Computer simulation investigation of diffusion selectivity in graphite slit pores

Equilibrium molecular dynamics simulations are reported of oxygen and nitrogen molecules confined in graphite slit pores. Self- and collective diffusion coefficients have been calculated as a function of pore width, temperature and density for each pure component in the pore space. The aim of this study was to elucidate the mechanism by which oxygen and nitrogen are kinetically separated when air is passed over an adsorbent bed consisting of molecular sieving carbon in the commercial production of oxygen. It was found that a critical pore width exists for each species at which there is a sharp drop in the rate of diffusion (both self- and collective diffusion) of each fluid. The critical pore width is one for which the individual molecules are prevented from rotating freely about one of their axes. The greater length of a nitrogen molecule means that the critical pore width is higher for this species than for oxygen. Consequently, oxygen molecules diffuse substantially faster than nitrogen molecules in the vicinity of the nitrogen critical pore width. From an analysis of correlation functions and their corresponding power spectra it is shown that the restricted rotations, which occur at or below the critical pore width, cause a decoupling of translational and rotational modes, with the net result being a lowering of translational diffusion. The nitrogen critical pore width lies within the range of the mean pore size of most commercial molecular sieving carbons, and so this mechanism may help to explain the high oxygen selectivities reported in the literature.     

Density profiles and solvation force for a liquid in a slit

Computer simulations and density functional theory results are reported for a Lennard-Jones liquid in a slit or pore formed by two parallel hard walls. Both density profiles and solvation forces are computed. Two classes of calculation are performed. In the first class, a high bulk density is selected and, starting from a high temperature, the temperature is reduced until the temperature corresponding to bulk liquid—vapour coexistence is reached. For small slit widths or exceedingly large widths, the density in the slit decreases continuously until the slit is virtually empty or ‘dry’. When the slit width is somewhat larger than a molecular diameter, but still finite, the density in the slit decreases continuously as the temperature is decreased until there is an abrupt change in the density in the slit. Below this temperature, the density is smaller. Further decreases in the temperature, result in a continuous decrease in the slit density until the slit is virtually empty. In the second class, the density and temperature for bulk coexistence are chosen and the bulk density is increased. At the temperature and bulk density for bulk coexistence, the slit is virtually empty and remains so for all widths that we consider. As the bulk density is increased at constant temperature, the slit remains empty as the width is increased until some specific width is reached and then starts to fill abruptly. The agreement of the density functional and simulation results is qualitative but good.     

Transmission enhancement through a metallic slit assisted by low scattering loss corrugations

A method to obtain large transmission of light through a nano-metallic slit bordered by nano trenches is demonstrated theoretically. The model is based on the composite diffraction of evanescent waves (CDEW) theory and utilizes a single trench design to effectively convert free-space light into surface plasma waves (SPW). The effectiveness is confirmed by the finite difference time domain (FDTD) method. The SPW loss due to scattering by the trench is also analyzed. It is found that when the width of the trench is slightly larger than λ_spp/2, the SPW becomes localized and resonates at the bottom edges performing as a dipole-like radiation source. At this time, the propagating SPW suffers from high scattering loss. Trenches can be used to enhance the transmission of a nano-scaled slit while simultaneously preserving high conversion efficiency and low scattering loss. A nano-scaled slit bordered by 10 pairs of trenches can be enhanced by a factor as high as 16. It is determined that a device designed to have a large clear aperture of 15 μm would have an advantage in terms of alignment.     

E.S.R. evidence for the planarity of the t-butyl radical

Monte Carlo calculations are reported for the radial distribution function g ₂(r; λ) of a fluid in which the intermolecular pair potential is [u ^ref(r) + λu ^p(r)], u ^ref(r) being the Weeks-Chandler-Andersen (WCA) reference fluid, and [u ^ref(r) + u ^p(r)] being the Lennard-Jones (6, 12) fluid. The calculations are performed for λ values in the range 0 to 1, at the state condition ρσ³ = 0·80, kT/ε = 0·719. It is shown that at high densities the perturbation expansion of g ₂(r; λ = 1) about g ₂(r; λ = 0) is rapidly convergent, but that the corresponding expansion for y ₂(r; λ) = exp [βu(r; λ)] × g ₂(r; λ) is not. In addition Monte Carlo estimates of the individual terms that contribute to the first-order perturbation term, (?g ₂/?λ)_λ=0, are presented. It is shown that these terms are individually large, but that (?g ₂/?λ)_λ=0 is small because there is strong cancellation between the various terms. Consequently, the calculation of (?g ₂/?λ)_λ=0 is highly sensitive to the approximation used to evaluate the individual terms.     

