Gas Sorption Characterization of Porous Materials Employing a Statistical Theory for Bethe Lattices.

In the present work, a recently developed statistical theory for adsorption and desorption processes in mesoporous solids, modeled by random Bethe lattices, has been applied to obtain pore size distributions and interpore connectivity from sorption isotherms in real random porous materials, employing a robust and validated methodology. Using the experimental adsorption-desorption N2 isotherms at 77.4 K on Vycor glass, a porous material with random pore structure, we demonstrate the solution of the inverse problem resulting in extracted pore size distribution and interpore connectivity, notably different from the predictions of earlier theories. The results presented are corroborated by the analysis of 3D digital images of reconstructed Vycor porous glass, showing excellent agreement between the predictions of geometric analysis and the new statistical theory.

Connecting dynamic pore filling mechanisms with equilibrium and out of equilibrium configurations of fluids in nanopores.

In the present study, using dynamic mean field theory complemented by grand canonical molecular dynamics simulations, we investigate the extent to which the density distributions encountered during the dynamics of capillary condensation are related to those distributions at equilibrium or metastable equilibrium in a system at fixed average density (canonical ensemble). We find that the states encountered can be categorized as out of equilibrium or quasi-equilibrium based on the magnitude of the driving force for mass transfer. More specifically, in open-ended slit pores, pore filling via double bridging is an out of equilibrium process, induced by the dynamics of the system, while pore filling by single bridge formation is connected to a series of configurations that are equilibrium configurations in the canonical ensemble and that cannot be observed experimentally by a standard adsorption process, corresponding to the grand canonical ensemble. Likewise, in closed cap slits, the formation of a liquid bridge near the pore opening and its subsequent growth while the initially detached meniscus from the capped end remains immobilized are out of equilibrium processes that occur at large driving forces. On the other hand, at small driving forces, there is a continuous acceleration of the detached meniscus from the capped end, which is associated with complete reversibility in the limit of an infinitesimally small driving force.

Free energy landscape within the hysteresis regime for fluids confined in disordered mesoporous solids.

Adsorption/desorption and melting/freezing in structurally disordered nanoporous solids exhibit strongly non-equilibrium behavior as revealed by the formation of a hysteresis region populated by the multitude of different states. Many questions concerning the free energy spectrum of these states, including the existence of the equilibrium transition, if any, their accessibility in the experiments, and internal relaxation dynamics toward the global energy minimum, still remain poorly addressed. By using a serially connected pore model with the statistical disorder as a minimal model of the pore networks, we explore the system free energies along the solid-liquid and liquid-gas transitions in the pore systems. The rigorous results obtained with this model shed light on the occurrence and nature of the equilibrium transition line in porous solids with arbitrary pore topology. We discuss further the free energies along the experimentally measured boundary and scanning transitions and how close the equilibrium states can be approached in these experiments.

Nonequilibrium Steady States in Fluid Transport through Mesopores: Dynamic Mean Field Theory and Nonequilibrium Molecular Dynamics.

We present a dynamic mean field theory (DMFT) and nonequilibrium dual control volume grand canonical molecular dynamics (GCMD) simulation study of steady-state fluid transport in slit-shaped mesopores under an applied chemical potential gradient. The main focus is on states where the bulk conditions on one side of the pore would lead to a capillary condensed state in the pore at equilibrium while those on the other side would lead to a vapor state in the pore. This choice of conditions is motivated by certain separation applications in which condensable vapors permeate through mesoporous membranes. Under these circumstances, we have found partially filled states with a liquid-like state at the high chemical potential end of the pore and a vapor-like state at the low chemical potential end. This phenomenon is accompanied by hysteresis. The existence of partially filled states has been hypothesized in previous work but the present paper reveals them as an emergent feature of the systems. We find that predictions of DMFT are in good qualitative agreement with the overall GCMD results. However, the GCMD results demonstrate that the transport is faster through the partially filled pore than through the unfilled pore, a feature not captured by DMFT.

A comparison of dynamic mean field theory and grand canonical molecular dynamics for the dynamics of pore filling and capillary condensation of fluids in mesopores.

We use results from grand canonical molecular dynamics (GCMD) to test the predictions from dynamic mean field theory (DMFT) for the pore filling and capillary condensation mechanisms of a fluid confined in slit shaped mesopores. The theory predicts that capillary condensation occurs by a nucleation process in which a liquid bridge forms between the two walls, and the pore is filled via the growth of this bridge. For longer pores, multiple bridging is seen. These mechanisms are confirmed by the molecular dynamics simulations. The primary difference between the theory and simulations lies in the role of fluctuations. DMFT predicts a single nucleation time and location, while in GCMD (and in nature) a distribution of nucleation times and locations is seen.

Dynamic density functional theory with hydrodynamic interactions: theoretical development and application in the study of phase separation in gas-liquid systems.

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van der Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.

