Modeling of submicrometer aerosol penetration through sintered granular membrane filters

We present a deep-bed aerosol filtration model that can be used to estimate the efficiency of sintered granular membrane filters in the region of the most penetrating particle size. In this region the capture of submicrometer aerosols, much smaller than the filter pore size, takes place mainly via Brownian diffusion and direct interception acting in synergy. By modeling the disordered sintered grain packing of such filters as a simple cubic lattice, and mapping the corresponding 3D connected pore volume onto a discrete cylindrical pore network, the efficiency of a granular filter can be estimated, using new analytical results for the efficiency of cylindrical pores. This model for aerosol penetration in sintered granular filters includes flow slip and the kinetics of particle capture by the pore surface. With a unique choice for two parameters, namely the structural tortuosity and effective kinetic coefficient of particle adsorption, this semiempirical model can account for the experimental efficiency of a new class of "high-efficiency particulate air" ceramic membrane filters as a function of particle size over a wide range of filter thickness and texture (pore size and porosity) and operating conditions (face velocity).     

Packing effects on argon and methanol adsorption inside graphitic cylindrical and slit pores: a GCMC simulation study

Using Grand Canonical Monte Carlo simulation, we have studied the effects of confinement on argon and methanol adsorption in graphitic cylindrical and slit pores. Linear chain, zigzag and incomplete helical packing are observed for argon adsorption in cylindrical pores. However, for methanol adsorption different features appear because the electrostatic interactions favour configurations that maximize the hydrogen bonding among methanol molecules. We have found zigzag chains with hydrogen-bonded structures for methanol adsorption in cylindrical and slit pores. To investigate how dense the adsorbed phase is and how many molecules could be packed per unit physical volume of the solid, we consider two different definitions of pore density; one based on the physical volume and the other on the accessible volume. That based on accessible volume gives a measure of the fluid density, while that based on the physical volume gives a measure of how much adsorbate can be stored per unit volume of the adsorbent. It is found that the adsorbate is denser in cylindrical pores, but that slit pores can pack more molecules per unit solid volume. We also discuss the effects on the isosteric heat of argon and methanol of pore size, pore geometry and loading.     

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.     

Isotherms of Capillary Condensation Influenced by Formation of Adsorption Films

Isotherms of capillary condensation are often used to determine the vapor sorption capacity of porous adsorbents as well as the pore size distribution by radii. In this paper, for calculating the volume of capillary condensate and of adsorption films in a porous body, an approach based on the theory of surface forces is used. Adsorption isotherms and disjoining pressure isotherms of wetting films are presented here in an exponential form discussed earlier. The calculations were made for straight cylindrical capillaries of different radii and slit pores of different width. The mechanisms of capillary condensation differ in cylindrical and slit pores. In cylindrical pores capillary condensation occurs due to capillary instability of curved wetting films on a capillary surface, when film thickness grows. In the case of slit pores, coalescence of wetting films formed on opposite slit surfaces proceeds under the action of attractive dispersion forces. Partial volumes of liquid in the state of both capillary condensate and adsorbed films are calculated dependent on the relative vapor pressure in a surrounding media. Copyright 2000 Academic Press.     

Synthesis, morphology, and magnetic characterization of iron oxide nanowires and nanotubes

We have explored the synthesis of iron oxide particles, tubes, and fibrils within the pores of nanoporous polycarbonate and alumina membranes. The membranes contain uniformly distributed cylindrical pores with monodispersed diameters (varying between 20 and 200 nm) and thicknesses of 6 and 60 microm, respectively. By hydrolysis and polymerization of iron salts, particles of different sizes and phases were formed in the pores, building iron oxide particle nanowires. Alternatively, by the sol-gel technique, using as reagents metalloorganic compounds, fibrils and tubes of different iron oxide phases were prepared. Structural and morphological investigations performed using scanning electron microscopy and transmission electron microscopy revealed ordered iron oxide particle wires, tubes, and fibrils formed inside the membrane nanopores. Magnetic characterization was accomplished with a vibrating sample magnetometer. Below the blocking temperature (T(B)), the magnetic behavior of the nanowires was governed by dipolar interaction between nearest-neighbor nanoparticles inside the pore, whereas the energy barrier, and therefore the T(B) value, was mainly governed by dipolar interaction between magnetic moments over larger (interpore) distances. As expected, crystalline iron oxide nanotubes exhibited magnetic perpendicular anisotropy due to their magnetocrystalline and shape anisotropy.     

