Water sorption, equilibrium

Most of these aspects of water-sorption equilibrium correspond to the equality of chemical potentials of water in the medium and in the polymer. The consequences of this principle are illustrated by the experiment of Fig. 14.2, where an interface is created between water and a nonmiscible liquid (oil, hydrocarbon, etc.), and a polymer sample is immersed into the organic liquid. It can be observed that, despite the hydrophobic character of the surrounding medium, the sample reaches the same level of water saturation as in direct water immersion or in a saturated atmosphere. What controls the water concentration in the polymer is the ratio C/Cs of water concentrations in the organic phase, where Cs is the equilibrium concentration, which can be very low but not zero. In other words, hydrophobic surface treatments can delay the time to reach sorption equilibrium but they cannot avoid the water absorption by the substrate. 

Drying kinetics was represented by a diffusive model. The models were completed with water sorption equilibrium equation, expressions for product and moist air properties, correlations for convective heat and mass transfer coefficients, and the kinetics of drying and of the selected quality changes in the product as functions of water content and temperature (Di Scala and Crapiste, 2005). Experimental data were obtained from Di Scala and Crapiste (2005) and Roura et al. (2001). 

Research into the aquatic chemistry of plutonium has produced information showing how this radioelement is mobilized and transported in the environment. Field studies revealed that the sorption of plutonium onto sediments is an equilibrium process which influences the concentration in natural waters. This equilibrium process is modified by the oxidation state of the soluble plutonium and by the presence of dissolved organic carbon (DOC). Higher concentrations of fallout plutonium in natural waters are associated with higher DOC. Laboratory experiments confirm the correlation. In waters low in DOC oxidized plutonium, Pu(V), is the dominant oxidation state while reduced plutonium, Pu(III+IV), is more prevalent where high concentrations of DOC exist. Laboratory and field experiments have provided some information on the possible chemical processes which lead to changes in the oxidation state of plutonium and to its complexation by natural ligands. 

Nguyen, T. H., Himmelstein, K. J., and Higuchi, T., Some equilibrium and kinetic aspects of water sorption in poly(ortho esters), Int. J. Pharm.. 25, 1-12, 1985. 

The equilibrium swelling degree is the most important property of a hydrogel it directly influences the rate of water sorption, the permeability to drugs, and the mechanical strength of the gel. It also affects the biocompatibility of the... 

Pure PHEMA gel is sufficiently physically cross-linked by entanglements that it swells in water without dissolving, even without covalent cross-links. Its water sorption kinetics are Fickian over a broad temperature range. As the temperature increases, the diffusion coefficient of the sorption process rises from a value of 3.2 X 10 8 cm2/s at 4°C to 5.6 x 10 7 cm2/s at 88°C according to an Arrhenius rate law with an activation energy of 6.1 kcal/mol. At 5°C, the sample becomes completely rubbery at 60% of the equilibrium solvent uptake (q = 1.67). This transition drops steadily as Tg is approached ( 90°C), so that at 88°C the sample becomes entirely rubbery with less than 30% of the equilibrium uptake (q = 1.51) (data cited here are from Ref. 138). 

Soil Sorption Constant - Soil/Water (Knp.). The distribution of a chemical between soil and water can be described with an equilibrium expression that relates the amount of chemical sorbed to soil or sediment to the amount in the water at equilibrium. 

The most fundamental manner of demonstrating the relationship between sorbed water vapor and a solid is the water sorption-desorption isotherm. The water sorption-desorption isotherm describes the relationship between the equilibrium amount of water vapor sorbed to a solid (usually expressed as amount per unit mass or per unit surface area of solid) and the thermodynamic quantity, water activity (aw), at constant temperature and pressure. At equilibrium the chemical potential of water sorbed to the solid must equal the chemical potential of water in the vapor phase. Water activity in the vapor phase is related to chemical potential by... 

