Micro-imaging of transient guest profiles in nanochannels

Zeolites of type ferrierite are exploited as a host system for monitoring the evolution of guest concentration (methanol) in nanoporous host materials upon adsorption. Additional transport resistances at the crystal surface have been removed so that uptake is exclusively controlled by the diffusion resistance of the pore space. Since the crystal shape deviates from a simple parallelepiped, the primary imaging data do not immediately reflect true local concentrations. A simple algorithm is developed which overcomes this complication. The determined transient concentration profiles ideally comply with the requirements for the application of the Boltzmann-Matano integration method for determining diffusivities. The resulting diffusivities (along the direction of the "10-ring channels") are found to exceed those along the 8-ring channels by three orders of magnitude.     

Sorption Kinetics and Intracrystalline Diffusion of Methanol in Ferrierite: An Example of Disguised Kinetics

Sorption kinetics of methanol in large crystals of ferrierite have been studied in detail by interference microscopy (IFM) and infra-red microscopy (IRM). The IFM measurements yield the transient concentration profiles, thus providing a direct measurement of both the surface resistance to mass transfer and the internal diffusion resistance. It is shown that, for this system, the uptake rate is controlled by the combined effects of surface resistance and diffusion through the 8-ring channels (in the y-direction). Transport through the 10-ring channels (in the z-direction) appears to be blocked by surface resistance. Although the overall uptake curves conform well to the “root t law” the diffusivity values derived from the uptake curves vary widely depending on the assumed direction of diffusion. Even if the correct direction of diffusion is assumed, the diffusivity values derived from the uptake curves are seriously in error as a result of the intrusion of surface resistance. The existence of transport resistances at the crystal surface is clearly apparent from the transient concentration profiles but is not obvious from the uptake curves.     

The options of interference microscopy to explore the significance of intracrystalline diffusion and surface permeation for overall mass transfer on nanoporous materials

After a short introduction into interference microscopy and its potentials in monitoring transient concentration profiles in nanoporous materials, we concentrate on the special options of an analysis of these profiles close to the crystal surfaces. We shall in particular introduce a novel route of correlating the overall uptake, at a certain instant of time, with the current boundary concentration. In this way, the significance of surface resistances to overall molecular uptake may be most vividly demonstrated. Considering a large variety of nanoporous host-guest systems, including methanol in zeolites ferrierite, methanol in MOF Manganese(II)-formate and methanol in SAPO STA-7, quite different patterns of surface resistivities may be observed. A generalized analysis is complicated by the fact that both the diffusivities and the surface permeabilities are found to notably depend on the actual concentration. As a consequence, for one and the same system and over identical pressure steps, the relative contributions of diffusion and surface permeation to the overall process may be quite different for desorption and adsorption.     

Molecular dynamics simulation of solvent-polymer interdiffusion: Fickian diffusion

The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a function of time. The weight gain is found to scale as t(1/2), which is expected for Fickian diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity. The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self-diffusion constant in the dilute solvent limit. We separately calculated the diffusivity as a function of concentration using the Darken equation and found that the diffusivity is essentially constant for the concentration range relevant for interdiffusion.     

Measuring diffusivity in supercooled liquid nanoscale films using inert gas permeation. II. Diffusion of Ar, Kr, Xe, and CH4 through methanol

We present an experimental technique to measure the diffusivity of supercooled liquids at temperatures near their T(g). The approach uses the permeation of inert gases through supercooled liquid overlayers as a measure of the diffusivity of the supercooled liquid itself. The desorption spectra of the probe gas are used to extract the low temperature supercooled liquid diffusivities. In the preceding companion paper, we derived equations using ideal model simulations from which the diffusivity could be extracted using the desorption peak times for isothermal or peak temperatures for temperature programmed desorption experiments. Here, we discuss the experimental conditions for which these equations are valid and demonstrate their utility using amorphous methanol with Ar, Kr, Xe, and CH(4) as probe gases. The approach offers a new method by which the diffusivities of supercooled liquids can be measured in the experimentally challenging temperature regime near the glass transition temperature.     

Effective diffusivities of BSA in cellulosic fiber beds measured with magnetic resonance imaging

The temporal and spatial evolution of concentration profiles of bovine serum albumin (BSA) in various cellulosic fiber beds is measured using magnetic resonance imaging. Effective diffusivities are calculated using a numerical one dimensional Fickian model to match experimental concentration profiles. Experimental values of the diffusivities are compared with predictions from a simple diffusion-adsorption model which accounts for porosity, tortuosity, and surface adsorption. BSA was found to have negligible adsorption in the concentration range studied, resulting in a simplified diffusion model based on fiber characteristics and geometry. Effective diffusivities agreed well with the predicted values and were within an order of magnitude of the estimated bulk diffusivity of BSA.     

