Sorption and Permeability

Observed values of permeability may also be expected to deviate from predictions based on a simple two-component model of an impermeable, noninteracting filler embedded in a permeable matrix (see Section 12.1.3.1). If an interphase exists, it may be more permeable than the matrix, as in some pigmented paint films (Funke et ai, 1969 Michaels 1965), or less permeable, as in several other filler-polymer systems now to be discusses. 

It has now been shown that recent studies of relaxation, sorptive, and diffusive behavior in many filled polymer systems amply confirm earlier observations of deviations from values predicted by simple additivity (Kumins, 1965). Such effects are not confined to high-surface-area fillers such as certain carbon blacks and fillers (typical reinforcing fillers for rubber) they are also observed frequently with low-surface-area fillers, such as pigments and even glass beads with average diameters in the range of tens of micrometers. 

In conclusion, the picture of an interphase surrounding a filler particle, whether induced by adsorption, by other phenomena such as thermal stresses, or by some combination of these, can help explain specific effects of filler-matrix interactions on behavior. However, the interphase itself may well not be well defined and monolithic, so that a gradation in properties is probably more realistic (Kaufman et al, 1971 Morgan, 1973). In addition, more than one component (e.g., both densified and rarefied) may coexist. Further studies of adsorption per se, the chemistry of cured matrix resins at interfaces, relaxation behavior, and thermal stress effects should be of great value. 

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The sorption of a penetrant by a class (a) membrane can be treated most simply, if the processes of sorption in the polymer matrix and into each kind of specific sorption site within it can be treated as mutually independent and hence additive. Under these conditions, each sorbed species may similarly be expected to contribute additively to the total diffusion flux. Hence, if there are N — 1 kinds of specific sorption sites, the overall sorption and permeability or diffusion coefficients can be written as... 

Before describing the details of the new technique, we shall present a concise review of the most popular methods used to study water vapor sorption and permeability of the stratum comeum. 

The fit of these expressions to experimental results is very good. At low pressure regimes, the fit was shown to be even better than that of dual sorption expressions. Except for these regimes, the two models seem to do equally well in describing sorption and permeability data. Concentration dependent diffusivity and permeability have been considered before mainly for vapors. The new aspect of the matrix model is that it broadens these effects to fixed gases. The important difference between the matrix and dual sorption models is in the physical picture they convey of gas transport and interaction with the polymer. Additional experimental evidence will be needed to determine the preference of these different physical representations. 

Diaz LA, Aburn GC, Corti HR (2012) Methanol sorption and permeability in Nafion and acid-doped PBl and ABPBI membranes. J Membr Sci 411-412 35-44... 

Boufatit, M, Ait-Amar, H. McWhinnie, W. R. (2007). Development of an Algerian material montmorillonite clay. Adsorption of phenol, 2-dichlorophenol and 2,4,6-trichlorophenol from aqueous solutions onto montmorillonite exchanged with transition metal complexes. Desalination, vol. 206, pp. 394-406. ISSN 0011-9164. Burns, S. E., Bartelt-Hunt, S. L. Smith, J. (2003). Sorption and permeability of gasoline hydrocarbons in organobentonite porous media. Journal of Hazardous Materials, vol. 96, pp. 91-97. ISSN 0304-3894. 

Since the dominant feature of packings of spheroidal particles is the constrictions between the tetrahedral cavities formed by the Alumina microspheres, a more realistic model is required, based on the random sphere packing models. Such models are obviously more complex. Conversely, they permit a more realistic representation of the pore space among the spheroidal particles. A preliminary model has been reported for sorption [47] and relative permeability Pr [48]. A more realistic model of the sorption and permeability at different porosities is under development, aiming at predicting the sorption and the condensed phase permeabilities, given the porosity and the spheroidal particle size distribution. 

Different approaches were studied for obtaining both water sorption coefficient and water permeability coefficient. For that, some authors cut rectangular specimens of polymer films which are dried in vacuum oven at 50°C and their weight was measured until reaching no weight loss change. The films were immersed in a deionized water bath at 37°C. All specimens were weighed as a function of immersion time until the sorption process was complete. Then, the mass uptake at time t, and water solubility were calculated and thereafter water diffusivity, sorption and permeability coefficients. 

Temperature. Considering that the diffusion, sorption, and permeability are activated processes, D, S and P are related to the temperature by an Arrhenius-type equation... 

