Adsorption-Sorption Models

Equilibrium between solution and adsorbed or sorbed phases is a condition commonly used to evaluate adsorption or sorption processes in soils or soil-clay minerals. As previously stated, equilibrium is defined as the point at which the rate of the forward reaction equals the rate of the reverse reaction. Two major techniques commonly used to model soil adsorption or sorption equilibrium processes are (1) the Freundlich approach and (2) the Langmuir approach. Both involve adsorption or sorption isotherms. A sorption isotherm describes the relationship between the dissolved concentration of a given chemical species (adsorbate) in units of micrograms per liter (pg L 1), milligrams per liter (mg L-1), microequivalents per liter (pequiv L-1), or millimoles per liter (mmol L-1), and the sorbed quantity of the same species by the solid phase (adsorbent) in units of adsorbate per unit mass of adsorbent (solid) (e.g., pg kg-1, mg kg-1, peq kg-1, or mmol kg 1) at equilibrium under constant pressure and temperature. Sorption isotherms have been classified into four types, depending on their general shape (Fig. 4.13)  

L-type describes high-affinity adsorption between the adsorbate and adsorbent and usually indicates chemisorption (e.g., phosphate-soil interactions) 

S-type describes adsorbate-adsorbate interactions on the adsorbent, often referred to as clustering, and/or the interaction of the adsorbate with solution ligands. When ligand saturation is reached, adsorption proceeds (e.g., aluminum-ful vie acid-clay interactions) 

C-type describes partitioning, which suggests interaction between a generally hydrophobic adsorbate with a hydrophobic adsorbent (e.g., pesticide-organic matter interactions) 

H-type describes strong chemisorption interactions, which is basically an extreme case of the L-type isotherms (e.g., phosphate-iron oxide interactions) 

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Another widely used sorption model is the Langmuir equation. It was developed by Irving Langmuir [140] to describe the adsorption of gas molecules on a planar surface. It was first applied to soils by Fried and Shapiro [ 141 ] and Olsen and Watanabe [142] to describe phosphate sorption on soils. Since that time, it has been heavily employed in many environmental fields to describe sorption on various solid surfaces [19,65]. The general Langmuir model is... 

Though not a general adsorption equilibrium model the Kelvin equation does provide the relationship between the depression of the vapor pressure of a condensable sorbate and the radius (r) of the pores into which it is condensing. This equation is useful for characterization of pore size distribution by N2 adsorption at or near its dew point. The same equation can also describe the onset of capillary condensation the enhancement of sorption capacity in meso- and macro-pores of formed zeolite adsorbents. 

Figure 7.12 Adsorption of water by skim milk and sorption isotherms predicted by the Braunauer-Emmett-Teller (BET), Kuhn and Guggenheim-Andersson-De Boer (GAB) sorption models (from Roos, 1997).

Adsorption-induced brittle fracture. This model is based on the hypothesis that adsorption of environmental species lowers the interatomic bond strength and the stress required for cleavage. This model of chemical adsorption can explain the fact that a certain alloy is susceptible to specific ions. An important factor in support of this mechanism is the existence of a critical potential below which the SCC does not occur in some systems, and this model underlines the relation between the potential value and the capacity of adsorption of the aggressive ion. It also explains the preventive action of SCC for some systems by cathodic protection. This model may interpret the rupture of plastic materials or glass. It is referred to as the stress-sorption model, and similar mechanisms have been proposed for HE and LME. In this model, the crack should propagate in a continuous way at a rate determined by the arrival of the embrittling species at the crack tip. The model does not explain how the crack maintains a sharp tip in a normally ductile material.156... 

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-... 

Given in Table 10.7 are the surface reactions and corresponding activity adsorption isotherm model equations used in MINTEQA2 as presented by Allison et al. (1991). In these expressions SOH and SOH M represent unoccupied surface sites and surface sites occupied by species M. Because the and Freundlich isotherm models assume an infinite number of available sorption sites, the con-... 

Laying aside, for the moment, all application problems, let us examine the inherent capabilities of kinetics. Reaction rates are the most obvious and most readily available output of these experiments. As with adsorption isotherms, empirical sorption or desorption data can simply be plotted as a function of time and the progress of the reaction can be visually examined. Such information as half-reaction time and time to establish a new equilibrium can be directly obtained from the plot. If, however, the objective of the research is to provide input for generalized sorption models, more quantita-live information will be necessary. 

