Vapor sorption isotherms

Fig. 6 Water vapor sorption isotherms for poly(vinylpyrrolidone) at 60°C(+) 30°C (x) -20°C ( ) and -40°C (A). Data were taken from Oksanen and Zografi [71,75]. A 0 represents the calculated water contents necessary to depress Tg to the temperature of the isotherms.

The experimental basis of sorption studies includes structural data (SANS, SAXS, USAXS), isopiestic vapor sorption isotherms,i and capillary isotherms, measured by the method of standard porosimetry. i 2-i44 Thermodynamic models for water uptake by vapor-equilibrated PEMs have been suggested by various groupThe models account for interfacial energies, elastic energies, and entropic contributions. They usually treat rate constants of interfacial water exchange and of bulk transport of water by diffusion and hydraulic permeation as empirical functions of temperature. 

Gibbs free energies of water sorption, AG "(/l), can be extracted from isopiestic vapor sorption isotherms this analysis shows that AG (T) < AG", where AG" = -44.7 kj moH is the Gibbs free energy for vapor sorption at a free water surface at ambient condihons. Water absorbed by the membrane is therefore more strongly bound than water at a free bulk water surface this affirms the hydrophilic nature of water sorption in PEMs. 

To begin, it is essential to rationalize the equilibration of water within the membrane at AP = 0, APs = 0, j = 0, and = 0. The suggested scenario of membrane swelling is based on the interplay of capillary forces and polymer elasticity. In order to justify a scenario based on capillary condensation, isopiestic vapor sorption isotherms for Nafioni in Figure 6.9(a) are compared with data on pore size distributions in Figure 6.9(b) obtained by standard porosimetry.i In Figure 6.9(a), a simple fit function. 

This relation can adequately reproduce the shape of experimental vapor sorption isotherms in the regime corresponding to capillary condensation. The approach to the limit of T, — 0 (only surface water remaining) is given by... 

Mauritz and Rogers constructed a water vapor sorption isotherm model for ionomers with inherently clustered morphologies, as applied to Nafion mono-... 

Figure 11.4 Vapor sorption isotherms of 1,3-dichlorobenzene on Woodbum soil at 20°C as a function of relative humidity (RH). Adapted from Chiou and Shoup (1985).

Water vapor adsorption isotherms have been obtained on cotton from room temperature up to 150°C [303,304]. Theoretical models for explaining the water vapor sorption isotherms of cellulose have been reviewed [303]. Only adsorption theories will be discussed here at ambient temperatures. The shape of the isotherm indicates that multilayer adsorption occurs and thus the Brunauer, Emmett and Teller (BET) or the Guggenheim, Anderson and deBoer (GAB) theory can be applied. In fact, the BET equation can only be applied at relative vapor pressures (RVPs) below 0.5 and after modification up to a RVP of 0.8 [305]. The GAB equation, which was not discussed in the chapter in the book Cellulose Chemistry and Its Applications [303], can be applied up to RVPs above 0.9 [306]. Initially as the RVP... 

Figure 6. Equilibrium water vapor sorption isotherms obtained on female stratum corneum (age 29) using salt solutions ( ) and the dynamic method (O) at 23.3 0.5°C...

Fig. 6 Water vapor sorption isotherm for crystalline and amorphous samples of indomethacin. ( ) Amorphous ( ) crystalline. (From Ref. " l)...

The three natural CDs form crystalline structures in the solid state that decompose above 200°C with no definite melting points. They are not considered hygroscopic, but they do form various stable hydrates. The water vapor sorption isotherms (Fig. 9) show two phases for the p- and y-CDs, and one phase for a-CD. At 11% RH, ot-CD absorbs 4 water molecules and upon long-term storage, forms a stable hydrate with 6 water molecules. The water content gradually increases with increasing humidity to a constant value of 6.6 water molecules per CD molecrJe at and above 79 /o Four different... 

Fig. 9 Water vapor sorption isotherms for a-, P-, and y-CD at 40 C. (Dashed line adsorption, solid line desorption). (Adapted from Ref...

Water Sorption. The water vapor sorption isotherm (293 K) is given in Figure 3. The general sigmoidal shape is evident, and the hysteretic phenomenon is quite pronounced, even when desorption is instigated from intermediate pressures (about 0.6 Pq), and vacuum closure... 

