Critical water content

This equation relates the temporal concentration of a diffusing chemical to its location in space. In real soil and aquifer materials, the diffusion coefficient can be affected by the temperature and properties of the solid matrix, such as mineral composition (which affects sorption, a process that can be difficult to separate from diffusion), bulk density, and critically, water content. 

Figure 4. Number of water molecules in a cluster Nc at RH = 0.9 against silica content. The inset shows the critical water content hc against silica content.

Figure 5.6. Water plasticization and sorption behavior typical of dairy powder showing critical water content and water activity resulting in glass transition at a typical room temperature.

Careri et al. (1986), using the framework of percolation theory, analyzed the explosive growth of the capacitance with increasing hydration above a critical water content (Fig. 14). The threshold for onset of the dielectric response was found to he 0.15 h for free lysozyme and 0.23 h for the lysozyme—substrate complex. In the percolation model the thresh-... 

As noted, for both the lysozyme—saccharide complex and the purple membrane, the critical point for protonic percoladon is at the onset of function. These observations may apply to other situations, in which a new property emerges suddenly at a critical water content, and may lead to understanding of function in terms of the building up of a statistical network of water-assisted pathways encompassing the system. Statistical... 

Equation (23) contains G, S, and as parameters. G kg Pit,/hTR) is a function of Tr and the psychrometric ratio. The psychrometric ratio can be calculated and is fairly constant. Therefore G is a function of Tr only (Pr, being the vapor pressure at Tr). < is a function of Tr and S is a function of Tr and Tw. In Figs. 3 and 4, moisture concentration and time, in dimensionless coordinates, have been plotted with Tr and Tr — Tyr as parameters. Given Tr, Tyy, and BhTRAo/ KWy, one can determine the drying schedule by using these plots. A /W is the area of heat transfer per pound of water at the critical water content. 

Since no constant-rate data were available for the rods, the initial moisture was taken as the critical water content. The theory deviated as much as 20% from experiment for this data. Because the errors involved were small, no attempt was made to obtain better values of the critical moisture content in this case. 

Water plasticized the food models and caused a substantial decrease of the glass-transition temperature. The Gordon-Taylor equation was successfully fitted to experimental glass transition temperatures of the three model systems, as shown in Figure 53.2b. The constant, k, for the Gordon-Taylor equation was found to be 7.6 0.8 for lactose/reactant systems, 7.2 0.7 for lactose/trehalose/reactant systems, and 7.9 0.9 for trehalose/reactant systems. The three model systems had corresponding glass-transition behaviors, which were typical of lactose-based dairy products. The critical water contents at 23°C obtained from Tg data for lactose/reactant, lactose/trehalose/reactant, and trehalose/reactant systems were 7.0, 7.4, and 7.1 g/100 g of dry solids, respectively. 

The obtained relationships will allow us to know the critical water content (CWC) and the critical water activity (CWA) at which the glass transition in the water-soluble phase occurs at a determined storage temperature of the product. Above these values, this phase in dried pear become sticky and rubber, and the crystallization of the amorphous compounds could take place. At 30°C (temperature at which the isotherms were obtained). 

The authors suggested that the critical water content wc at which the Tg of the plasticized glass falls below that of the storage temperature (Ts) may be predicted from... 

It was mentioned above that the crystallization of lactose can occur at a critical water content, just above the glass transition. It was further (implicitly) assumed that this would happen at the same mass fraction of water i/fw in skim milk powder. Experiments show that this is not precisely correct but that the critical conditions for crystallization are at the same water activity. Does this imply that the glass transition is determined by aw rather than i//w ... 

Usually, this part of water is nonfreezable and, therefore, not available for chemical reactions or as plasticizers (Okos et al., 1992). The water that does not freeze is normally considered to correspond to the monomolecular layer of adsorbed water and has been suggested to be the critical water content above which deteriorative changes may occur. The nonfreezable water content, in percentage (%) of total water for various foodstuffs, is given in Table 7.1. 

A separate conducting aqueous phase separates above the critical water content of about 35%, as already demonstrated by ultracentrifugation. 

Thus, when an oil-in-water emulsion inverts to become a water-in-oil system (e.g., cream to butter), conductivity decreases drastically. Figure 5.3b also demonstrates the importance of the liquid phase in breadmaking. Dough expansion in a baking test only occurs once a separate liquid phase is present and the test bake loaf volume, similarly to conductivity, extrapolates to zero expansion near the critical water content of about 35%. 

There is a correlation between the corrosion rate of the steel and the water concentration in the gasoline. A similar phenomenon was found in mixtures of naphtha and kerosene with water. The critical concentration of water in gasoline is 200 ppm, in naphtha it is 1000 ppm The general corrosion rate in the pure (without water) gasoline, naphtha and kerosene is 0.002-0.004 mm/year. Injection of the critical water content into gasoUne, naphtha and kerosene results in a drastic increase of the general corrosion rate to 0.6-0.8 mm/year. 

At the macroscopic level, proton transport can be studied with electrochemical impedance spectroscopy (EIS). Cappadonia et al. (1994,1995) performed EIS studies to explore variations of proton conductivity with water content and temperature for Nafion 117. The Arrhenius representation of conductivity data revealed activation energies between 0.36 eV at lowest hydration and 0.11 eV at highest hydration, as shown in Figure 2.6. The transition occurs at a critical water content of A-crit 3. At fixed X, the transition between low and high activation energies was observed at 260 K for well-hydrated membranes. This finding was interpreted as a freezing point suppression due to confinement of water in small pores. 

The value of the activation energy of proton transport in PEMs is low ( 0.1 eV), for water contents above X 3, and it is similar to the value in bulk water, as depicted in Figure 2.6. This similarity suggests that the widely studied relay-type mechanism of prototropic mobility in bulk water is relevant for PEMs above a critical water content. 

As discussed, this approach works surprisingly well above a critical water content Xc. 

It should be emphasized again that hydraulic permeation models do not rule out water transport by diffusion. Both mechanisms contribute concurrently. The water content in the PEM determines relative contributions of diffusion and hydraulic permeation to the total backflux of water. Hydraulic permeation prevails at high water contents, that is, under conditions for which water uptake is controlled by capillary condensation. Diffusion prevails at low water contents, that is, under conditions for which water strongly interacts with the polymeric host (chemisorption). The critical water content that marks the transition from diffusion-dominated to hydraulic permeation-dominated transport depends on water-polymer interactions and porous network morphology. Sorption experiments and water flux experiments suggest that this transition occurs at A. 3 for Nafion with equivalent weight 1100. 

The results presented here indicate that there is an important change in the pore structure on going from 20 to 30 wt. % of water in the polymerization mixture. Previously it has been suggested that the critical water content leading to heterogeneous PHEMA is closer to 45 % (Chirila et al. and references therein) 28) on consideration that the equilibrium water content of PHEMA hydrogels is related to the polymer-solvent interaction parameter and hence solvent quality. 

Since the hydrolysis and condensation of metal alkoxides are extremely sensitive to water, the thickness of electrodeposited non-sihcon sol-gel films is also dependent on the content of water in the deposition solution, as shown in Figure 12.8. A critical water content was observed for both anodic and cathodic electrodeposition, at which the film deposited had the highest thickness. Almost no film was electrodeposited when the water content was very low, about <10 ppm. This indicates that both anodic and cathodic electrodeposition are based on the electrolysis of water. However, it is still unclear why the thickness of the film decreased as the water content was higher than 100 ppm. One possible explanation is that the sol-gel precursor underwent condensation in the solution forming oligomers that were not active enough for further film deposition. 

---