Micropore Transport

Pore diameters are in the molecular size range, where the distinction between whether the molecules are gas or liquid ceases to exist. The molecules aie under the effect of the interaction potential from the pore wall and their transport is according to the hopping diffusion like a solid-state vacancy mechanism. This mechanism can be applied well for amorphous stmctures and molecules that fit tightly in the pore. Membiane pore system is then considered as a Langmuir lattice of the sites that can be either vacant or occupied by the molecules. In such a case the flux of species /j can be written by 

In which b° is the mechanical mobility for a molecule on an otherwise empty lattice, the concentration of available sites, R the universal gas eonstant, T absolute temperature, and 0 6 1 is the average site occupation. Equilibrium between the site occupation and feed eoncentration on both sides of the membrane can be used as the boundary condition to solve the above eqnation. Non-eqnilibrinm correction factor 0 j 1 is often very close to nnity bnt can be very small for the molecule of low occupancy (low 0) when the other molecnle occnpies the sites strongly and hinders the movement of the former molecnle. The above generic expression leads to the following two types of microporous and surface diffusion separation  

Which is a simple Pick s first law for a single species with the chemical diffusion coefficient Di = b iRT, which is independent of 0. In type 1 mechanism, the Hemy s isotherm 9i = Ki pi/p is applicable so that the diffusion penneance can be written as 

Where p° is the standard pressure and X is the apparent membrane thickness. The above equation shows that that represents the permeance in the micropoie is in- 

Furthermore, the significant modification of Eq. (8.23) leads to o(l l2 = a/,/2, which means the selectivity becomes the ideal selectivity. 

---

Considering only micropore transport with constant parameters, the single component uptake by pore diffusion in RS-10, following a step change in gas concentration, is given by... 

In principle, the separation properties of a multilayer porous ceramic membrane, such as permselectivity, should be dependent only on the pore size distribution of the top separation layer. However, they can be compromised if resistances in the intermediate layers and the macroporous support become significant. For transport through macro- and meso-pores, molecular diffusion, Knudsen diffusion and viscous flow all contribute to the total transport, while the activated surface flow of the adsorbed phase will affect microporous transport. Therefore, any theoretical models used in analysing the transport data of gases through a porous ceramic membrane with a distributed pore size must take the following contributions into consideration (1) viscous flow, (2) Knudsen flow, (3) surface flow and (4) molecular sieving... 

This division is somewhat arbitrary siace it is really the pore size relative to the size of the sorbate molecule rather than the absolute pore size that governs the behavior. Nevertheless, the general concept is useful. In micropores (pores which are only slightly larger than the sorbate molecule) the molecule never escapes from the force field of the pore wall, even when ia the center of the pore. Such pores generally make a dominant contribution to the adsorptive capacity for molecules small enough to penetrate. Transport within these pores can be severely limited by steric effects, leading to molecular sieve behavior. 

The tme driving force for any diffusive transport process is the gradient of chemical potential rather than the gradient of concentration. This distinction is not important in dilute systems where thermodynamically ideal behavior is approached. However, it becomes important at higher concentration levels and in micropore and surface diffusion. To a first approximation the expression for the diffusive flux may be written... 

For a macroporous sorbent the situation is slightly more complex. A differential balance on a shell element, assuming diffusivity transport through the macropores with rapid adsorption at the surface (or in the micropores), yields... 

Ceramic, Metal, and Liquid Membranes. The discussion so far implies that membrane materials are organic polymers and, in fact, the vast majority of membranes used commercially are polymer based. However, interest in membranes formed from less conventional materials has increased. Ceramic membranes, a special class of microporous membranes, are being used in ultrafHtration and microfiltration appHcations, for which solvent resistance and thermal stabHity are required. Dense metal membranes, particularly palladium membranes, are being considered for the separation of hydrogen from gas mixtures, and supported or emulsified Hquid films are being developed for coupled and facHitated transport processes. 

Although microporous membranes are a topic of research interest, all current commercial gas separations are based on the fourth type of mechanism shown in Figure 36, namely diffusion through dense polymer films. Gas transport through dense polymer membranes is governed by equation 8 where is the flux of component /,andare the partial pressure of the component i on either side of the membrane, /is the membrane thickness, and is a constant called the membrane permeability, which is a measure of the membrane s ability to permeate gas. The ability of a membrane to separate two gases, i and is the ratio of their permeabilities,a, called the membrane selectivity (eq. 9). 

Adsorption of supercritical gases takes place predominantly in pores which are less than four or five molecular diameters in width. As the pore width increases, the forces responsible for the adsorption process decrease rapidly such that the equilibrium adsorption diminishes to that of a plane surface. Thus, any pores with widths greater than 2 nm (meso- and macropores) are not useful for enhancement of methane storage, but may be necessary for transport into and out of the adsorbent micropores. To maximize adsorption storage of methane, it is necessary to maximize the fractional volume of the micropores (<2 nm pore wall separation) per unit volume of adsorbent. Macropore volume and void volume in a storage system (adsorbent packed storage vessel) should be minimized [18, 19]. 