The data for the crystal structure, NMR structure, powder x-ray diffraction pattern, water vapor sorption isotherms, glass transition temperature as a function of water, heat capacity, heat of solution properties, vapor pressure, and osmotic pressure are described in the literature. 

Figure 3.4.24 Vapor sorption isotherms for benzene(open circle) and n-hexane(solid circle) at 20 °C (a) and the pressure selective on-off adsorption (b). The difficulty of fitting these large guests into the a-crystal phase is illustrated by the negligible adsorption before crystal phase transition into the (3-crystal phase.

Vapor sorption isotherms in a polymer as computed from Flory-Huggins theory by using interaction parameters shown. 

Base on minimum RH for stable hydrate form at different temperature (from water vapor sorption isotherms)... 

Water vapor sorption Isothermal microcalorimetry Intrinsic dissolution Triboelectric property... 

H. D. Orchiston, Adsorption of water vapor. I Soils at 25 C, Soil Sci. 76 453 (1953). J. P. Quirk, Significance of surface areas calculated from water vapor sorption isotherms by use of the BET equation. Soil Sci. 80 423 (1955). 

FIG U RE 1.21 Water vapor sorption isotherms on polyvinyledene chloride (PVDC and urea formaldehyde resin (UF) carbons before and after outgassing and oxidation. (From Bansal, R.C., Dhami, T.L., and Prakash, S., Carbon, 16, 389, 1978. With permission.)... 

FIGURE 6 Water vapor sorption isotherms on smectites exchanged with Ca, Ba, Cs, and Na ions. (Adapted from Ref. 89.)... 

The conventional approach to perform water vapor sorption kinetics is based on the measnrement of the film sample mass until reaching constant value corresponding to a saturation level in a hydrated environment. For each hydrated enviromnent, the mass of sample is measured allowing to obtain the mass gain, ejqtressed in percent, or, in other word, the water concentration, expressed in mass of water soibed per mass of polymer or in mmol of water soibed per mass of polymer, inside sample. The combination of mass gain at each humidity level leads to build the water vapor sorption isotherm. The water vapor sorption and the isotherm shape are depending on the moisture resistance of polymer and its ability to interact with water. 

The experimental basis of sorption studies includes isopiestic vapor sorption isotherms (Morris and Sun, 1993 Pushpaet al., 1988 Rivin et al., 2001 Zawodzinski et al., 1993c) and capillary isotherms, measured by standard porosimetry (Divisek et al., 1998 Vol fkovich and Bagotsky, 1994 Vol fkovich et al., 1980). A number of thermodynamic models of water uptake by vapor-equilibrated PEMs have been... 

A necessary consistency check of a water sorption model is the calculation of vapor sorption isotherms. Equation 2.49 gives A V/Vb as a function of oo.c- The input for the calculation includes the environmental parameters T, P, P"), materials parameters (sr, G, PsQ-) probability density distribution n (ao). The value of t]c can be... 

The water content is the state variable of PEMs. Water uptake from a vapor or liquid water reservoir results in a characteristic vapor sorption isotherm. This isotherm can be described theoretically under a premise that the mechanism of water uptake is sufficiently understood. The main assumption is a distinction between surface water and bulk water. The former is chemisorbed at pore walls and it strongly interacts with sulfonate anions. Weakly bound bulk-like water equilibrates with the nanoporous PEM through the interplay of capillary, osmotic, and elastic forces, as discussed in the section Water Sorption and Swelling of PEMs in Chapter 2. Given the amounts and random distribution of water, effective transport properties of the PEM can be calculated. Applicable approaches in theory and simulation are rooted in the theory of random heterogeneous media. They involve, for instance, effective medium theory, percolation theory, or random network simulations. 

The second boundary condition in Equation 5.12 involves an approximation of the vapor sorption isotherm in the form of Henry s law ... 

Using this linear approximation might be considered oversimplistic, but it renders the mathematical problem amenable to analytical solution by Laplace transformation. Moreover, it does not affect the agreement with experimental data. Of course, one may always resort to a numerical solution of the complete problem with a more accurate representation of the vapor sorption isotherm. 

Using the same linear approximation for the vapor sorption isotherm in Equation 5.8, similar expressions can be obtained as well for the VE case. In Monroe et al. 

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