Theoretical modeling of water vapor transport in cellulose-based materials

The theory of mass transport in porous media is of fundamental importance for different applications such as food, paper packaging, textiles, and wood for building materials. In this study, a theoretical water vapor transport model has been developed for cellulose-based materials, such as paper and regenerated cellulose film. Pore diffusivities were determined from the dynamic moisture breakthrough experiments comprising a stack of paper sheets and regenerated cellulose films in a configuration similar to a packed adsorption column. Other mass transfer parameters were determined from transient moisture uptake rate measurements. The model incorporates pore and surface diffusion as a lump parameter into a variable effective diffusion coefficient. The mass transport, involving both pore and surface diffusions, is evaluated independently. The theoretical water vapor transmission rates (WVTRs) obtained from the model were compared with experimentally determined WVTRs measured under steady-state conditions. The theoretical model, based on intrinsic diffusion, stipulates higher WVTR values compared to the experimental results. However, the theoretical water vapor transfer rates agree well with the experimental results when external mass transfer resistance is incorporated in the model.     

Interface chemistry of nanostructured materials: ion adsorption on mesoporous alumina

This paper presents a part of our work on understanding the effect of nanoscale pore space confinement on ion sorption by mesoporous materials. Acid-base titration experiments were performed on both mesoporous alumina and alumina particles under various ionic strengths. The point of zero charge (PZC) for mesoporous alumina was measured to be approximately 9.1, similar to that for nonmesoporous alumina materials, indicating that nanoscale pore space confinement does not have a significant effect on the PZC of pore surfaces. However, for a given pH deviation from the PZC, (pH-PZC), the surface charge per mass on mesoporous alumina was as much as 45 times higher than that on alumina particles. This difference cannot be fully explained by the surface area difference between the two materials. Our titration data have demonstrated that nanoscale confinement has a significant effect, most likely via the overlap of the electric double layer (EDL), on ion sorption onto mesopore surfaces. This effect cannot be adequately modeled by existing surface complexation models, which were developed mostly for an unconfined solid-water interface. Our titration data have also indicated that the rate of ion uptake by mesoporous alumina is relatively slow, probably due to diffusion into mesopores, and complete equilibration for sorption could take 4-5 min. A molecular simulation using a density functional theory was performed to calculate ion adsorption coefficients as a function of pore size. The calculation has shown that as pore size is reduced to nanoscales (<10 nm), the adsorption coefficients of ions can vary by more than two orders of magnitude relative to those for unconfined interfaces. The prediction is supported by our experimental data on Zn sorption onto mesoporous alumina. Owing to their unique surface chemistry, mesoporous materials can potentially be used as effective ion adsorbents for separation processes and environmental cleanup.     

A network model for the permeability of condensable vapours through mesoporous media

The paper aims at introducing a discrete (network) approach to modelling transport of condensable vapours in mesoporous structures. Such models possess the potential for improving the understanding of the mechanisms responsible for the observed transport behaviour. The basic elements of a typical pore network representing a mesoporous medium are summarized and the current state concerning the simulation of the related phenomena is given. The main processes involved (adsorption, mass diffusion, surface flow, capillary condensation) are simulated over the entire range of relative pressure. Finally, the effects of material structural parameters (average pore radius, pore size distribution and standard deviation, pore connectivity) and other relevant factors (relative pressure, temperature, resistance to surface flow, total pressure drop) on vapour permeability are presented and the future research directions are pointed out.     

Three-dimensional pore evolution of nanoporous metal particles for energy storage

A well characterized and predictable aging pattern is necessary for practical energy storage applications of nanoporous particles that facilitate rapid transport of ions or redox species. Here we use STEM tomography with segmentation to show that surface diffusion and grain boundary diffusion are responsible for pore evolution at intermediate and higher temperatures, respectively. This unprecedented three dimensional understanding of pore behavior as a function of temperature suggests routes for optimizing pore stability in future energy storage materials.     

Nanoporous Glass as a Model System for a Consistency Check of the Different Techniques of Diffusion Measurement

The remarkable differences in the guest diffusivities in nanoporous materials commonly found with the application of different measuring techniques are usually ascribed to the existence of a hierarchy of transport resistances in addition to the diffusional resistance of the pore system and their differing influence due to the differing diffusion path lengths covered by the different measuring techniques. We report diffusion measurements with nanoporous glasses where the existence of such resistances could be avoided. Molecular propagation over diffusion path lengths from hundreds of nanometers up to millimeters was thus found to be controlled by a uniform mechanism, appearing in coinciding results of microscopic and macroscopic diffusion measurement.     

