Self-Diffusion Coefficients for Pure and Mixed Adsorbate Fluids in Narrow Pores

The equilibrium distribution and the concentration dependence of the local and average self-diffusion coefficients for pure fluid and binary mixture components in narrow slitlike pores were analyzed. The coefficients were calculated using the lattice gas model in the quasi-chemical approximation on the assumption of a spherical shape and approximately equal sizes of the components. For the pure adsorbate, these calculations were compared with molecular dynamics simulations. Both methods gave similar concentration profile changes and dynamic characteristics of interlayer particle redistributions in strong nonuniform adsorption fields for dense fluids. A satisfactory agreement was obtained for the temperature dependences of the self-diffusion coefficients along the pore axis. The influence of the molecule–wall potential and of intermolecular interaction were considered. The self-diffusion coefficients of the adsorbate were shown to strongly depend on the density of the mixture and the distance from pore walls.     

分子在ITQ-3分子筛窄孔道内扩散的过渡态理论模型

建立了一个基于过渡态理论的分子在ITQ-3窄孔道方向扩散的模型. 该模型中, 由于分子从空腔中的一个吸附位越过势垒到相邻的另一个空腔中的吸附位需要克服很大的势垒能, 因而分子在势垒处可以简化处理为只存在排斥势, 可得到扩散系数依赖温度和Lennard-Jones作用参数的解析关系. 用分子动力学方法对CF₄在ITQ-3上扩散进行了模拟并验证了解析关系的合理性. 分子动力学模拟计算得到的扩散活化能、势垒能和吸附位势能与实际值相吻合. 模拟结果也显示了扩散系数依赖于附载量, 表现为先增大后减小的变化模式. 扩散活化能的计算证实了这一变化机理, 即当附载量增加时, 由于处于空腔中的分子彼此抬高了势能, 降低了扩散活化能, 使得扩散系数随附载量的增加而增大, 之后由于堵塞效应, 扩散系数随附载量的增加而逐步减小.     

A diffusion model for the fluids confined in micropores

The self-diffusion coefficients were calculated by molecular dynamics simulations and the effects of pore width, temperature, and fluid density on diffusion behavior of simple fluid argon and polar fluid water confined in micropores were analyzed and studied. A mathematical model describing diffusion behavior of fluids confined in micropores was proposed from the theories of molecular dynamics and molecular kinematics, and validated on the basis of the simulation results at various conditions. The model indicates that the diffusion coefficient is proportional to the square root of the pore width and to the temperature divided by the density squared. It is applicable to either liquid or gas states and only two parameters are required.     

Investigation of the concentration dependence of mass transfer coefficients in reversed-phase liquid chromatography

In order to investigate the concentration dependence of mass transfer coefficients in RPLC, experimental breakthrough curves obtained by staircase frontal analysis (FA) were fitted to the simplified models such as multiplate (MP) model, equilibrium dispersive (ED) model, and transport model, and the sophisticated models such as lumped pore diffusion (POR) model and general rate (GR) model. The MP model was used to obtain the initial guesses of the parameters of the ED and the transport models. Then the best values were obtained by minimizing the differences between theoretical and experimental values with a nonlinear fitting procedure. The values of the parameters of the POR and the GR models can be calculated by using the expressions derived from the plate height equations, which was further validated by using the fitting method. It was found that the mass transfer coefficients would depend on the solute concentration. This can be ascribed to the surface diffusivity, which correlates with the concentration and is lumped into the mass transfer coefficients for both simplified and sophisticated models.     

Direct determination of the concentration dependence of diffusivities using combined model-based Raman and NMR experiments

Diffusion in liquids can still be predicted only with high uncertainty due to a lack of sufficient experimental data. Diffusion experiments are complex and time-consuming. Furthermore, the determination of the concentration dependence of the diffusion coefficients requires usually several experiments even for binary mixtures. A powerful model identification framework based on two fast experimental techniques is presented here. Raman inter-diffusion experiments in combination with a novel incremental identification technique establish the concentration dependence directly from the data without requiring a priori specification of the model structure. In regions where this technique is sensitive to error noise, it is complemented with NMR intra-diffusion measurements. Models describing the concentration dependence are identified in two steps. Based on the combined data suitable model candidates are proposed and initialized through basic curve fitting in the first identification step. A statistically sound dynamic optimization step yields the final model parameters. The methodology is exemplarily used to determine the diffusion coefficient in the mixture ethyl acetate–cyclohexane in the full concentration space.     

Concentration dependences of heat conductivity coefficients of inert gases in narrow pores

Calculation of the transfer of molecules in porous systems requires self-consistent expressions describing the kinetic transfer coefficients for various concentrations and temperatures. The concentration dependences of heat conductivity and self-diffusion coefficients for fluids with different densities, ranging from rarefied gases to liquids, were considered in terms of a unified model. For monoatomic gases (argon), the model takes into account two energy transfer channels, namely, the vacancy mechanism and energy transfer through collisions of molecules. The former channel is characteristic of rarefied gases, while the latter is noted for condensed phases. The energy parameters of the model were determined on the basis of data on the heat conductivity coefficient in the bulk phase. The heat conductivity coefficient follows a linear temperature dependence for low density; in the medium and large density regions, these dependences follow a more complex pattern that changes depending on temperature. The influence of the interaction of atoms with the pore walls on the concentration dependences of the heat conductivity coefficients was investigated for different total amounts of the adsorbate. These coefficients depend appreciably on the distance to the pore wall and on the direction of heat transfer.     

