Calculated Self-diffusion Coefficients Research Articles

Molecular Dynamics Simulations of the Diffusion of Small Chain Hydrocarbons in 8-Ring Zeolites

Molecular dynamics (MD) simulations were performed to study the microscopic motion of methane, ethane, propene, and propane adsorbed in three pure silica zeolites with windows made of 8 SiO4 tetrahedral units: Si-LTA, Si-IHW, and Si-ITE. The zeolite framework and guest structures have been simulated allowing full flexibility, using the well-known BKS model and the potential of Oie et al., respectively. The MD approach followed allows us to calculate the intra- and intercage dynamics of the smaller adsorbates, that is, methane and ethane, in statistically meaningful time and length scales in the temperature range studied, whereas for the larger size guest molecules the analysis of intercage motion is limited to higher temperatures. Calculated self-diffusion coefficients for methane, ethane, and propene show a decreasing trend correlated with increasing guest kinetic diameter sizes and decreasing critical window size, confirming experimental measurements on the molecular sieving properties of 8-ring zeolite...

Diffusivity calculation on noble gas silica systems using first-principles molecular simulations

First-principles molecular dynamics simulations are carried out to investigate the diffusivity of noble gases dissolved in silica melts. The simulations are performed for a range of molar volumes, corresponding to pressures ranging from ambient pressure to ∼50 GPa at temperatures above the SiO2 melting point. The Chi-square merit function, weighted by the statistical certainty of the data, was used to regress the mean-square displacement against time relationship and to calculate self-diffusion coefficients for noble gases, Si, and O atoms. The results are in good agreement with the available literature data. We found that the higher the temperature and smaller the noble gas atom, the higher the diffusivity; noble gas diffusivity decreased almost linearly with the square of the atomic radius. With molar volume decreasing, the self-diffusion coefficient of small noble gases decreased, while Si and O showed an abnormal dependence on molar volume. In the temperature range simulated, the diffusivity for He, Si and O could be described by an Arrhenius equation with activation energies consistent with available experimental data within simulation accuracy.

Molecular Dynamics Simulations of Ionic Liquids: Cation and Anion Dependence of Self-Diffusion Coefficients of Ions

Molecular dynamics simulations of a series of ionic liquids [1-alkyl-3-methylimidazolium (alkyl = methyl, ethyl, butyl, hexyl, and octyl), 1-butylpyridinium, N-butyl-N,N,N-trimethylammonium and N-butyl-N-methylpyrrolidinium cations combined with a (CF(3)SO(2))(2)N(-) anion ([mmim][TFSA], [emim][TFSA], [bmim][TFSA], [C(6)mim][TFSA], [C(8)mim][TFSA], [bpy][TFSA], [(n-C(4)H(9))(CH(3))(3)N][TFSA], and [bmpro][TFSA]) and a 1-butyl-3-methylimidazolium combined with BF(4)(-), PF(6)(-), CF(3)CO(2)(-), CF(3)SO(3)(-), and (C(2)F(5)SO(2))(2)N(-) anions ([bmim][BF(4)], [bmim][PF(6)], [bmim][CF(3)CO(2)], [bmim][CF(3)SO(3)], and [bmim][BETA])] were carried out using the OPLS force field for ionic liquids. The force field was refined on the basis of ab initio molecular orbital calculations of isolated ions and experimental densities for four ionic liquids. The densities calculated for the 13 ionic liquids agreed with the experimental values within a 2% error. The self-diffusion coefficients calculated for the ions in the 13 ionic liquids were compared with the experimental values obtained by the NMR measurements. Although the calculated self-diffusion coefficients were about 1 order smaller than the experimental ones, the cation and anion dependence (the effects of alkyl chain length in imidazolium, cation structures, and anion species) of the experimental self-diffusion coefficients was reproduced by the simulations quite well in most cases. The translational motion of the terminal carbon atoms in the alkyl chains of the imidazolium cations on the time scale of a few nanoseconds is significantly faster than that of the atoms in the imidazolium rings and anions, which suggests that the dynamics of atoms in the polar domains of the ionic liquids is significantly different from that in the nonpolar domains. The factors determining the self-diffusion coefficients of the ions are also discussed.

