Diffusion permeant

Values for Po, So, Do, Ep, AHs, and Ep can be derived from isostatic permeation experiments. In this experiment, one side of the membrane is exposed to a higher concentration of the permeant, and at the other side is swept with a carrier gas (N2 or H2) that delivers the diffused permeant to a sensor so that the concentration in this side is always near zero. 

Nonporous Dense Membranes. Nonporous, dense membranes consist of a dense film through which permeants are transported by diffusion under the driving force of a pressure, concentration, or electrical potential gradient. The separation of various components of a solution is related directiy to their relative transport rate within the membrane, which is determined by their diffusivity and solubiUty ia the membrane material. An important property of nonporous, dense membranes is that even permeants of similar size may be separated when their concentration ia the membrane material (ie, their solubiUty) differs significantly. Most gas separation, pervaporation, and reverse osmosis membranes use dense membranes to perform the separation. However, these membranes usually have an asymmetric stmcture to improve the flux. 

Fig. 37. Diffusion coefficient as a function of molar volume for a variety of permeants in natural mbber and in poly(vinyl chloride) (PVC) (81—83).

Fig. 38. Permeability as a function of molar volume for a mbbery and glassy polymer, illustrating the different balance between sorption and diffusion in these polymer types. The mbbery membrane is highly permeable the permeability increases rapidly with increasing permeant size because sorption dominates. The glassy membrane is much less permeable the permeability decreases with increasing permeant size because diffusion dominates (84).

The Permeation Process Barrier polymers limit movement of substances, hereafter called permeants. The movement can be through the polymer or, ia some cases, merely iato the polymer. The overall movement of permeants through a polymer is called permeation, which is a multistep process. First, the permeant molecule coUides with the polymer. Then, it must adsorb to the polymer surface and dissolve iato the polymer bulk. In the polymer, the permeant "hops" or diffuses randomly as its own thermal kinetic energy keeps it moving from vacancy to vacancy while the polymer chains move. The random diffusion yields a net movement from the side of the barrier polymer that is ia contact with a high concentration or partial pressure of the permeant to the side that is ia contact with a low concentration of permeant. After crossing the barrier polymer, the permeant moves to the polymer surface, desorbs, and moves away. 

Permeant movement is a physical process that has both a thermodynamic and a kinetic component. For polymers without special surface treatments, the thermodynamic contribution is ia the solution step. The permeant partitions between the environment and the polymer according to thermodynamic rules of solution. The kinetic contribution is ia the diffusion. The net rate of movement is dependent on the speed of permeant movement and the availabiHty of new vacancies ia the polymer. 

The diffusion coefficient, sometimes called the diffusivity, is the kinetic term that describes the speed of movement. The solubiHty coefficient, which should not be called the solubiHty, is the thermodynamic term that describes the amount of permeant that will dissolve ia the polymer. The solubiHty coefficient is a reciprocal Henry s Law coefficient as shown ia equation 3. 

The diffusion and solubihty coefficients for oxygen and carbon dioxide in selected polymers have been collected in Table 5. Determination of these coefficients is neither common, nor difficult. Methods are discussed later. The values of S for a permeant gas do not vary much from polymer to polymer. The large differences that are found for permeabihty are due almost entirely to differences in D. 

Figures 4 and 5 show how the diffusion coefficient and solubility coefficient vary for a series of linear esters in low density polyethylene film. The trends are generally tme for other permeants in other films. As the size of the permeant increases, the diffusion coefficient decreases and the solubility coefficient increases. Since the increase in solubility coefficient is larger than the decrease in the diffusion coefficient, the permeability actually increases as the permeant size increases.

Reasonable prediction can be made of the permeabiUties of low molecular weight gases such as oxygen, nitrogen, and carbon dioxide in many polymers. The diffusion coefficients are not compHcated by the shape of the permeant, and the solubiUty coefficients of each of these molecules do not vary much from polymer to polymer. Hence, all that is required is some correlation of the permeant size and the size of holes in the polymer matrix. Reasonable predictions of the permeabiUties of larger molecules such as flavors, aromas, and solvents are not easily made. The diffusion coefficients are complicated by the shape of the permeant, and the solubiUty coefficients for a specific permeant can vary widely from polymer to polymer. 

To measure gas and water vapor permeability, a film sample is mounted between two chambers of a permeability cell. One chamber holds the gas or vapor to be used as the permeant. The permeant then diffuses through the film into a second chamber, where a detection method such as infrared spectroscopy, a manometric, gravimetric, or coulometric method isotopic counting or gas-liquid chromatography provides a quantitative measurement (2). Die measurement depends on the specific permeant and the sensitivity required. 

For gases, both permeation and diffusion data are best measured by permeation tests, many different types been described elsewhere. The same sheet membrane permeation test can quantify permeation coefficient Q, diffusion coefficient D, solubility coefficient s, and concentration c. The membrane, of known area and thickness, must be completely sealed to separate the high-pressure (initial) region from that containing the permeated gas it may need an open-grid support to withstand the pressure. The permeant must be suitably detected and quantified (e.g., by pressure or volume buildup, infrared (IR) spectroscopy, ultraviolet (UV), gas chromatography, etc.). 

FIG. 20-77 Permeant-concentration profile in a pervaporation membrane. 1— Upstream side (swollen). 2—Convex curvature due to concentration-dependent permeant diffusivity. 3—Downstream concentration gradient. 4—Exit surface of membrane, depleted of permeant, thus unswollen. Courtesy Elsevier.)... 

Studies of the effect of permeant s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. Kinks may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational kink g tg ) isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks. 

X10 cm /s. This is over 1,000 X smaller than the Hiffusion coefficient for this osmium complex diffusing freely in the acetonitrile solvent (obtained from the limiting current at the naked Pt electrode), and the observed PD corresponds to a very low permeability of the polymer film to luch bulky permeants. 

The paracellular route is the pathway of diffusion of a permeant between cells growing in a monolayer. The ability of solutes to move through this space is... 

The aqueous diffusivities of charged permeants are equivalent to those of uncharged species in a medium of sufficiently high ionic strength. The product DF(r/R) is the effective diffusion coefficient for the pore. It is implicit in k that adsorption of the cations does not occur, so that the fixed surface charges on the wall of the pore are not neutralized. Adsorption is more likely to occur with multivalent cations than with univalent ones. 

Figure 10 Paracellular permeability of charged solutes as a consequence of their molecular radius illustrates the mechanism of molecular restricted diffusion across negatively charged pores. Solid line depicts the curve drawn through the permeability coefficients of neutral solutes, and the neutral image of positively and negatively charged permeants.

VIII. TRANSCELLULAR DIFFUSION OF HIGHLY MEMBRANE INTERACTIVE PERMEANTS... 

Hydration can be an important factor in diffusion and mass transport phenomena in pharmaceutical systems. It may alter the apparent solubility or dissolution rate of the drug, the hydrodynamic radii of permeants, the physicochemical state of the polymeric membrane through which the permeant is moving, or the skin permeability characteristics in transdermal applications. 

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