Zinc is electrodeposited from the sodium zincate electrolyte during charge. As in the zinc/bromine battery, two separate electrolytes loops ("posilyte" and "nega-lyte") are required. The only difference is the quality of the separator The zinc/ bromine system works with a microporous foil made from sintered polymer powder, but the zinc/ferricyanide battery needs a cation exchange membrane in order to obtain acceptable coulombic efficiencies. The occasional transfer of solid sodium ferrocya-nide from the negative to the positive tank, to correct for the slow transport of complex cyanide through the membrane, is proposed [54],... 

The aim of the newly introduced mesoporosity is to enhance the utilization of the microporous network by improved accessibihty of the active sites that are mostly present in the micropores. Although numerous papers have reported on the improved catalytic performance of desihcated zeolites in catalysis (details in Section 2.4.5), only few works are available that reaUy tackle the hierarchical nature of the desihcated zeohtes and demonstrate that selective sihcon removal leads to an enhanced physical transport in the zeohte crystals. 

Theory and Computer Simulation of Structure, Transport, and Flow of Fluid in Micropores... 

Other microporous materials have been synthesized using the porogen polyethylene glycol in polyethylene oxide-urethane gels [27]. Micropores were formed in the gel, and it was found that the diffusion of larger species, vitamin B12, was enhanced relatively more than that of a smaller species, proxyphylline. This result is in qualitative agreement with that found for electrophoretic transport by RiU et al. [322] discussed earher, where the mobility of larger species was preferentially enhanced in the templated media. 

Bone is a porous tissue composite material containing a fluid phase, a calcified bone mineral, hydroxyapatite (HA), and organic components (mainly, collagen type). The variety of cellular and noncellular components consist of approximately 69% organic and 22% inorganic material and 9% water. The principal constiments of bone tissue are calcium (Ca ), phosphate (PO ), and hydroxyl (OH ) ions and calcium carbonate. There are smaller quantities of sodium, magnesium, and fluoride. The major compound, HA, has the formula Caio(P04)g(OH)2 in its unit cell. The porosity of bone includes membrane-lined capillary blood vessels, which function to transport nutrients and ions in bone, canaliculi, and the lacunae occupied in vivo by bone cells (osteoblasts), and the micropores present in the matrix. 

In the light of the wide variety of complex pore spaces where microscopic transport features are of interest, we decided to concentrate on a special type of microporous systems suitable for testing NMR mapping methods and to examine... 

The in vitro system we have been using to study the transepithelial transport is cultured Madin-Darby canine kidney (MDCK) epithelial cells (11). When cultured on microporous polycarbonate filters (Transwell, Costar, Cambridge, MA), MDCK cells will develop into monolayers mimicking the mucosal epithelium (11). When these cells reach confluence, tight junctions will be established between the cells, and free diffusion of solutes across the cell monolayer will be markedly inhibited. Tight junction formation can be monitored by measuring the transepithelial electrical resistance (TEER) across the cell monolayers. In Figure 1, MDCK cells were seeded at 2 X 104 cells per well in Transwells (0.4 p pore size) as described previously. TEER and 14C-sucrose transport were measured daily. To determine 14C-sucrose... 

Figure 1. The correlation of transepithelial electrical resistance (TEER) with the transepithelial transport of 14C-sucrose in MDCK cell monolayers grown on microporous filters.

The intent of this chapter is to establish a comprehensive framework in which the physicochemical properties of permeant molecules, hydrodynamic factors, and mass transport barrier properties of the transcellular and paracellular routes comprising the cell monolayer and the microporous filter support are quantitatively and mechanistically interrelated. We specifically define and quantify the biophysical properties of the paracellular route with the aid of selective hydrophilic permeants that vary in molecular size and charge (neutral, cationic, anionic, and zwitterionic). Further, the quantitative interrelationships of pH, pKa, partition... 

It is important to stress that the capacitive behaviour of the microporous carbons could be further improved by enhancing the mesopore volume. The presence of mesopores plays a crucial role for the ion transportation to the active surface. Hence, a development of mesopores in these materials, and a strict control of the micropore-mesopore volume ratio is necessary. 

Materials with uniform pore structures offer a wide range of applications, including catalysis, adsorption, and separation. These materials have the benefit ofboth specific pore systems and intrinsic chemical properties [1-3]. The pores in the materials are able to host guest species and provide a pathway for molecule transportation. The skeletal pore walls provide an active and/or affinity surface to associate with guest molecules. According to the International Union of Pure and Applied Chemistry (IUPAC), porous materials can be classified into three main categories based on the diameters of their pores, that is, microporous, mesoporous, and macroporous... 

---