Adsorption hysteresis of nitrogen and argon in pore networks and characterization of novel micro- and mesoporous silicas

We report results of nitrogen and argon adsorption experiments performed at 77.4 and 87.3 K on novel micro/mesoporous silica materials with morphologically different networks of mesopores embedded into microporous matrixes: SE3030 silica with worm-like cylindrical channels of mode diameter of approximately 95 angstroms, KLE silica with cage-like spheroidal pores of ca. 140 angstroms, KLE/IL silica with spheroidal pores of approximately 140 angstroms connected by cylindrical channels of approximately 26 angstroms, and, also for a comparison, on Vycor glass with a disordered network of pores of mode diameter of approximately 70 angstroms. We show that the type of hysteresis loop formed by adsorption/desorption isotherms is determined by different mechanisms of condensation and evaporation and depends upon the shape and size of pores. We demonstrate that adsorption experiments performed with different adsorptives allow for detecting and separating the effects of pore blocking/percolation and cavitation in the course of evaporation. The results confirm that cavitation-controlled evaporation occurs in ink-bottle pores with the neck size smaller than a certain critical value. In this case, the pressure of evaporation does not depend upon the neck size. In pores with larger necks, percolation-controlled evaporation occurs, as observed for nitrogen (at 77.4 K) and argon (at 87.3 K) on porous Vycor glass. We elaborate a novel hybrid nonlocal density functional theory (NLDFT) method for calculations of pore size distributions from adsorption isotherms in the entire range of micro- and mesopores. The NLDFT method, applied to the adsorption branch of the isotherm, takes into account the effect of delayed capillary condensation in pores of different geometries. The pore size data obtained by the NLDFT method for SE3030, KLE, and KLE/IL silicas agree with the data of SANS/SAXS techniques.     

Computer simulation study on the concentration distribution of spherical colloids within confined spaces of well‐defined pores

Aside from the virial expansion and density functional methods, theoretical results on the concentration partitioning behavior for charged colloids within cylindrical pores have not been presented so far. With the increase of relative solute size as well as solute concentration, however, the approximate analytic methods have proven to be unreliable. A suitable Monte Carlo simulation, which is proved as a rigorous technique for concentrated colloids, has been applied in the present study. The concentration profiles within the pore representing the effects of solute concentration as well as solution ionic strength are obtained via a stochastic process, from which the partition coefficient is estimated. Previously developed analyses on the linearized Poisson‐Boltzmann (P‐B) equation are employed for the estimation of long‐range electrostatic interaction. Both the singularity method and the analytical solution with series representation properly determine respective interaction energies between pairs of solute particles and between the solute particle and the pore wall. The effect of solute‐solute and solute‐wall interactions associated with repulsive energy is presented on the partitioning of colloids. Simulation results show that the partition coefficient is evidently enhanced when no particle‐wall interaction exists. Hindered diffusion can be predicted by the simplifying assumption of the centerline approximation analogy, where a dependence on the solute concentration becomes greater as the solution ionic strength decreases.     

