Pseudo-Restricted Self-Diffusion of Molecules in Biporous Structures: Study by Pulsed Field Gradient NMR

The mobility of liquid (n-decane) that fills the system of primary and secondary pores of a biporous sample (granular Vycor porous glass) is studied by the pulsed field gradient NMR technique. The anomalous time dependence of the slow component of diffusion decay is revealed: the self-diffusion coefficient decreases with an increase in diffusion time t_d and, at large t_d values, this dependence satisfies the feature of completely restricted self-diffusion. It is established that this component is related to the mobility of liquid molecules filling the system of primary pores. By use of computer simulation, it is shown that the effect of “pseudo-restricted” diffusion is explained by the exchange processes between the phases, where the molecules of the liquid that are present in the systems of primary and secondary pores and differ in self-diffusion coefficients are understood as the phases. The effect of interfacial exchange is confirmed by the time dependence of the fraction of molecules with the lowest self-diffusion coefficients. The revealed phenomenon of “pseudo-restricted” diffusion is not related to real spatial constraints and can be observed in any systems with two (or more) phases with different self-diffusion coefficients, provided that these “phases” are bulky and can be subjected to molecular exchange.     

Modeling the concentration dependence of the methanol self-diffusivity in faujasite systems: comparison with the liquid phase

Molecular dynamics simulations were performed to understand further the concentration dependence of the self-diffusion of methanol in the faujasite zeolite systems. The evolution of the self-diffusivity was investigated as a function of coverage for DAY and NaY systems to study the effect of both the pore confinement and the presence of the extraframework cations within the supercage. It was found that the self-diffusivity decreases with loading for DAY, whereas for NaY it passes through a maximum at intermediate coverage, in agreement with pulse-field gradient NMR and quasi elastic neutron scattering data reported in similar systems. The activation energies of the methanol diffusion corresponding to a combination of both intra- and intercage motions were evaluated as a function of the coverage. The simulated trends are interpreted on the basis of the predominant interactions which take place in both systems. Finally, the preferential arrangement of the adsorbate molecules are provided and compared with those simulated in the liquid phase. For the fully loaded materials, it was seen that the methanol molecules form a one-dimensional hydrogen-bonded chain along the channels in DAY whereas only dimers are present in NaY.     

The use of the cohen–turnbull model for calculation of the self-diffusion coefficients of liquid dichloroalkanes

The paper presents the self-diffusion coefficients calculated for liquid dichloroalkanes C₆H₁₂Cl₂, C₈H₁₆Cl₂, C₁₀H₂₂Cl₂ and C₁₂H₂₄Cl₂, with the use of the Cohen and Turnbull model. Determination of self-diffusion coefficients permits a separate analysis of intra- and intermolecular motions and provides information on geometrical and dynamical properties of molecules. The self-diffusion coefficients of selected dichloroalkanes have been determined by X-ray diffraction and compared with the corresponding NMR results. The suitability of the Cohen–Turnbull model of the translating motion for prediction of self-diffusion coefficients for molecules whose shape significantly differs from the spherical symmetry is analysed. Angular distributions of X-ray scattered intensity were measured, and differential radial distribution functions of electron density (DRDFs) were calculated. The mean coordination numbers were obtained from the area delimited by the minima of the DRDFs, and their dependence on the length of the methylene chain is also presented subsequently. On the basis of the DRDFs the average free volume of the molecules and total free volume of the liquids were calculated. The activation volume of the diffusion was found to make about 0.6 of the van der Waals volume of the molecule. As expected the diffusion coefficients decrease with increasing molecular weight. The equation relating the self-diffusion coefficient with the volume of the coordination spheres in the liquid has been derived.     

The Potentials of Pulsed Field Gradient NMR for Investigation of Porous Media

PFG NMR self-diffusion studies provide information on the translational mobility of fluid molecules. Since in porous media the diffusion path of fluid molecules in the pore space is affected by interaction with the pore wall, PFG NMR measurements are sensitive to structural peculiarities of the confining porous medium. The pore space properties which can be investigated depend on length scales set by the PFG NMR experiment in respect to the typical size of the structural feature studied. Based upon these length scales, an interpretation pattern for PFG NMR self-diffusion studies in porous media is given. PFG NMR self-diffusion studies in macro- and microporous systems such as sedimentary rocks and zeolite crystallites, respectively, are reviewed.     