Self-diffusion and transport diffusion of light gases in metal-organic framework materials assessed using molecular dynamics simulations

Metal-organic framework (MOF) materials pose an interesting alternative to more traditional nanoporous materials for a variety of separation processes. Separation processes involving nanoporous materials can be controlled by either adsorption equilibrium, diffusive transport rates, or a combination of these factors. Adsorption equilibrium has been studied for a variety of gases in MOFs, but almost nothing is currently known about molecular diffusion rates in MOFs. We have used equilibrium molecular dynamics (MD) to probe the self-diffusion and transport diffusion of a number of small gas species in several MOFs as a function of pore loading at room temperature. Specifically, we have studied Ar, CH4, CO2, N2, and H2 diffusion in MOF-5. The diffusion of Ar in MOF-2, MOF-3, and Cu-BTC has been assessed in a similar manner. Our results greatly expand the range of MOFs for which data describing molecular diffusion is available. We discuss the prospects for exploiting molecular transport properties in MOFs in practical separation processes and the future role of MD simulations in screening families of MOFs for these processes.     

Preparative weak cation-exchange chromatography of monoclonal antibody variants I. Single-component adsorption

The retention behavior of a monoclonal antibody has been characterized on a weak cation exchanger, Fractogel EMD COO(-)(s). This new generation of resin materials comprise of a higher mechanical strength compared to softer gel-type matrices while maintaining elevated capacities, resulting in higher productivity and longer lifetimes. These parameters are extremely important when working with large bio-molecules such as proteins, and in particular monoclonal antibodies. In the first part of this work a parameter estimation strategy is presented to fully characterize the retention behavior of a single monoclonal antibody and determine suitable model parameters. Literature correlations were used for the estimation of mass transfer rates. The transport limiting parameter, pore diffusion, was regressed experimentally. Various methods for the adsorption isotherm determination have been applied, their combinations resulting in little experimental effort and accurate predictions of elution profiles. The process has been modelled with a complete pore diffusion model and the agreement between experimental and predicted profiles is good in general. However, a very marked sensitivity to changes in the effective pore diffusion coefficient has been observed. A correlation describing the effect of the separation conditions on the diffusion rate is therefore needed in order to have a fully predictive mathematical model.     

Multicomponent effective medium-correlated random walk theory for the diffusion of fluid mixtures through porous media

Molecular transport in nanoconfined spaces plays a key role in many emerging technologies for gas separation and storage, as well as in nanofluidics. The infiltration of fluid mixtures into the voids of porous frameworks having complex topologies is common place to these technologies, and optimizing their performance entails developing a deeper understanding of how the flow of these mixtures is affected by the morphology of the pore space, particularly its pore size distribution and pore connectivity. Although several techniques have been developed for the estimation of the effective diffusivity characterizing the transport of single fluids through porous materials, this is not the case for fluid mixtures, where the only alternatives rely on a time-consuming solution of the pore network equations or adaptations of the single fluid theories which are useful for a limited type of systems. In this paper, a hybrid multicomponent effective medium-correlated random walk theory for the calculation of the effective transport coefficients matrix of fluid mixtures diffusing through porous materials is developed. The theory is suitable for those systems in which component fluxes at the single pore level can be related to the potential gradients of the different species through linear flux laws and corresponds to a generalization of the classical single fluid effective medium theory for the analysis of random resistor networks. Comparison with simulation of the diffusion of binary CO(2)/H(2)S and ternary CO(2)/H(2)S/C(3)H(8) gas mixtures in membranes modeled as large networks of randomly oriented pores with both continuous and discrete pore size distributions demonstrates the power of the theory, which was tested using the well-known generalized Maxwell-Stefan model for surface diffusion at the single pore level.     

About the Dominance of Mesopores in Physisorption in Amorphous Materials

Amorphous, porous materials represent by far the largest proportion of natural and men-made materials. Their pore networks consists of a wide range of pore sizes, including meso- and macropores. Within such a pore network, material moisture plays a crucial role in almost all transport processes. In the hygroscopic range, the pores are partially saturated and liquid water is only located at the pore fringe due to physisorption. Therefore, material parameters such as porosity or median pore diameter are inadequate to predict material moisture and moisture transport. To quantify the spatial distribution of material moisture, Hillerborg’s adsorption theory is used to predict the water layer thickness for different pore geometries. This is done for all pore sizes, including those in the lower nanometre range. Based on this approach, it is shown that the material moisture is almost completely located in mesopores, although the pore network is highly dominated by macropores. Thus, mesopores are mainly responsible for the moisture storage capacity, while macropores determine the moisture transport capacity, of an amorphous material. Finally, an electrical analogical circuit is used as a model to predict the diffusion coefficient based on the pore-size distribution, including physisorption.     