Synthesis and characterization of TiFe(0.7-x)Mn(0.3)V(x) (x = 0.05, and 0.1) and Ti(1-y)Ta(y)Fe(0.7)Mn(0.3) (y = 0.2, and 0.4) nanostructured metal hydrides for low temperature applications.

Metal hydrides (MH) are often preferred to absorb and desorb hydrogen at ambient temperature and pressure with a high volumetric density. These hydrogen storage alloys create promising prospects for hydrogen storage and can solve the energetic and environmental issues. In the present research work, the goal of our studies is to find the influence of partial substitution of small amounts of vanadium and tantalum on the hydrogenation properties of TiFe(0.7-x)Mn(0.3)V(x) (x = 0.05, and 0.1) and Ti(1-y)Ta(y)Fe(0.7)Mn(0.3) (y = 0.2, and 0.4) alloys, respectively. The nominal compositions of these materials are TiFe(0.6)Mn(0.3)V(0.05), TiFe(0.6)Mn(0.3)V(0.1), Ti(0.8)Ta(0.2)Fe(0.7)Mn(0.3), and Ti(0.6)Ta(0.4)Fe(0.7)Mn(0.3). All samples were synthesized by arc-melting high purity elements under argon atmosphere. The structural and microstructural properties of the samples were studied by using XRD and SEM, respectively, while the corresponding microchemistry was determined by obtaining EDS measurements at specific regions of the samples. Mapping was obtained in order to investigate atomic distribution in microstructure. Moreover, to ensure the associations between the properties and structure, all samples were examined by an optical microscope for accessional characterization. From all these microscopic examinations a variety of photomicrographs were taken with different magnifications. The hydrogenation properties were obtained by using a Magnetic Suspension Balance (Rubotherm). In this equipment, the hydrogen desorption and re-absorption, can be investigated at constant hydrogen pressures in the range of 1 to 20 MPa (flow-through mode). At least 3.43 wt.% of absorbed hydrogen amount was measured while the effect of substitutions was investigated at the same temperature.

Structural, microchemistry, and hydrogenation properties of TiMn0.4Fe0.2V0.4, TiMn0.1Fe0.2V0.7 and Ti0.4Zr0.6Mn0.4Fe0.2V0.4 metal hydrides.

In this work, TiFe-based alloys have been developed according to the stoichiometry Ti1-xAx Fe1-yBy (A [triple bond] Zr; B [triple bond] Mn, V). The hydrogen solubility properties have been investigated to develop dynamic hydrides of Ti-based alloys for hydrogen storage applications. The hydrogenation behavior of these alloys has been studied, and their hydrogen storage capacities and kinetics have been evaluated. Several activation modes, including activation at high temperatures under hydrogen pressure, have been attempted for the as-milled powders. In order to clarify the structural/microstructural characteristics, and chemical composition before and after hydrogenation, X-Ray Diffraction (XRD), EDAX-Mapping Analysis and Scanning Electron Microscopy (SEM), have been carried out for the samples. Modeling of the isotherms has been performed by using MATLAB programming. The maximum gravimetric density of 4.3 wt%, has been obtained on the sample with the BCC main phase. The calculated enthalpy of reaction (deltaH) is found to be about 4 kJ/mol.

Thermodynamic consistency of liquid-gas lattice Boltzmann methods: interfacial property issues.

In the present study we examine the thermodynamic consistency of lattice Boltzmann equation (LBE) models that are based on the forcing method by comparing different numerical treatments of the LBE for van der Waals fluids. The different models are applied for the calculation of bulk and interfacial thermodynamic properties at various temperatures. The effect of the interface density gradient parameter, kappa , that controls surface tension, is related explicitly with the fluid characteristics, including temperature, molecular diameter, and lattice spacing, through the employment of a proper intermolecular interaction potential. A comprehensive analysis of the interfacial properties reveals some important shortcomings of the LBE methods when central finite difference schemes are employed in the directional derivative calculations and proposes a proper treatment that ensures thermodynamically consistent interfacial properties in accord with the van der Waals theory. The results are found to be in excellent quantitative agreement with exact results of the van der Waals theory preserving all the major features of the interfacial characteristics of vapor-liquid systems of different shapes and sizes.

Numerical and experimental investigation of the diffusional release of a dispersed solute from polymeric multilaminate matrices.

In the present work the release behavior of special, multilaminate matrix-type polymer systems, is studied both theoretically and experimentally. Two different mathematical models have been employed to describe the release of a dispersed solute from both single- and multilayer matrices. A parameter sensitivity study shows that the incorporation of supersaturated matrices in the formation of multilaminate devices, with a nonuniform initial solute loading, can provide a delivery system with optimized performance compared to monolithic ones. Finally, the findings of this theoretical analysis show good agreement with measurements of the release rates of a model disperse dye from both single- and multilayer matrices.

A two-phase model for controlled drug release from biphasic polymer hydrogels.