Adsorption-desorption isotherm hysteresis of phenol on a C18-bonded surface

Single component adsorption and desorption isotherms of phenol were measured on a high-efficiency Kromasil-C18 column (N = 15000 theoretical plates) with pure water as the mobile phase. Adsorption isotherm data were acquired by frontal analysis (FA) for seven plateau concentrations distributed over the whole accessible range of phenol concentration in pure water (5, 10, 15, 20, 25, 40, and 60 g/l). Desorption isotherm data were derived from the corresponding rear boundaries, using frontal analysis by characteristic points (FACP). A strong adsorption hysteresis was observed. The adsorption of phenol is apparently modeled by a S-shaped isotherm of the first kind while the desorption isotherm is described by a convex upward isotherm. The adsorption breakthrough curves could not be modeled correctly using the adsorption isotherm because of a strong dependence of the accessible free column volume on the phenol concentration in the mobile phase. It seems that retention in water depends on the extent to which the surface is wetted by the mobile phase, extent which is a function of the phenol concentration, and of the local pressure rate, which varies along the column, and on the initial state of the column. By contrast, the desorption profiles agree well with those calculated with the desorption isotherms using the ideal model, due to the high column efficiency. The isotherm model accounting best for the desorption isotherm data and the desorption profiles is the bi-Langmuir model. Its coefficients were calculated using appropriate weights in the fitting procedure. The evolution of the bi-Langmuir isotherm parameters with the initial equilibrium plateau concentration of phenol is discussed. The FACP results reported here are fully consistent with the adsorption data of phenol previously reported and measured by FA with various aqueous solutions of methanol as the mobile phase. They provide a general, empirical adsorption model of phenol that is valid between 0 and 65% of methanol in water.     

Guest diffusion in interpenetrating networks of micro- and mesopores

Pulsed field gradient NMR is applied for monitoring the diffusion properties of guest molecules in hierarchical pore systems after pressure variation in the external atmosphere. Following previous studies with purely mesoporous solids, also in the material containing both micro- and mesopores (activated carbon MA2), the diffusivity of the guest molecules (cyclohexane) is found to be most decisively determined by the sample "history": at a given external pressure, diffusivities are always found to be larger if they are measured after pressure decrease (i.e., on the "desorption" branch) rather than after pressure increase (adsorption branch). Simple model consideration reproduces the order of magnitude of the measured diffusivities as well as the tendencies in their relation to each other and their concentration dependence.     

The effect of concentration on Li diffusivity and conductivity in rutile TiO2

Li transport characteristics are studied by means of density functional theory (DFT) and molecular dynamics (MD) simulations in order to investigate concentration effects on Li chemical diffusivity and conductivity in TiO(2) rutile. Our MD simulations predict one-dimensional diffusion of Li ions via jumps between the octahedral sites along the channels parallel to the c-axis. The diffusion barrier and diffusion coefficient (at room temperature) for the isolated Li, determined by means of DFT calculations, correspond to 60 meV and 9.1 × 10(-6) cm(2) s(-1), respectively. Such a small barrier suggests rapid mass transport along the channels. MD simulations are performed to evaluate the concentration dependent diffusivity profiles. The changes in Li energetics and dynamics are studied as a function of Li content, which is varied primarily between 10% and 50%. In addition, we consider a couple of compositions over 50% although this is above the intercalation limit. Our results suggest that Li diffusivity is strongly dependent on the Li?∶?TiO(2) ratio, and it decreases with increasing Li concentration. For instance, at room temperature, we find Li diffusivity for high concentrations (50% Li) to be three orders of magnitude slower than that for lower concentrations (10% Li). Our analyses on the energetics and dynamics suggest that the changes in the diffusivities originate from successive increases in the barriers with increasing concentration. The decrease in diffusivity as a function of increasing Li content is attributed to the fact that additional Li ions successively block the energetically preferred vacant sites along the channels. Our analyses also show that increasing Li concentration enhances the Li-Li repulsion within the channels, and as a result, diffusion is hindered. We also compare concentration-dependent diffusivities for Li diffusion in anatase, rutile and amorphous TiO(2). Interestingly, we find differing concentration dependence of the diffusivity in these chemically identical but structurally non-equivalent TiO(2) polymorphs. Our study suggests that these differences result from intrinsic structural characteristics of TiO(2) polymorphs, which ultimately contribute to intercalation limit, diffusivity, ionic conductivity, and the electrochemical performance in energy storage applications.     