Nematodynamics and structures in junctions of cylindrical micropores

ABSTRACT

We explore equilibrium structures and flow-driven deformations of nematic liquid crystals confined to 3D junctions of cylindrical micropores with homeotropic surface anchoring. The topological state of the nematic ordering field in such basic unit of porous networks is controlled by nematic orientation profiles in individual pores, anchoring frustration along the edges of joining pores and coupling to the material flow field. We numerically investigate formation of the flow-aligned configurations in single cylindrical pores and pore junctions. Depending on the arrangement of inlet and outlet flows in the junction, we demonstrate existence of numerous stationary nematic configurations, characterised by specific bulk defects and surface disclinations along joining edges. Observed bulk defects are nonsingular escaped structures, disclinations in the form of loops or disclination lines pinned to the joining edges of the pores. Furthermore, we show examples of defect dynamics during the flow-induced topological transformations.     

Modeling of adsorption in pores with strongly heterogeneous walls: parametric lattice-site wall model

We present results of grand canonical Monte Carlo simulations of adsorption in cylindrical pores with rough surface modeled by a parametric lattice-site approach. The sites are randomly distributed over the pore walls. They could be attractive, neutral or repulsive with respect to the smooth pore model. Each site is characterized by two amplitudes (structural and energetic) which modify locally the structure and energetic properties of the surface. The results presented here show how different parameters of the model affect the mechanism of adsorption and, consequently, the form of the isotherm.     

Mobility of protein through a porous membrane

The electrophoretic mobility of proteins in membrane pores has been investigated experimentally. When the size of the protein is small relative to the pore size, the protein mobility is identical to the free protein mobility. As the pore radius approaches the protein radius the mobility of the protein is significantly reduced. This phenomenon has been explained in terms of electrokinetic theory. Using a method of reflections, and taking into account the effect of the back-flow, an approximation has been developed for the average mobility in a closed system of a spherical particle moving under electrophoresis parallel to the axis of a cylindrical pore. This approximation assumes that the surface potential of the particle is low, and is valid for arbitrary double layer thickness relative to particle size, provided that there is minimal overlap between the double layers at the pore surface and around the particle. It is also predicted that when the protein and the membrane have surface potentials of the same sign, there can be a significant increase in protein mobility for medium-sized pores.     

Effect of electrostatic, hydrodynamic, and Brownian forces on particle trajectories and sieving in normal flow filtration

Particle deposition and fouling are critical factors governing the performance of microfiltration and ultrafiltration systems. Particle trajectories were evaluated by numerical integration of the Langevin equation, accounting for the combined effects of electrostatic repulsion, enhanced hydrodynamic drag, and Brownian diffusion. In the absence of Brownian forces, particles are unable to enter the membrane pores unless the drag associated with the filtration velocity can overcome the electrostatic repulsion. Brownian forces significantly alter this behavior, allowing some particles to enter the pore even at low filtration velocities. The average particle transmission, evaluated from the probability of having a particle enter the pore, increases with increasing filtration velocity due to the greater hydrodynamic drag force on the particle. These results provide important insights into particle behavior in membrane systems.     

Design parameters for rotating cylindrical filtration

Rotating cylindrical filtration displays significantly reduced plugging of filter pores and build-up of a cake layer, but the number and range of parameters that can be adjusted complicates the design of these devices. Twelve individual parameters were investigated experimentally by measuring the build-up of particles on the rotating cylindrical filter after a fixed time of operation. The build-up of particles on the filter depends on the rotational speed, the radial filtrate flow, the particle size and the gap width. Other parameters, such as suspension concentration and total flow rate are less important. Of the four mechanisms present in rotating filters to reduce pore plugging and cake build-up, axial shear, rotational shear, centrifugal sedimentation and vortical motion, the evidence suggests rotational shear is the dominant mechanism, although the other mechanisms still play minor roles. The ratio of the shear force acting parallel to the filter surface on a particle to the Stokes drag acting normal to the filter surface on the particle due to the difference between particle motion and filtrate flow can be used as a non-dimensional parameter that predicts the degree of particle build-up on the filter surface for a wide variety of filtration conditions.     