Structures and autocorrelation functions of liquid Al and Mg modelled via Lennard-Jones potential from molecular dynamics simulation

The structures and autocorrelation functions of Al and Mg in the liquid state are investigated through the pair distribution functiong(r), the diffusion coefficients as well as the shear viscosity via the Green-Kubo and Einstein relations. From the structure and the Enskog relation we determined the frequency of collisions of atoms in the first shell ofg(r) in the systems. We also discovered that the packing fraction of Lennard-Jones liquids should be approximately half the reduced density value. This approximation is accurate to within 99%. The temperature dependence of the pair distribution function and the atomic mean square displacement are investigated by performing simulations at various experimental temperatures and corresponding densities. The structures of the systems are affected by temperature via movements of atoms in the first minimum ofg(r). The Lennard-Jones model shows that density dependence of the shear viscosity is in agreement with what is expected of simple liquids in the range of investigated temperatures and densities. In the gas limit, the Stoke-Einstein relationDη =K _BT /2πσ is grossly overestimated by Lennard-Jones model. This could not be attributed to deficiencies in the model, as other investigators using first principle method could not obtain the gas limit of the Stoke-Einstein relation.     

Distribution of the amplitude of the magnetic potential of diffractive beams generated in a ferrite slab by a surface spin wave incident on a slit in an opaque screen

The total magnetic potential generated in the far field of a ferrite slab as a result of a plane noncollinear surface spin wave incident on a slit in an opaque screen is investigated. The dependence of the potential amplitude from the polar angle in the plane of a ferrite slab is calculated for different orientations of the screen with relative to an external magnetic field magnetizing the slab. It is found that two diffractive beams are generated in the slab as a result of spin diffraction on the slit. The angular width of each beam depends largely on the slit’s orientation and can be greater or smaller than value λ _n /D (where D is the slit’s width and λ _n is the length of the spin wave corresponding to each beam).     

Perturbation theory for the radial distribution function

Perturbation theory is used to consider expansions for the radial distribution function, g ₂(r), of a fluid with a soft core. We consider the Lennard-Jones (12, 6) potential and divide it into repulsive and attractive regions. In the repulsive region we expand the function exp (β u(r))g ₂(r) about a hard sphere value. For the first-order contribution of the attractive region we consider a simple approximation to the exact analytical expression. The resulting g ₂(r) is accurate at densities below about ρσ ³=0·5.     

Angular momentum and temperature dependence of fission barriers with a realistic force

Angular distributions and excitation functions were measured for 30 2⁺ resonances in the³⁹K(p,p₀) and₃₉K(p, α⁰) reactions. Partial reduced widths have been extracted for three proton channels; the relative signs of the reduced width amplitudes for two of these channels were also determined. Reduced widths are generally consistent with a Gaussian distribution for the reduced width amplitudes, but the amplitudes themselves are not. These data represent the first measurement of correlation coefficients in an entrance channel and suggest that the large correlations previously observed in exit channels are generic features of this mass region.     

The mechanism of surface heterodiffusion at elevated temperatures

Molecular dynamics simulations employing the Lennard-Jones potential have been performed on Kr/Ar(111) to investigate the nature of high-temperature surface heterodiffusion. These suggest that high activation energies and preexponential factors observed experimentally at temperatures above approximately 0.70 T_m arise from adatom-vacancy pair formation, which sharply increases the number of mobile species. Evidence is also obtained that at intermediate temperatures (0.45 T_m < T < 0.66 T_m), Arrhenius curves mass transfer diffusivity can depend on both coverage and adsorbate interactions. For adsorbates which exhibit islanding, low coverage diffusion is characterized by an activation energy equal to the enthalpy of migration, whereas at moderate coverage the activation energy contains an additional term due to the enthalpy of formation of mobile adatoms from immobile islands.     

