Permeability Convertion factors

Given this relationship between CA(t) and Co(t), where retention is factored in, we can proceed to convert Eq. (7.3) into Eq. (7.5), where a is the same as before, and b now needs to be multiplied by the partition-related factor, 1 — R. The so-modified ordinary differential, Eq. (7.5), is solved by standard methods, using integration limits from xLAG to t (not 0 to t), and the desired effective permeability derived as... 

The particle size and surface area distributions of pharmaceutical powders can be obtained by microcomputerized mercury porosimetry. Mercury porosimetry gives the volume of the pores of a powder, which is penetrated by mercury at each successive pressure the pore volume is converted into a pore size distribution. Two other methods, adsorption and air permeability, are also available that permit direct calculation of surface area. In the adsorption method, the amount of a gas or liquid solute that is adsorbed onto the sample of powder to form a monolayer is a direct function of the surface area of the sample. The air permeability method depends on the fact that the rate at which a gas or liquid permeates a bed of powder is related, among other factors, to the surface area exposed to the permeant. The determination of surface area is well described by the BET (Brunauer, Emmett, and Teller) equation. 

In real cells, multiple transmembrane pumps and channels maintain and regulate the transmembrane potential. Furthermore, those processes are at best only in a quasi-steady state, not truly at equilibrium. Thus, electrophoresis of an ionic solute across a membrane may be a passive equilibrative diffusion process in itself, but is effectively an active and concentra-tive process when the cell is considered as a whole. Other factors that influence transport across membranes include pH gradients, differences in binding, and coupled reactions that convert the transported substrate into another chemical form. In each case, transport is governed by the concentration of free and permeable substrate available in each compartment. The effect of pH on transport will depend on whether the permeant species is the protonated form (e.g., acids) or the unprotonated form (e.g., bases), on the pfQ of the compound, and on the pH in each compartment. The effects can be predicted with reference to the Henderson-Hasselbach equation (Equation 14.2), which states that the ratio of acid and base forms changes by a factor of 10 for each unit change in either pH or pfCt ... 

Eq. (7.15) can be used to estimate the optimum particle size squared over the column length. Typical values for the column permeability factor, ko, is I x 10 the Knox parameter, C, is 0.1 and the molecular diffusion coefficient 1 x 10 cm-/s for small molecules and 1 x 10 cm /s for proteins. The SI units for solving these equations are AP (pascal or N/m-), p (Pas or N s/m ) and D, (m /s) to give dp and L in m. Thus, typical units for pressure are converted from psi to pascal, typical units for viscosity are converted from centipoise to poise and typical units for diffusion coefficient are converted from cm /s to m /s. 

P (properdin) can also bind to the C3 convertase. Its role is to stabilize the complex and hence it is considered a cofactor-activator in the alternative pathway. These components plus additional C3b molecules form the C5 convertase, an enzyme complex that peoteolytically converts C5 to C5a and CSb. Properdin stabilizes C3b and Bb in the complex and protects these proteins from proteolytic inactivation by factor I. Factor H competes for Bb in the C5 convertases, the same as it does in the C3 convertase. The alternative pathway has also been called the properdin pathway because of properdin s participation in alternative pathway C3 and C5 convertases. C5b is a component in the terminal complex of the complement activation process, the MAC. The MAC is composed of a self-assembled, noncovalent complex of C5b, C6, C7, C8, and C9. Together these components produce a pore-like structure that makes the membrane of the cell to which it is attached permeable and causes cell death. Under the electron microscope the MAC appears like an impact crater similar to those observed on the surface of the moon. C5a is also an anaphylatoxin like C3a, but it is more potent. C5a is also a chemokine and attracts phagocytic cells to the site of complement activation. 

Fig. 1. Modulation of apoptosis by v-FLIP and v-Bcl-2. v-FLIPs specifically inhibit apoptosis mediated by death receptors. v-lCA specifically targets caspase-8 and inhibits its activation. v-Bcl-2 and vMIA inhibit those apoptotic pathways that are signaled through mitochondrial release of cytochrome c. FADD, Fas-associated death domain FLICE, FADD-like interleukin-converting enzyme CARD, cas-pase-recruiting domain PTPC. permeability transition pore complex FLIP, FLICE-inhibitory protein vie A, viral inhibitor of caspase 8-induced-apoptosis MIA. viral mitochondrial inhibitor of apoptosis Apcif-l, apoptotic protease-activating factor 1...

Each of the above conversion technique has different advantages and limitations. The selection of the technique depends on several factors such as the measured S-parameters, sample length, desired output properties, speed of conversion and accuracies in the converted results. Among above-mentioned procedures, Nicolson-Ross-Weir (NRW) technique [1,88,89] is the most widely used regressive/iterative analysis as it provides direct calculation of both the permittivity (e ) and permeability from the input S-parameters. It is the most commonly used technique for performing such conversions where the measurement of reflection ( T) and transmission (T) coefficient requires all four (S, S, S 22) or a pair (Sjj, S j) of S-parameters of the material under test to be measured. The procedure proposed by NRW method is deduced from the following set of equations ... 

At low or medium water/cement ratios the porosity and permeability of hydrated non-converted aluminous cement pastes are sufficiently low to confine the corrosive action of any external chemical agents to the surface region of the concrete structure. However, as the porosity increases in the course of conversion, the susceptibility to chemical attack of concrete based on aluminous cement increases. An effective way to prevent this from happening is to use initial water/cement ratios that are too low for complete hydration. Under these conditions the water liberated in the conversion of the hexagonal calcium aluminate hydrate phases, formed initially, reacts with the non-hydrated fraction of the cement, thus preserving a low porosity of the hardened paste. Note that the permeability is the main factor determining the resistance of aluminous cement concrete to chemical agents, and this has to be kept in mind when calcium aluminate cement is used in practice. 

The second set of units, in the preceding equation, is obviously the smaller collective unit, which would be obtained from the first by a factor of 1000. In other words, a permeability value of, say, 2 in the first set of units would convert as follows ... 

Their applications and improved long-term stability for gas separation and pervaporation were further investigated. A maximum in the separation factor and rate was obtained for the PTMSP copolymer with 12 mol% PDMS. The membrane was able to convert a 7 wt% ethanol mixture to over 70 wt% in ethanol [120]. Good oxygen permeability and stability of over a month was also achieved for the PTMSP copolymers with over 60% PDMS [121]. In a separate study, PPP was foimd to have good permselectivity to water while PTMSP is alcohol permselective. These copolymers as well as a series of poly(phenyl acetylene) graft PTMSP copolymers were further studied for pervaporation applications [122]. 

Flow through fibrous media was modeled considering the nanofiber diameter, nanofiber arrangement, and porosity of the mat. The permeability factor for the nanoliber mat was modified to take into account the effect of sandwich structure as per the resistances-in-series law and converted to permeation in cc-mm/m day for comparison with the experimental values. The presence of GO was not taken into account here. 

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