of a light particle between two heavier species in the micropores of silicalite and ZK4 zeolites has been studied through molecular dynamics (MD) simulations. A three-body potential controls the exchange of the light particle between the heavier ones; an effective barrier of a few kBT separates the two stable regions corresponding to symmetric "reactant" and "product" species. Harmonic forces always retain the reactants at favorable distances so that in principle only the energetic requirement must be fulfilled for the transfer to occur. The rate constant for the process (obtained from a correlation analysis of equilibrium MD trajectories) decreases by more than one order of magnitude when the barrier height is increased from 2kBT to 5kBT following an Arrhenius-type behavior. The transfer rates are always lower in ZK4. When the reaction is studied in a liquid solvent the calculated rate constants are closer to those obtained in silicalite. Since with this model the diffusive approach of the reactants is almost irrelevant on the reactive dynamics, only the different ability of each environment to transfer the appropriate energy amount to the reactants and then promote the barrier passage could be invoked to explain the observed behavior. We found that structural, rather than energetic, effects are mainly involved on this point. The lower efficiency of ZK4 seems to arise from the frequent trapping of the reactive complex in the narrow ZK4 windows in which the transfer is forbidden and from the weaker interaction of the reactive complex with the host framework compared to silicalite

A CTRW interpretation of simulated single-file diffusion in zeolites

Single-file diffusion of molecules adsorbed in the channels of zeolite is a phenomenon occurring at different time and length scales, which is difficult to simulate by standard methods, because it often occurs for large molecules adsorbed in microporous materials showing parallel non-crossing channels, with large energy barriers to diffusion.. Two interesting examples are given by water adsorbed in two different Li containing zeolites, Li-ABW and bikitaite, which show parallel straight channels where hydrogen-bonded linear chains of water molecules run along the axis of the channels, parallel to regular rows of lithium ions sticking to the channel surface. Extensive Molecular Dynamics (MD) simulations of the dynamical of water in these zeolites at different loading and temperature were performed by this research group. It resulted that the energy barrier for water molecules to cross one another in the same channel is much larger than kT event at any reasonably high temperature, so that the diffusion resulted single-file in all the simulation conditions. The simulation details and results are reported in Refs. [3] and [4], were it was shown that for time scales ranging from a few to some hundreds of picoseconds depending on temperature and loading the mean square displacement (MSD) is proportional to the square root of time as expected for single-file diffusion

"Two-step" model of molecular diffusion in silicalite

The influence of the particle "memory" on long-range diffusion in the channel network of silicalite is taken into account by considering pairs of subsequent steps between the channel intersections. It is shown that in this case the correlation rule between the principal elements of the diffusion tensor has to be modified by including an additional term, which takes account of the deviation of molecular propagation from complete randomness. The obtained relations are discussed in terms of molecular dynamics simulations of ethane in silicalite

Dynamical behavior of one-dimensional water molecule chains in zeolites: nanosecond time-scale molecular dynamics simulations of bikitaite

Nanosecond scale molecular dynamics simulations of the behavior of the one-dimensional water molecule chains adsorbed in the parallel nanochannels of bikitaite, a rare lithium containing zeolite, were performed at different temperatures and for the fully and partially hydrated material. New empirical potential functions have been developed for representing lithium–water interactions. The structure and the vibrational spectrum of bikitaite were in agreement both with experimental data and Car–Parrinello molecular dynamics results. Classical molecular dynamics simulations were extended to the nanosecond time scale in order to study the flip motion of water molecules around the hydrogen bonds connecting adjacent molecules in the chains, which has been observed by NMR experiments, and the dehydration mechanism at high temperature. Computed relaxation times of the flip motion follow the Arrhenius behavior found experimentally, but the activation energy of the simulated system is slightly underestimated. Based on the results of the simulations, it may be suggested that the dehydration proceeds by a defect-driven stepwise diffusion. The diffusive mechanism appears as a single-file motion: the molecules never pass one another, even at temperatures as high as about 1000 K, nor can they switch between different channels. However, the mean square displacement (MSD) of the molecules, computed with respect to the center of mass of the simulated system, shows an irregular trend from which the single-file diffusion cannot be clearly evidenced. If the MSDs are evaluated with respect to the center of mass of the molecules hosted in each channel, the expected dependence on the square root of time finally appears

Application of the Wolf method for the evaluation of Coulombic interactions to complex condensed matter systems: aluminosilicates and water

The application of the method recently proposed by Wolf et al. [J. Chem. Phys. 110, 8254 (1999)] for the evaluation of Coulombic energy in condensed state systems by spherically truncated, pairwise r–1 summation is verified for liquid water and anhydrous and hydrated aluminosilicates. Criteria for the estimation of the optimum values for the truncation radius and the damping parameter are discussed. By several examples it is verified that the new method is computationally more efficient than the traditional Ewald summations. For the considered systems the performances of the new method are good, provided that the truncation radius and the damping parameter are carefully chosen