A comprehensive two phase model is developed to describe the sustained release of a solute or drug from a biphasic hydrogel substrate. Such a material consists of a continuous hydrophilic phase (polymer backbone in water) and a dispersion of spherical microdomains made of the hydrophobic side chains of the polymer organised in a micelle like fashion. The solute or drug is assumed to be encapsulated within the dispersed microdomains, and to diffuse from the interior to the surface of the microdomain where it exchanges following a Langmuir isotherm. Mass transfer to the bulk phase occurs by desorption of the drug from the surface through a driving force that is proportional to the difference of surface and bulk concentration. Accordingly the drug is released to the surroundings by diffusion through the bulk. Depending on the values of the Langmuir constant and assuming well stirred behaviour in the interior of the microdomain, the present model results in either of the two asymptotic models developed in previous studies. The results of a parametric study show that the desired steady state flux of a specific drug to the surroundings may be obtained given appropriate values of structural properties of the material. This conclusion is further supported when using this model to simulate earlier experimental results. The polymer structural properties can be manipulated easily during the fabrication of dispersed-phase networks, as indicated by preliminary experiments.

Correlation of structural and permeation properties in sol-gel-made nanoporous membranes.

The aim of the present work was to establish a fundamental link between the basic structural properties of ceramic nanoporous membranes made by the sol-gel process and their respective transport properties, for a systematic evaluation of their performance in gas and liquid applications. For this purpose, supported and unsupported gamma-Al2O3 and TiO2 membranes were prepared from different colloidal dispersions (sols) by a sol-gel dipping process followed by drying and calcination, resulting in structures of crystallites of different shape and stacking arrangement. Accordingly, the pore structure of each membrane was simulated employing process-based reconstruction techniques and the permeation properties were predicted by solving the appropriate transport equations in the generated structures. Excellent agreement was achieved between the computed and experimental permeability values in the Knudsen and viscous flow regimes, validating the considerations made regarding the basic structural characteristics and the procedure for generation of the membrane structures. Moreover, it was shown that the shape and stacking arrangement of the primary particles (crystallites) of the sol have a major impact on the formation of pathways in the membrane pore structures and control the transport and therefore also the separation properties of these materials.

Lattice Boltzmann method for Lennard-Jones fluids based on the gradient theory of interfaces.

In the present study we propose a lattice Boltzmann equation (LBE) model derived from density gradient expansions of the discrete BBGKY evolution equations. The model is based on the mechanical approach of the gradient theory of interfaces. The basic input is the radial distribution function, which is related exclusively to the molecular interaction potential, rather than semiempirical equations of state used in previous LBE models. This function can be provided from independent molecular simulations or from approximate theories. Evidently the accuracy of the interaction potential, and thus the radial distribution function, reflects on the accuracy of the thermodynamic properties and consistency of the derived LBE model. We have applied the proposed model to obtain equilibrium bulk and interfacial properties of a Lennard-Jones fluid at different temperatures, T, close to critical, T(c). The results demonstrate that the LBE model is in excellent agreement with gradient theory as well as with independent literature results based on different molecular simulation approaches. Hence the proposed LBE model can recover accurately bulk and interfacial thermodynamics for a Lennard Jones fluid at T/T(c)>0.9.

Structural and flow properties of binary media generated by fractional Brownian motion models.

In the present paper, the structural and flow properties of binary media generated by two-dimensional lattices that follow fractional Brownian motion statistics are studied. A modification of the midpoint displacement and random addition method is employed in order to generate multicell binary media with sizes that are considerably larger than the correlation length of the medium. Several structural properties, such as the autocorrelation function, the surface area, and the percolation threshold, are studied for different values of porosity and degree of correlation. In addition, transport properties are investigated in the above media, by solving numerically the momentum and continuity equations, to determine the absolute permeability of the medium in directions parallel and normal to the fractional Brownian motion (fBm) plane. It is found that multicell fBm porous media possess very interesting structural properties that are functions of the Hurst exponent and porosity, and are independent of the lattice size, in contrast to the traditional single-cell fBm media. In addition, they exhibit stronger structural correlation, lower specific surface area, higher percolation threshold, and lower permeabilities than those of the corresponding single-cell porous media.

A study on structural and diffusion properties of porcine stratum corneum based on very small angle neutron scattering data.

PURPOSE: Generation of valuable information about the biphasic geometrical configuration of porcine stratum corneum from Very Small Angle Neutron Scattering (VSANS) data and investigation of its effect on the corresponding effective diffusivity. METHODS: Spectra of porcine stratum corneum are mathematically transformed in order to obtain the corresponding auto-correlation function (ACF). Model stratum corneum structures, matching this experimentally determined ACF, are then produced based on the "brick-and-mortar" configuration. The effective diffusivity through these model domains is calculated using an appropriate numerical method. RESULTS: The most appropriate geometry of porcine stratum corneum's lipid and protein phases in a "brick-and-mortar" configuration is quantitatively determined and correlated with the barrier properties (diffusivity) of the stratum corneum model structures. CONCLUSIONS: The ACF analysis indicates the most appropriate values for the dimensions of the corneocyte thickness and the surrounding lipid gap, while the corneocyte length is estimated from the diffusion study.