Intracrystalline diffusivities and surface permeabilities deduced from transient concentration profiles: methanol in MOF manganese formate

The intracrystalline concentration profiles during molecular uptake of methanol by an initially empty, single crystal of microporous manganese(II) formate (Mn(HCO2)2), representing an ionic inorganic-organic hybrid within the MOF family, are monitored by interference microscopy. Within these profiles, a crystal section could be detected where over the total of its extension ( approximately 2 microm x 50 microm x 30 microm) molecular uptake ideally followed the pattern of one-dimensional diffusion. Analysis of the evolution of intracrystalline concentration in this section directly yields the permeability of the crystal surface and the intracrystalline diffusivity as a function of the concentration of the total range of 0 相似文献   

Lysozyme transport in p-HEMA hydrogel contact lenses

Protein binding in hydrogels adversely affects their performance and can interfere with their usage in several biomedical applications including contact lenses. In this study we focus on understanding and modeling the mechanisms of protein transport in hydrogels, specifically focusing on the effect of protein concentration and gel crosslinking on transport. Specifically, we focus on lysozyme, the most abundant protein in tear fluid, and hydrogels of poly-hydroxyethyl methacrylate (p-HEMA), a common contact lens material. Protein uptake experiments with gels of different thicknesses showed a time scale increase as the square of the thickness suggesting diffusion controlled transport. Partition coefficient was found to be dependent on the equilibrium concentration of lysozyme, and also on the degree of crosslinking. Since transport is related to mesh size, gel modulus was obtained for various crosslinkings and utilized to estimate the mesh size. The transport data were fitted to a diffusion model and the fitted diffusivity was compared to diffusivity predicted from a model based on hydrogel mesh size. Both protein absorption and desorption data fitted the diffusion model with the same value of diffusivity, but the experimentally measured diffusivities were significantly smaller than those estimated on the basis of the gel mesh size. Models were modified to take into account protein binding to the polymer but the modified predictions were still larger than the measured values. The results of this study could assist in the development of contact lens materials that exhibit minimal protein binding, in designing cleaning regimens for protein removal from contact lenses, and in applications related to protein binding in several other biomaterials.     

Imaging of transient guest profiles in nanoporous host materials: a new experimental technique to study intra-crystalline diffusion

The application of interference microscopy (IFM) and infrared microscopy (IRM) to monitoring transient concentration profiles during uptake and release of guest molecules in nanoporous materials has opened a novel technique for diffusion studies with adsorbed molecules. For the first time, the coefficients of transport diffusion and the surface permeabilities have become accessible by direct observation under non-equilibrium conditions. The examples presented in this communication include diffusion and permeation measurements with zeolites of the ferrierite type and with metal-organic frameworks (MOFs) of type ZIF-8     

Rapid monoclonal antibody adsorption on dextran-grafted agarose media for ion-exchange chromatography

The binding capacity and adsorption kinetics of a monoclonal antibody (mAb) are measured for experimental cation exchangers obtained by grafting dextran polymers to agarose beads and compared with measurements for two commercial agarose-based cation exchangers with and without dextran grafts. Introduction of charged dextran polymers results in enhanced adsorption kinetics despite a dramatic reduction of the accessible pore size as determined by inverse size-exclusion chromatography. Incorporation of neutral dextran polymers in a charged agarose bead results instead in substantially lower binding capacities. The effective pore diffusivities obtained from batch uptake curves increase substantially as the protein concentration is reduced for the resins containing charged dextran grafts, but are much less dependent on protein concentration for the resins with no dextran or uncharged dextran grafts. The batch uptake results are corroborated by microscopic observations of transient adsorption in individual particles. In all cases studied, the adsorption kinetics is characterized by a sharp adsorption front consistent with a shell-progressive, diffusion limited mechanism. Greatly enhanced transport rates are obtained with an experimental resin containing charged dextran grafts with effective pore diffusivities that are 1-9 times larger than the free solution diffusivity and adsorption capacity approaching 300 mg/cm3 of particle volume.     

Diffusion kinetics for methanol in polycrystalline ice

Quantitative analyses of the isothermal desorption kinetics from methanol-doped H2O films on Pt(111) reveal that transport kinetics for CH3OH in polycrystalline ice are much slower than previously reported. They also indicate that MeOH displays first-order desorption kinetics with respect to its instantaneous surface concentration below 0.1 mole fraction in ice. These observations allow isothermal desorption rate measurements to be interpreted in terms of a depth profiling analysis providing one-dimensional concentration depth profiles from methanol-doped polycrystalline ice films. Using a straightforward approach to inhibit ice sublimation, transport properties are extracted from the evolution of concentration depth profiles obtained after thermal annealing of binary ice films at high temperature. Heterodiffusion coefficients for methanol in polycrystalline (cubic) ice Ic films are reported for temperatures between 145 and 195 K and for concentrations below 10(-3) mole fraction. Finally, diffusion kinetics for methanol in ice are shown to display a very strong concentration dependence that may contribute, in addition to variations in laboratory samples microstructure, to the disagreements reported in the literature regarding the transport properties of ice.     