Entrance channel correlations for 2+ resonances inp+27Al

Angular distributions for²⁷Al(p, α ₀) and excitation functions for²⁷Al(p, p ₀) and²⁷Al(p, α ₀) have been measured for 2⁺ resonances in thep+²⁷Al system. For 10 of these resonances, partial widths have been determined for three proton channels, and the relative sign between the reduced width amplitudes in two of these channels has been deduced. Linear correlation coefficients between reduced widths and between reduced width amplitudes in different channels have been calculated. The amplitudes appear consistent with the expected Gaussian distribution.     

A systematic elimination procedure for Ito stochastic differential equations and the adiabatic approximation

We study a class of nonlinear Ito stochastic differential equations (with possibly state dependent diffusion coefficients), in which the variables can be divided into linearly damped (slaved) variables s and linearly undamped variablesu (order parameters). We devise a systematic and constructive procedure to eliminate the slaved variables. We take explicit time and chance dependence of the slaved variables into account, the latter via a family of diffusion processesZ _t ^(v) . These act as fluctuating coefficients of the Center Manifolds _t=s(u _t, t,Z _t ^(v) (v=2, 3, ...)) and appear explicitly in the elimination procedure. We show how in the Ito calculus fluctuating and deterministic coefficients of the Center Manifold are more completely separated than in the previously treated Stratonovich case [1]. The adiabatic approximation is defined as a partial summation of the elimination expansion and the stochastic generalization ofs=0 is derived. We show how thus ambiguity of stochastic calculi is removed. Closed form summations are given in two examples. We briefly indicate the potential use of perturbation theory techniques in the systematic elimination procedure.     

Surface diffusion and entrapment of simple molecules on porous silica

Interactions of simple molecules with the surface of porous silica have been investigated using time-of-flight secondary ion mass spectrometry and temperature programmed desorption. A monolayer of water diffuses into pores at temperatures higher than 110 K. Multilayers of water are also incorporated in pores via sequential surface diffusion. In contrast, a methanol monolayer tends to stay on the surface up to 150 K, and carbon dioxide diffuses into pores rather gradually. Results can be explained as the contribution of hydrogen bonds between the adsorbate–substrate and adsorbate–adsorbate interactions. The predominance of the former (latter) might be responsible for single-molecule migration of methanol and carbon-dioxide (collective diffusion of water molecules) on the surface. These molecules are entrapped at higher coordination sites in pores, as revealed from thermal desorption peaks appearing at higher temperatures than those from non-porous silica. However, no significant difference is observed in desorption kinetics of CF₂Cl₂, Kr, CH₄, and N₂ molecules between the porous and non-porous silica substrates.     

Ab initio SCF CI study of the electronic spectrum of s-tetrazine

Configuration interaction (CI) studies of ground, n→ π* and π→ π* electronically excited states are reported for s-tetrazine. The first n→ π* singlet excited state (¹ B _3u ), which is responsible for the purple-red colour of the molecule, is calculated at 2·80 eV, compared to the experimental transition energy of 2·22–2·70 eV. The singlet-triplet split of the first n→ π* states (¹ B _3u and ³ B _3u states) is calculated to be 0·76 eV.

The interaction of nitrogen lone pair orbitals (n-orbitals) is studied in terms of the ordering of the n π* excited states and found that the SCF orbital ordering is qualitatively in accord with the ordering of the n π* excited states in the CI level.

The first π→ π* excited state (¹ B _2u ) is calculated at 5·99 eV, slightly above the observed range of absorption. Numerous other high-lying singlet states as well as the triplet states have been calculated and they are used to verify several proposals relating to the excited state dynamics in the photo-physical studies of s-tetrazine.     

Spinodal decomposition in a Lennard-Jones fluid

A microscopic theory for the early stages of spinodal decomposition in a one-component fluid is presented. We show that in the unstable region of the phase diagram the amplitude of density fluctuations with wave vectors less than some critical value q_c , where q_c is the position of the pole in the static density response function of the uniform fluid, increases exponentially with time. The corresponding amplification factor is related to the Ornstein-Zernike direct correlation function of the uniform fluid. We have calculated the amplification factor for a Lennard-Jones fluid at several densities and temperatures. We find that these amplification factors are qualitatively different from those obtained from the analogue of Cahn's linearized theory of spinodal decomposition. Our calculated value of q_c at reduced density 0·35 and temperature 0·8 is in fairly good agreement with the result of a recent molecular dynamics simulation of a Lennard-Jones fluid quenched to this state.     

