Diffusion polymer membrane

A first limit rate expression is obtained when surface rate contributions are rate determining.The concentration profile is plotted in Fig. 18.22. Although the use of Henry s law (Equation [18.1]) as boundary conditions is usually limited to the case of molecular diffusion (polymer membranes), it can also be used to describe permeation across metallic membranes with surface rate-determining step (rds). In such cases, the dissociative physisorption step of H2 into H is assumed to be fast and at equilibrium. Steps (3) and (5) of the sorption mechanism are rds and the relationship between surface hydrogen ad-atoms and pressure is given by Equation [18.8] ... 

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). 

Diffusion. Diffusional dmg delivery systems utilize the physicochemical energy resulting from concentration differentials. Dmg molecules diffuse through a polymer matrix or through a polymer membrane film from a region of high concentration to one of low concentration. 

A monolithic system is comprised of a polymer membrane with dmg dissolved or dispersed ia it. The dmg diffuses toward the region of lower activity causiag the release of the dmg. It is difficult to achieve constant release from a system like this because the activity of the dmg ia the polymer is constantly decreasiag as the dmg is gradually released. The cumulative amount of dmg released is proportional to the square root of time (88). Thus, the rate of dmg release constantly decreases with time. Again, the rate of dmg release is governed by the physical properties of the polymer, the physical properties of the dmg, the geometry of the device (89), and the total dmg loaded iato the device. 

With capsules, the polymer usually completely encloses the drug in the form of a membrane. The rate of dissolution of the polymer and the thickness of the membrane then determine the time at which the drug is exposed fully to body fluids. Of course, the drug can also diffuse through the polymer membrane to the surface with subsequent dissolution. In this instance, the rate of release is more constant. 

Note that in the component mass balance the kinetic rate laws relating reaction rate to species concentrations become important and must be specified. As with the total mass balance, the specific form of each term will vary from one mass transfer problem to the next. A complete description of the behavior of a system with n components includes a total mass balance and n - 1 component mass balances, since the total mass balance is the sum of the individual component mass balances. The solution of this set of equations provides relationships between the dependent variables (usually masses or concentrations) and the independent variables (usually time and/or spatial position) in the particular problem. Further manipulation of the results may also be necessary, since the natural dependent variable in the problem is not always of the greatest interest. For example, in describing drug diffusion in polymer membranes, the concentration of the drug within the membrane is the natural dependent variable, while the cumulative mass transported across the membrane is often of greater interest and can be derived from the concentration. 

The permeation technique is another commonly employed method for determining the mutual diffusion coefficient of a polymer-penetrant system. This technique involves a diffusion apparatus with the polymer membrane placed between two chambers. At time zero, the reservoir chamber is filled with the penetrant at a constant activity while the receptor chamber is maintained at zero activity. Therefore, the upstream surface of the polymer membrane is maintained at a concentration of c f. It is noted that c f is the concentration within the polymer surface layer, and this concentration can be related to the bulk concentration or vapor pressure through a partition coefficient or solubility constant. The amount... 

GM Zentner, JR Cardinal, J Feijen, S-Z Song. Progestin permeation through polymer membranes. IV. Mechanism of steroid permeation and functional group contributions to diffusion through hydrogel films. J Pharm Sci 68 970-975, 1979. 

DR Paul, M Garcin, WE Garmon. Solute diffusion through swollen polymer membranes. J Appl Polym Sci 20 609-625, 1976. 

H Yasuda, CE Lamaze, LD Ikenberry. Permeability of solutes through hydrated polymer membranes I. Diffusion of sodium chloride. Makromol Chem 118 196-206, 1968. 

H Yasuda, CE Lamaze, A Peterlin. Diffusive and hydraulic permeabilities of water in water-swollen polymer membranes. J Polym Sci A-2 9 1117-1131, 1971. 

Figure 14 The reversibilities of insulin permeation through polymer membranes in a two-compartment diffusion cell AH20 ( ), AS 15 (A), AS20 ( ), H ( ). Numbers indicate the content of styrene or HEMA in feed compositions in moles. H represents a cross-linked poly(2-hydroxyethyl methacrylate) (HEMA). (From Ref. 34.)... 

S Sato, SW Kim. Macromolecular diffusion through polymer membranes. Int J Pharm 22 229-255, 1984. 

Some of the polymeric membranes are suitable for bulk separation of hydrogen from impurities to enrich a dilute hydrogen stream. Dense polymers permeate gases by solution diffusion mechanism. The permeation rate of a gas species through a polymer membrane... 

Approaches to make a polymeric membrane selective to C02 attempt to enhance the solubility selectivity of the polymer material for C02 and reduce the diffusivity selectivity of the polymer that favors smaller hydrogen molecule. The permeability of a polymer membrane for species A, PA, is often expressed as (Ghosal and Freeman, 1994)... 

Water also diffuses across the polymer membrane to a limited extent. Therefore the electrode response is unstable and unreliable if there is a significant difference between the osmotic pressure of the filling solution and the unknown solution. To partially alleviate this problem,data were taken with filling solutions containing 0, 1.0, and 2.0 M additional KC1. 

The main emphasis in this chapter is on the use of membranes for separations in liquid systems. As discussed by Koros and Chern(30) and Kesting and Fritzsche(31), gas mixtures may also be separated by membranes and both porous and non-porous membranes may be used. In the former case, Knudsen flow can result in separation, though the effect is relatively small. Much better separation is achieved with non-porous polymer membranes where the transport mechanism is based on sorption and diffusion. As for reverse osmosis and pervaporation, the transport equations for gas permeation through dense polymer membranes are based on Fick s Law, material transport being a function of the partial pressure difference across the membrane. 

Divisek et al. presented a similar two-phase, two-dimensional model of DMFC. Two-phase flow and capillary effects in backing layers were considered using a quantitatively different but qualitatively similar function of capillary pressure vs liquid saturation. In practice, this capillary pressure function must be experimentally obtained for realistic DMFC backing materials in a methanol solution. Note that methanol in the anode solution significantly alters the interfacial tension characteristics. In addition, Divisek et al. developed detailed, multistep reaction models for both ORR and methanol oxidation as well as used the Stefan—Maxwell formulation for gas diffusion. Murgia et al. described a one-dimensional, two-phase, multicomponent steady-state model based on phenomenological transport equations for the catalyst layer, diffusion layer, and polymer membrane for a liquid-feed DMFC. 

Figure 5.7 shows a typical application of gas-diffusion membranes isolation of the circulating sample from a voltammetric or potentiometric electrode for the electrochemical determination of gaseous species. The ion-selective electrode depicted in this Figure includes a polymer membrane containing nonactin that is used for the potentiometric determination of ammonia produced in biocatalytic reactions. Interferences from alkali metal ions are overcome by covering the nonactin membrane with an outer hydro-... 

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