Values of reaction orders (Table 3) and competitive sorption effects mentioned in Section 3.3 could be quantified more satisfactorily using a adsorption kinetic model. The model was derived under the assumptions of constant volume reaction, nitrous oxide reacting from the gas phase (because of the small influence of nitrous oxide feed concentration on phenol selectivity), three times higher phenol sorption constant than benzene sorption constant (Kc6H5oh 3 Kc6H6, 3s derived from sorption simulation calculations), but without considering the dependency on temperature (reaction temperature 400°C) [5,7]. 

H2O, n-hexane and cyclohexane sorption capacities of SAPO-31 were determined gravimetrically using a vacuum microbalance (Cahn Instruments, USA). The size and the morphology of the crystals of SAPO-31 were examined using a JEOL (JSM-840 A) scanning electron microscope. The BET surface area was determined using a volumetric adsorption apparatus ( Model Omnisorb lOOCX, Coulter, USA). 

Simulation of Mo(VI) breakthrough by the equilibrium sorption model is compared with the experimental data from the 0.043 mmol/1 column in Figure 3. Results for the 0.096-, 0.01- and 0.0016-mmol/l columns were similar and are not shown. The model simulates a very steep slope for the adsorption limb of the breakthrough curve and complete site saturation by the second pore volume. Experimental data from the column show that complete breakthrough did not occur until the sixth pore volume, which indicates the effects of a rate process. The equilibrium model also simulated complete rinse-out of Mo(VI) by the 9th pore volume whereas Mo(VI) in the column effluent did not reach zero until the 15th pore volume, which indicates that desorption also was affected by a rate process. 

However, the two-sink model as well as other existing adsorption (sink) models do not seem to be able to describe the strong asymmetry between the adsorption/desorption of VOCs on/from indoor surface materials (the desorption process is much slower than the adsorption process). Diffusion combined with internal adsorption is assumed to be capable of explaining the observed asymmetry. Diffusion mechanisms have been considered to play a role in interactions of VOCs with indoor sinks. Dunn and Chen (1993) proposed and tested three unified, diffusion-limited mathematical models to account for such interactions. The phrase unified relates to the ability of the model to predict both the ad/absorption and desorption phases. This is a very important aspect of modeling test chamber kinetics because in actual applications of chamber studies to indoor air quality (lAQ), we will never be able to predict when we will be in an accumulation or decay phase, so that the same model must apply to both. Development of such models is underway by different research groups. An excellent reference, in which the theoretical bases of most of the recently developed sorption models are reviewed, is the paper by Axley and Lorenzetti (1993). The authors proposed four generic families of models formulated as mass transport modules that can be combined with existing lAQ models. These models include processes such as equilibrium adsorption, boundary layer diffusion, porous adsorbent diffusion transport, and conveetion-diffusion transport. In their paper, the authors present applications of these models and propose criteria for selection of models that are based on the boundary layer/conduction heat transfer problem. 

The values for the exudation rate F, interaction coefficient (A), buffer power of exudate in soil b and the decomposition rate constant for the exudate k were adopted from Kirk (1999). The value of the forward rate constant was estimated from Scheckel and Sparks (2001), who evaluated kinetic adsorption data of Ni to different minerals where ranged from 2.5 x 10 to 9.78 X 10 s For the simulation, an average value of 5.00 x 10 was used. This value also coincides with the values that Kirk and Staunton (1989) suggested for the kinetic adsorption of Q to soil, where the values ranged from lO" to 10 2 s f This same value was assumed for the rate constant for the two-stage sorption model, a2- The fraction of type 1 sites (F ) was assumed to be 0.3. Table 7 summarizes all input parameter values. 

The sorption model was derived from studies to determine the quantity of solvent adsorbed to the surface of silica. Experimental evidence suggests that silica adsorbs water to its surface, some of which can be removed by either heating to 110 °C, or by sequential organic phase extraction. More can be removed at very high temperatures, but this also results in the breakdown of silanol groups (Scott, 1982). Measurement of the adsorption of different concentrations of polar modifiers in an inert solvent allows the adsorption isotherms to be calculated (Fig. 6.2). When the concentration of the modifier is low, the isotherm fits closest to a monolayer function. When the polar modifier is present at a high concentration a bilayer adsorption isotherm function is produced ... 

In the context of the DRM, sorption by soft carbon is described as a partitioning process, and is represented by a linear model. Conversely, sorption by hard carbon is treated as a nonlinear adsorption process and described by the Langmuir sorption model. Because the sorption sites and associated energies of hard carbon matrices are typically heterogeneous (i.e., N is large), the second right-hand term in Equation 4 can be approximated well by the Freundlich equation (37)... 

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