Langmuir isotherm, glassy polymer

Earlier work on the application of the concept of dual mode sorption and diffusion to glassy polymer-gas systems has been reviewed in detail 6) and important aspects of more recent work have been dealt with in more recent reviews 7 10). Eq. (5) was first applied by Michaels et al U). Sorption in the polymer matrix and in the specific sorption sites was represented by linear (Henry s law) and Langmuir isotherms respectively so that Sj in Eq. (5) is given by... 

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. 

The permeation of a gas through a porous polymer is generally described by equations based on the kinetic theory of gases. The sorption isotherm described by Eq. 1 is concave to the pressure axis and is commonly observed for a penetrant gas in a glassy polymer. It is composed of Henry s law and Langmuir-terms [20] ... 

Type-IV sorption isotherm is a combination of type-11 sorption at low concentration and type-111 sorption at high concentration. Type-V isotherm as dehned here (Figure 5.1) is exhibited by glassy polymers/polymers containing adsorptive fillers. This type of sorption is dehned as dual mode sorption, which is a combination of Henry s type and Langmuir type. The former applies to the bulk polymer and the latter to the hller/micro-voids in the polymer. Netke et al. [35] have studied the permeation of acetic acid-water mixmres in silicalite hlled PDMS. Equations governing type-V isotherm are... 

In glassy polymers the interactions of the penetrant molecules with the polymer matrix differ from one sorption site to another. A limiting description of the interaction distribution is known imder the name of the dual-sorption model [59, 60]. In this model, the concentration of the penetrant molecules consists of two parts. One obeys Henry s law and the other a Langmuir isotherm ... 

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. 

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. ... 

The solubility of a penetrant in a polymer matrix is described by the sorption isotherm. It correlates, at a constant temperature, the amount of sorbed penetrant to the pressure or to the activity of the phase outside the polymer (Fig. 11.1). Depending on the nature of the polymer-penetrant system, sorption isotherms may show considerable differences in shape. The micro-voids in a glassy polymer can immobilize a portion of the penetrant molecules by entrapment or by binding at high energy sites at their molecular peripheries (Langmuir type isotherm). As a result, this system typically shows concave shaped sorption isotherms (I in Fig. 11.1). On the contrary, for high penetrant concentration of vapours in rubbery polymers, the sorption isotherm turns upwards into a convex shaped curve (II in Fig. 11.1). This kind of isotherm can be explained by a... 

It was found in several glassy polymers that a gas permeability depended onp and that sorption must be interpreted as occurring by two mechanisms the usual Fickian mechanism described above and a second mechanism resembling a Langmuir-type isotherm. The total concentration in the polymer in this duai-sorption model was then expressed as [30]... 

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