Diffusion permeability

Electrical conductance of an ion-exchange membrane Xm in various ionic forms can be used for an approximate estimation of the ions self-diffusion coefficients Dj using the Nernst-Einstein equation  

The diffusion coefficient calculated in this way is usually higher than values measured by independent methods. This can be explained by the fact that during the self-diffusion measurements ions are moving toward each other and the water present in the ion-exchange resin is motionless. At the time of electric conductance measurements aU counterions are moving in one direction and create electroosmotic flow. It is obvious that in this case the ion s movement would have less resistance as they move along with the fiquid flow. 

The counterion diffusion coefficients obtained by a kinetic study or by conductivity measurements caimot be used as membrane diffusion coefficients, because counterions and co-ions are moving in opposite directions in electrodialysis. However co-ions are motionless at the time of ion exchange between equal activity solutions. Therefore the ion-migration conditions are totally different in these cases. 

It should be noted that ion-exchange membrane swelling depends on the external solution concentration. This fact has a significant impact on the membranes diffusion permeabifity. Moreover, the real-life situation often includes an ion-exchange membrane facing a concentrated solution on one side and a dilute 

By order of magnitude the diffusion permeability of commercial membranes 

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Hydration of polymeric membranes may be influenced by the chemical identity of the polymers. A hydrophilic polymer has a higher potential to hydrate than a hydrophobic one. Sefton and Nishimura [56] studied the diffusive permeability of insulin in polyhydroxyethyl methacrylate (37.1% water), polyhydroxy-ethyl acrylate (51.8% water), polymethacrylic acid (67.5% water), and cupro-phane PT-150 membranes. They found that insulin diffusivity through polyacrylate membrane was directly related to the weight fraction of water in the membrane system under investigation (Fig. 17). 

Figure 10. Calculated and measured metal permeabilities for different microorganisms. Permeabilities have been calculated using data given in each of the original references (P. tricornutum, Zn, [4] T. pseudonana, Mn, [4] C. kesslerii, Zn, [90] C. kesslerii, Pb, [160] C. pyrenoidosa, Cd, [205] C. reinhardtii, Ag, Mn, [91] T. oceanica, T. pseudonana, Zn, [311] T. oceanica, E. huxleyi, Cd, [214] T. pseudonana, Mn, [92]). The grey circles correspond with observed permeabilities, calculated by dividing the observed internalisation flux by the concentration of free ion (P = /int/[M]). The range of limiting diffusive permeabilities, / ,)] "njrl and / ,)] "n.lx, as calculated by equations (55) and (57), are given by the black rectangle...

While modeling the structure and properties of porous materials one usually is interested in structural properties of a desirable hierarchical level. For example, for chemical properties the molecular structure is major, and the specific adsorption and catalytic properties are guided by the structure and composition of particle surface. Diffusion permeability is determined by the supramolecular... 

Du 1986). This reflects the importance of smaU pores in order to apply effectively capillary condensation as a separation mechanism. Uhlhom (1990) demonstrated the effect of multilayer diffusion of propylene through a modified y-alumina membrane at 0°C. The separation factor for the N2/CjHg mixture was 27, where propylene is the preferentially permeating component, while the permeability increased to 7 times the Knudsen diffusion permeability. Although this mechanism appears to be very effective because of a high separation factor and a high permeability, it is limited by the obvious need for a condensable component. This in turn restricts the applicability range, due to limits set by temperature and pressure, needed for formation of multilayers or capillary condensation. 

For the pressure studies, two phase" compact ion behavior is observed with an inflection point between 7 and 11 atms. For the aqueous solution studies, the hydraulic permeability K and the g-ratio are hardly effected by solute type (within experimental error). The solute diffusive permeability however, varies with solute type in good qualitative agreement with free energy parameters, infrared overtone shifts, and spin echo and continuous wave nuclear magnetic resonance spectroscopy results from the literature. 

Water Transport. The dependence of the diffusive permeability of tritiated water Pq., (HTO) and hydraulic permeability LpAX on the lEC are presented in Figures 4 and 5. Both Pj and LpAX can be seen to increase exponentially as a function of lEC. Since the volume fraction of water, (J>, is also a linear function of the lEC, a similar exponential relation is obtained for these parameters vs. (J>. In terms of the pore model, the increase in either diffusion permeability or the hydraulic permeability may be caused by one or both of the following possibilities (a) an increase in the number of passageways, or (b) by increase in the radius of the pores. This question may be resolved by examining the g factor, defined as a ratio of two permeabilities (15) ... 

Figure 4. Diffusive permeability, Pt v. lEC (9) SPS obtained by sulfonation of P-3500 resin (X) SPS obtained by sulfonation of P-1700 resin...

Diffusive Salt Permeability Through PVA Membranes. In order to verify the Interdependence between the water and salt transport through PVA, the diffusive permeability of salt through an un-pressurlzed PVA membrane was measured. The diffusion system employed In this experiment Is described schematically In Figure 8. The diffusion cell consists of an upper cell and a lower cell, separated by the tested membrane, a 150 micron thick, untreated PVA membrane. Initially, the lower cell contalnes distilled water, which Is circulated through a conductivity cell, and the... 