Theoretical effects of macromolecule concentration and charge on membrane rejection coefficients

A hydrodynamic model for the convection of rigid, spherical solutes through cylindrical pores, which includes both steric and electrostatic interactions between pairs of solute particles and between solutes and the pore wall, has been developed to examine the effects of solute concentration and charge on solute rejection by membrane pores during ultrafiltration. Calculations have been performed for a wide range of charge conditions and the results are presented in terms of the membrane rejection coefficient at infinite dilution and a correction factor which accounts for the first-order effects of concentration. For pores and solutes of like charge, the rejection coefficient is predicted to decrease with increasing feed concentration or ionic strength.     

Effects of radially dependent parameters on proton transport in polymer electrolyte membrane nanopores

A three-dimensional continuum model is explored to investigate the effects of radially dependent system parameters, such as relative permittivity and viscosity, on the transport of proton and water in nanoscale cylindrical pores of a fully hydrated polymer electrolyte membrane (PEM). The model employs Poisson, Nernst-Planck, and Stokes equations. Based on evidence from the literature for the presence of a stagnant water layer near the pore surface, we assume that a no-slip surface is located inside the pore, a few Angstroms from the pore wall. To solve the system numerically, the steady-state solution for the transport of protons and water is considered to be a perturbation around the equilibrium solution. Our results indicate that a radial variation of relative permittivity has the greatest influence on pore conductivity, reducing it by about 50% when compared to that of constant permittivity. On the other hand, viscosity plays the dominant role when the effective water drag within such pores is considered. We conclude that a continuum approach, including constant viscosity, is applicable in nanoscale models provided that the location of the no-slip surface is properly specified and the radial variation of the relative permittivity is taken into consideration.     

Lower closure point of adsorption hysteresis in ordered mesoporous silicas

To examine the nature of the lower closure point of adsorption hysteresis in ordered mesoporous silicas, we measured the temperature dependence of the adsorption-desorption isotherm of nitrogen for three kinds of ordered silicas with cagelike pores and three kinds of ordered silicas with cylindrical pores. The lower closure point pressure of nitrogen in the cagelike pores with sufficiently small necks, that is, the cavitation pressure of a confined liquid, did not depend appreciably on the cage size in the temperature region far away from a hysteresis critical temperature (Tch) but its cage-size dependence was noticeable in the vicinity of Tch. The lower closure point in the cylindrical pores depended on the pore size, and its thermal behavior was totally different from that in the cagelike pores. Nevertheless, the hysteresis critical points of nitrogen in the ordered mesoporous silicas, which are defined as a threshold of temperatures (Tch) and pressure above which reversible capillary condensation takes place in a given size and shape of pores, fell on a common line in a temperature-pressure diagram regardless of the pore geometries. We consider this finding as evidence that capillary evaporation in the cylindrical pores follows a cavitation process in the vicinity of Tch in the same way as that in the cagelike pores and also that the low limit of the hysteresis loop that has been long recognized since 1965 is due to the occurrence of a vapor bubble in a stretched metastable liquid confined to the pores with decreasing pressure (cavitation).     

Grand canonical Monte Carlo simulation of argon adsorption at the surface of silica nanopores: effect of pore size, pore morphology, and surface roughness

Argon adsorption (77 K) in atomistic silica nanopores of various sizes and shapes has been studied by means of grand canonical Monte Carlo simulations (GCMC). We discuss the effects of confinement (pore size), pore morphology (ellipsoidal, hexagonal, constricted pore), and surface texture (rough/smooth) on the thickness variation of the adsorbed film with pressure onto the disordered inner surface of porous materials (usually called t-plot or t-curve). We show that no confinement effect occurs when the diameter of the regular cylindrical pore is larger than 10 nm. For pores smaller than 6 nm, we find that the film thickness increases as the pore size decreases. We show that the adsorption isotherm in the rough pore can be described as the sum of an adsorbed amount similar to that found for a smooth pore (of the same radius) and a constant contribution due to atoms "trapped" in the infractuosities of the rough surface which act as a microporous texture. Simulation snapshots for Ar adsorption in hexagonal and ellipsoidal smooth pores indicate that at low pressures the gas/adsorbate interface retains memory of the pore shape and becomes cylindrical prior to the capillary condensation of the fluid in the pore. The film thickness in the hexagonal pore is close to that obtained for a cylindrical pore having a similar dimension. By contrast, we find that the film thickness for an ellipsoidal pore is always larger than that for an equivalent cylindrical pore (having the same length and volume but a circular section). We show that this effect strengthens as the pore size decreases and/or the pore asymmetry increases. Ar adsorption in a cylindrical constricted pore shows that the presence of the narrower part considerably modifies the adsorption mechanism. Finally, we report GCMC simulations of Ar adsorption (77 K) on a plane silica reference substrate for different intermolecular potentials. We discuss the effect of the interaction on the shape of the adsorption isotherm and compare our results with experiments.     

