Local sorption isotherms

Distributed Reactivity Model. Isotherm relationships observed for natural systems may well be expected to reflect composite sorption behavior resulting from a series of different local isotherms, including linear and nonlinear adsorption reactions. For example, an observed near-linear isotherm might result from a series of linear and near-linear local sorption isotherms on m different components of soft soil organic matter and p different mineral matter surfaces. The resulting series of sorption reactions, because they are nearly linear, can be approximated in terms of a bulk linear partition coefficient, KDr that is... 

In Eq. (9), [solute] is the molar solute concentration in the solution, 6 is the surface coverage (adsorbed amount of solute divided by total amount of surface sites), / is the fraction of surface sites of class j, Tif soiute is the affinity constant for the local sorption isotherm describing the interaction between the solute and the surface site y the index t stands for the overall (total) adsorption. 

In the present symposium, Dr. Raucher argued that the observed curvature in gas sorption isotherms does not arise from a site saturation mechanism such as we have described in the preceding discussion. The form of the sorption isotherm and local concentration dependent diffusion coefficient proposed by Raucher and Sefcik are given below ... 

Humidity control The question of humidity control was examined in several ways. The moisture sorption isotherm showed moisture levels from 3-6% over a relative humidity range of 20-95%. Also, samples held at 65°C for over 2 weeks remained within this range of water content, which was within pharmacopeial specification. Finally, samples which were heated did not show a change in crystal form by X-ray powder diffraction, such as partial conversion to an anhydrate. Based on these results, humidity control was not deemed necessary for comparative stress studies. Samples to be compared were all stored under identical conditions, i.e., in the same oven. Any local change in humidity around each sample was therefore a function of the sample itself. 

Most field-scale modeling studies of contaminant plumes make the local equilibrium assumption (LEA) [18,19]. The LEA is based on the premise that the interactions between the contaminant and the aquifer material are so rapid compared to advective residence times that it can be assumed that the interactions are instantaneous [3]. Linear equilibrium sorption assumes that the binding of contaminants to aquifer solids is instantaneous and that the concentration of sorbed contaminant is directly proportional to the concentration of the dissolved contaminant. This can be modeled by a linear sorption isotherm [2] ... 

Rockland (1969) has introduced the concept of local isotherm to provide a closer relationship between sorption isotherms and stability than is possible with other methods. He suggested that the differential coefficient... 

For polymer/penetrant combinations where strong interactions between specific functional groups occur and binding to specific sites predominates, a localized sorption model is more appropriate. Figure 5.15(b) represents such a model, which is equivalent to the Langmuir and Freundlich isotherm models presented in the context of adsorption in the previous section. This behavior has been ob-... 

Figure 5.15(d) resembles a BET adsorption isotherm and represents a combination of two interactions indicated by the broken curves speciHc localized sorption at low concentrations, followed by clustering or aggregate formation at high concentrations (note that clustering is not associated with capillary condensation as it is in the BET case). Sorption of water by hydrophobic polymers such as cellulosic materials follows this behavior. 

DFT and molecular simulation methods have been applied to the analysis of adsorbents in two main capacities. For nonporous adsorbents, DFT can be used to provide a local isotherm r(P,e) in order to solve eq. (2) for the distribution of site energies on the adsorbent surface [1] A sample result is shown in Fig. 5 for the site energy distribution of a heterogeneous activated carbon obtained from DFT analysis of the nitrogen sorption isotherm. 

It is assumed that the instant local equilibrium described by Eq. (21) is established. The Langmuir equation or other sorption isotherms can be utilized to represent the equilibrium relationship. The initial and boundary conditions are... 

If a series of local isotherms can be identified, the total sorption at any solution concentration will be the sum of those isotherms produced by the individual local sorption mechanisms. 

The development of accurate sorption relationships for contaminants in natural environments requires characterization of dominant local sorption phenomena operating within a particular system and determination of the extent to which they are expressed. This chapter focuses on the nature of local sorption behavior and associated isotherm relationships commonly observed in natural aquatic systems. These local isotherm relationships are then incorporated into descriptions of overall sorption behavior to demonstrate how distributed local concentration dependencies translate into deviations from sorption predictions predicated on single-mechanism and limiting-condition models. 

Distributed Reactivity. Natural systems commonly are composed ol a variety of different solid phases and interfaces, each of which might well yield distinctly individual local sorption behavior with respect to a particula] solute and thus an identifiable local isotherm. Figure 3 is a schematic illustration of four different types of local sorption phenomena, ranging from a specific adsorption reaction of a solute molecule with a sorbent surface on the left to the absorption of the molecule into the matrix of a sorbing substance on the right. 

The experimental results given in Figure 7 provide confirmation of the importance of such small but highly reactive nonlinearly sorbing components to the overall sorption behavior of hydrophobic contaminants in subsurface systems. This figure presents a comparison of the carbon-normalized contribution of the nonlinear local TCB isotherm for the shale isolated from the Wagner soil to the composite sorption isotherm for the soil itself. 

Several common local sorption processes have been examined here by way of illustrating such effects sorption by geologically immature soft-carbon organic matter, which results in quasi-linear sorption isotherms, sorption by common mineral phases within concentration regions where linear behavior is exhibited, and sorption by diagenetically altered hard-carbon organic matter... 

Localized sorption occurs when adsorbed water is tightly bound to the polymer molecules. In these cases, two populations of water are considered to exist in the polymer a bound population and a liquid like population. This sorption isotherm is described by ... 

The different units (sites or cells) of the sorbent will be localized in the crystal and, therefore, are distinguishable. If they are independent in the sense that there are no interactions between sorbate particles in different units, we may hypothetically group all units of one kind together in space without changing the sorption behavior. The sorption characteristics would be the same as those of a macroscopic mixture of different solids, each containing sorption units of only one kind (index i) and obeying a sorption isotherm d (p). 

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