Visualization-based analysis of structural and dynamical properties of simulated hydrous silicate melt

We have explored first-principles molecular dynamics simulation data for hydrous MgSiO3 liquid (with 10 wt% water) to gain insight into its structural and dynamical behavior as a function of pressure (0–150 GPa) and temperature (2,000–6,000 K). By visualizing/analyzing a number of parameters associated with short- and mid-range orders, we have shown that the melt structure changes substantially on compression. The speciation of the water component at low pressures is dominated by the isolated structures (with over 90% hydrogen participated) consisting of hydroxyls, water molecules, O–H–O bridging and four-atom (O–H–O–H and H–O–H–O) groups, where every oxygen atom may be a part of polyhedron or free (i.e., bound to only magnesium atom). Hydroxyls favor polyhedral sites over magnesium sites whereas molecular water is almost entirely bound to magnesium sites, and also interpolyhedral bridging (Si–O–H–O–Si) dominates other types of bridging. Water content is shown to enhance and suppress, respectively, the proportions of hydroxyls and molecular water. As compression increases, these isolated structures increasingly combine with each other to form extended structures involving a total of five or more O and H atoms and also containing threefold coordination species, which together consume over 80% hydrogen at the highest compression studied. Our results show that water lowers the mean coordination numbers of different types including all cation–anion environments. The hydrous melt tends to be more tetrahedrally coordinated but with the Si–Si network being more disrupted compared to the anhydrous melt. Protons increase the content of non-bridging oxygen and decrease the contents of bridging oxygen as well as oxygen triclusters (present at pressures above 10 GPa). The calculated self-diffusion coefficients of all atomic species are enhanced in the presence of water compared to those of the anhydrous melt. This is consistent with the prediction that water depolymerizes the melt structure at all pressures. Our analysis also suggests that proton diffusion involves two processes—the transfer of H atoms (requiring the rupture and formation of O–H bonds) and the motion of hydroxyls as hydrogen carriers (requiring the rupture and formation of Si–O and/or Mg–O bonds). Both the processes are operative at low compression whereas only the first process is operative at high compression.

Theory and atomistic simulation of krypton fluid

An ab initio interaction potential available in literature is scaled via an empirical procedure and used in an extensive computer simulation study to investigate the thermodynamic properties and self-diffusion coefficient of krypton over a wide range of densities and temperatures. The thermodynamic properties of the fluid phase equilibriums are computed utilizing the Gibbs ensemble Monte Carlo simulation technique. The equation of state and the pair correlation function are obtained using the NVT-Monte Carlo simulation method. The time-correlation function formalism of Green-Kubo is applied in molecular dynamics simulations to calculate the self-diffusion coefficient. Furthermore, the modified Cohen-Turnbull theory is employed to determine the self-diffusion coefficient and the mean free volume needed for this purpose is provided via the generic van der Waals theory. The virial minimization method is used to compute the effective diameter and the results are applied within the generic van der Waals theory as the repulsion-attraction splitting distance of the interaction potential. A remarkable agreement is observed between the computed and empirical results for the orthobaric densities, the vapor pressure, the critical point, and the equation of state. A detailed analysis is presented for the calculated self-diffusion coefficient.

CONFINEMENT EFFECTS ON ADSORPTION AND DIFFUSION OF HEXANE IN NANOPOROUS MCM-41 WITH DIFFERENT PORE SIZES: A MOLECULAR DYNAMICS STUDY

We report the results of molecular dynamics (MD) simulations using a new semi-empirical intermolecular interaction potential on the adsorption and diffusion of hexane in siliceous MCM-41 at 300 K. The potential function is tuned to give an adsorption energy of − 9.1 kcal/mol, reproducing the experimental value for a corresponding pore size. We investigated MCM-41 models with four different pore sizes and studied loadings from one molecule of hexane up to a loading corresponding to the density of liquid hexane. As a result of confinement in MCM-41, the free energy of adsorption of hexane increases when the pore sizes decrease; for example, the adsorption energy increases from − 9.1 to 13.7 kcal/mol for the largest to the smallest pore size for a loading of one molecule. Also, the adsorption energy increases by 3–4 kcal/mol for all pore sizes when the loading is increased from one hexane molecule to the density of liquid hexane. The calculated self-diffusion coefficients of hexane in MCM-41 with a pore diameter of 27 Å are in the order of 1 × 10−5 cm2/s, depending on the loading, which is in reasonable agreement with available experimental data. The self-diffusion coefficients decrease with increasing loadings and when the pore sizes decrease. The average distance between the centers of the mass of hexane molecules in the smallest pores is only marginally less than in the larger pores and in the liquid phase. For low loadings the hexane molecules lie parallel to the pore channel for every pore size. When the loading is increased, they build up concentric rings. These rings of hexane molecules are less well separated from each other in the larger models, and thus their structure more resembles the liquid phase.