Comparisons of porous and adsorption properties of carbons activated by steam and KOH

In this work, fir woods and pistachio shells were used as source materials to prepare porous carbons, which were activated by physical (steam) and chemical (KOH) methods. Pore properties of these activated carbons including the BET surface area, pore volume, pore size distribution, and pore diameter were first characterized by a t-plot method based on N(2) adsorption isotherms. Highly porous activated carbons with BET surface area up to 1009-1096 m(2)/g were obtained. The steam and KOH activation methods produced carbons with mesopore content in the range 9-15 and 33-49%, respectively. The adsorption equilibria and kinetics of tannic acid, methylene blue, 4-chlorophenol, and phenol from water on such carbons at 30 degrees C were then investigated to check their chemical characteristics. The Freundlich equation gave a better fit to all adsorption isotherms than the Langmuir equation. On the other hand, the intraparticle diffusion model could best follow all adsorption processes. In comparison with KOH-activated carbons, it was shown that the rate of external surface adsorption with steam-activated carbons was significantly higher but the rate of intraparticle diffusion was much lower.     

Electrokinetic and surface chemical characterizations of an irradiated microfiltration polysulfone membrane: comparison of two irradiation doses

The effect of ionizing radiation on the surface and electrokinetic characteristic parameters for a porous membrane of pore size 0.2 mum is determined and correlated with the irradiation dose (10 and 80 J/kg). Changes in NaCl permeability and membrane system electrical resistance determined from diffusion and impedance spectroscopy measurements are consistent with the increase of membrane pore radii/porosity, in agreement with SEM micrographs and reported results. Low irradiation dose seems to clean the membrane surface of impurities, according to XPS results, but the increase of irradiation doses could affect surface roughness. Due to the relatively high pore radius, ion transport numbers are practically independent of radiation and dose, but irradiation slightly modifies the membrane solution interface by increasing its weakly electronegative character, which could be of interest in the ultrafiltration of proteins or macromolecules.     

An experimental and theoretical analysis of molecular separations by diffusion through ultrathin nanoporous membranes

Diffusion based separations are essential for laboratory and clinical dialysis processes. New molecularly thin nanoporous membranes may improve the rate and quality of separations achievable by these processes. In this work we have performed protein and small molecule separations with 15 nm thick porous nanocrystalline silicon (pnc-Si) membranes and compared the results to 1- and 3- dimensional models of diffusion through ultrathin membranes. The models predict the amount of resistance contributed by the membrane by using pore characteristics obtained by direct inspection of pnc-Si membranes in transmission electron micrographs. The theoretical results indicate that molecularly thin membranes are expected to enable higher resolution separations at times before equilibrium compared to thicker membranes with the same pore diameters and porosities. We also explored the impact of experimental parameters such as porosity, pore distribution, diffusion time, and chamber size on the sieving characteristics. Experimental results are found to be in good agreement with the theory, and ultrathin membranes are shown to impart little overall resistance to the diffusion of molecules smaller than the physical pore size cutoff. The largest molecules tested experience more hindrance than expected from simulations indicating that factors not incorporated in the models, such as molecule shape, electrostatic repulsion, and adsorption to pore walls, are likely important.     

A microfluidic approach for measuring capillary pressure in PEMFC gas diffusion layers

A dearth of experimental capillary pressure data limits our understanding and optimization of liquid water transport in PEMFC gas diffusion layers (GDLs). A microfluidic device and method is described for measuring the capillary pressure as a function of liquid water saturation for these thin porous materials with complex, heterogeneous wetting properties. A sample sandwich (hydrophilic membrane–GDL–hydrophobic membrane) is key for probing the entire hydrophilic and hydrophobic pore volume of the GDL during sequential liquid intrusion and gas intrusion experiments. The capillary pressure curves for an as-purchased Toray 090 and two differentially-processed Avcarb P75T GDLs were evaluated; each material displayed highly repeatable, but quantitatively different, room temperature capillary pressure curves that matched qualitative differences in their macroscopic wettability. The measurements show that hysteresis between the liquid intrusion and gas intrusion curves is significant. For example, both the Toray and fully wet-proofed Avcarb GDLs appear hydrophobic during most of the liquid intrusion curve and hydrophilic during most of the gas intrusion curve. The implications of this work for water management, and future device designs and experiments are described.     

