Swelling isothermal

Since specific dilation isotherms are not usually available in open literature data, use of Equation (7.7) allows reasonable and simple procedures in the absence of dilation isotherm data, one single solubility datum at high pressure can be used in Equations (7.5) and (7.7) to obtain the swelling coefficient so that the swelling isotherm of the matrix at all other pressures can then be obtained through Equation (7.7). 

It must, of course, be emphasized that, in reality—as the swelling isotherms have shown—the three types of binding outlined above are continually overlapping and it means that certain liberties are taken in our definitions of the boundary they are, however, in line with the experimental methods available. If we wish to proceed more formally, we might speak simply of a part of the bound quantity of liquid greatly dependent on temperature and a part independent of temperature, so that the tempera-... 

The water intake of initially dry hydrogels was followed for a short time. Swelling isotherm of poly [N, N-DAPB/N, V-DMAAm/PNAAe] hydrogels (A -A ) is... 

Fig. 21.4. Swelling isotherms of poly(methyl methacrylate), polystyrene and poly(vinyl pyridine) in carbon dioxide at 308 K [22].

Figure 10.14 Swelling isotherm (V/Vo) for DNA gels (1% crosslinker) immersed in solutions of the cationic surfactants CigTAB, Ci4TAB, Ci2TAB and CgTAB. The concentration range 0-0.2 mM is also represented in detail (see inset). Temperature 25 °C, pH 9. From Ref [83].)...

Bauer et al. performed humidity scans of the Nafion 117-H+ membrane swelling isotherms. The results indicated that the length swell ratio increased with the humidity and the increase in length is more pronounced at high humidity and at temperature more than 15°C. A similar behavior for the sorption isotherm of Nafion at room temperature has been described by Laporta et al. and Zawodzinski et al. ... 

A tremendous variety of structures is known, and some of the three-dimensional network ones are porous enough to show the same type of swelling phenomena as the layer structures—and also ion exchange behavior. The zeolites fall in this last category and have been studied extensively, both as ion exchangers and as gas adsorbents (e.g.. Refs. 185 and 186). As an example, Goulding and Talibudeen have reported on isotherms and calorimetric heats of Ca -K exchange for several aluminosilicates [187]. 

The swelling of the adsorbent can be directly demonstrated as in the experiments of Fig. 4.27 where the solid was a compact made from coal powder and the adsorbate was n-butane. (Closely similar results were obtained with ethyl chloride.) Simultaneous measurements of linear expansion, amount adsorbed and electrical conductivity were made, and as is seen the three resultant isotherms are very similar the hysteresis in adsorption in Fig. 4.27(a), is associated with a corresponding hysteresis in swelling in (h) and in electrical conductivity in (c). The decrease in conductivity in (c) clearly points to an irreversible opening-up of interparticulate junctions this would produce narrow gaps which would function as constrictions in micropores and would thus lead to adsorption hysteresis (cf. Section 4.S). 

The equilibrium stress-strain isotherms in elongation, and the swelling ratios in benzene, were measured at 25°C for these networks. Network chain densities calculated from these measurements exceeded the values predicted from stoichiometry. 

The two network precursors and solvent (if present) were combined with 20 ppm catalyst and reacted under argon at 75°C to produce the desired networks. The sol fractions, ws, and equilibrium swelling ratio In benzene, V2m, of these networks were determined according to established procedures ( 1, 4. Equilibrium tensile stress-strain Isotherms were obtained at 25 C on dumbbell shaped specimens according to procedures described elsewhere (1, 4). The data were well correlated by linear regression to the empirical Mooney-Rivlin (6 ) relationship. The tensile behavior of the networks formed In solution was measured both on networks with the solvent present and on networks from which the oligomeric PEMS had been extracted. 

Hysteresis is observed not only in the sorption isotherms but also in calorimetric measurements of heat of wetting at different moisture contents, and it is thus a combined entropy and enthalpy phenomenon. A reliable explanation for this effect is not currently available, but there is speculation that it is due to the stresses which are induced as the cellulose swells. Since the swelling of cellulose is not completely reversible, mechanical recovery is incomplete and hysteresis will therefore be present both in the internal stress-strain curve of the sample, and also in the water adsorption isotherm. 

As water swells cellulose in an intercrystalline way (i.e. only within the non-crystalline amorphous regions), a relationship would be expected between accessibility and moisture uptake, and this is indeed found (Figure 5.5). Refining causes cellulosic fibres to swell and it would therefore be expected to cause a change in the water adsorption isotherm. This is indeed observed (Figure 5.6). 

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. 

In milk powders, the caseins are the principal water sorbants at low and intermediate values of aw. The water sorption characteristics of the caseins are influenced by their micellar state, their tendency towards self-association, their degree of phosphorylation and their ability to swell. Sorption isotherms for casein micelles and sodium caseinate (Figure 7.14) are generally sigmoidal. However, isotherms of sodium caseinate show a marked increase at aw between 0.75 and 0.95. This has been attributed to the... 

In recent years the Coal Research Laboratory has been investigating the kinetics and isotherm behavior of methanol sorption on coal (6, 7, 10) along with the sorption of other vapors on coal (6) and of polar vapors on swelling gels (9, 10). Methanol sorption was shown to be reversible on coal, and its sorption behavior supports the model of coal as a gel or mixture of gels in its physical structure. All indications (I, 6, 7) are that its interaction is with specific and a fixed number of sites for a particular coal sample. Although the sorption of methanol is reversible, coal exhibits sorption behavior which is interpreted in terms of an irreversible swelling of the coal gel upon initial exposure to methanol vapor. As a result of these studies, an isotherm and experimental rate equation for the sorption and desorption were derived that fit the observed data. The isotherm derived for methanol sorption on coal was ... 

Maurice M. Mitchell This term accounts for the swelling property of the gel. For a derivation of the isotherm equation see ref. 9. 

It must be remembered, in interpreting adsorption isotherms on coal, that coal expands sizably when temperature is increased, and coal swells appreciably during adsorption. These factors are relatively unimportant for porous inorganic solids. On heating from —195°C. to room temperature the volume of coal expands about 10%, and at least more or less consistent with this, pore openings at —195°C. seem to be 4A. while at room temperature they are about 5A. Further, on adsorption of water or methanol the volume of coal increases 10-20%, and with some exceptional polar adsorbates coal eventually dissolves. 

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