Loading dependence of the diffusion coefficient of methane in nanoporous materials

In this work, we use molecular simulations to study the loading dependence of the self-and collective diffusion coefficients of methane in various zeolite structures. To arrive at a microscopic interpretation of the loading dependence, we interpret the diffusion behavior in terms of hopping rates over a free-energy barrier. These free-energy barriers are computed directly from a molecular simulation. We show that these free-energy profiles are a convenient starting point to explain a particular loading dependence of the diffusion coefficient. On the basis of these observations, we present a classification of zeolite structures for the diffusion of methane as a function of loading: three-dimensional cagelike structures, one-dimensional channels, and intersecting channels. Structures in each of these classes have their loading dependence of the free-energy profiles in common. An important conclusion of this work is that diffusion in nanoporous materials can never be described by one single effect so that we need to distinguish different loading regimes to describe the diffusion over the entire loading range.     

Concentration dependence of the diffusion coefficient of polydisperse polystyrene in dilute solution

The concentration dependence of the diffusion coefficients (D) of two different polystyrenes in toluene was measured. The concentration dependence of D of a standard monodisperse sample (M = 498,000) for concentrations up to 1 · 25 g/dl is not linear. The dependence is adequately described by the theory of dilute polymer solutions up to about 0·7 g/dl and the second virial coefficients of the osmotic pressure can be evaluated. For a polystyrene sample having a broad molecular weight distribution, the concentration dependence of four different average diffusion coefficients was determined so indirectly characterizing the molecular weight distribution. These dependences are not linear and differ from each other owing to the different sensitivity of the individual averages to high-molecular and low-molecular weight fractions. The apparent distribution of the diffusion coefficients becomes narrower with increasing concentration. When evaluating polydispersity from the free diffusion data obtained in good solvents, it is necessary to determine directly the differential diffusion coefficients; an extrapolation of the integral diffusion coefficients can be misleading.     

Mass dependence of mutual diffusion coefficient: computer simulation study

Molecular dynamic computer simulations are performed to study the mass dependence of mutual diffusion coefficient in an isotopic, equimolar binary system. The particles of the system are assumed to be interacting via Lennard-Jones potential. The self- and mutual diffusion coefficients are calculated from the time dependence of the mean square displacement and from the velocity correlation function using the Green–Kubo formula. The study has been carried out at different densities and temperatures. Like the self-diffusion coefficient, the mutual diffusion coefficient is also found to be weakly dependent on the mass ratio. Our study also shows that the temperature of the system has a negligible effect on the mass dependence of the diffusion coefficients.     

The concentration dependence of the diffusion and permeability in a homogeneous membrane

For the sorption and diffusion coefficient dependence on the concentration of the penetrant the transport properties of a homogeneous medium are calculated. The diffusion current is assumed to be proportional to the negative gradient of the chemical potential. This is in contrast with the first Fick's law that assumes this current to be proportional to the negative gradient of the concentration of the penetrant. The difference between the two cases depends on the concentration dependence of the sorption coefficient. In a homogeneous membrane the chemical potential formulation leads to an equation which is very similar to the Fickian expression. The apparent diffusion coefficient, however, depends not onlly on the transport resistance but also on the deviation of the sorption coefficient from constancy.     

Temperature dependence of the diffusion coefficient of copper(II) chloride in porous-glass membranes

Diffusion transport of a 0.5 M aqueous solution of CuCl₂ was studied in a set of porous-glass membranes with predominant pore radii of 4.5 to 70 nm in the temperature range 25–70°C. Raising the temperature causes a rise in diffusion coefficients and their gradual equalization, which eliminates their dimension dependence on the radius of membrane channels.     

Non-hydrodynamic contribution to the concentration dependence of the self diffusion of interacting brownian macroparticles

One-dimensional single-channel scattering calculations on an effective potential are used to discuss resonances in collinear reactions and to predict their energetic location almost quantitatively. The effective potential includes the vibrationally adiabatic potential and the adiabatic diagonal correction in Delves' mass-weighted polar coordinates (hyperspherical coordinates). This $\text{di}$agonal corrected $\text{v}$ibrational $\text{a}$diabatic $\text{h}$yperspherical (DIVAH) model is tested for a variety of reactions (H + H₂, H + MuH, I + HI, F + H₂) and a detailed discussion of the effective potential and its physical implications is given.     