Permeability to specific drugs Sorption and permeability to water... 

McBain J W 1932 Sorption by chabasite, other zeolites and permeable crystals The Sorption of Gases and Vapors by So//ds (London Routledge) pp 167-76... 

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 gas sorption and transport properties also depend on the bisphenol connector groups [210]. The permeability coefficients for all gases rank in the order ... 

The equilibrium swelling degree is the most important property of a hydrogel it directly influences the rate of water sorption, the permeability to drugs, and the mechanical strength of the gel. It also affects the biocompatibility of the... 

N2 injection rapidly increases the methane production rate. The timing and magnitude depends on the distance between injection and production wells, on the natural fracture porosity and permeability, and on the sorption properties. N2 breakthrough at the production well occurs at about half the time required to reach the maximum methane production rate in this ideal case. The N2 content of the produced gas continues to increase until it becomes excessive, i.e., 50% or greater. 

The sorption and degradation characteristics listed for most pesticide compounds in terms of partition coefficients and half-lives relate only to a (standard) fertile, organic clayey soil and must not to be taken as representative of the permeable sandy soils widely developed on aquifer outcrops. Thus leaching of 1% of original application rates, and perhaps significantly higher, could easily occur for certain compounds on permeable soils. 

This condition has been recently used in a vaporization-exchange model for water sorption and flux in phase-separated ionomer membranes. The model allows determining interfacial water exchange rates and water permeabilities from measurements involving membranes in contact with flowing gases. It affords a definition of an effective resistance to water flux through the membrane that is proportional to... 

From Fig. 19.3a-c, and as opposed to purely sorption controlled processes, it can be seen that during pervaporation both sorption and diffusion control the process performance because the membrane is a transport barrier. As a consequence, the flux 7i of solute i across the membrane is expressed as the product of both the sorption (partition) coefficient S, and the membrane diffusion coefficient Di, the so-called membrane permeability U, divided by the membrane thickness f and times the driving force, which maybe expressed as a gradient of partial pressures in place of chemical potentials [6] ... 

Figure 1. Core processing (scale in cm). Samples taken for area and pore-size distribution measurements (A), petrographic thin sections (Bj, B2, and B3), sorption experiments (Ci and C2), and permeability measurements (D).

In the absense of any dependence of S and DT on penetrant concentration, the sorption and steady-state permeation properties of the membrane are described by effective solubility and permeability or diffusion coefficients given by... 

One can easily show that the appropriate equation derived from the dual mode sorption and transport models for the steady state permeability of a pure component in a glassy polymer is given by Eq (7) (18) when the downstream receiving pressure is effectively zero and the upstream driving pressure is p ... 

Nonlinear, pressure-dependent solubility and permeability in polymers have been observed for over 40 years. Meyer, Gee and their co-workers (5) reported pressure-dependent solubility and diffusion coefficients in rubber-vapor systems. Crank, Park, Long, Barrer, and their co-workers (5) observed pressure-dependent sorption and transport in glassy polymer-vapor systems. Sorption and transport measurements of gases in glassy polymers show that these penetrant-polymer systems do not obey the "ideal sorption and transport eqs. (l)-(5). The observable variables,... 

Nonlinear, pressure-dependent sorption and transport of gases and vapors in glassy polymers have been observed frequently. The effect of pressure on the observable variables, solubility coefficient, permeability coefficient and diffusion timelag, is well documented (1, 2). Previous attempts to explain the pressure-dependent sorption and transport properties in glassy polymers can be classified as concentration-dependent and "dual-mode models. While the former deal mainly with vapor-polymer systems (1) the latter are unique for gas-glassy polymer systems (2). 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

The second key factor determining permeability in polymers is the sorption coefficient. The data in Figure 2.18 show that sorption coefficients for a particular gas are relatively constant within a single family of related materials. In fact, sorption coefficients of gases in polymers are relatively constant for a wide range of chemically different polymers. Figure 2.25 plots sorption and diffusion coefficients of methane in Tanaka s fluorinated polyimides [23], carboxylated polyvinyl trimethylsiloxane [37] and substituted polyacetylenes [38], all amorphous glassy polymers, and a variety of substituted siloxanes [39], all rubbers. The diffusion... 

Figure 2.59 Sorption, diffusion, and permeability coefficients, as a function of temperature for polyethylene and methyl bromine at 600 mm of Hg.

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