Langmuir mode sorption

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. 

Here, the heat of sorption, AH j, is a composite parameter involving both sorption mechanisms. The Henry s law mode requires both the formation of a site and the dissolution of the species into that site. The formation of a site involves an endothermic contribution to this process. In the case of the Langmuir mode, the site already exists in the polymer matrix and, consequently, sorption by hole filling yields more exothermic heats of sorption. 

Theoretical sorption isotherm model. I) Langmuir type isotherm II) Flory-Hugginstype isotherm III) Dual sorption (BET-mode) type isotherm. 

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 sorption and diffusion behaviour of gas mixtures is of particular interest from the point of view of membrane gas separation, which is steadily gaining in importance by virtue of its low energy requirements. On the basis of the dual mode sorption model, one may reasonably expect that sorption of a binary gas mixture A, B in the polymer matrix will exhibit little gas-gas interaction and hence will tend to occur essentially additively. In the Langmuir-like mode of sorption, on the other hand, there will be competition between A and B for the limited number of available sites. These considerations led 67) to the following reformulation of Eqs. (8) and (9)... 

Because of non-adherence of the site sorption mode to a strict Langmuir mechanism, as noted previously, Eq. (18), as well as Eqs. (20) or (20 a), must, at the quantitative level, be validated experimentally. This can be done most conveniently by varying the partial pressure of one component at various constant partial pressures of the other. Sorption data of this type have recently been reported for PMMA-C02, C2H4 at 35 °C69 70). As shown in Fig. 7, the agreement between experiment and calculation from the pure component isotherms, though not perfect, is nevertheless quite impressive. 

It is particularly interesting and instructive to note that application of Henry + Langmuir dual-mode sorption and diffusion models is not confined to glassy polymer-gas systems. Sorption and transport of high affinity ionic species, exemplified by anionic dyes, in charged polymers, exemplified by polyamides at low pH, has been treated in the same way. These systems are of considerable importance both from the bio-mimetic and from the textile processing point of view, but have received limited atten-... 

NR and — CO groups, measured after prior washing of the resin with water 85), was well represented by a Langmuir + Nernst dual mode sorption model at salt concentrations not exceeding 0.2 mol dm 3. A detailed physical interpretation of the relevant parameters was not given, however, neither was the dual mode concept utilized in a corresponding diffusion study 86). 

The sorption of a weak electrolyte by a charged polymer membrane is another case where Nernst + Langmuir-like dual mode sorption, involving the undissociated and dissociated species respectively, may be expected. The concentration of each species in solution follows, of course, from the dissociation constant of the electrolyte. The sorption isotherms of acetic acid and its fluoroderivatives have been analysed in this manner, and the concentration dependence of the diffusion coefficient of acetic acid interpreted resonably successfully, using Nylon 6 as the polymer substrate 87). In this case the major contribution to the overall diffusion coefficient is that of the Nernst species consequently DT2 could not be determined with any precision. By contrast, in the case of HC1, which was also investigated 87 no Nernst sorption or diffusion component could be discerned down to pH = 2 and the overall diffusion coefficient obeyed the relation D = DT2/( 1 — >1D), which is the limiting form of Eq. (25) when p — 00. 

In the dual-mode sorption and transport model the pressure-dependence of a (= C/p), P and 0 in gas-glassy polymer systems arises from the pressure-dependent distribution of the sorbed gas molecules between Langmuir sites and Henry s law dissolution. Although k, Dg and are assumed to be constant, the average or effective solubility and diffusion coefficients of the entire ensemble of gas molecules change with pressure as the ratio of Henry s to Langmuir s population, C /C, changes continuously with pressure [eq. (14)]. 

The experimental evidence presented here and in the literature (15) show that the real diffusion coefficient depends on concentration. These results are incompatible with the notion of concentration-independent diffusion coefficients for the dissolved and Langmuir sorbed molecules [D and Djj in equation (15)] as proposed by the dual-mode sorption and transport model ( 13). 

This equation has become known as the "dual sorption model", because obviously two separate sorption mechanisms are operative for gases in glassy polymers. One mode (first term on the right in Eq. (18.36)) follows the Henry s law the other mode (second term) follows a Langmuir form. This additional mode is attributed to sorption into micro-voids that apparently pre-exist in the glassy state of the polymer (and only there ) it disappears above Tg (see Fig. 18.9b). 

Thus, poly(4a) can be easily cast into a thin, tough membrane. Furthermore, the gas permeation through this polyacetylene is connected with the dual-mode sorption mechanism involving Langmuir adsorption, whereas... 

The basic assumptions of the dual mode sorption theory as it applies to the transport model of Vieth and Sladek, have been stated by Vieth et al. in their excellent review of the subject The sorption isotherm was described by the combination of a Henry s law dissolved component, Cp, and a Langmuir hole filling term, Ch, i.e.. 

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... 

FIGURE 9.4 Dependence of constants (a, b, and c present Henry constant, sorption affinity constant, and Langmuir sorption capacity respectively) of the model of dual-mode sorption of hydrocarbons by glassy polyphenylene oxides on boiling temperatures of hydrocarbons Z), is pDMePO, poly-2,6-dimethyl-l,4-phenylene oxide o is pDPhPO, poly-2,6-diphenyl-l,4-phenylene oxide is pDMePO/pDPhPO copolymer (97.5/2.5% mol) v is pDMePO/pDPhPO copolymer (75/25% mol). (From analysis of results presented in Lapkin, A.A., Roschupkina, O.P., and Ilinitch, O.M., J. Membr. Sci., 141, 223, 1998.)... 

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