Molecular dynamics study of oxygen self-diffusion in reduced CeO 2

The oxygen self-diffusion in partially reduced CeO 2 has been investigated by large-scale Molecular Dynamics simulations, in the temperature range between 800 and 2200 K. Simulation boxes with ~ 4100 and ~ 33,000 ions were investigated for randomly distributed oxygen vacancies and Ce 3+ ions. Our calculated self-diffusion coefficients vary between 10 −8 and 10 −6 cm 2/s in the temperature range studied. The activation energy and D 0 values are also reported. The oxygen diffusion mechanism has also been analyzed: only a 〈100〉 vacancy mechanism is observed.

Mixed micelles of octane-1,8 bis(dodecyl dimethyl ammonium chloride) and n-dodecyl-β- d-maltoside by 1H NMR study

Nuclear magnetic resonance (NMR) spectroscopy is a versatile technique at a molecular level for the study of surfactants. Mixed micellization of nonionic sugar-based surfactant n-dodecyl-β- d-maltoside (DM) and cationic surfactant octane-1,8 bis(dodecyl dimethyl ammonium chloride) gemini (12-8-12) was studied using NMR by self-diffusion coefficient, spin–spin and spin–lattice relaxation time, and two-dimensional nuclear Overhauser enhancement (2D NOESY). NMR results reveal the relative arrangement of the surfactant molecules in the mixed micelles. It is shown that the methylene group next to the ammonium head is in the near vicinity of penultimate sugar ring, and the hydrophobic chain of DM molecule and the two hydrophobic chains of 12-8-12 gemini are side by side in the interior of the micellar core. At fixed total surfactant concentrations of DM and 12-8-12 gemini, calculated self-diffusion coefficient suggests that the size of the mixed micelles is largely dependent on the DM concentration, higher the DM concentration, larger the mixed micelles in size. From 2D NOESY maps of mixed micelles, it is found that at fixed DM concentration, surfactant interaction between DM and 12-8-12 gemini in their mixed solutions increases gradually with increase of 12-8-12 gemini concentration from DM/12-8-12 ratio of 1:1–1:3. Interestingly, with further increase of 12-8-12 gemini concentration from DM/12-8-12 ratio of 1:4–1:8, the inter-molecular interaction starts to decrease, which is attributed to the more and more dominant intra-molecular proton–proton dipolar coupling of two surfactant molecules.

Diffusion of methane in a mica slit pore: Molecular dynamics simulations and correlation models

Equilibrium molecular dynamics simulations have been used to calculate the self-diffusion coefficients of fluid methane confined in mica slit pore at different temperatures, densities and pore widths. On the other hand, based on the Chapman–Enskog theory and Heyes relationships, two simple correlation models which can describe the self-diffusion coefficient of fluid methane in mica slit pore are proposed as a function of the temperature, density and pore width. Both models are written in terms of Lennard-Jones (LJ) dimensionless variables, which are defined in terms of the LJ parameters σ and ε . These parameters are meaningful at molecular level. The validity of these models is evaluated by comparing with the calculated self-diffusion coefficient data at different state points. The average error of both these two models is usually less than 13%.

Investigation of Atomistic Scale Transport Phenomena of the Proton Exchange Membrane Fuel Cell

This paper studies the transport phenomena inside the electrolyte of proton exchange membrane fuel cells (PEMFCs) using atomistic simulation techniques. The investigated material of the electrolyte is Nafion®, which is the most widely adapted polymer membrane in low-temperature fuel cells. The molecular dynamics simulation system includes part of the Nafion structure, numerous water molecules, and the transporting cations. The cations are assumed to be hydroxoniums (H3O+), which are a hydrogen proton combined with a water molecule. Simulation results indicated that the electrostatic energy dominated the other potential energies in the total internal energy analysis. Clusters of water molecules tend to move toward the sulfonic acid group in the Nafion fragment, where the hydrophilic/hydrophobic characteristics can be observed. The transport phenomena of hydroxoniums are classified into two categories—continuous migration and noncontinuous hopping. The self-diffusion coefficients of the hydroxoniums and the water molecules in the membrane were evaluated to be 3.476×10−5cm2∕s and 4.993×10−5cm2∕s respectively, based on the Einstein relation. The calculated self-diffusion coefficients are of the same order of magnitude as the experimental results, which indicates this atomistic simulation is reaching more and more practical in engineering analysis.

