Uptake isotherm

Unfortunately, the literature is relatively sparse with examples showing the water uptake profile onto crystalline, nonhydrating substances below RHq. This is most likely due to the difficulty in accurately measuring the small amounts of water that are sorbed. Alkali halides are an exception, however, likely due to their well-characterized particle morphologies [34—37]. Figure 2 shows a water uptake isotherm onto recrystallized sodium chloride [37]. Note that the amount of water sorbed as a function of relative humidity is normalized to the specific surface area of the sample. Since water is sorbed only to the external surface of... 

Since water molecules occupy regular positions within the lattice of a hydrate with a specific stoichiometry (e.g., 1 1 monohydrate, 2 1 dihydrate, 5 1 pentahydrate) to the solid, relatively large quantities of water are sorbed. Figure 3 shows a moisture uptake isotherm for ipratropium bromide [39]. This substance undergoes an apparent hydration of the crystal between 63% and 75% relative humidity. Above 75% relative humidity, approximately 4.6% water is sorbed (theoretical monohydrate is 4.4 g/g). Interestingly, as anhydrous ipratropium bromide is equilibrated for extended time periods (e.g., 2 months and 5 months respectively, as shown in Fig. (3), hydration of the crystal appears to occur at... 

Table 3 Wm Values for Various Starches Obtained from BET Analysis of Moisture Uptake Isotherms...

Combining solids that have previously been equilibrated at different relative humidities results in a system that is thermodynamically unstable, since there will be a tendency for moisture to distribute in the system so that a single relative humidity is attained in the headspace. As shown in Fig. 7, moisture will desorb into the headspace from the component initially equilibrated at a higher relative humidity and sorb to the component initially equilibrated at a lower relative humidity. This process will continue until both solids have equilibrated at the final relative humidity. The final relative humidity can be predicted a priori by the sorption-desorption moisture transfer (SDMT) model [95] if one has moisture uptake isotherms for each of the solid components, their initial moisture contents and dry weights, headspace volume, and temperature. Final moisture contents for each solid can then easily be estimated from the isotherms for the respective solids. 

The simultaneous solution of the equations for ai, 02, and K will yield an a versus X curve if all the underlying parameters were known. To this end, Futerko and Hsing fitted the numerical solutions of these simultaneous equations to the experimental points on the above-discussed water vapor uptake isotherms of Hinatsu et al. This determined the best fit values of x and X was first assumed to be constant, and in improved calculations, y was assumed to have a linear dependence on 02, which slightly improved the results in terms of estimated data fitting errors. The authors also describe methods for deriving the temperature dependences of x and K using the experimental data of other workers. 

Different models determine A in different ways. Nation exhibits a water-uptake isotherm as shown in Figure 7. The dashed line in the figure shows the effects of Schroeder s paradox, where there is a discontinuous jump in the value of A. Furthermore, the transport properties have different values and functional forms at that point. Most models used correlate A with the water-vapor activity, since it is an easily calculated quantity. An exception to this is the model of Siegel et al., ° which assumes a simple mass-transfer relationship. There are also models that model the isotherm either by Flory—Huggins theory" or equilibrium between water and hydrated protons in the membrane and water vapor... 

There is a need to be able to describe both types of behavior, diffusive and hydraulic, in a consistent manner, which also agrees with experimental data. For example, a membrane with a low water content is expected to be controlled by diffusion, and an uptake isotherm needs to be used (see Figure 7). The reasons for this are that there is not a continuous liquid pathway across the medium and that the membrane matrix interacts significantly with the water due to binding and solvating the sulfonic acid sites. A hydraulic pressure in this system may not be defined. 

Figure 5. Moisture uptake isotherms for sorbitol samples.

In solution culture experiments both strontium and caesium show hyperbolic absorption isotherms with respect to the external concentration of the element. Figure 7-15 (a) shows an example of a typical uptake isotherm for Sr while Shaw and Bell (1989) have demonstrated a similar isotherm for Cs. Baker (1981) has referred to such plant uptake responses as accumulator functions and has identified these as being typical of the absorption of elements over which plants can exert some degree of physiological control. Typically, the nutrient elements, including K and Ca, exhibit such isotherms and it can be postulated from the similarity in the uptake patterns of K and Cs on the one hand and Ca and Sr on the other that the radioions share, to some extent, the same uptake mechanisms as the nutrient ions. This has several important implications. Firstly, the direct competition for uptake sites between radioions and nutrient ions means that the external (soil) concentration of one is increased at the expense of the uptake of the other as the nutrient ions in question are vastly more abundant in soils than radioions it is K and Ca which will be effective in competitively excluding Cs and Sr, respectively. Secondly, the kinetics of this competition are concentration-dependent, so the assumption of first order kinetic movements of... 

Keywords volume phase transition (VPT) PNIPA phenol resorcinol phloroglucinol swelling uptake isotherm dynamic light scattering (DLS) small angle neutron scattering (SANS)... 

Table 2. Parameters obtained from the equilibrium uptake isotherms in Figure 1.