On the shape of wedding cakes

The large-scale morphology of a growing surface is characterized for a simple model of crystal growth in which interlayer transport is completely suppressed due to the Ehrlich-Schwoebel effect. In the limit where the ratio of the surface diffusion coefficient to the deposition rateD/F the surface consists of wedding-cake-like structures whose shape is given by the inverse of an error function. The shape can be viewed as a separable solution of the singular diffusion equationu ₁=[u ^–2 u _x ] _x . As an application, expressions for the number of exposed layers as a function of coverage and diffusion length are derived.     

Molecular simulation study of triangle-well fluids confined in slit pores

Grand canonical Monte Carlo simulations are used to study the behaviour of triangle-well (TW) fluids with variable well widths confined inside slit pores. The effect of individual factors influencing the properties of confined fluids such as fluid–fluid interactions, pore size and pore wall–fluid interactions are obtained using simulations as it is difficult to experimentally determine the same. An interesting observation of this study is that inside the narrow pore of slit height h* = 5 at the high-pressure condition of P* = 0.8, for the TW fluid with long-range attraction or for the fluid at a low temperature for even a short-range attraction, the density profiles show layering such that there is a sticking tendency of the particles at centre, while there is a depletion of particles near the wall (as the layers at the centre have higher density peak heights than near the walls).     

Variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation

We give an integral variational characterization for the speed of fronts of the nonlinear diffusion equationu _t =u _xx +f(u) withf(0)=f(1)=0, andf>0 in (0,1), which permits, in principle, the calculation of the exact speed for arbitraryf.     

On the Dimensions of the Chiral and Dilatation Symmetry Breaking Hamiltonian Densities

Denoting by l_u and l_δ the dimensions (if any) of the chiral and dilation symmetry breaking Hamiltonian densities u(x) and δ(x), respectively, the property (4 – l_u) (l_u – l_δ) > 0 (which is already known in special cases) is derived for a much larger class of models. We furthermore obtain a simple and general explicit expression for u(x) in terms of the current divergences, and review the physical applications of this (or an analogous, almost obvious) expression.     

Diffusion and transport of a magnetic field in a turbulent medium with helicity

An analysis is made of the relation between accurate formulas for the coefficients of turbulent diffusion D _T and the alpha effect α _T for a magnetic field in the Lagrange and Euler representations. It is shown that the quadratic term with respect to α _T in the diffusion coefficient derived by Moffatt and Kraichnan is incorrect and should be dropped. First, a numerical solution of the nonlinear equation (DIA equation) for the Green function is presented, describing the transport of a magnetic field for the case of incompressible, uniform, isotropic, steady-state turbulence possessing helicity. These solutions are used to calculate the steady-state coefficients D _T and α _T for various values of the parameters ξ ₀=u ₀ σ ₀/R ₀, a=H ₀/u ₀ ² p ₀, σ ₀/σ ₁, and R ₀/R ₁, where u ₀, σ ₀, and R ₀ are the characteristic velocity, lifetime, and scale of the turbulent pulsations, and H ₀, σ ₁, and R ₁ are similar values describing the helicity of the medium h(1,2)=〈u(1)· (∇×u(2))〉, and the parameter α characterizes the degree of helicity. The DIA values of D _T and α _T and the self-consistent values of these quantities calculated using the Green tensor in the diffusion approximation are in qualitative agreement. It is shown that the coefficient of turbulent diffusion is always positive for all the types of turbulence studied. Nonsteady-state values of D _T(t) and α _T(t) calculated by a self-consistent method are given. Zh. éksp. Teor. Fiz. 112, 1312–1331 (October 1997)     

Self-diffusion coefficients and orientational correlation times in aqueous NaCl solutions: Complementarity with structural investigations

The dynamical properties of pure water and aqueous NaCl solutions over a wide range of salt concentrations (0-6 m) at ambient conditions are characterized by molecular dynamics (MD) simulations. MD simulations are performed with a flexible SPC water model as a solvent, while the ions are treated as charged Lennard-Jones particles. In this paper, attention has been focused on the self-diffusion coefficients (D_i) of ions and water molecules and on orientational correlation time of water molecules. It is found that the self-diffusion coefficients decrease with ion concentration. Moreover, the self diffusion coefficients of sodium and chloride at higher salt concentrations are very comparable which may be due to the formation of clusters of these ions. The deduced rotational dynamics speeds up as the salt concentration increases. Some complementarities between dynamical properties and structural ones, recently obtained, are carried out.