Hailwood-Horrobin

Many models have been developed that deal with the sorption properties of wood in the presence of moisture these have been discussed in a number of works (e.g. Skaar, 1972 Siau, 1984). They can be approximately divided into sorption models, such as the Brunauer-Emmett-Teller (BET) model, or solution models (such as the Hailwood-Horrobin, H-H, model). The sigmoidal shapes of sorption or desorption isotherms can be deconvoluted into two components. These are often taken to represent a monomolecular water layer (associated with the primary sorption sites, OH groups), and a multilayer component where the cell wall bound water molecules are less intimately associated with the fixed cell wall OH groups. 

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). 

Figure 29 shows curves of H/M ( = h/m) vs. H = lOOh) calculated from experimental sorption data (also plotted) on wood and bark at 25 °C, for both adsorption and desorption. Figure 30 shows the curves of the total moisture content M, and of Mi and M2, all expressed in percent (M = 100 m). These curves were obtained using values of m, ki, and 2 calculated from the curve in Figure 29 for the adsorption isotherm of wood. The curves labelled Mh and M, are derived from the Hailwood-Horrobin sorption isotherm model. 

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-... 

The Hailwood-Horrobin single hydrate model predicts a sorption isotherm of the same form as the Dent model, that is, a parabolic relationship between h/m and h as given in Equation 33. Furthermore, two of the fundamental constants, and K2 are identical with the Dent constants and 2- The third constant Ki is analogous to of the Dent model but not identical. They are related by... 

The derivative of air relative humidity (p with respect to moisture content u is calculated from the Hailwood-Horrobin equation adopted for wood by Simpson [37] and given as ... 

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. 

In this connexion also see the recent paper by A, J. Hailwood and S. Horrobin, Tram. Faraday Soc., 47 B (1946) 84, Gen. Discussion on Smiling and Shrinking, held at London (1946). 

For the system wool-water a theory of this kind has been developed by Cassie and in a particularly interesting paper by Hailwood and Horrobin The latter postulated formation of a monohydrate, i. e., binding of one water molecule by each monomeric residue of the fibre portion taking part in absorption. For the isotherm they gave the equation ... 

The next point of interest is to seek an explanation for the initial disappearance of the narrow band in cellulose II. Making use of Hailwood and Horrobin s [Id] theory we calculate the amounts of adsorbed water at the critical points indicated by the initial raise, maximum and final decline of the broad band second... 

The conditions are slightly different in the case of cellulose II. Accomodating the first water uptake in the crystalline zone we exclude it from participation in the equilibrium described by the theory of Hailwood and Horrobin [id]. The total water content at a regain R = 2.25% is 0.2025 H2O/C6. Concentrating this water in the crystalline zone one obtains... 

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