Linear sorption isotherm description

Geochemical models of sorption and desorption must be developed from this work and incorporated into transport models that predict radionuclide migration. A frequently used, simple sorption (or desorption) model is the empirical distribution coefficient, Kj. This quantity is simply the equilibrium concentration of sorbed radionuclide divided by the equilibrium concentration of radionuclide in solution. Values of Kd can be used to calculate a retardation factor, R, which is used in solute transport equations to predict radionuclide migration in groundwater. The calculations assume instantaneous sorption, a linear sorption isotherm, and single-valued adsorption-desorption isotherms. These assumptions have been shown to be erroneous for solute sorption in several groundwater-soil systems (1-2). A more accurate description of radionuclide sorption is an isothermal equation such as the Freundlich equation ... 

The appearance of the conjugate sorption data presented so far qualitatively indicates a shift from a more to a less Fickian character as the initial surface moisture content increases. That is, the appearance of the conjugate sorption isotherms obtained by totally immersing the samples violate two of the criteria by which Fickian behavior is defined. The same cannot be said for those samples exposed to less than 100% R.H., particularly at 25°C. This qualitative trend for PMC is further demonstrated by Figures 16 and 17. Here MjVWq is presented as a function of time. For both the thick and the thin sample, as either temperature or relative humidity is increased, the character of the curves progresses towards pure Case II description. That is, the moisture uptake becomes linear with time up to the point where a plateau is achieved in the behavior. 

A quantitative description of penetrant solution and diffusion in microheterogeneous media has evolved over the past forty years and has become known as the duad mode sorption theory (4). OriginaJly, this theory postulated that two concurrent modes of sorption are operative in a microheterogeneous medium. Nonlinear sorption isotherms can be decomposed into a linear part that accounts for normal solution (Henry s law-type domain) and a nonlinear Langmuir-type domain that accounts for immobilization of the penetrant molecules at fixed sites in the medium. 

The two-phase kinetic model developed by Karickhoff (65) is capable of fitting either the sorption or desorption of a sorbing solute. For linear isotherms, the mathematical description given by Karickhoff (1) and others (67, 70, 71) is virtually identical to that of a mass transfer process (72). 

For example, if the reaction controlling the sorption of each molecule of a contaminant is identical and the capacity of a sorbent for these molecules is operationally limitless, a linear isotherm relationship is prescribed in which the sorbed-phase concentration is a constant proportion of the solution-phase concentration. When the sorption reactions are identical but sorption capacity is limited, an asymptotic approach to a maximum sorbed-phase concentration might be expected. These two limiting-condition models have been described and compared with others for description of the sorption of hydrophobic contaminants on a variety of natural soils, sediments, and suspended solids... 

Considering aU the above-discussed data, we conclude that the linear dependence in the coordinates of the BET equation does not yet imply that the general conclusions of the polymolecular adsorption theory can be applied to the description of sorption on hypercrosslinked polystyrenes. These cannot be regarded as rigid sorbents with a constant heterophase structure. Accordingly, calculation of the pore size distribution from the desorption branch of the isotherms for carbon dioxide using the Kelvin equation (Eq. [3.4], Chapter 3) results in the unrealistic pore dimensions of about 0.1 A. The isotherms for water produce more sensible data for pore diameters, 20—40 A, but one should not assume that the plots presented in Fig. 10.4 correspond correcdy to the real pore size distribution of the material. 

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