Simple models of adsorption in nanotubes

We present two very simple models of adsorption in cylindrical pores. It is assumed that a layer-by-layer mechanism occurs similarly to that in the BET theory. The major assumption is that in the pores having an adsorption space with cylindrical geometry, the surface area of the upper surface (in comparison with the bottom surface) should be diminished in proportion to the radii of a cylinder. Two cases are considered: the adsorbate-adsorbate interactions are neglected or they are taken into account according to the lattice model developed by Fowler and Guggenheim. It is shown that the data simulated by Ohba and Kaneko for adsorption of nitrogen in the internal space of carbon nanotubes are successfully described by our models. On the basis of the fitted data we show that the relation between the monolayer capacity in cylindrical pores and on flat surfaces is in excellent agreement with the equation developed recently by Salmas and Androutsopoulos. Moreover, our models are verified for two sets of experimental data reported by Kaneko et al. We obtain excellent agreement between the values of the pore diameters calculated by us and suggested by these authors (from HRTEM, the GCMC simulations, and the IDBdB model). It is concluded that proposed simple and fast models can be applied as a first approximation to the estimation of the internal nanotube diameters if they do not exceed ca. 5 nm and are slightly dispersed.     

Equilibrium adsorption in cylindrical mesopores: a modified Broekhoff and de Boer theory versus density functional theory

This paper presents a thermodynamic analysis of capillary condensation phenomena in cylindrical pores. Here, we modified the Broekhoff and de Boer (BdB) model for cylindrical pores accounting for the effect of the pore radius on the potential exerted by the pore walls. The new approach incorporates the recently published standard nitrogen and argon adsorption isotherm on nonporous silica LiChrospher Si-1000. The developed model is tested against the nonlocal density functional theory (NLDFT), and the criterion for this comparison is the condensation/evaporation pressure versus the pore diameter. The quantitative agreement between the NLDFT and the refined version of the BdB theory is ascertained for pores larger than 2 nm. The modified BdB theory was applied to the experimental adsorption branch of adsorption isotherms of a number of MCM-41 samples to determine their pore size distributions (PSDs). It was found that the PSDs determined with the new BdB approach coincide with those determined with the NLDFT (also using the experimental adsorption branch). As opposed to the NLDFT, the modified BdB theory is very simple in its utilization and therefore can be used as a convenient tool to obtain PSDs of all mesoporous solids from the analysis of the adsorption branch of adsorption isotherms of any subcritical fluids.     

Influence of surface properties of the titanium dioxide porous films on the characteristics of solar cells

Porous films formed by cylindrical geometrically anisotropic fragments of TiO₂ have been produced by electrochemical anodization of titanium. The specific surface area and pore volume of the samples were determined by the BET method. It is shown that the samples have a bimodal pore-size distribution with maxima depending on the anodization voltage: by increase in voltage the inner diameter of the cylindrical pores grows, which leads to a decrease in the specific surface area. Dye sensitized solar cells were assembled on the basis of the obtained materials to study the effect of certain characteristics on the efficiency of solar energy conversion. The electrical transport properties of the films were studied by impedance spectroscopy.