Diffusion anomaly as a function of molecular length of linear molecules: levitation effect

Previous work on monatomic spherical sorbates has shown the existence of an anomalous peak in self-diffusivity (D) when plotted as a function of size of the diffusant. Molecular dynamics studies on linear molecules of different lengths l in zeolite NaY at 140 and 200 K are reported. It is seen that there is a peak in D as a function of l, suggesting that the levitation effect exists for linear molecules, the simplest member of polyatomics. This is confirmed by the lowering of the activation energy for the molecule whose length l exhibits highest D. Related quantities of interest such as the guest-host interaction energy and preexponential factor are discussed.     

The central cell model: a mesoscopic hopping model for the study of the displacement autocorrelation function

On the mesoscale, the molecular motion in a microporous material can be represented as a sequence of hops between different pore locations and from one pore to the other. On the same scale, the memory effects in the motion of a tagged particle are embedded in the displacement autocorrelation function (DACF), the discrete counterpart of the velocity autocorrelation function (VACF). In this paper, a mesoscopic hopping model, based on a lattice-gas automata dynamics, is presented for the coarse-grained modeling of the DACF in a microporous material under conditions of thermodynamic equilibrium. In our model, that we will refer to as central cell model, the motion of one tagged particle is mimicked through probabilistic hops from one location to the other in a small lattice of cells where all the other particles are indistinguishable; the cells closest to the one containing the tagged particle are simulated explicitly in the canonical ensemble, whereas the border cells are treated as mean-field cells in the grand-canonical ensemble. In the present paper, numerical simulation of the central cell model are shown to provide the same results as a traditional lattice-gas simulation. Along with this a mean-field theory of self-diffusion which incorporates time correlations is discussed.     

Understanding diffusion in confined systems: methane in a ZK4 molecular sieve. A molecular dynamics simulation study

The equilibrium probability distribution of N methane molecules adsorbed in the interior of n alpha cages of the ZK4 zeolite, the all-silica analogue of zeolite A, is modeled by a modified hypergeometric distribution where the effects of mutual exclusion between particles are extracted from long molecular dynamics simulations. The trajectories are then analyzed in terms of time-correlation functions for the fluctuations in the occupation number of the alpha cages. The analysis digs out the correlations induced by the spatial distribution of the adsorbed molecules coupled with a migration mechanism where a molecule can pass from one alpha cage to another, one-by-one. These correlations lead to cooperative motion, which manifests itself as a nonexponential decay of the correlators. Our results suggest ways of developing improved lattice approaches that may be useful for studying diffusion in much larger systems and for a much longer observation time.     

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.     

The behavior of silicalite-1 under high pressure conditions studied by computational simulation

Completely siliceous zeolite ZSM-5 (silicalite-1) under high external pressures, up to 7 GPa, was investigated by energy minimization techniques. Classical empirical potentials have been used to study the phase transformation of the silicalite crystal to a new one with a lower symmetry. The analysis of the unit cell geometry and vibrational spectra at selected pressures suggest the loss of crystallinity of the silicalite structure. We found that a low-density amorphous phase is reached at pressures around 2.5–3.5 GPa. These results are compatible with recent Raman and X-Ray diffraction studies. We report the structural and vibrational properties of the new phase. In addition, we report the simulated elastic constants and the Young’s modulus of silicalite at selected pressures. The simulated results are in semi-quantitative agreement with the experiment.     

Introducing a cellular automaton as an empirical model to study static and dynamic properties of molecules adsorbed in zeolites

A new lattice gas cellular automaton (LGCA) simulation approach to study static and dynamic properties of molecules adsorbed in zeolites is proposed. The motivation for the present work arises from the ongoing effort to develop efficient numerical tools where conventional approaches like molecular dynamics and Monte Carlo have been revealed as inefficient for a real extension of length and time scales in such inhomogeneous systems. Our LGCA is constituted by a constant number of interacting 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. The main input for our model comes from data such as (i) local density dependent mean-field potentials and transition probabilities obtained from atomistic simulations that will be used as the starting point to derive adsorption and diffusion properties and (ii) thermodynamic and kinetic data obtained from experiments and/or other simulation methods. Our numerically less demanding LGCA has been tested over three different systems. The obtained results are in excellent agreement with the experimental and theoretical reported data.     