A series of experiments was also conducted by Bowman et al. [34] to ascertain the effects of differing environmental factors on the sediment-water interactions of natural estrogens (estradiol and estrone) under estuarine conditions. Sorption onto sediment particles was in this case relatively slow, with sorption equilibrium being reached in about 10 and 170 h for estrone and estradiol, respectively. On the other hand, true partition coefficients calculated on colloids were found to be around two orders of magnitude greater that those on sediment particles. Hence, it was concluded that under estuarine conditions, and in comparison to other more hydrophobic compounds, both estrone and estradiol... 

Because of the similarity of transport in biotilms and in stagnant sediments, information on the parameters that control the conductivity of the biofilm can be obtained from diagenetic models for contaminant diffusion in pore waters. Assuming that molecular diffusion is the dominant transport mechanism, and that instantaneous sorption equilibrium exists between dissolved and particle-bound solutes, the vertical flux ( ) through a stagnant sediment is given by (Berner, 1980)... 

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... 

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. 

We consider a flat sediment surface which is overlain by a completely mixed water column. A sorbing chemical is exchanged between the water and the sediment. Immediate sorption equilibrium at every local point in space is assumed. 

The sorption equilibrium is expressed by (Kf solid-water distribution ratio Eq. 9-7) ... 

Next we analyze the sorption kinetics of a sorbate with constant aqueous concentration, C°, sorbing into a porous spherical aggregate with radius rQ. More precisely, the macroparticle is a homogeneous aggregate of microparticles which are separated by micropores filled with water (Fig. 19.17). The sorbate diffuses in these pores and sorbs to the microparticles. It is not relevant whether sorption occurs at the surface or in the interior of the microparticles as long as we can assume that sorption equilibrium between the solute concentration and the microparticles at each position within the aggregate is attained instantaneously. 

In cases (b) and (b ) there is no equilibrium the mass increases continuously or decreases after a maximum, which indicates the existence of an irreversible process - chemical, hydrolysis, or physical, damage microcavitation increases the capacity of the material for water sorption. The experimental curves having the shape of curves (b) or (b7), indicate that the irreversible processes induce significant mass changes in the timescale of diffusion. When the irreversible processes are significantly slower than diffusion, the behavior shown by curves (c) or (d) is observed. The sorption equilibrium is reached at t to, and a plateau can be observed in the curve... 

However, more recently, Perlinger et al. (1993) observed a solids concentration effect with benzene on aluminum oxide that could not be explained by incomplete phase separation, nonattainment of sorption equilibrium, or aggregation of particles. Perlinger et al. (1993) suggested that the observed effect resulted from changes in the activities of water and/or benzene sorbed at the mineral surface. This was thought to occur when the structure of water near the mineral surface increased due to particle interactions. 

Barrie (1968) collected all the known data on water sorption. From these data it is possible to estimate the effect of the different structural groups on water sorption at different degrees of humidity. Table 18.14 presents the best possible approach to the sorptive capacity of polymers versus water, i.e. the amount of water per structural group at equilibrium, expressed as molar ratio. From these data the solubility (cm3 water vapour (STP) per cm3 of polymer) can be easily calculated. (The multiplication factor is 22.4 x 103/V, where V is the molar volume per structural polymer unit.)... 

Lewin and coworkers [255-260] developed an accessibility system based on equilibrium sorption of bromine, from its water solution at pH below 2 and at room temperature, on the glycosidic oxygens of the cellulose. The size of the bromine molecule, its simple structure, hydrophobicity, nonswelling, and very slow reactivity with cellulose in acidic solutions, contribute to the accuracy and reproducibility of the data obtained. The cellulose (10 g/1) is suspended in aqueous bromine solutions of 0.01-0.02 mol/1 for 1-3 h, depending on the nature of the cellulose, to reach sorption equilibrium. The diffusion coefficients of bromine in cotton and rayon are 4.6 and 0.37 x 10 cm /min, respectively. The sorption was found to strictly obey the Langmuir isotherm, which enables the calculation of the accessibility of the cellulose as follows ... 

Figure 2. Sorption Equilibrium of phenanthrene onto soil. (SpiK,eq=Equilibrium concentration of phenanthrene in soil, Cphe,eq = Equilibrium concentration of phenanthrene in water)...

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