Sorption isotherm Henry

Thus, in terms of a, the sorption isotherm for osmotically ideal solutions is of Type III in Brunauer s classification (29) and reduces to Henry s law for (Mi/M2)a< 1. 

This picture fits very well with the tendency of the sorption isotherm curvature (and hence of the site sorption mode) to disappear at T > Tg. On a more quantitative level, the above characterization of the Henry sorption mode is supported by the smooth temperature dependence of K, found in the PET-C02 system 12), which indicates a roughly unchanged enthalpy of sorption AH, above and below Tg. Additional support is provided by the correlation between K, and the Lennard-Jones parameter s/k characteristic of the gaseous penetrant, in accordance with... 

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] ... 

Fig. 3 Shift of the resonance wavelength of the surface plasmons of a layer of 200 nm caused by different concentrations of the three analytes. The sorption isotherms follow the Henry-Langmuir-equation...

In this chapter we will mostly focus on the application of molecular dynamics simulation technique to understand solvation process in polymers. The organization of this chapter is as follow. In the first few sections the thermodynamics and statistical mechanics of solvation are introduced. In this regards, Flory s theory of polymer solutions has been compared with the classical solution methods for interpretation of experimental data. Very dilute solution of gases in polymers and the methods of calculation of chemical potentials, and hence calculation of Henry s law constants and sorption isotherms of gases in polymers are discussed in Section 11.6.1. The solution of polymers in solvents, solvent effect on equilibrium and dynamics of polymer-size change in solutions, and the solvation structures are described, with the main emphasis on molecular dynamics simulation method to obtain understanding of solvation of nonpolar polymers in nonpolar solvents and that of polar polymers in polar solvents, in Section 11.6.2. Finally, the dynamics of solvation with a short review of the experimental, theoretical, and simulation methods are explained in Section 11.7. 

Precise studies of sorption of non-permanent gases in glassy polymers showed that the sorption isotherms do not follow Henry s law (see Fig. 18.9a). A very good approximation of the isotherm is ... 

Equations 1 and 4 are equivalent only when the diffusion and sorption processes are ideal, i.e. when the diffusion coefficient is a constant and when Henry s law, which states that there is a linear relation between the external concentration or vapor pressure and the equilibrium concentration in the material, is obeyed (or, in other words, when the sorption isotherm is linear). In this case. Equation 1 may be interpreted to give... 

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.. 

Figure 5. Validity of the y/T law in a constant-volume variable-pressure system where the sorption isotherms approach Henry s law (2)...

For ideal systems (usually as in elastomers), the solubility wiU be independent of concentration and the sorption curve will follow Henry s law (Equation 4.6), i.e., gas concentration within the polymer is proportional to the applied pressure. For nonideal systems (usually as in glassy polymers), the sorption isotherm is generally curved and highly nonlinear. Such behavior can be described by free-volume models and Flory-Huggins thermodynamics—comprehensive discussions on this may be found elsewhere [1,25,26]. 

The basic transport mechanism through a polymeric membrane is the solution diffusion as explained in Section 4.2.1. As noted, there is a fundamental difference in the sorption process of a rubbery polymer and a glassy polymer. Whereas sorption in a mbbery polymer follows Henry s law and is similar to penetrant sorption in low molecular weight liquids, the sorption in glassy polymers may be described by complex sorption isotherms related to unrelaxed volume locked into these materials when they are quenched below the glass transition temperature, Tg. The various sorption isotherms are illustrated in Figure 4.6 [47]. 

Rogers [34] described four different types of sorption isotherms. For very dilute feed solution sorption isotherm is linear obeying Henry s law (Equation 5.6). It is also called type-I sorption isotherm. 

For polymeric membranes filled with absorptive fillers, sorption in the filler occurs in accordance with the Langmuir adsorption isotherm while Henry s law governs that in the polymer matrix. This kind of sorption isotherm is designated as type-II isotherm. 

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... 

If the sotted concentration at the upstream face obeys Henry s Law as shown in Fig. 20.3-3a. then C2 = Sp2, and we can express the time lag directly in terms of pressure. If a more complex polynomial fit to the sorption isotherms shown in Fig. 2C.3-3o is necessaiy, II is clear that C versusp2 conld still be suberituted into Eq. (20.3-14) to obtain the presesre-explicit prediction of 8 versus pressure for comparison to the eaperimentally measured data. 

It follows from this that all solutions of mass transport problems taking into account only advective-dispersive dispersion are also applicable for cases of linear sorption (Henry s sorption isotherm). It is sufficient for... 

Water vapour has anomalous solubility characteristic, because of the strong hydrogen bonding between the molecules. Figure 11.2 shows that the sorption isotherms can curve steeply upwards as the relative pressure approaches 1. However, hydrophobic polymers such as polyolefins still obey Henry s law. 

ABSTRACT. An isosteric sorption system has been used to study the sorption of methane, ethane, ethene, propane, N2 and CO2 and some of their binary mixtures in silicalite-1. Isotherms of some of these sorbates have been determined at equilibrium pressures up to 20 atmospheres. Isosteric heats of sorption have been obtained from the slopes of the isosteres. Separation factors calculated from the Henry s Law constants determined from the initial slopes of the single conq>onent isotherms are found to be in good agreement with experim tal separation factors. The Langmuir-Freundlich equation has be used to lit the single component data and the Ideal Adsorbed Solution theory has be used to predict a binary sorption isotherm from the respective single component data. Comparison of the sorption behaviour of the hydrocarbons in silicalite-1 and NaY zeolites has been made. 

By introducing a solubility coefficient S, that is, the ratio of concentration over pressure C /p2, when sorption isotherm can be represented by the Henry s law, the permeability coefficient may be expressed simply as... 

Both Equations [18.1] and [18.5] describe ideal cases. In many experimental situations, sorption isotherms are non-linear, showing a negative behavior compared to Henry s law. Some cases can be described using a dual sorption theory (Paul and Koros, 1976) in which the global sorption capacity is the result of two different contributions, one that follows Henry s law and a second that follows Langmuir behavior ... 

Monte Carlo simulation has been used to simulate the optimized structures for zeolites, metal oxides and metals. In addition, it has been used to simulate the siting of sorbates, Henry s Law constants, heat capacities, isosteric sorption isotherms and other thermodynamic properties. 

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