Calculations of the distribution of trace impurities in cylindrical pores

The equilibrium distribution of a trace impurity and the self-diffusion coefficients of molecules of the base component and the trace impurity in narrow cylindrical pores were calculated using the lattice-gas model. Two types of lattice structures with six and eight closest neighbors were considered. The sizes of the base component and impurity molecules were taken to be identical. Lateral interactions were taken into account in the quasi-chemical approximation. The equilibrium distributions of the trace impurity across a pore section in the gas and liquid phases of the base component and at the interface for the case of capillary condensation were considered. The probability of existence of isolated dimeric clusters was estimated and the self-diffusion coefficients of the base component and trace impurity for a single-phase distribution of the base component were calculated. The effects of the energy of interaction of impurities with the pore walls and the concentration of the base component on the diffusion mobility of the impurities were analyzed. The concentration dependences of the partition coefficient for the trace impurity between the pore center and the pore wall and the concentration dependences of the self-diffusion coefficients for the trace impurity molecules become nonmonotonic with an increase in the base component concentration. These effects are due to the displacement of the impurity from the near-surface area to the bulk of a pore following an increase in the pore coverage by the base component and to higher mobility of the impurity in the free bulk of the pore. Further filling of the pore bulk reduces the mobility of all molecules. The energetics of intermolecular interactions also plays a certain role. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 605–615, April, 2000.     

Dependence of the Self-Diffusion Coefficient of Liquid Molecules in a Porous Medium on Its Geometric Parameters

Based on the most general concepts of the translational mobility and geometry of a porous medium, an expression is derived for the self-diffusion coefficient of liquid molecules in such a medium. An analytical relation between the self-diffusion coefficient and the effective geometric parameters of the pores, as well as the sizes of diffusant molecules, is proposed. The derived expression agrees well with experimental results.     

Influence of concentration on the activation energy for diffusion in polymer-solvent systems

The self-diffusion of benzene, toluene, and ethylbenzene in polystyrene have been analyzed using the Vrentas/Duda free-volume diffusion model. Diffusion coefficient predictions suggest an exponential concentration dependence of the activation energy required to overcome attractive forces, E. Without the use of any diffusion data approximating E as zero over the entire concentration range yields self-diffusion coefficient predictions which are in good agreement with experimental data. © 1992 John Wiley & Sons, Inc.     

Diffusion-Ordered Spectroscopy (DOSY) as a Powerful NMR Method to Investigate Molecular Mobilities and Intermolecular Interactions in Complex Oil Mixtures

Studying the characteristics and molecular mechanisms of liquid self-diffusion coefficient and viscosity changes is of great significance for, e. g., chemical and petroleum processing. As examples of highly complex liquid,an asphaltene-free high-acid and high-viscosity crude oil and its extracted fractions were studied by comparing their ¹H DOSY diffusion maps. The crude oil exhibited a polydisperse diffusion distribution, including multiple diffusion portions with diffusion coefficients much smaller than that of any single fraction in independent diffusion. The main mechanism that leads to the decreases in the diffusion coefficients of crude oil is attributed to diffusion resistance enhanced by Dynamical Molecular-Interaction Networks (DMINs), rather than by enlargement of the diffusion species caused by molecular aggregation. Constructed through the synergistic interactions of various polar molecules in crude oil, DMINs dynamically bind polar molecules, trap polarizable molecules, and spatially hinder the free motion of non-polar molecules. Overall, this reduces the mobility of all molecular species, as illustrated by the decreased diffusion coefficients. This study demonstrates that DOSY is a powerful NMR method to investigate molecular motion abilities also in complex mixtures. In addition, the insights in the influence of the interaction matrix on the molecular mobility also help to understand the contribution of “structural viscosity” to the viscosity of heavy oil.     

NMR self-diffusion study of polyethylene and paraffin melts

The self-diffusion coefficient D of paraffin and polyethylene melts—covering the range between N = 19 and 10³ where N is the number of monomeric units—was measured by the pulsed-magnetic-field-gradient NMR method for diffusion times between 3 ms and 1 s. For the paraffins, D is proportional to N^?2 though the molecular weights are smaller than the critical molecular weight for entanglement. In polyethylene, melts a strong dependence of the diffusion coefficient on the diffusion time is observed, whereas no such dependence is found in paraffin melts. A mathematical formalism for describing spin-echo attenuation in terms of a velocity autocorrelation function is shown to yield qualitative agreement with the experimental results.     