Temperature and concentration dependence of diffusion coefficients in ethylene–propylene-diene copolymers

Self-diffusion and partition coefficients were measured for two commercial ethylene–propylene-diene copolymers (EPDM) and five solvents at infinite dilution using inverse gas chromatography. Mutual diffusion coefficients for solvents in EPDM also were measured for finite concentration using gravimetric sorption for three of the solvents. From the inverse gas chromatography experimental values for self-diffusion coefficients were obtained. Free-volume parameters were obtained through regression of the self-diffusion coefficient as a function of temperature. Mutual diffusion coefficients as a function of concentration were predicted using free volume theory and compared with experimental data obtained using gravimetric sorption. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1713–1719, 1998     

Simulation of ion mass transfer processes with allowance for the concentration dependence of diffusion coefficients

The system of equations describing ion transport in a binary electrolyte z _a-z _c with allowance for the linear dependence of the diffusion coefficients on the concentration was analyzed in the framework of the phenomenological Nernst-Planck approach. The expressions are obtained that define concentration profiles of ions and conditions favorable for the limiting current caused by the achievement of the concentration of a saturated solution (in the case of the anodic reaction) and depletion of the near-electrode region in electroactive cations (in the case of the cathodic reaction). The revealed theoretical dependence of the limiting current on the volume concentration of the salt agrees with published experimental data. The voltammetric characteristics of the corresponding systems were calculated. The role of the migrational component of the ion flow is discussed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 638–642, April, 2006.     

Generalizations of the diffusion equation

The mass flux entering the Fick's diffusion equation is considered as an arbitrary analytical function of concentration, concentration gradient, and of the gradient of concentration gradient. The restrictions imposed on the flux by the principle of material objectivity are stated and briefly discussed.     

Determination of the concentration dependence of polyelectrolyte diffusion coefficients by application of the Boltzmann gradient method

The concentration dependence of a polyelectrolyte diffusion coefficient in aqueous low salt solution (KCl, 1 mM) is determined from a single dynamic gradient experiment. The Boltzmann method is applied to calculate the diffusion coefficient. A special diffusion cell is constructed that minimizes aberrations in the optical detection of the polyion concentration profile. Bovine serum albumin (BSA) is chosen as a model polyion. To get information about the diffusion process down to very small polyion concentrations, the BSA molecule is fluorescently labeled. The fluorescence intensity is used as a measure of the polyion concentration. The change of the polyion net charge caused by labeling is discussed. The cell is illuminated by an LED, and the fluorescence intensity profile is detected by a CCD camera. Experiments at 5 and 17 degrees C show that the diffusion coefficient of labeled BSA remains constant in the very low polyion concentration range below a threshold of about 1.5 g/l. This is in contradiction to the linear concentration dependence of polyion diffusion coefficients at very low concentrations often postulated in the literature without reference to direct experimental evidence. Our finding is confirmed by dynamic light scattering experiments published recently. An explanation for this behavior based on a modified Donnan osmotic compressibility approach is given.     

Translational diffusion in sucrose benzoate near the glass transition: probe size dependence in the breakdown of the Stokes-Einstein equation

