Sorption Henry’s Law

Permeability P, can be expressed as the product of two terms. One, the diffusion coefficient, reflects the mobility of the individual molecules in the membrane material the other, the Henry s law sorption coefficient, reflects the number of molecules dissolved in the membrane material. Thus equation 9 can also be written as equation 10. 

The concept of unrelaxed volume in glassy polymers is used to interpret sorption and transport data for pure and mixed penetrants A review of recent sorption and permeation data for mixed penetrants indicates that competition for sorption sites associated with unrelaxed gaps between chain segments is a general feature of gas/glassy polymer systems This observation provides convincing support for the use of the Langmuir isotherm to describe deviations from simple Henry s law sorption behavior. 

Figure 2.28 An illustration of the two components that contribute to gas sorption in a glassy polymer according to the dual sorption model. Henry s law sorption occurs in the equilibrium free volume portion of the polymer. Langmuir sorption occurs in the excess free volume between polymer chains that exists in glassy polymers...

The concept of two or mote modes of sorption of penetrants in polymers is very familiar to cellulose and protein chemists for the case of water vapor. In fact combined Lan uir and Henry s law sorption was proposed and correctly formulated by Matthes in 1944 for water in cellulose The discovery of dual mode sorption of gases in assy polymers and the aibsequent realization that diffusion constants determined by the time lag method did not have the same ple fundamental significance a ociated whh these parameters for mbbery polymers was of profound importance. Not only were the many carefully determined diffusion coefficients in the literature of questionable value for polymers below their ass transition but a good deal of the careful peculation about solution and diffusion and the effect of... 

The effect of the Lat uirian sorption mode per se on miration kinetics is ex(dored further in Fig. 18. The total immobilization limit (F = 0) has been arbitrarily selected in preparing curve (a) of Fig. 18. Clearly, other values of F could be treated as well. The K = 0 limit (Henry s law sorption) gives rise to mudi more rapd desorption than for K > 0 since the mean diffusion coeffident corre nding to Eq. (27) is equal to Dd when K = 0. For all values of K > 0, D < Do and desorption is retarded, Imwever total evacuation of the samfde is eventually predicted at times which, although non-infinite, ate indeed extraordinarily long. 

Fig. 18. Comparison of desorption kinetics for the case where only Henry s law sorption occurs (K = 0 as in a rubbery polymer) with the case in which Langmuirian and Henry s law sorption occur (K > 0) in local equilibrium with each other for the case of F = 0 1...

Alternatively, a Henry s Law sorption can be written for the polymer component and the water component, each term multiplied by the volume of the component, and the contributions summed to give ... 

There is a decrease in the permeability of both CO2 and CH4 as a result of exposure to hexane at different partial pressures (Figme 11.15) as the result of competitive sorption. The decrease is more pronounced for CO2, because the solubility of this gas within the polymer is more strongly influenced by Langmuir adsorption. Indeed at the hexane concentrations used, almost all the carbon dioxide is displaced from the Langmuir voids by hexane with the permeability approaching that predicted by Henry s Law sorption alone. The greater reduction in CO2 permeability results in a net loss of selectivity from 16 to around 10. 

TWo modes of sorption, Henry s law sorption and Langmuir sorption, take place simultaneously. 

Figure 4.3.4. Henry s law sorption coefficient of vapors and gases as a function of molar volume for natural rubber membranes. From Figure 3, p. 361, in "Membrane Separation of Organic Vapors from Gas Streams ", R.W. Baker and J.G. Wijmans, Chapter 8 in Polymeric Gas Separation Membranes, D.K Paul and Y.P. Yampolskii (eds.) 1994, CRC Press reprinted by permission of the publisher (Taylor Francis Group, http //www. informaworld.com.)...

DJD is the ratio of the diffusion coefficients of the two molecules and can be viewed as the mobil-ity or diffusivity selectivity, reflecting the different sizes of the two molecules is the ratio of the Henry s law sorption coefficients of the two molecules and can be viewed as the sorption or solubility selectivity of the two molecules. The balance between the solubility selectivity and the diffusivity selectivity determines whether a membrane material is selective for molecule A or molecule B in a feed mixture. Either the diffusivity or the solubility needs to be enhanced to increase membrane selectivity however, polymers that are more permeable are generally less selective and vice versa [19]. The schematic diagram of polymer membrane is given in Figure 6.1. The driving force behind the transport process which involves sorption, diffusion and permeation is the concentration difference between the two phases [21]. 

A combination of Henry s law sorption with that of the Langmuir type has been used to explain the sorption isotherm commonly observed for the sorption of gases in glassy polymers. The dualmode theory views sorption occurring in glassy polymers in two distinct modes. ... 

Coefficient 5(C) depends on gas condensability as well as polymer-penetrant interactions. Equation (24.2) can be expressed differently using various sorption modes in polymers. These modes, shown in Figure 24.1, are Henry s law sorption, Langmuir-mode sorption, Flory-Huggins mode sorption, dual-mode sorption, and Brunauer-Emmett-Teller (BET) mode sorption. 

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