Effect of temperature on the diffusion mechanism of xylene isomers in a FAU zeolite: a molecular dynamics study

The diffusion of o-, m-, and p-xylene in a FAU zeolite at 300-900 K was investigated using molecular dynamics simulations. Calculated self-diffusion coefficients of xylene isomers showed that the mobility of p-xylene was the fastest, m-xylene the second fastest, and o-xylene the slowest in the FAU zeolite at the same temperature. The diffusion activation energy of o-xylene, m-xylene and p-xylene was, respectively, determined to be 9.04, 7.45 and 6.44 kJ mol(-1) within the temperature range of 400 to 900 K, while to be 14.12, 13.59 and 15.47 kJ mol(-1) within the temperature range of 300 to 400 K. Xylene density profiles and orientational analysis suggested that this can be attributed to the xylene molecules that diffuse in the FAU zeolite by two different mechanisms at high and low temperatures. The behavior of motion for xylene in the FAU zeolite exhibits a "fluid-like" mode at high temperatures and exhibits a "jump-like" mode at low temperatures.     

交换La^3＋对NaX型分子筛Na^＋电导的影响

用X-射线衍射、原子吸收、差热热重、化学分析等方法测定了交换La3 离子NaX型分子筛的物相及组成。用交流阻抗谱仪测量了其离子电导。由电导率随温度的变化得到NaX的Na 电导表观活化能为38．8kJ／mol，适度交换La3 ，NaLaX的Na 电导表观活化能降低至27．9kJ/mol。讨论了交换La3 对分子筛中Na 迁移扩散的影响。     

Study of intracrystalline diffusion in zeolites 6. Comparison of the results obtained by the method of densitometry of light and the adsorption method

The use of the method of densitometry of light passing through a layer of zeolite crystals permits determining the limiting stage of diffusion during adsorption by zeolites. Diffusion in transport pores and external heat exchange play the basic role in adsorption of benzene by NaX zeolite, while diffusion in crystals is the determining mechanism of transport in adsorption of water by NaA and NaX zeolites. The diffusion coefficients of water in NaX zeolite have an order of magnitude of 10^–17 m²/sec and increase with an increase in the degree of filling. An explanation for the anomalous behavior of the kinetic adsorption curve for brief times of adsorption of water by zeolite is proposed.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1224–1228, June, 1990.     

Diffusion coefficients in a halocarbon–polybutene system

The diffusion coefficient of 1,1,2-trichlorotrifluoroethane (TTE) in a liquid polybutene was determined at 25°C. as a function of concentration over the range 1.0–19.5 g. TTE/100 cc. The diffusion coefficient increase with increasing TTE concentration, rising continuously from 3 × 10^?8 cm.²/sec. at the lowest concentration to 15 × 10^?8 cm.²/sec. at the highest. The magnitudes of the diffusion coefficients indicate that the diffusion mechanism for small molecules in polymeric media must afford vastly greater opportunities for diffusion than the Stokes-Einstein relation allows. Similarly, self-diffusion coefficients for the liquid polymer are much lower than the observed mutual diffusion coefficients. An explanation for this behavior is presented.     

Permeation through a single crystal of Zeolite NaX

Steady state permeation through a 120 μm single crystal of zeolite NaX has for the first time been observed. Each crystal was imbedded in an epoxy film, polished to expose opposite faces to feed and permeate gases, and mounted in an apparatus with pmol/s permeation rate sensitivity. Permeation was constrained to occur by an intracrystalline diffusion mechanism, confirmed by temperature dependence and selectivity measurements. Rates decreased at higher temperatures due to opposing sorption and diffusion effects. Intracrystalline butane diffusivity at 25°C was 3 x 10^?4 cm²/sec, in agreement with other methods. Anomalously long time lags for approach to steady state are explained by a transition between two states of the zeolite, differing in permeability by 10²-10⁴. The state with lower permeability was selectively permeable to isobutane from a methaneísobutane mixture.     

A model for predicting solvent self-diffusion coefficients in nonglassy polymer/solvent solutions

Cohen-Turnbull diffusion theory is used to develop a model for predicting solvent self-diffusion coefficients D₁ in nonglassy polymer/solvent solutions. Polymer molecules are envisioned as hindering solvent mobility by reducing the average free volume per unit mass in the system and through the lower mobility of polymer segments relative to solvent molecules. The concentration dependence of D₁ predicted by the model is in reasonable agreement with data for the solvents heptane, hexadecane, benzene, cyclohexane, and decalin in polyisobutylene (PIB), and for toluene in polystyrene, poly(methyl mothacrylate), and PIB. Although none of the data is for high concentrations of polymer (volume fractions ?≥0.9) it is anticipated the model will be less representative in this regime where the assumptions in its development are unsure. The model also demonstrates the correct temperature and concentration dependence of the apparent activation energy for diffusion. The only experimental data needed to use the model are the viscosity and critical volume of the pure solvent, and the specific volume of both the solvent and mixture. No binary transport data are required.     

