Composite isotherms

It is important to note that the experimentally defined or apparent adsorption no AN 2/, while it gives F, does not give the amount of component 2 in the adsorbed layer Only in dilute solution where N 2 0 and = 1 is this true. The adsorption isotherm, F plotted against N2, is thus a composite isotherm or, as it is sometimes called, the isotherm of composition change. 

Equation XI-27 shows that F can be viewed as related to the difference between the individual adsorption isotherms of components 1 and 2. Figure XI-9 [140] shows the composite isotherms resulting from various combinations of individual ones. Note in particular Fig. XI-9a, which shows that even in the absence of adsorption of component 1, that of component 2 must go through a maximum (due to the N[ factor in Eq. XI-27), and that in all other cases the apparent adsorption of component 2 will be negative in concentrated solution. 

More often, however, microporosity is associated with an appreciable external surface, or with mesoporosity, or with both. The effect of microporosity on the isotherm will be seen from Fig. 4.11(a) and Fig. 4.12(a). In Fig. 4.11(a) curve (i) refers to a powder made up of nonporous particles and curve (ii) to a solid which is wholly microporous. However, if the particles of the powder are microporous (the total micropore volume being given by the plateau of curve (ii)), the isotherm will assume the form of curve (iii), obtained by summing curves (i) and (ii). Like isotherm (i), the composite isotherm is of Type II, but because of the contribution from the Type 1 isotherm, it has a steep initial portion the relative enhancement of adsorption in the low-pressure region will be reflected in a significantly increased value of the BET c-constant and a shortened linear branch of the BET plot. 

Figure 4.12(a) refers to the case where micropores are present along with mesopores. The composite isotherm (iii), like the isotherm (ii) of the mesoporous substance itself, is of Type IV, and again has a steep initial branch with an increased value of c. 

A high value of the BET constant c is a useful preliminary indication of the presence of microporosity, but it does not enable one to estimate the micropore volume itself, that is in effect to break down the composite isotherm (iii) into its components (i) and (ii). 

Even so, it is of interest to calculate the BET monolayer capacity from the composite isotherm of Fig. 5.12(b). Though the isotherm did not conform very closely to the BET equation, the isosteric net heat of adsorption was... 

Figure 1. Ideal pressure-composition isotherms showing the hydrogen solid-solution phase, a, and the hydride phase, j3. The plateau marks the region of coexistence of the a and fl phases. As the temperature is increased the plateau narrows and eventually disappears at some consolule temperature...

There are few systematic guidelines which can be used to predict the properties of AB2 metal hydride electrodes. Alloy formulation is primarily an empirical process where the composition is designed to provide a bulk hydride-forming phase (or phases) which form, in situ, a corrosion— resistance surface of semipassivating oxide (hydroxide) layers. Lattice expansion is usually reduced relative to the ABS hydrides because of a lower VH. Pressure-composition isotherms of complex AB2 electrode materials indicate nonideal behaviour. 

The successive fractions may be obtained by lowering the temperature in suitable increments rather than by varying the solvent composition isothermally. If a poor solvent is found from which the polymer precipitates in a convenient temperature range, it may be used alone without addition of another component. 

A range of different methods measures the solubility of hydrogen in metals and alloys. Manometric methods [98] and gas volumetric methods [99] have been used to determine pressure-composition isotherms at selected temperatures for a range of alloys [100-103],... 

Typically, sorption isotherms are constructed for a single food ingredient or food system. An alternative approach is to plot the moisture content versus water activity (or relative vapor pressure) values for a variety of as is food ingredients and food systems. The result is a composite food isotherm (Figure 17). The composite isotherm fits the typical shape observed for a sorption isotherm for an individual food system, with a few products falling above or below the isotherm curve (chewing gum, honey, raisins, bread, and colby and cheddar cheeses). Slade and Levine (1991) were the first to construct such a plot using moisture content and aw values from van den... 

Fig. 6. Pressure-composition isotherms at 300°C for MgH2 with ceramic catalyst addition.

The Li-Mg-B-N-H structure possesses storage capacity of more than 10 wt.% at around 150-200 "C. However, the reversibility of the hydrogen sorption characteristics was determined using pressure-composition isotherms as shown in Figure 6. From this study, we found reversible hydrogen absorption-desorption behavior (-3-4 wt.%) of the new complex hydride Li-Mg-B-N-H. The improvement in temperature and reversible hydrogen storage capacity were unaffected even after ten... 

Figure 6. Pressure-composition isotherms of Li-Mg-B-N-Fl prepared by different synthesis procedures...

Adsorption Isotherm Measurements and Site-Selective Thermodynamics. For heterogeneous surfaces like CSPs, the adsorption isotherms are usually composite isotherms and often a Bi-Langmuir model (Equation 1.15) describes reasonably well the adsorption behavior [54]. 

When one or more of the component elements of sorption is governed by a nonlinear relationship between the solution and the sorbed phase, the composite isotherm deviates from linearity. In these cases, modifications to the Freundhch isotherm have been developed (e.g., Lambert 1967 Weber et al. 1992) to express these conditions. 

Figure 5.23 Pressure composition isotherms for critical temperature 7. The construction of the hydrogen absorption in atypical metal (left). The van t Hoff plot is shown on the right. The slope of solid solution (a-phase), the hydride phase the line is equal to the enthalpy of formation (p-phase) and the region ofthe coexistence ofthe divided by the gas constant and the intercept with two phases. The coexistence region is the axis is equal to the entropy of formation...

The thermodynamic aspects of hydride formation from gaseous hydrogen are described by means of pressure-composition isotherms in equilibrium (AG = 0). While the solid solution and hydride phase coexist, the isotherms show a flat plateau, the length of which determines the amount of H2 stored. In the pure P-phase, the H2 pressure rises steeply vfith increase in concentration. The two-phase region ends in a critical point T, above which the transition from the a- to the P-phase is continuous. The equilibrium pressure peq as a function of temperature is related to the changes AH° and AS° of enthalpy and entropy ... 

Figure 5.36 Pressure-composition isotherms for NaAIH4 and Na3AIH6,2-...

Figure 5.55 Examples of bcc alloys and corresponding pressure-composition isotherms. The bcc structure offers three times more interstitial sites than the fee and hep structures.

The second concept that has to be considered is that of absolute adsorption or adsorption of an individual component. This can be considered as the true adsorption isotherm for a given component that refers to the actual quantity of that component present in the adsorbed phase as opposed to its relative excess relative to the bulk liquid. It is a surface concentration. From a practical point of view, the main interest lies in resolving the composite isotherm into individual isotherms. To do this, the introduction of the concept of a Gibbs dividing surface is necessary. Figure 10.6 shows the concept of the surface phase model. 

Absorption pressure-composition isotherms were established by metering fixed amounts of hydrogen into the system and determining the pressure after equilibrium. In each case, the sample chamber was isolated before hydrogen... 

Figure 1. Pressure-composition isotherms for the Dy2Co7-H system. Hydrogen concentration is expressed as atoms of H per formula unit of Dy2Co7. X designates absorption O designates desorption.

Typical pressure-composition isotherms for the LaNi5-H2 system are shown in Figure 2 (14). From plots of In Pplateau vs- 1 / T, several workers determined the experimental heats and entropies of Reaction 1. The enthalpies are the heats of formation for the /J-phase hydride from the a-phase hydrogen-saturated alloy (see Table I). 

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