A molecular dynamics study and molecular level explanation of pressure dependence of ionic conductivity of potassium chloride in water

Experimental ionic conductivity of different alkali ions in water shows markedly different dependences on pressure. Existing theories such as that of Hubbard-Onsager are unable to explain these dependences on pressure of the ionic conductivity for all ions. We report molecular dynamics investigation of potassium chloride solution at low dilution in water at several pressures between 1 bar and 2 kbar. Two different potential models have been employed. One of the models successfully reproduces the experimentally observed trend in ionic conductivity of K(+) ions in water over the 0.001-2 kbar range. We also propose a theoretical explanation, albeit at a qualitative level, to account for the dependence of ionic conductivity on pressure in terms of the previously studied Levitation Effect. It also provides a microscopic picture in terms of the pore network in liquid water.     

NMR studies of carbon dioxide and methane self-diffusion in ZIF-8 at elevated gas pressures

Self-diffusion measurements with methane and carbon dioxide adsorbed in the Zeolitic Imidazolate Framework-8 (ZIF-8) were performed by ¹H and ¹³C pulsed field gradient nuclear magnetic resonance (PFG NMR). The experiments were conducted at 298 K and variable pressures of 7 to 15 bar in the gas phase above the ZIF-8 bed. Via known adsorption isotherms these pressures were converted to loadings of the adsorbed molecules. The self-diffusion coefficients of carbon dioxide measured by PFG NMR are found to be independent of loading. They are in good agreement with results from molecular dynamic (MD) simulations and resume the trend previously found by IR microscopy at lower loadings. Methane diffuses in ZIF-8 only slightly slower than carbon dioxide. Its experimentally obtained self-diffusion coefficients are about a factor of two smaller than the corresponding values determined by MD simulations using flexible frameworks.     

Use of anisotropic atom-atom potential functions in lattice-dynamical calculations for solid nitrogen

For solid nitrogen, a set of ‘anisotropic’ atom-atom semi-empirical potential functions, which are easily derived from the usual ‘6-exp’ or ‘12-6’, eliminates the difficulties encountered in demonstrating the stability of the γ-phase in lattice-dynamical calculations according to the Born-von Karman procedure.

Negative eigenvalues of the dynamical matrices in certain regions of the Brillouin zone disappear, the agreement with experimental data improves and the α-γ transition is foreseen.     

High-temperature dynamic behavior in bulk liquid water: A molecular dynamics simulation study using the OPC and TIP4P-Ew potentials

Classical molecular dynamics simulations were performed to study the high-temperature (above 300 K) dynamic behavior of bulk water, specifically the behavior of the diffusion coefficient, hydrogen bond, and nearest-neighbor lifetimes. Two water potentials were compared: the recently proposed “globally optimal” point charge (OPC) model and the well-known TIP4P-Ew model. By considering the Arrhenius plots of the computed inverse diffusion coefficient and rotational relaxation constants, a crossover from Vogel–Fulcher–Tammann behavior to a linear trend with increasing temperature was detected at T* ≈ 309 and T* ≈ 285 K for the OPC and TIP4P-Ew models, respectively. Experimentally, the crossover point was previously observed at T* ± 315–5 K. We also verified that for the coefficient of thermal expansion α _P (T, P), the isobaric α _P (T) curves cross at about the same T* as in the experiment. The lifetimes of water hydrogen bonds and of the nearest neighbors were evaluated and were found to cross near T*, where the lifetimes are about 1 ps. For T < T*, hydrogen bonds persist longer than nearest neighbors, suggesting that the hydrogen bonding network dominates the water structure at T < T*, whereas for T > T*, water behaves more like a simple liquid. The fact that T* falls within the biologically relevant temperature range is a strong motivation for further analysis of the phenomenon and its possible consequences for biomolecular systems.