On the Knudsen transport of gases in nanochannels

We investigate the diffusion of gas molecules in nanochannels under the combinational effect of the vibration of the channel, gas-wall binding energy, and channel size through molecular dynamics simulations. It is found that the molecular vibration of the channel plays a critical role in gas transport process when the gas-wall binding energy is strong. For small binding energies, the influence of the flexibility of the wall can be neglected. In rigid channels, the gas self-diffusion coefficient increases with increasing gas-wall binding energy, while it decreases in nonrigid channels. The effect of the channel size on the self-diffusion coefficient is not significant except that a local maximum in the gas self-diffusion coefficient is found in 2 nm channels due to the strong repulsive force caused by the surface curvature of the channels.     

Effective removal of uranium ions from drinking water using CuO/X zeolite based nanocomposites: effects of nano concentration and cation exchange

For the first time, effects of CuO nanoparticles concentration (from 1 to 24.2 wt%) in CuO/NaX nanocomposite and replacing various cations (Ag⁺, K⁺, Ca²⁺, and Mg²⁺) with Na⁺ ions in NaX zeolite on removal of uranium ions from drinking water are reported. The removal of uranium was performed under natural conditions of pH, laboratory temperature and the presence of competing cations and anions that are available in tap water of Isfahan city. Characterization of parent NaX zeolite and modified samples were investigated using X-ray fluorescence, X-ray powder diffraction patterns, scanning electron microscopy, and atomic absorption spectroscopy methods. Using Langmuir, Freundlich, and C-models, isotherms of equilibrium adsorption were studied. Results show the removal efficiency and distribution coefficient of NaX zeolite decrease in the presence of other competing anions and cations that exist in drinking water. But, modification of NaX zeolite with various cations and CuO nanoparticles might enhance the ability of X zeolite in removing uranium from drinking water.     

Tracing pore-space heterogeneities in X-type zeolites by diffusion studies

Pore-space homogeneity of zeolite NaX was probed by pulsed field gradient (PFG) NMR diffusion studies with n-butane as a guest molecule. At a loading of 0.75 molecules per supercage, a wide spectrum of diffusivities was observed. Guest molecules in the (well-shaped) zeolite crystallites were thus found to experience pore spaces of quite different properties. After loading enhancement to 3 molecules per supercage, however, molecular propagation ideally followed the laws of normal diffusion in homogeneous media. At sufficiently high guest concentrations, sample heterogeneity was thus found to be of no perceptible influence on the guest mobilities anymore.     

Is the wall of a cellulose fiber saturated with liquid whether or not permeable with CO2 dissolved molecules? Application to bubble nucleation in champagne wines

In this paper, the transversal diffusion coefficient D perpendicular of CO2 dissolved molecules through the wall of a hydrated cellulose fiber was approached, from the liquid bulk diffusion coefficient of CO2 dissolved molecules modified by an obstruction factor. The porous network between the cellulose microfibrils of the fiber wall was assumed being saturated with liquid. We retrieved information from previous NMR experiments on the self-diffusion of water in cellulose fibers to reach an order of magnitude for the transversal diffusion coefficient of CO2 molecules through the fiber wall. A value of about D perpendicular approximately 0.2D0 was proposed, D0 being the diffusion coefficient of CO2 molecules in the liquid bulk. Because most of bubble nucleation sites in a glass poured with carbonated beverage are cellulose fibers cast off from paper or cloth which floated from the surrounding air, or remaining from the wiping process, this result directly applies to the kinetics of carbon dioxide bubble formation from champagne and sparkling wines. If the cellulose fiber wall was impermeable with regard to CO2 dissolved molecules, it was suggested that the kinetics of bubbling would be about three times less than it is.     

Adsorption and adsorption-induced deformation of NaX zeolite under high pressures of carbon dioxide

Isotherms of carbon dioxide adsorption and adsorption-induced deformation of pelletized crystalline NaX zeolite at pressures of 0.2--5.4 MPa and temperatures of 195--423 K are measured. The adsorption deformation is positive at low zeolite micropore filling (a < 1 mmol g^-1) at all temperatures, i.e., the zeolite suffers expansion. Further, as the amount of the adsorbed substance increases, the adsorption deformation curves pass first through a maximum and then through a minimum. In the range of high fillings (a > 7 mmol g^-1) the NaX zeolite shows dramatic expansion.