The translational diffusion coefficient D(trans) for rubrene, 9,10-bis(phenylethynyl)anthracene (BPEA), and tetracene in the fragile molecular glass-former sucrose benzoate (SB) (Tg=337 K) was studied as a function of temperature from Tg+3 K to Tg+71 K by use of the holographic fluorescence recovery after photobleaching technique. The values of D(trans) vary by five to six orders of magnitude in this temperature range. Contrary to the predictions of the Stokes-Einstein equation, the temperature dependence of probe diffusion in SB over the temperature range of the measurements is weaker than that of T/eta, where eta is the shear viscosity. In going from the crossover temperature Tx approximately 1.2Tg to Tg, D(trans)eta/T increases by factors of 2.4+/-0.2 decades for rubrene, 3.4+/-0.2 decades for BPEA, and 3.8+/-0.4 decades for tetracene. The decoupling between probe diffusion in SB and viscosity is characterized by the scaling law D(trans) approximately T/eta(xi), with xi=0.621 for tetracene, 0.654 for BPEA, and 0.722 for rubrene. Data for probe diffusion in SB are combined with data from the literature for probe diffusion in ortho-terphenyl and alphaalphabeta-tris(naphthyl)benzene in a plot of enhancement versus the relative probe size parameter rho(m)=(m(p)m(h))(1/3), where m(p) and m(h) are, respectively, the molecular weights of the probe and host solvent. The plot clearly shows a sharp increase in enhancement of translational diffusion at rho(m) approximately 1. By applying temperature shifts, D(trans) for probe diffusion in SB and the dielectric relaxation time tau(D) can be superimposed on a single master curve based on the Williams-Landel-Ferry equation. This suggests that the dynamics of probe diffusion in SB is described by the scaling relationship D(trans) approximately 1/tau(D)(T+DeltaT), where tau(D)(T+DeltaT) is the temperature-shifted dielectric relaxation time. The results from this study are discussed within the context of dynamic heterogeneity in glass-forming liquids.     

Effective concentration difference model to study the effect of various factors on the effective diffusion coefficient in the dialysis membrane

Cellulose acetate dialysis membrane (CDM) has been used in the diffusive gradients in thin films (DGT) technique, where accurate diffusion coefficients are essential for the assessment of the concentrations of labile metal in solution. Effective concentration difference model (ECDM), based on the assumption that the effective diffusion coefficient of metal ion in the dialysis membrane is determined by the effective concentration difference (ΔC(e)) across the dialysis membrane, is proposed and applied to study the effect of ionic strength, binding agent, ligands and Donnan potential on the effective diffusion coefficient. The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in receptor solutions with binding agent were almost the same as those in receptor solutions without binding agent at higher ionic strengths (0.01-1 M) but much higher than those at lower ionic strengths (0.001-0.0001 M). The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in deionized water receptor solutions with binding agent were not significantly different from those in synthetic receptor solutions (receptor solutions with various ionic strengths) with binding agent. The DGT-labile fractions were measured in synthetic solutions and natural waters, which indicated that the effective diffusion coefficients, through the dialysis membrane immersed in the deionized water solution with binding agent as receptor solution and in the spiked natural water as source solution, were more suitable for DGT application.     

Experimental study of the concentration dependence of the soret coefficient by thermal field-flow fractionation: the case of polystyrene in decalin

Summary Thermal field-flow fractionation separates polymers with high selectivity according to their Soret coefficient,S _τ, hence, according to their molar mass, and therefore consitutes an efficeint physicochemical tool for the determination of the Soret coefficient of a given polymer in the carrier liquid from its retention time. However, the polymer concentration in the sample influences the retention time and, hence, the value ofS _τ derived from it. An experimental study of the influence of sample concentration on retention,S _τ, and peak shape was performed for the polystyrene-decalin system over a relatively large temperature domain and for various molar masses. It is found that the retention time and the value ofS _τ increase with increasing sample concentration, the more so as the cold wall temperature is lower. This appears to be in contradiction with the general non-equilibrium thermodynamic expression derived for polymer-solvent systems with positive second virial coefficients, such as the present system over the temperature range investigated. There seems to be a temperature for which the dependence ofS _τ on sample concentration vanishes. This temperature is about 375 K for the polystyrene-decalin system. As the sample concentration increases, the peak barycentre and the standard deviation increases. As the peaks are fronting, the skewness is negative and becomes more negative as the sample concentration increases. The peak skewness appears to be a good indicator of the onset of sample concentration effects. The threshold concentration, for which these effects begin to become significant, decreases with increasing molar mass.     

Calculation of the binary diffusion second virial coefficient

Calculations of the first density correction to the binary diffusion coefficient are presented for several mixtures. These calculations are based on the classical kinetic theory for mixtures developed by Bennett and Curtiss. The theoretical predictions agree well with experimental data.     

Effect of micropores on the effective diffusion coefficient

The effective diffusion coefficient for catalysts differing in their porous structure has been derived from experimental data on H₂S conversion in the Claus reaction. The effective diffusion coefficient increases under conditions of catalyst deactivation due to sulfur condensation in micropores. A mathematical model is suggested to describe the micropore effect on the effective diffusion coefficient.