Hydrophobic interaction chromatography of proteins III. Transport and kinetic parameters in isocratic elution

The effective pore diffusivities, D(e), of five model proteins (ribonuclease A, lysozyme, alpha-lactalbumin, ovalbumin, and BSA) in eight commercial phenyl hydrophobic interaction chromatography (HIC) media were determined by analyzing the plate height data from isocratic elution using the first two moments of the general linear rate model. The adsorbents represent a diverse set of HIC media that are widely used for protein purification. The estimated pore diffusivities were used to calculate the elution profiles of proteins in these adsorbents and were compared with the elution profiles obtained experimentally. High protein loading and sample protein concentration led to the underestimation of the pore diffusivity by the linear rate model. Comparisons between the calculated and the experimental profiles suggest that the pore diffusivities obtained from the linear rate model are generally accurate for proteins with low structural flexibility but not for more flexible ones, presumably because conformational change effects contribute significantly to the overall HETP. The general linear rate model was modified to account for the protein folding/unfolding kinetics, and parameter values could be estimated by fitting the experimental elution profiles to the modified model. In addition to conformational change, adsorbent type also had a significant effect on the accuracies of the pore diffusivities estimated by the linear rate model. The results also show that pore diffusion was the rate-limiting step in all absorbents for rigid proteins such as ribonuclease A and lysozyme. For structurally flexible proteins, conformational change contributed significantly to the overall reduced plate heights of the isocratic elution peaks. The physical properties of adsorbents, such as protein accessible porosity, pore size distribution, pore radius and pore connectivity, play important roles in determining the effective protein pore diffusivities.     

Gas diffusion in polycrystalline silicalite membranes investigated by 1H pulse field-gradient NMR

1H pulse field-gradient (PFG) spin-echo NMR was performed to measure the diffusivity of methane in a polycrystalline MFI-type silicalite membrane. Measured diffusivities decreased with an increase in the diffusion distance and converged to the constant value. This result suggests the presence of a transport barrier in the membrane. The long-time diffusivity in the membrane was 3.7 x 10(-9) m2/s, which was a factor of 3 smaller than reported values in a single crystal. The distance between the transport barriers was estimated to be much larger than 6 mum from the relationship of diffusivity with displacement. It should be noted that the estimated distances were larger than the smallest dimension of the crystals appearing in the membrane surface. Gas permeation and pervaporation tests were carried out on the same sample for which NMR measurements were taken. The estimated methane flux using measured long-time diffusivity by the permeation theory overestimated the experimental value, although it is closer to the experimental value than the value estimated using the short-time diffusivity. These results mean that the methane diffusivity in a silicalite membrane is much smaller than that in a single crystal.     

Measuring diffusivity in supercooled liquid nanoscale films using inert gas permeation. I. Kinetic model and scaling methods

We describe in detail a diffusion model used to simulate inert gas transport through supercooled liquid overlayers. In recent work, the transport of the inert gas has been shown to be an effective probe of the diffusivity of supercooled liquid methanol in the experimentally challenging regime near the glass transition temperature. The model simulations accurately and quantitatively describe the inert gas permeation desorption spectra. The simulation results are used to validate universal scaling relationships between the diffusivity, overlayer thickness, and the temperature ramp rate for isothermal and temperature programmed desorption. From these scaling relationships we derive simple equations from which the diffusivity can be obtained using the peak desorption time or temperature for an isothermal or set of TPD experiments, respectively, without numerical simulation. The results presented here demonstrate that the permeation of gases through amorphous overlayers has the potential to be a powerful technique to obtain diffusivity data in deeply supercooled liquids.     

Interdiffusion of solvent into glassy polymer films: a molecular dynamics study

Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time t as t(1/2) in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the one-dimensional Fick's model of the diffusion equation is compared to the diffusivity calculated using the Darken equation from simulations of equilibrated solvent-polymer solutions. The diffusivity calculated using these two different approaches are in good agreement. The behavior of the diffusivity strongly depends on the state of the polymer and is related to the shape of the solvent concentration profile.     

Diffusion of guest molecules in MCM-41 agglomerates

The pulsed field gradient nuclear magnetic resonance method has been used to study self-diffusion of cyclohexane in a commercial MCM-41 material at different external gas pressures from zero to saturated vapor pressure. It is found that the effective diffusivities exhibit three different regions with increasing pressure: decrease at low pressures, a sudden drop at intermediate pressures, and increase at higher pressures. In addition, in the region of irreversible adsorption (hysteresis loop) the diffusivities are also found to differ on the adsorption and the desorption branches. A simple analytical model taking account of different molecular ensembles with different transport properties due to the complex architecture of the porous structure is developed which provides a quantitative prediction of the experimental data. The analysis reveals that the effective diffusivity is predominantly controlled by the adsorption properties of the individual mesoporous MCM-41 crystallites which, in combination with high transport rates, provide a simple instrument for fine tuning of the transport properties by a subtle variation of the external conditions.