The shape of a zeolite sorption uptake isotherm, a quantitation of the amount of a given sorbate taken up as a function of its partial pressure in the gas phase in equilibiitun with the zeolite sorbent, depends both on the zeolite sorbate interaction and on the sorbate - sorbate interactions. Simulation of such isotherms for one or more sorbates is accomplished by the Grand Canonical Monte Carlo method. Additional to the molecular reorientation and movement attempts is a particle creation or annihilation, the probability of which scales with the partial pressure [100,101]. This procedure thus simulates the eqmlibrium between the sorbed phase in the zeolite and an infinite gas / vapor bath. Reasonable reproduction of uptake isotherms for simple gases has been achieved for a small number of systems (e.g. [100,101]), and the molecular simulations have, for example, explained at a molecular level the discontinuity observed in the Ar - VPI-5 isotherm. 

We have examined whether a simple non-bonded potential can be developed to be (i) transferable from one zeolite to another and (ii) to simulate without parameter adjustment isosteric heats at different temperatures and sorption uptake isotherms. The sorption of methane into Na- and K- zeolite X, and Na-and K-clinoptilolites was considered. Models for Na-X and K-X were constructed based on the averaged crystallographic results. The non-bonded parameters in a Lennard-Jones potential were iteratively adjusted so as to best reproduce the experimental isosteric heats in Na-X and K-X over a small temperature range. Methane-methane interaction parameters were taken from earlier work [89] and a final iteration was made so as to better fit the experimental sorption isotherms in clinoptilolite. This single and simple non-bonded potential parameter set then reproduces to a reasonable degree... 

Table 3 BA values for various starches obtained from BET analysis of moisture uptake isotherms...

Water uptake isotherms for the two crystal forms at different temperatures. Open symbols represent adsorption curves, closed symbols represent desorption. 

Reactions were chosen from this set by trial and error fitting to the 0.1 mM ZCo uptake isotherm. Reactions 203 and 204 (Table I) proved necessary and adequate, while 202 produced unacceptably low uptake curve slopes. The solution is not unique. Other combinations of reactions and equilibrium constants (K) can fit the 0.1 mM data equally well, but K-values significantly different from the selected range degrade the fit at higher ECo. 

Figure 5.1. Water-uptake isotherm at 25°C showing the effect of Schroder s paradox.

As the membrane becomes more hydrated, the sulfonic acid sites become associated with more water allowing for a less bound and more bulk-like water to form. This is why there is a flattening out of the slope above X = 6 in the uptake isotherm, Figure 5.1. The extreme case is when the membrane is placed in a liquid-water reservoir, where the ionic domains swell and a bulklike liquid-water phase comes into existence throughout the membrane. The way in which water does this is unknown but is probably due to the interfadal properties of the membrane, such as the fluorocarbon-rich skin on the surface of Nafion [26,27] or the removal of a liquid-vapor meniscus at the membrane surface [28]. In essence, the reorganization results in a porous structure with an average pore size between 1 and 2 nm [29]. 

Chemical potential and water content, X, can be related through an uptake isotherm. Uptake isotherms of k as a function of water-vapor activity or relative humidity, such as that given in Figure 5.1, are prevalent in the literature [4, 6, 42, 43]. They have been used in almost every model that deals with vapor-equilibrated membranes and treats the membrane as a single phase [1]. As discussed in the proposed physical model, the water uptake is described by the hydration of the sulfonic acid sites in the membrane clusters and a balance between osmotic, elastic, and electrostatic forces. The approach taken here is to calculate the isotherms using the chemical model of Meyers and Newman [5] with some modifications [39]. 

Figure 5.4. Water uptake isotherms from the modified chemical model for a membrane in contact with water vapor the temperatures are 25,45,65, and 85°C. (The figure is reproduced from Ref [39] with permission of The Electrochemical Society, Inc.)...

Fig. 11.10 Water uptake isotherms of various ionomers and sulfuric acid at 80 C. Dowex 50 is an ion-exchange resin made of 4% cross-linked polystyrene divinyl benzene BPSH 40 is a 2-mil 40% randomly sulfonated biphenol sulfone 700 EW PFSA is a 1-mil membrane with a structure similar to Nafion Nafion 112 is a 2-mil extruded membrane and, PAEK triblock is a 1-mil triblock polyaryl ether ketone with a sulfonated middle block (Reproduced from C.K. Mittelsteadt and H. Liu. [30] by permission from John Wiley Sons)...

Figure 14 Total gravimetric gas uptake isotherms at various temperatures for CH4 for NU-111 (Reproduced from Ref. 39 with permission from The Royal Society of Chemistry.)...

Carrying out the reaction at increased pH, achieved by the addition of further equivalents of triethylamine, results in the isolation of a three-dimensional network, [Ni2,5(0H)(L-Asp)2]-6.55H20. Analogous onedimensional helices are observed, which are linked across the plane by [Ni(L-Asp)2] subunits (Figure 5c) to yield a three-dimensional structure (Figure 5d), which is permanently porous with a BET surface area from N2 uptake isotherm data of 157 m g . This second aspartate dianion coordinates the linking Ni " " ion in a fac motif through the... 

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