Atomic dynamics in liquid alkali metals at the melting point

The atomic dynamics in liquid alkali metals at the melting point has been studied with the help of an equation of motion in terms of the velocity autocorrelation function. An atom is considered to be moving in a mean-time-dependent field, in a series of steps much smaller than the average interatomic spacing (small-step diffusion approximation). The theoretical formulation presented here is a special case of our generalized formulation for simple monatomic liquids [Phys. Rev. E. 70, 51201 (2004)]. It gives a good account of the single-particle motion in liquid Li, Na, K, Rb, and Cs. The calculated self-diffusion coefficients are found to be in excellent agreement with the experiments. The formulation is also used to investigate the collective excitations arising due to density fluctuations. The dispersion curves for the collective excitations for Li, Na, and K show a decent overall agreement with the inelastic neutron scattering and inelastic x-ray scattering results. The effect of quantum-mechanical correction has been observed for Li, Na, and K. It suggests a significant improvement over the classical results. Since the applicability of the small-step diffusion approximation is limited to weak electron-ion coupling at high electron densities, the present formulation gives satisfactory dispersion curves for Rb and Cs in a small intermediate $q$ range. It has been observed that an abrupt change in the dynamical properties occurs at the position of potassium in accordance with the change in atomic number density.

Molecular Dynamics Simulation Studies of p-Xylene in OH-free Si-MCM-41

We report on modeling efforts and molecular dynamics computer simulations of the structure and self-diffusion of p-xylene in OH-free Si-MCM-41 as a function of loading. Both the guest molecules and Si-MCM-41 are modeled as flexible entities. With this newly developped intermolecular force field the average potential energy of p-xylene in the pore increases with increasing loading. The adsorption of p-xylene in MCM-41 is primarily associated with the van der Waals interactions of the model, whereas the contribution from electrostatic interactions is relatively small (about 2 kcal/mol), in accordance with other aromatic hydrocarbons adsorbed in zeolite catalysts. The calculated selfdiffusion coefficients of p-xylene in Si-MCM-41 are well comparable with diffusion coefficients of pyridine in MCM-41 and of the same order of magnitude as in liquid p-xylene. Increasing the loading results in non-negligible mutual p-xylene interaction, thus leading to a decrease of the self-diffusion coefficient.

Quantum diffusion in liquid water from ring polymer molecular dynamics

We have used the ring polymer molecular-dynamics method to study the translational and orientational motions in an extended simple point charge model of liquid water under ambient conditions. We find, in agreement with previous studies, that quantum-mechanical effects increase the self-diffusion coefficient D and decrease the relaxation times around the principal axes of the water molecule by a factor of around 1.5. These results are consistent with a simple Stokes-Einstein picture of the molecular motion and suggest that the main effect of the quantum fluctuations is to decrease the viscosity of the liquid by about a third. We then go on to consider the system-size scaling of the calculated self-diffusion coefficient and show that an appropriate extrapolation to the limit of infinite system size increases D by a further factor of around 1.3 over the value obtained from a simulation of a system containing 216 water molecules. These findings are discussed in light of the widespread use of classical molecular-dynamics simulations of this sort of size to model the dynamics of aqueous systems.

System-Size Dependence of Diffusion Coefficients and Viscosities from Molecular Dynamics Simulations with Periodic Boundary Conditions

We study the system-size dependence of translational diffusion coefficients and viscosities in molecular dynamics simulations under periodic boundary conditions. Simulations of water under ambient conditions and a Lennard-Jones (LJ) fluid show that the diffusion coefficients increase strongly as the system size increases. We test a simple analytic correction for the system-size effects that is based on hydrodynamic arguments. This correction scales as N-1/3, where N is the number of particles. For a cubic simulation box of length L, the diffusion coefficient corrected for system-size effects is D0 = DPBC + 2.837297kBT/(6πηL), where DPBC is the diffusion coefficient calculated in the simulation, kB the Boltzmann constant, T the absolute temperature, and η the shear viscosity of the solvent. For water, LJ fluids, and hard-sphere fluids, this correction quantitatively accounts for the system-size dependence of the calculated self-diffusion coefficients. In contrast to diffusion coefficients, the shear viscos...

Molecular dynamics simulation data of self-diffusion coefficient for Lennard–Jones chain fluids

The knowledge of the diffusion coefficient of a molecule in dense fluids at a given density and temperature plays an important role in many chemical processes. Molecular dynamics (MD) simulation has been recognized as a useful tool to provide exact results of theoretical models, thus affording a database for the development of empirical models that can be readily accessible for engineering purposes. The aim of this work is to provide self-diffusion coefficient data from MD simulation for freely jointed Lennard–Jones (LJ) chain fluids of lengths 2, 4, 8, and 16 at the reduced densities ranging from 0.1 to 0.9 and at the reduced temperature interval of 1.5–4. Based on both Chapman–Enskog formalism and MD simulation data, we propose an equation to calculate self-diffusion coefficients of polyatomic fluids. The new model represents the self-diffusion coefficients with an absolute average deviation (AAD) of 15.3%.