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.     

Equilibrium and kinetics of water adsorption in carbon molecular sieve: theory and experiment

Measurements of water adsorption equilibrium and kinetics in Takeda carbon molecular sieve (CMS) were undertaken in an effort to characterize fundamental mechanisms of adsorption and transport. Adsorption equilibrium revealed a type III isotherm that was characterized by cooperative multimolecular sorption theory. Water adsorption was found to be reversible and did not display hysteresis upon desorption over the conditions studied. Adsorption kinetics measurements revealed that a Fickian diffusion mechanism governed the uptake of water and that the rate of adsorption decreased with increasing relative pressure. Previous investigations have attributed the observed decreasing trend in the rate of adsorption to blocking of micropores. Here, it is proposed that the decrease is attributed to the thermodynamic correction to Fick's law which is formulated on the basis of the chemical potential as the driving force for transport. The thermodynamically corrected formulation accounted for observations of transport of water and other molecules in CMS.     

Dielectric exclusion of ions from membranes

Dielectric exclusion is caused by the interactions of ions with the bound electric charges induced by ions at interfaces between media of different dielectric constants. It is considered as one of mechanisms of nanofiltration. The transport properties of capillary model are expressed through ion distribution and diffusion coefficients. Due to local equilibrium the distribution coefficient is directly related to the excess solvation energy of ion. First, this energy is considered for single ions in single neutral pores in terms of pore size, ion charge, dielectric constants of solvent and membrane matrix and pore geometry. The dielectric exclusion from pores with closed geometry like circular cylinders is shown to be essentially stronger than that from pores with relatively open geometry like slits. Furthermore, the role of finite membrane porosity is analysed for the model of infinite slabs with alternating dielectric constants. The presence of other ions is accounted for within the scope of a mean-field approach, and the screening of dielectric exclusion is thus introduced and considered in some detail. A fixed electric charge is shown to cause additional screening. At the same time the dielectric exclusion makes the Donnan exclusion of ions stronger. Therefore the interaction between those two rejection mechanisms turns out to be non-trivial. Finally, the effect of solvent molecular structure is considered within the scope of non-local electrostatics. It is shown that the solvent non-locality typically results in somewhat stronger dielectric exclusion, however, its most important effect is slowing down the decline of dielectric exclusion with increasing bulk electrolyte concentration.     

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.     

A kinetic model for nonisothermic homogeneous nucleation

A model for isothermal homogeneous nucleation is proposed that improves the classical model. A quasiequilibrium distribution of clusters was calculated on a basis of the Frenkel’-Lothe-Pound theory. The dependence of the free energy of clusters on their size was represented by an interpolation formula relating the free energy of dimers and large clusters to which a notion of macroscopic surface tension is applicable. The nucleation rate and the dependence of the cluster temperature on their size were calculated by balance equations describing the heating of from a cluster due to the condensation of monomers and its cooling due to collisions with an ambient gas. It is shown that the nucleation rate in excess buffer gas is higher than for the pure condensing gas by approximately two orders of magnitude. The model adequately describes the experimental data for the nucleation of methanol supersaturated vapor.     

Effect of hindered diffusion on the adsorption of proteins in agarose gel using a pore model

The hindered diffusion and binding of proteins of different sizes (lysozyme, BSA and IgG) in an agarose gel is described using adsorption kinetic and diffusional data together with an experimentally determined pore size distribution in the gel. The validity of the pore model, including variable diffusion coefficients and porosities is tested against experimental confocal microscopy data. No fitting parameters were used in the present model. The importance of knowing the gel structure is demonstrated especially for large proteins such as IgG. Experimental confocal microscopy data can be explained by the present model.     

Kinetics of the desorption of surfactants and proteins from adsorption layers at the solution/air interface

It is shown by experiments that the DeSNa desorption kinetics is governed by a pure diffusion mechanism, while the desorption of more surface active surfactants such as C13DMPO and Triton X-100 obeys a mixed mechanism. The BLG desorption kinetics, as shown by experiments, is determined by a barrier mechanism. From the analysis of the temperature dependence of the BLG desorption kinetics it is possible to calculate the activation energy of this process, which is quite close to the free energy of BLG adsorption. The theoretical model of desorption kinetics predicts that these two energetic parameters are approximately equal to each other if the adsorption activation energy is low. This can explain the fact that the higher the adsorption activity of a substance is, the lower is its desorption rate.     