Figure 8. Diffusive permeability measurement system (1) thermostated bath (2) diffusion cell (3) membrane (4) thermometer (5) stirrer (6) circulation pump (7) conductivity cell (8) conductivity meter (9) recorder.

Stewart, P. S., A review of experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms , Biotechn. Bioeng., 59,261-272 (1998). 

On the Energy of Activation. The temperature dependence of many processes, such as diffusion, permeability, and partition coefficients, has been represented often in terms of the Arrhenius plots (52). It would appear that ki in Equation 14 also could be treated in this manner by defining... 

For the tortuous and irregular capillaries of porous media, it has been reported theoretically and experimentally that a minimum in the permeability of adsorbates at low pressures is not expected to appear. In our study of n-hexane in activated carbon, however, a minimum was consistently observed for n-hexane at a relative pressure of about 0.03, while benzene and CCI4 show a monotonically increasing behavior of the permeability versus pressure. Such an observation suggests that the existence of the minimum depends on the properties of permeating vapors as well as the porous medium. In this paper a permeation model is presented to describe the minimum with an introduction of a collision-reflection factor. Surface diffusion permeability is found to increase sharply at very low pressure, then decrease modestly with an increase in pressure. As a result, the appearance of a minimum in permeability was found to be controlled by the interplay between Knudsen diffusion and surface diffusion for each adsorbate at low pressures. 

One would physically expect that as pressure increases the solid surface may get smoother due to the filling of small pores and cavities with adsorbed molecules, and as a result the reflection time of gas phase molecules from the surface may become shorter. The values of / in Table 1 are close to unity as expected and they are in an increasing order of n-hexane, carbon tetrachloride and benzene. On the other hand, the parameter a for n-hexane is much higher than that of the others. Since the parameter a in Eq. 3 represents how fast the Knudsen diffiisivity increases with pressure, one would expect a substantial contribution of the Knudsen diffusion for n-hexane to the total permeability at very low pressures. Also the parameter is a measure of how fast the activation energy for surface diffusion decreases with adsorbed concentration. As Table 1 indicates, the surface diffusion permeabilities of n-hexane and carbon tetrachloride are expected to increase more sharply than that of benzene. 

Fig. 13 The controlled release of drug molecules from a (membrane-matrix) hybrid-type drug delivery system in which solid drug is homogeneously dispersed in a polymer matrix, which is then encapsulated inside a polymeric membrane, where D, P, and h are the diffusivity, permeability, and thickness, respectively, and the subscripts p, m, and d denote the drug depletion zone in the polymer matrix, polymer coating membrane, and diffusion layer, respectively.

An investigator in this area typically has precise information on composition of casting solutions and other physicochemical factors affecting membrane formation. Functional measurements of transport in terms of convective permeability, selectivity or diffusive permeability are usually also available. However, without proper techniques for quantitative description of membrane pore structures, and their shape and size distributions, membrane development efforts remain largely empirical. 

Transport Properties. Important transmembrane transport parameters of the fibers are Lp, the hydraulic conductivity Pm, the diffusive permeability for a given solute o, the solute reflection coefficient and R, the solute rejection. These coefficients appear in the following equations, which are assumed to be valid at the steady state at each position Z along the fiber wall ... 

Myoglobin, cytochrome-C, inulin, and vitamin B-12 were the solutes studied in saline, calf serum, and BSA systems at 37 C and pH 7.4. Observed solute rejections were corrected to intrinsic values by using uniform-wall-flux boundary layer theory for the developing and fully-developed asymptotic regions. The Splegler-Kedem equation ( ) for rejection versus volume flow was used to calculate reflection coefficients and diffusive permeabilities for each solute. There was no significant difference between rejection parameters measured in saline and protein solutions. 

It is known that an elevated permeability of usual SPC based on liquid glass is intimately connected with the big porosity and filtering defects. Because of this, application of commonly used SPC requires a leak proof and chemically stable lining of expensive materials (lead, polyisobutylene, etc.). Filtration and diffusive permeability of SPC with monomeric additives (TFS, FA) in aggressive environments were studied. 

Adhesive composition no. 5 is optimal from the standpoint of chemical resistance, and adhesive strength was tested on diffusion permeability by sulfuric acid. 

Yasuda and coworkers found the following relationships between diffusive permeability and membrane structure ... 

Aller, R. C. 1983. The importance of the diffusive permeability of animal burrow linings in determining marine sediment chemistry. J. Mar. Res. 41 299-322. 

Information on diffusive permeability of electret coatings is presented in Table 3.3. Based on these results, an analytical dependence between the liquid mass absorbed by the coating and the polarizing charge value has been derived [16]. 

The presence of an unstirred layer which may adhere to a given cell membrane can be treated operationally as a barrier with its own permeability property in series with the actual membrane. Its importance in membrane transport processes depends essentially on the permeability of the membrane itself relative to that of the unstirred layer to the particular molecule being transported. Consequently, only molecules which permeate membranes at high rates are affected, since diffusion in the unstirred layer is quite rapid. Water transfer across human red cell membrane and those of most other cells and tissues studied falls within this category. Dainty [22] has given the following equation by which the apparent diffusion permeability coefficient may be corrected for the effect of an unstirred layer of thickness, 8 ... 

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