Mesoporous zirconium titanium oxides. Part 1: Porosity modulation and adsorption properties of xerogels

A series of zirconium titanium oxide mesophases containing 33 atom % Zr have been prepared using carboxylic acids of different alkyl chain lengths (Cy ) from y=4-18 through organic-inorganic polymer phase segregation as the gel transition is approached. Thermal treatment of these transparent gels up to 450 degrees C eliminated the organic template, and domain coarsening occurred affording stable worm-hole mesoporous materials of homogeneous composition and pore diameters varying from about 3 to 4 nm in fine increments. With such materials, it was subsequently possible to precisely study the adsorption of vanadium oxo-anions and cations from aqueous solutions and, more particularly, probe the kinetics of intraparticle mass transport as a function of the associated pore dimension. The kinetics of mass transport through the pore systems was investigated using aqueous vanadyl (VO2+) and orthovanadate (VO3(OH)2-) probe species at concentrations ranging from 10 to 200 ppm (0.2 to 4 mmol/L) and pH values of 0 and 10.5, respectively. In the case of both of these vanadium species, the zirconium titanate mesophases displayed relatively slow kinetics, taking in excess of about 500 min to achieve maximum uptake. By using a pseudo-second-order rate law, it was possible to extract the instantaneous and overall rate of the adsorption processes and then relate these to the pore diameters. Both the instantaneous and overall rates of adsorption increased with increasing surface area and pore diameter over the studied pore size range. However, the equilibrium adsorption capacity increased linearly with pore diameter only for the higher concentrations and was independent of pore diameter for the lower concentration. These results have been interpreted using a model in which discrete adsorption occurs at low concentrations and is then followed by multilayer adsorption at higher concentration.     

Preparation of organic-inorganic composite anion-exchange membranes via aqueous dispersion polymerization and their characterization

Organic-inorganic composite membranes based on poly(vinyl alcohol)/SiO(2) were prepared via an aqueous dispersion polymerization route and anion-exchange groups were introduced in the membrane matrix by the chemical grafting of 4-vinylpyridine with the desired content. These membranes were extensively characterized for their surface morphology, thermal stability, water content, and surface-charge properties using SEM, TEM, FTIR, TGA, water uptake, and ion-exchange capacity measurements. Counterion transport numbers across these membranes were estimated from membrane potential data. Membrane conductance measurements were also performed and these data were used for the estimation of values of counterion diffusion coefficients in the membrane phase. Physicochemical and electrochemical properties of these membranes and equivalent pore radius (estimated from electroosmotic flux measurements) were found to be highly dependent on the 4-vinylpyridine (4-VP) content in the membrane phase. It was also observed that for better selectivity and membrane conductivity of anion-exchange membranes complete optimization of the loading of 4-VP in the membrane phase is necessary. Furthermore, among these, membrane with 25% loading with 4-VP exhibited very good selectivity, water content, and ion-exchange capacity along with moderate membrane conductivity, which may be used for their application in electro-driven separation at elevated temperatures or for other electrochemical processes.     

Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed.     

In situ study on molecular diffusion phenomena in nanoporous catalytic solids

As an omnipresent phenomenon in nature, diffusion is among the rate-determining processes in many technological processes. This is in particular true for catalytic conversion in nanoporous materials. We provide a critical review of the possibilities of exploring diffusion phenomena over microscopic dimensions in such media by direct experimental observation. By monitoring the probability distribution of molecular displacements as a function of time, the pulsed field gradient technique of NMR (PFG NMR) records the rate of molecular re-distribution. By varying the observation time, PFG NMR is thus able to trace even hierarchies of transport resistances as occurring, e.g., in catalyst particles in the form of binder-compacted assemblages of zeolite crystallites. Alternatively, and complementary to this information, interference microscopy (IFM) and IR microscopy (IRM) are able to follow the evolution of intracrystalline concentration profiles during uptake and release. This allows, in particular, an accurate quantification of the transport resistances on the surface of the individual crystallites and of the probability that reactant molecules from the gas phase, upon colliding with the external surface, are able to penetrate through such "surface barriers" into the crystal bulk phase. Being able to distinguish between different molecular species, IRM is able to record the evolution of intracrystalline concentration profiles even during multi-component adsorption and catalytic reactions (169 references).     

Characterization and modeling of nonlinear hydrophobic interaction chromatographic systems

A general rate model was employed in concert with a preferential interaction quadratic adsorption isotherm for the characterization of HIC resins and the prediction of solute behavior in these separation systems. The results indicate that both pore and surface diffusion play an important role in protein transport in HIC resins. The simulated and experimental solute profiles were compared for two model proteins, lysozyme and lectin, for both displacement and gradient modes of chromatography. Our results indicate that a modeling approach using the generate rate model and preferential interaction isotherm can accurately predict the shock layer response in both gradient and displacement chromatography in HIC systems. While pore and surface diffusion played a major role and were limiting steps for proteins, surface diffusion was seen to play less of a role for the displacer. The results demonstrate that this modeling approach can be employed to describe the behavior of these non-linear HIC systems, which may have implications for the development of more efficient preparative HIC separations.