Two- and <i>N</i>-step correlated models for the analysis of molecular dynamics trajectories of linear molecules in silicalite

Recent molecular dynamics data on the diffusion of linear diatomic and triatomic molecules in the zeolite silicalite are analyzed in terms of a new correlated model [F. Jousse, S. M. Auerbach, and D. P. Vercauteren, J. Chem. Phys. 112, 1531 (2000)] capable to account for both first- and higher-order correlation effects. This "N-step" model reproduces very well our calculated mean square displacements and diffusion coefficients of the molecules considered. The improvements with respect to the results obtained with our previous "two-step" model [P. Demontis, J. Kärger, G. B. Suffritti, and A. Tilocca, Phys. Chem. Chem. Phys. 2, 1455 (2000)] are remarkable for all molecules except chlorine, showing that only in this case the effect of (negative) correlations spanning more than two jumps between channel intersections (~20 Å) can be neglected. The basic trajectory analysis in terms of single- and two-step models, besides being an useful reference, provides all the input data needed for the application of the N-step model. Indeed, in its silicalite formulation, the N-step model is strongly linked to the two-step one because it calculates the probability of a sequence of jumps in the same channel by means of the correlations between any two consecutive jumps. Finally, the possibility to obtain qualitative insight into the diffusive mechanism through various kind of correlation coefficients is discussed

Diffusion in tight confinement: a lattice-gas cellular automaton approach. I. Structural equilibrium properties

The thermodynamic and transport properties of diffusing species in microporous materials are strongly influenced by their interactions with the confining framework, which provide the energy landscape for the transport process. The simple topology and the cellular nature of the α cages of a ZK4 zeolite suggest that it is appropriate to apply to the study of the problem of diffusion in tight confinement a time-space discrete model such as a lattice-gas cellular automaton (LGCA). In this paper we investigate the properties of an equilibrium LGCA constituted by a constant number of noninteracting identical particles, distributed among a fixed number of identical cells arranged in a three-dimensional cubic network and performing a synchronous random walk at constant temperature. Each cell of this network is characterized by a finite number of two types of adsorption sites: the exit sites available to particle transfer and the inner sites not available to such transfers. We represent the particle-framework interactions by assuming a differentiation in binding energy of the two types of sites. This leads to a strong dependence of equilibrium and transport properties on loading and temperature. The evolution rule of our LGCA model is constituted by two operations (randomization, in which the number of particles which will be able to try a jump to neighboring cells is determined, and propagation, in which the allowed jumps are performed), each one applied synchronously to all of the cells. The authors study the equilibrium distribution of states and the adsorption isotherm of the model under various conditions of loading and temperature. In connection with the differentiation in energy between exit and inner sites, the adsorption isotherm is described by a conventional Langmuir isotherm at high temperature and by a dual-site Langmuir isotherm at low temperature, while a first order diffuse phase transition takes place at very low temperature

Diffusion in tight confinement: a lattice-gas cellular automaton approach. II. Transport properties

In this second paper the authors study the transport properties of the lattice-gas cellular automaton presented in Paper I [J. Chem. Phys. 126, 194709 (2007)] to model adsorption and dynamics of particles in a lattice of confining cells. Their work shows how a surprisingly simple parallel rule applied to a static network of cells joined by links set in space and time can generate a wide range of dynamical behaviors. In their model the cells are the elementary constituent objects of the network. They are a portion of space structured in sites which are energetically different. Each cell can accommodate a given maximum number of particles, and each pair of neighboring cells can exchange at most one particle at a time. The predictions of the model are in qualitative agreement with both experimental observations and molecular dynamics simulation results

Cellular Automata modeling of diffusion under confinement

Both thermodynamic and transport properties of molecular species are strongly influenced by the effect of confinement exerted by microporous materials such as zeolites. The nature of particle-framework interactions, along with geometric effects (size, shape, and connectivity of the pores), provides the energy landscape for the transport process and plays a major role in determining the aptitude of the diffusing species to migrate from pore to pore. Geometrical restrictions can cause a sharp separation on the time scales involved in the diffusion process: intracage motion (short times) and intercage migration (long times). Zeolites provide a three-dimensional framework (connected channels and cages with finite capacity) which, when reduced to its essential constituents, can be represented as a set of structured lattice points (cells) evolving in time according to well defined local rules: these are the basic ingredients of Cellular Automata (CA) models. With their parallel, space-time discrete nature, CA algo-rithms represent a very convenient environment in which physical systems can be modelled in a reductionistic approach, in order to cover large scales of space and time. We constructed a CA satisfying detailed balance to model intercage diffusion and equilibrium properties of particles adsorbed in a ZK4 zeolite