Water sorption theory

Kapsalis, J.G. 1987. Influence of hysteresis and temperature on moisture sorption isotherms. In Water Activity Theory and Application to Foods (L.B. Rockland and L.R. Beuchat, eds), pp. 173-213. Dekker, New York. 

In spite of the composite nature of the stratum corneum, its water sorption isotherm is qualitatively identical to those of the more simple protein systems shown, suggesting that water interacts predominately with the protein components of the corneum. This conclusion is supported further by the results of chloroform-methanol (3/1 by volume) extraction which removed as much as 25% of the original dry weight (lipids and low molecular weight water-soluble components) but did not quantitatively alter the isotherm in the low relative humidities (18). The application of the Zimm-Lundberg cluster theory (56, 57) to the isotherm yields additional information as to the state of the sorbed water in the corneum. The tendency of water to cluster is expressed in this theory by the cluster function CiGn ... 

Since water vapor dissolves in the solid during absorption, several models based on solution theory, proposing that the sorbate is taken up into the solid as a solid solution, have been derived and used to describe water sorption on polymers (e.g., Flory-Huggins, Hallwood-Horrobin ). More recently, Vrentas et developed a solution-based model... 

Most subsequent sorption theories, including those discussed here, have followed this general approach and postulate two forms of sorbed water. These theories may be classified into at least two general types based on the sorption mechanism assumed. One type assumes sorption on internal surfaces and is represented by the Dent theory (52), which is a modification of the classic Brunauer, Emmett, and Teller (BET) theory (53). The second type assumes that the wood-water system forms a solution, exemplified by the Hailwood-Horrobin theory. There have been other theories, not discussed here, that have also been applied to explain water sorption by hygroscopic materials (JO, 54, 55). 

Dent s Surface Sorption Theory. The Dent sorption theory or model (52), in the simple form, is a modification of the BET model, which is itself an extension of the earlier Langmuir model (56). The Langmuir model assumes that a gas (water vapor in the case of wood) is sorbed onto sorption sites on the substrate or sorbent in a mono-layer only. The fraction of sorption sites occupied by the vapor or sorbate is a function of the vapor pressure of the sorbate and approaches unity as the vapor pressure increases. 

Hailwood-Horrobin Solution Sorption Theory. The Hailwood-Horrobin (57) model treats moisture sorption as hydration of the polymer, taken here to be dry wood, by some of the sorbed water called water of hydration, m. The hydrate forms a partial solution with the remaining sorbed water, called water of solution, m,. An equilibrium is assumed to exist between the dry wood and water and the hydrated wood with an equilibrium constant K. Equilibrium is also assumed to exist between the hydrated wood and water vapor at relative vapor pressure h, with equilibrium constant K2. A third constant is defined as the moisture content corresponding to com-... 

In general, water sorption data must be determined experimentally. Some 80 correlations, ranging from those based on theory to those that are purely empirical, have appeared in the literature. Two of the most extensive compilations are due to Wolf et al. (1985) and Iglesias and Chirife (1982). Aside from temperature, water sorption is also affected by the physical structure as well as the composition of the material. The pore structure and size, as well as the physical and/or chemical transformations during processing can cause significant variations in the moisture binding ability of the solid. 

For true adsorption, several equations for adsorption isotherms have been derived, based on various theories. Such equations often are applied to water sorption isotherms of foods as well. However, one cannot speak of adsorption in the case of most foods, as mentioned above, because there is no (or a very limited) phase surface onto which water can adsorb. Moreover, most foods contain numerous components even if phase surfaces were present they must be very inhomogeneous. In the author s opinion, it therefore makes little sense to use such equations. Only for relatively simple and homogeneous systems, like pure starch granules, can some theories be more or less applicable, but not for real foods. Mathematical fitting of experimental data may be useful for practical purposes, and since the equations generally have three or four adjustable parameters, a reasonable fit can often be obtained. But one cannot attribute physical significance to the parameters derived in this way, such as a monolayer water content. ... 

That is, if water sorption occurs on two types of sites, a polymer site and a pol3rmer-water site, the influence of the former will predominate as P and the amount of sorbed water simultaneously approach zero. A plot of vs P with a slope of k] (the inverse of Equation 2), as shown in Figure 1, is tangent to the experimental Isotherm at the origin. The analysis outlined allows a unique specification of x interaction parameter, through use of the limiting (Henry s Law) approximation of the Flory-Hugglns theory ( 3). That is... 

