Magnitude, isotherm nonlinearity

Composite Sorption Magnitude and Isotherm Nonlinearity. Accurate assessment of the extent to which the global isotherm for a system is nonlinear is important for accurate portrayal of sorption processes in that system. From a practical point of view, the extrapolation of linear approximations of weakly nonlinear or near-linear sorption isotherms to concentration ranges beyond which they are valid can result in significant errors in projections of contaminant fate and transport (1). From a conceptual point of view, observations of isotherm nonlinearity over specific concentration ranges may be employed in conjunction with models such as the DRM to probe and evaluate the extent to which multiple sorption mechanisms are operative in a particular system. 

In summary, we should realize that, when applying Kioi values determined at high concentrations or derived from LFERs such as Eq. 9-26 (Table 9.2), we may underestimate equilibrium sorption at low concentrations (i.e., below 1% of the compound s solubility) by a factor of 2 or more. Due to competition with other sorbates present in a natural system, the effect of specific adsorption could, however, be significantly attenuated (Chiou et al., 2000). Furthermore, the abundance of specific adsorption sites may be rather low in certain environments. Hence, in cases in which the effect can be expected to be moderate and in which we need only to get an order of magnitude estimate of Kioc, we may decide to neglect the nonlinearity of the isotherm. In other situations, however, such as the PAH case discussed in Illustrative Example 9.3, adsorption to carbonaceous materials or other high-affinity sorbents present in significant abundances has to be taken into account. 

Despite the similar reaction mechanism, a completely different type of behavior was found for the TAME process [71-73]. This is due to the fact that the rate of reaction is one order of magnitude slower for TAME synthesis compared to MTBE synthesis. The behavior of the TAME process is illustrated in Fig. 10.14. In contrast to the MTBE process the TAME column is operated in the kinetic regime of the chemical reaction at a pressure of 2 bar. Under these conditions large parameter ranges with multiple steady states occur. The more detailed analysis by Mohl et al. [73] reveals that steady state multiplicity of the TAME process is caused by self-inhibition of the chemical reaction by the reactant methanol, which is adsorbed preferably on the catalyst surface. Steady state multiplicity is therefore caused by the nonlinear concentration dependence of the chemical reaction rate. Consequently, a similar type of behavior can be observed for an isothermal CSTR. This effect is further in-... 

Figures 5 and 6 illustrate the utility of the DRDM for describing sorption in rubbery and glassy matrices. At 5 C, both the humic acid (Tg = 43 C, water-wet) and a synthetic poly(isobutyl methacrylate (PIMA) polymer (Tg = 50"C, water-wet) display significant nonlinear contributions to the overall sorption isotherm, while at 45 C (i.e., at or near their water-wet values) these non-linear contributions disappear for the PIMA, and are several orders of magnitude less than the linear contributions for the humic acid, giving rise to almost complete partitioning behavior, consistent with the existence of a predominantly rubbery state.

In one method adsorption isotherms are determined first and the specific surface areas are calculated from these isotherms by means of the BET method. The specific surface area of the sohd, S, can be determined at ideal, nonlinear chromatographic conditions, if the magnitude of monolayer adsorption, a, and the area occupied by a molecule of the adsorbate in the monolayer, lo, are known ... 

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