Modeling Self-Diffusion in Mixed-Solvent Electrolyte Solutions

A comprehensive model has been developed for calculating self-diffusion coefficients in mixed-solvent electrolyte solutions. The model includes methods for calculating the self-diffusion coefficients of ions and neutral species at infinite dilution and for predicting the effect of finite concentrations of electrolytes. For limiting diffusivities, a mixing rule has been developed for predicting the diffusivity in multicomponent mixed solvents using the limiting diffusivities or ion conductivities in pure solvents. The effect of finite concentrations of electrolytes is modeled by combining the contributions of long-range (Coulombic) and short-range interactions. The long-range interaction contribution is obtained from the mean spherical approximation theory of the relaxation effect, while the short-range interactions are represented using the hard-sphere model of diffusion. Aqueous species are characterized by effective species diameters, which are defined to reflect the interactions between the components of the solution. The model has been integrated with a thermodynamic speciation model, which makes it possible to take into account the effects of complexation or other reactions in the solution. The model accurately reproduces experimental self-diffusion coefficients of ions and neutral molecules in mixed solvents over wide ranges of concentrations.

Modeling of Liquid Silicon at Pressures up to 23 GPa from Diffraction Data

Earlier reported diffraction data for silicon at pressures of 4, 8, 14, and 23 GPa and temperatures 50 K above the melting point are used to develop models of liquid silicon (2997 particles in a cubic central box with periodic boundary conditions) and reconstruct the effective pair potential, which is found to depend little on density and temperature. It is shown that, between 8 and 14 GPa, the structure of liquid silicon becomes markedly denser. The calculated self-diffusion coefficient of liquid silicon decreases almost twofold with increasing pressure.

Structure and Dynamics of the TIP3P, SPC, and SPC/E Water Models at 298 K

Molecular dynamics simulations of five water models, the TIP3P (original and modified), SPC (original and refined), and SPC/E (original), were performed using the CHARMM molecular mechanics program. All simulations were carried out in the microcanonical NVE ensemble, using 901 water molecules in a cubic simulation cell furnished with periodic boundary conditions at 298 K. The SHAKE algorithm was used to keep water molecules rigid. Nanosecond trajectories were calculated with all water models for high statistical accuracy. The characteristic self-diffusion coefficients D and radial distribution functions, gOO, gOH, and gHH for all five water models were determined and compared to experimental data. The effects of velocity rescaling on the self-diffusion coefficient D were examined. All these empirical water models used in this study are similar by having three interaction sites, but the small differences in their pair potentials composed of Lennard-Jones (LJ) and Coulombic terms give significant differences in the calculated self-diffusion coefficients, and in the height of the second peak of the radial distribution function gOO.

Nonideality in Binary Mixtures: Correlations between Excess Volume, Excess Viscosity, and Diffusion Coefficients

Although many experimental studies over the years have shown strong (inverse) correlation between excess viscosity and excess volume of a binary mixture, there does not seem to exist any microscopic theoretical study of such behavior. In this work, we introduce and study two new models of binary mixture with the aim of removing this lacuna. Our models consist of a mixture of two molecular species (1 and 2) with the same diameter and mass but varying solute−solvent Lennard−Jones interactions. In model I, the two different species are strongly attractive, while in model II, the attraction is weaker than that between the pure components. That is, model I encourages structure formation, while the reverse is true for model II. Extensive constant pressure−constant temperature (NPT) molecular dynamics (MD) simulations have been carried out which show that these models can indeed reproduce the strong inverse correlation between the calculated excess volume and excess viscosity. The two models show opposite trends in the composition dependence. Another interesting result is the observation of a re-entrant behavior in the excess volume dependence of total viscosity of the mixturethe same re-entrance is also observed in the dependence of excess viscosity on excess volume. In addition, we derive the first two terms in the virial expansion for the composition dependence for the infinite frequency shear modulus, G∞. These terms can explain the composition dependence at low composition in terms of partial radial distribution functions and interaction potentials. The calculated self-diffusion coefficients have nonmonotonic behavior and show considerable deviations from Stokes−Einstein relation.

Calculation of self-diffusion coefficients in liquid metals based on hard sphere diameters estimated from viscosity data

Temperature-dependent hard sphere diameters are determined from viscosity data for sixteen liquid metals. These diameters are then used to calculate diffusion coefficients using the hard sphere model as well as the Stokes–Einstein model. Both models predict a temperature dependence of the diffusivity that is weaker than that observed experimentally. However, the predictions are comparable to those obtained using the Protopapas–Parlee hard sphere diameters which were determined from the diffusivity data.