R. Schlogl and F. Helfferich, Theory of exchange membrane potentials, Z. Elektro-chem, 1952, 56, 644-647 N. Ishibashi, T. Seiyama and W Sakai, Electrochemical studies on ion exchangers (Part 10) Mobilities of Ca+ and Cl- in the cation exchange membrane, Denki Kagaku (J. Electrochem. Soc. Jpn.), 1955, 23, 182-186 E.E. Boakye and H.L. Yeager, Water sorption and ionic diffusion in short side chain perfluorosulfonate ionomer membranes, J. Membr. Sci., 1992, 69, 155-167. 

Hailwood and Horrobin ( ) develqped an equation for water sorption of cellulose based on a solution theory. It permits the calculation of the fraction of the san )le inaccessible to water vapor. However, Hailwood and Horrobin assumed in the development of their equation that an ideal solid solution of polymer, hydrated polymer and water is formed. This assutrption has laeen questioned in the general discussion following the presentation of their paper and also by McLaren and Rcwen (29). 

Water vapor at room temperature will not penetrate well-defined crystallites but will be adsorbed in the amorphous regions. Consequently, moisture sorption measured gravimetrically at a given relative vapor pressure and temperature has been used to determine order in cellulosic materials. In the case of Valentine [252] and Jeffries [253], the fraction of ordered material was obtained by correlating moisture sorption with values obtained by the deuterium oxide method. Hailwood and Horrobin [254] developed an equation for water sorption of cellulose based on a solution theory that allowed the calculation of the fraction of the sample inaccessible to water. 

Spiess, W.E.L. and Wolf, W., Critical evaluation of methods to determination of moisture sorption isotherms, in Water Activity Theory and Applications to Food, Rockland, L.B. and Beuchat, L.R. (eds.), Marcel Dekker, New York, 1981. 

The distinguishing feature of the classical diffusion model of Springer et al. [39] (hereafter SZG) is the consideration of variable conductivity. SZG relied on their own experimental data to determine model parameters, such as water sorption isotherms and membrane conductivity as a function of the water content. Alternative approaches include the use of concentrated solution theory to describe transport in the membrane [45], and invoking simplifying assumptions such as thin membrane with uniform hydration [46]. 

Eigure 2.26 compares calculated water sorption isotherms to two independent sets of experimental data for Nafion (Maldonado et al., 2012 Zawodzinski et al., 1991). A fixed amount of surface water is subtracted in experimental isotherms, since the theory describes bulk-like water only. After this modification, the agreement that can be achieved is good. 

The theory of bundle formation in the section Aggregation Prenomena in Solutions of Charged Polymers provides sizes, as well as electrostatic and elastic properties of ionomer bundles. The theory of water sorption and swelling, described in this section, gives a statistical distribution of pore size and local stress in pores. The merging point of both theories is a theory of fracture formation in charged polymer... 

Percolation theory can be applied to parameterize the effective properties of CLs. Specific parameters employed could be determined from structural diagnostics, including porosimetry measurements, water sorption studies, as well as rapidly evolving tomographical approaches using scanning electron microscopy and transmission... 

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. 

Eikerling, M. and Berg, P. 2011. Poroelectroelastic theory of water sorption and swelling in polymer electrolyte membranes. 7(13), 5976-5990. 

In membrane research, Michael has developed a poroelectroelastic theory of water sorption and swelling together with Peter Berg (NTNU Trondheim). It rationalizes the impact of external conditions, statistical distribution of anionic head groups, and microscopic elastic properties of the polymer on water sorption and swelling. This work has opened up an intriguing research area the study of internal mechanical stresses in charged elastic media, induced by water sorption. 

The equilibrium degree of water sorption cannot be accurately calculated a priori from theory. However, theoretical illustrations of the effects of different parameters do agree qualitatively with experimental results. Flory-Huggins theory introduces the polymer-solvent interaction parameter, Xp and defines n jx, as follows ... 

As has been shown in the previous section, for the considered elastoplastics the structure fractal dimension value i is equal to 2.0. In turn, this means that = 1.0 [27]. Now the water sorption coefficient for the considered nanocomposites can be calculated according to Equation 7.17. In Figure 7.19 the comparison of experimental Q and water sorption coefficient values calculated according to the proposed multifractal treatment for two series of PU/montmorillonite nanocomposites (PTMG/ MMT and PBAD/MMT) at experiment duration 1 and 5 days is assumed. As one can see, good correspondence of theory and experiment was obtained - the average discrepancy between and Q makes up about 20%, which is quite sufficient for preliminary estimations. 

Despite the fact that there have been many attempts to correlate the sorption behavior of water with the microstructure of the polymer matrix, very few studies have been attempted to correlate water sorption with localized water structure that is induced by the microstructure of the polymer [41]. Zimm and Lundberg [42] have carried out this type of analysis by a cluster theory. 

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