Water sorption model

The water sorption model proposed in Eikerhng and Berg (2011) treats the water-filled PEM as a poroelectroelastic medium. Starting from a definition of the laws of swelling of such a medium, the model establishes a correlation between microscopic and macroscopic swelling. It correlates vapor sorption data, structural data, polymer elasticity, and volumetric swelling. 

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 basic assumption for a mass transport limited model is that diffusion of water vapor thorugh air provides the major resistance to moisture sorption on hygroscopic materials. The boundary conditions for the mass transport limited sorption model are that at the surface of the condensed film the partial pressure of water is given by the vapor pressure above a saturated solution of the salt (Ps) and at the edge of the diffusion boundary layer the vapor pressure is experimentally fixed to be Pc. The problem involves setting up a mass balance and solving the differential equation according to the boundary conditions (see Fig. 10). 

V. WATER SORPTION BY CRYSTALLINE SOLIDS A. General Model... 

Lievonen, S.M. and Roos, Y.H. 2002b. Water sorption of food models for studies of glass transition and reaction kinetics. J. Food Sci. 67, 1758-1766. 

Escher, B. I., Schwarzenbach, R. P. and Westall, J. C. (2000). Evaluation of liposome-water partitioning of organic acids and bases 1. Development of a sorption model, Environ. Sci. Technol., 34, 3954-3961. 

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. 

The subsequently presented model of water sorption in PEMs reconciles vapor sorption and porosity data. At sufficiently large water contents exceeding the amount of surface water, T > equilibrium water uptake is controlled by capillary forces. Deviations from capillary equilibrium arising at A < can be investigated by explicit ab initio calculations of water at dense interfacial arrays of protogenic surface groups. ° In the presented model, the problem of Schroeder s paradox does not arise and there is no need to invoke vapor in pores or hydrophobicity of internal channels. Here, we will present a general outline... 

This condition has been recently used in a vaporization-exchange model for water sorption and flux in phase-separated ionomer membranes. The model allows determining interfacial water exchange rates and water permeabilities from measurements involving membranes in contact with flowing gases. It affords a definition of an effective resistance to water flux through the membrane that is proportional to... 

To illustrate this a model transesterification reaction catalyzed by subtilisin Carls-berg suspended in carbon dioxide, propane, and mixtures of these solvents under pressure has been studied (Decarvalho et al., 1996). To account for solvent effects due to differences in water partitioning between the enzyme and the bulk solvents. Water sorption isotherms were measured for the enzyme in each solvent. Catalytic activity as a function of enzyme hydration was measured, and bell-shaped curves with maxima at the same enzyme hydration (12%) in all the solvents were obtained. The activity maxima were different in all media, being much higher in propane than in either CO2 or the mixtures with 50 and 10% CO2. Considerations based on the solvation ability of the solvents did not offer an explanation for the differences in catalytic activity observed. The results suggest that CO2 has a direct adverse effect on the catalytic activity of subtilisin. 

Water sorption isotherms may be determined experimentally by gravimetric determination of the moisture content of a food product after it has reached equilibrium in sealed, evacuated desiccators containing saturated solutions of different salts. Data obtained in this manner may be compared with a number of theoretical models (including the Braunauer-Emmett-Teller model, the Kuhn model and the Gruggenheim-Andersson-De Boer model see Roos, 1997) to predict the sorption behaviour of foods. Examples of sorption isotherms predicted for skim milk by three such models are shown in Figure 7.12. 

Figure 7.12 Adsorption of water by skim milk and sorption isotherms predicted by the Braunauer-Emmett-Teller (BET), Kuhn and Guggenheim-Andersson-De Boer (GAB) sorption models (from Roos, 1997).

The radial diffusion model and the linear sorption model are compared in Fig. 18.76. Since according to Eq. 19-76 the total mass of the chemical associated with the particle aggregate, (M(r), and the macroscopic solid-water distribution ratio, Kd(t), are linearly related ... 

NR and — CO groups, measured after prior washing of the resin with water 85), was well represented by a Langmuir + Nernst dual mode sorption model at salt concentrations not exceeding 0.2 mol dm 3. A detailed physical interpretation of the relevant parameters was not given, however, neither was the dual mode concept utilized in a corresponding diffusion study 86). 

Two parameters of excipients that are important to the compatibility formulator are (i) the ability of the excipients to absorb water at variable humidity and (ii) the pH that the excipient will impart in the solid-state environment. Knowledge of water sorption of excipients is well documented (27) and is used to estimate the amount of water the excipients will introduce into a solid-formulation mixture (30). The percentage of water and the dispensation of water, whether bound or variably adsorbed, was shown to have a dramatic effect on the hydrolytic stability of aspirin (31). It is well known that water will redistribute within solid pharmaceutical systems and this redistribution has been modeled and studied extensively (18). The pH influence that an excipient imparts to the formulation matrix can be directly related to... 

Composite formulations were prepared as follows The straw samples as received from INEEL were ground to 0.69 mm in a hammer mill and oven dried to 1.1% moisture. The dried straw samples were then blended with various amounts of high-density polyethylene (HDPE), lubricants, and maleated polyethylene blends (MAPE) (see Table 2). The mixed formulations were then extruded with a 35-mm Cincinnati Milacron Model CMT 35 counterrotating conical twin screw extruder (Cincinnati Milacron, Batavia, OH), which produced a 9.525 x 38.1 mm2 solid cross-section. Flexural strength, density, and water sorption were measured for the extruded samples according to ASTM Standard Methods (13,14). 

The sorption isotherm for many substances in polymers in the glassy state, as well as water in cellulose, can be described by two processes that are independent of one another (dual sorption model) ... 

Water sorption isotherms for hep show marked hysteresis. Powers and Brownyard (P20) found that, while it was difficult to obtain reproducible desorption curves, the low-pressure part of the water vapour resorption curve varied little with w/c ratio, between different Portland cements, or, if allowance was made for the contents of unreacted cement, with the degree of hydration. This was their main direct evidence for the conclusion (Section 8.2.1) that the properties of the hydration product considered in their model were essentially independent of these variables. However, the water sorption iostherms obtained by different investigators have varied considerably (e.g. Refs P20 and S79), and it is not clear to what extent the above conclusion would stand had different desorption conditions been used. 

Equation [1.5.38] is still fairly general. Except for the premises of localization, surface homogeneity and absence of lateral interaction, we only have the restriction that at given J there is only one type of subsystem, l.e. only one q(J). This generality implies that, for instance, [1.5.38] also applies to the three-dimensional analogue, like water sorption on a non-expanding gel. Furthermore, a number of models are compatible with this expression. 

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