Isotherm Flory-Huggins

Figure 3. Tg of PVC vs. content of VC (V) data measured by means of deviation from Flory-Huggins isotherm (5) (X) data measured thermomechanically (IS) (O) data obtained from limiting conversion (4).

Finally, the Flory-Huggins isotherm has the advantage of considering the size of the molecules as well as the replacement of adsorbed solvent molecules by the adsorbing molecule. However, its applicability to ionic systems depends on the parameters included in the term p—lateral interactions, surface heterogeneity, etc. 

We see that it becomes Henry s Law for k2 0, and speculate that the substitution of the Flory-Huggins isotherm for ki4i to give ... 

V) deviation from Flory-Huggins isotherm (X) thermomechanical measurements. 

Haeany Solution Model The initial model (37) considered the adsorbed phase to be a mixture of adsorbed molecules and vacancies (a vacancy solution) and assumed that nonideaUties of the solution can be described by the two-parameter Wilson activity coefficient equation. Subsequendy, it was found that the use of the three-parameter Flory-Huggins activity coefficient equation provided improved prediction of binary isotherms (38). 

Flory-Huggins-type isotherms and the Bockris-Swinkels isotherm in particular. If n is assumed equal to 3 in the latter case, the value of 01 becomes 0.582." ... 

Different models determine A in different ways. Nation exhibits a water-uptake isotherm as shown in Figure 7. The dashed line in the figure shows the effects of Schroeder s paradox, where there is a discontinuous jump in the value of A. Furthermore, the transport properties have different values and functional forms at that point. Most models used correlate A with the water-vapor activity, since it is an easily calculated quantity. An exception to this is the model of Siegel et al., ° which assumes a simple mass-transfer relationship. There are also models that model the isotherm either by Flory—Huggins theory" or equilibrium between water and hydrated protons in the membrane and water vapor... 

Irreversible reaction, 1251, 1419 Isoconic, definition, 933, 978, 982 Isotherm, 932, 964, 1197 applicability, 941 and charge transfer, 954, 955 Conway and Angersein-Kozlowska, 943 definition, 933 in electrode kinetics, 1197 Flory—Huggins type, 941,942, 944, 965 Frumkin, 938, 942, 965 Frumkin-Temkin, 1197, 1198 Habib-Bockris, 943... 

The Flory-Huggins-Type Isotherm A Substitutional Isotherm... 

According to the Flory-Huggins formalism (Section 6.8.11), the isotherm corresponding to this equilibrium is given by... 

With this in mind, some important adsorption isotherms were introduced, and we found that each of them describes important characteristics of the adsorption process (Table 6.10). Thus, the Langmuir isotherm considers the basic step in the adsorption process the Frumkin isotherm was one of the first isotherms involving lateral interactions the Temkin is a surface heterogeneity isotherm and the Flory-Huggins-type isotherms include the substitution step of replacing adsorbed water molecules by the adsorbed entities (Fig. 6.98). 

For a higher accuracy of the isotherm, the activities in the liquid phase instead of the concentrations can be used. If a thermodynamic model for the computation of the solid-phase activities exists, the equilibrium concentration q and qi can also be calculated from the condition of equal activity, as was done for example for the esterification of acetic acid on Amberlyst 15 using the Flory-Huggins activity model for the solid phase and a UNI FAC model for the liquid phase [17]. 

Type III is the sorption isotherm of Flory-Huggins. Here the solubility coefficient increases continuously with pressure. It represents a preference for formation of penetrant pairs and clusters it is observed when the penetrant acts as a swelling agent for the polymer without being a real solvent. An example is water in relatively hydrophobic polymers containing also some polar groups. 

FIG. 18.8 Typical isotherm plots of sorbed concentration versus ambient vapour pressure. (I) Henry s law, S is a constant (II) Langmuir equation (III) Flory-Huggins equation (IV) BET equation, site saturation at point B (from C.F. Rogers, 1985). 

For isothermal ternary systems, Geveke and Danner (1991) have modified the Flory-Huggins theory to account for the concentration dependency of the parameters. The reduced total Gibbs free energy of mixing is given by... 

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]. 

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