Langmuir, polymer penetrant mode

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. 

Although not necessary in terms of phenomenological applications, it is interesting to consider possible molecular meanings of the coefficients, Dq and D If two penetrants exist in a polymer in the two respective modes designated by "D" and "H" to indicate the "dissolved (Henry s law) and the "hole" (Langmuir) environments, then the molecules can execute diffusive movements within their respective modes or they may execute intermode jumps ... 

The concept of two or more modes of sorption of penetrants in polymers is very familiar to cellulose and protein chemists for the case of water vapor. In fact combined Langmuir and Henry s law sorption was proposed and correctly formulated by Matthes in 1944 for water in cellulose29. The discovery of dual mode sorption of gases in glassy polymers and the subsequent realization that diffusion constants determined by the time lag method did not have the same ample fundamental significance associated with these parameters for rubbery polymers was of profound importance. Not only were the many carefully determined diffusion coefficients in the literature of questionable value for polymers below their glass transition but a good deal of the careful speculation about solution and diffusion and the effect of... 

It is generally accepted that mass transport in dense polymer membranes takes place according to the well-known solution-diffusion mechanism [18,19]. For non-swelling and non-plasticizing species the amount of penetrant that can dissolve in the glassy polymer matrix depends on the available sorption sites and often a typical dual mode sorption behaviour is observed [20]. The number of Langmuir sorption sites is strongly related to the free volume distribution of the sample. 

The sorption isotherms for ethanol and methanol reported in Figure 4 and 5 cannot be interpreted on the basis of the well known dual mode model (/,2). This model assumes that the penetrant content in the glassy polymer matrix may be expressed as fimction of pressure through the sum of two contributions the first refers to the penetrant molecules which are considered to be adsorbed onto the surface of microvoids in the interior of the solid polymer, and the second represents the contribution due to penetrant molecules which are strictly dissolved into the solid phase. In the original formulation of the dual mode model the first contribution is expressed as fimction of pressure in terms of the Langmuir equation and the second through Henry s law. 

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