Reduced adsorption isotherms

Scamehorn et. al. (20) also presented a simple, semi—empirical method based on ideal solution theory and the concept of reduced adsorption isotherms to predict the mixed adsorption isotherm and admicellar composition from the pure component isotherms. In this work, we present a more general theory, based only on ideal solution theory, and present detailed mixed system data for a binary mixed surfactant system (two members of a homologous series) and use it to test this model. The thermodynamics of admicelle formation is also compared to that of micelle formation for this same system. 

Figure 3. Reduced Adsorption Isotherms of CgSO, and 2 04 on Alpha Aluminum Oxide.

The thermodynamic description of micropore filling of a supercritical gas introduces the difference in the micropore field strength into the Wl and Poq values. Consequently, if we express the amount of high pressure adsorption per Wl and the equilibrium pressure per Poq, the obtained adsorption isotherms must coincide with each other. Fig. 15 shows the reduced adsorption isotherm. Although the abscissa is 0.5 at best, the isotherm has the type I character. This reduced adsorption isotherm is described by the reduced DR equation ... 

This idea was applied to high pressure CH4 adsorption by ACF at 303 K. The high pressure CH4 adsorption isotherms of five ACF samples (P5-P25) were measured. The adsorption tendency was similar to that of supercritical N2 the smaller the micropore width, the greater the CH4 adsorption. These high pressure CH4 adsorption isotherms were also described by the reduced adsorption isotherm, although the deviation of the reduce adsorption data was greater compared with that for N2. Hence, this quasivapour model should be widely applied to adsorption of other supercritical gases on activated carbon. 

The intercept on the adsorption axis, and also the value of c, diminishes as the amount of retained nonane increases (Table 4.7). The very high value of c (>10 ) for the starting material could in principle be explained by adsorption either in micropores or on active sites such as exposed Ti cations produced by dehydration but, as shown in earlier work, the latter kind of adsorption would result in isotherms of quite different shape, and can be ruled out. The negative intercept obtained with the 25°C-outgassed sample (Fig. 4.14 curve (D)) is a mathematical consequence of the reduced adsorption at low relative pressure which in expressed in the low c-value (c = 13). It is most probably accounted for by the presence of adsorbed nonane on the external surface which was not removed at 25°C but only at I50°C. (The Frenkel-Halsey-Hill exponent (p. 90) for the multilayer region of the 25°C-outgassed sample was only 1 -9 as compared with 2-61 for the standard rutile, and 2-38 for the 150°C-outgassed sample). 

Adsorption of dispersants at the soHd—Hquid interface from solution is normally measured by changes in the concentration of the dispersant after adsorption has occurred, and plotted as an adsorption isotherm. A classification system of adsorption isotherms has been developed to identify the mechanisms that may be operating, such as monolayer vs multilayer adsorption, and chemisorption vs physical adsorption (8). For moderate to high mol wt polymeric dispersants, the low energy (equiUbrium) configurations of the adsorbed layer are typically about 3—30 nm thick. Normally, the adsorption is monolayer, since the thickness of the first layer significantly reduces attraction for a second layer, unless the polymer is very low mol wt or adsorbs by being nearly immiscible with the solvent. 

In the limit of zero association, x — 0 the latter equation reduces to the adsorption isotherm of hard spheres, evaluated within the singlet Percus-Yevick approximation, whereas for xx 1 (i-S- the limit of complete association) one obtains the adsorption isotherm of tangent dimers... 

For the case of a binary system with linear adsorption isotherms, very simple formulas can be derived to evaluate the better TMB flow rates [19, 20]. For the linear case, the net fluxes constraints are reduced to only four inequalities, which are assumed to be satisfied by the same margin /3 (/3 > 1) and so ... 

Knox and Piper (13) assumed that the majority of the adsorption isotherms were, indeed, Langmuir in form and then postulated that all the peaks that were mass overloaded would be approximately triangular in shape. As a consequence, Knox and Piper proposed that mass overload could be treated in a similar manner to volume overload. Whether all solute/stationary phase isotherms are Langmuir in type is a moot point and the assumption should be taken with some caution. Knox and Piper then suggested that the best compromise was to utilize about half the maximum sample volume as defined by equation (15), which would then reduce the distance between the peaks by half. They then recommended that the concentration of the solute should be increased until dispersion due to mass overload just caused the two peaks to touch. 

Surface areas were determined from the adsorption isotherms of nitrogen at 77 K, using a Micromeritics ASAP 200 instrument. Powder X-ray diffraction patterns were obtained with a CGR theta 60 instrument using CuKa monochromated radiation. Reducibility and the amount of Cu species were determined by temperature programmed reduction (TPR) with H2 (H2/Ar 3/97, vol/vol). The experimental set up has been described previously [6]. 

The adsorption free energy and other parameters may be determined, provided that a proper adsorption isotherm is identified and is fitted to experimental data. However, it is usually difficult to unequivocally choose an appropriate isotherm an experimental isotherm may well be fitted to a multitude of theoretical isotherms having several adjustable parameters. If the adsorption isotherm at a very small surface coverage is accessible experimentally, the adsorption free energy can be determined from the limiting slope of the isotherm, as all isotherms reduce to Henry s law when 6 0 ... 

Figure 11. Adsorption isotherms for CsHi on the surface reduced with CtHi and on the surface used for the reaction at 91 °C. Key O, in He and 3, in C02-He.

Figure 12. Adsorption isotherms at 91 °C for COs on the differently treated catalyst surfaces. Key I, , in He (oxidized surface) II, , in He (surface reduced by CtHJ HI, O, in He (surface used for the reaction) and IV, , in CeH -He (surface reduced by CtHk) and O, in He (surface reduced by Ht).

Predominantly, Freundlich s fitted adsorption isotherms computed by means of simple linear regression were proposed for the mathematical description of the process studied. Unlike the Langmuir equation, the Freundlich model did not reduce to a linear adsorption expression at very low nor very high solute concentrations, as above resulted. 

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