Macrokinetic Analysis of Passivation of Pyrophoric Powders

A model of ignition and passivation of a layer of a pyrophoric nanopowder was proposed and studied by analytical and numerical methods. Under the assumption that the passivation wave propagation is controlled by the oxidant diffusion, the dependence of the maximum nanopowder temperature on governing parameters was characterized. Passivation was proposed to be performed in two stages with increasing oxidant concentration in the gas phase, which makes it possible to reach the complete passivation of a sample several times faster at permissible temperature rise and opens up new opportunities for improving nanopowder production performance.     

Diffusion of polarizable colloids in electromagnetic fields

Diffusion of polarizable colloids in electromagnetic fields is considered. Extensive and intensive thermodynamic formulations of magnetic and electric polarization energy is used to establish driving forces that generate diffusion of colloids. Effects of concentration, activity coefficient, and interfacial and polarization energies are formulated in terms of corresponding concentration dependent diffusion coefficients. Magnetic and electric diffusion coefficients are defined and it is shown that the former can be made comparable and even larger than ordinary diffusion coefficients of polarizable colloids. Magnetic diffusion coefficients are derived for mono- and polydisperse colloid mixtures relative to the fluid and then are transformed to the dispersion frame of reference. It is shown that ordinary and magnetic diffusion coefficients of polydisperse colloids can be resolved into four and three basic coefficients, respectively.     

Single-stage conversion of associated petroleum gas and natural gas to syngas in combustion and auto-ignition processes

Single-stage conversion of alkane mixtures simulating associated petroleum gas (APG) to syngas is studied in a static installation and in a flow reactor based on the rocket combustion chamber. Yields of the desired reaction products close to their thermodynamically equilibrium values are obtained. A range of experimental parameters, in which ignition delays of APG-oxygen mixtures exhibit negative or zero temperature coefficients, is determined for the first time. Such a behavior of ignition delays is proved to be a fundamental property of fuel-rich APG mixtures. The range of abnormal temperature dependence of ignition delays is shown to be extended as the initial pressure rises, which makes it possible to significantly increase the reaction rate by increasing the initial working pressure.     

Incremental vapor sorption in a phase-segregated polyurethane elastomer

Incremental vapor sorption and desorption runs have been carried out with o-dichlorobenzene (ODCB) a strongly swelling solvent, in 2, 6, and 10 mil polyether polyurethane films. Two-stage sorption behavior occurs at intermediate and higher concentrations but is generally absent in the desorption runs. Analysis of the two-stage curves, using the Berens-Hopfenberg model of independent Fickian diffusion and first-order relaxation processes, leads to apparent diffusion coefficients which increase with thickness and show a pronounced maximum with concentration, whereas the relaxation rate constant decreases with concentration. Correction for the pressure drift during the runs, due to the low vapor pressure of ODCB, reduces the thickness dependence. The negative concentration dependence of the relaxation rate constant is related to the distribution of microdomain stabilities. Calculated values of the self-diffusion coefficient show that the maximum in the apparent diffusion constant with concentration can be accounted for largely, but not entirely, by the thermodynamic contributions. It is proposed that the additional factor is relaxation-controlled swelling which arises from the strong coupling between the matrix and hard-segment responses.     

Relation between pore sizes of protein crystals and anisotropic solute diffusivities

The diffusion of a solute, fluorescein, into lysozyme protein crystals with different pore structures was investigated. To determine the diffusion coefficients, three-dimensional solute concentration fields acquired by confocal laser scanning microscopy (CLSM) during diffusion into the crystals were compared with the output of a time-dependent 3-D diffusion model. The diffusion process was found to be anisotropic, and the degree of anisotropy increased in the order: triclinic, tetragonal and orthorhombic crystal morphology. A linear correlation between the pore diffusion coefficients and the pore sizes was established. The maximum size of the solute, deduced from the established correlation of diffusion coefficients and pore size, was 0.73 +/- 0.06 nm, which was in the range of the average diameter of fluorescein (0.69 +/- 0.02 nm). This proves that size exclusion is the key mechanism for solute diffusion in protein crystals. Hence, the origin of solute diffusion anisotropy can be found in the packing of the protein molecules in the crystals, which determines the crystal pore organization.     

Diffusion of methane and carbon dioxide in carbon molecular sieve membranes by multinuclear pulsed field gradient NMR

Carbon molecular sieve (CMS) membranes are promising materials for energy efficient separations of light gases. In this work, we report a detailed microscopic study of carbon dioxide and methane self-diffusion in three CMS membrane derived from 6FDA/BPDA(1:1)-DAM and Matrimid polymers. In addition to diffusion of one-component sorbates, diffusion of a carbon dioxide/methane mixture was investigated. Self-diffusion studies were performed by the multinuclear (i.e., (1)H and (13)C) pulsed field gradient (PFG) NMR technique which combines the advantages of high field (17.6 T) NMR and high magnetic field gradients (up to 30 T/m). Diffusion measurements were carried out at different temperatures and for a broad range of the root-mean-square displacements of gas molecules inside the membranes. The diffusion data obtained from PFG NMR are compared with the corresponding results of membrane permeation measurements reported previously for the same membrane types. The observed differences between the transport diffusivities and self-diffusion coefficients of carbon dioxide and methane are discussed.