Nonlinear sorption isotherm

Equilibrium considerations alone may partly explain the nonlinear sorption isotherm, i.e., when n in the Freundlich model (Eq. 8) is less than unity, intraparticle retardation will increase as the concentration inside the particle declines. However, in some studies it appears that the concentration dependence is steeper than expected based on equilibrium nonlinearity. 

The simplest monofunctional carboxylic adds have boiling points at atmospheric pressure without decomposition and, hence, can be analyzed directly by GC. However, owing to the high polarities of carboxyl compounds, the typical problem of their GC analysis with standard nonpolar phases is a nonlinear sorption isotherm. As a result, these compounds yield broad, nonsymmetrical peaks that lead to poor detection limits and unsatisfactory reprodudbility of their retention indices. The recommended stationary phases for direct analysis of free carboxylic acids are polar polyethylene glycols (Carbowax 20M, DB Wax, SP-1000, FFAP, etc.). However, these phases have less thermal stability compared with polydimethyl siloxanes (approximately 220-230°C versus 300-350°C). This means that the upper limit of GC columns with these polar phases in RI units is not more than 3000-3500 lU. High homologs, even of monocarboxylic acids, cannot be eluted within this RI window (keep in mind that the absence of RI data for palmitic acid C15H31COOH on the mentioned type of polar phases). 

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. 

Use of a partition coefficient without reference to the absolute chemical concentration at which it was measured implies that a linear relationship exists between the concentration of dissolved chemical and the concentration of sorbed chemical. In some cases, the ratio between dissolved and sorbed chemical concentrations does vary with concentration, and therefore it must be expressed as a nonlinear sorption isotherm. (Use of the term isotherm indicates that measurements are made at a constant temperature.) Laboratory measurements of sorption may fit a Freundlich isotherm. 

Huang et al. (1997) measured sorption isotherms for phenanthrene on 21 soils and sediments. All isotherms were nonlinear with Freundlich exponents n,- (Eq. 9-1) between 0.65 and 0.9. For example, for a topsoil (Chelsea 1) and for a lake sediment (EPA-23), interpolating the isotherm data yields the following observed sorbed concentrations, Cis, in equilibrium with dissolved concentrations, Ciw, of 1 /zg L-1 and 100 /zg-L-1, respectively ... 

Xia and Ball (1999) measured sorption isotherms for a series of chlorinated benzenes and PAHs for an aquitard material (foc = 0.015 kg oc kg-1 solid) from a formation believed to date to the middle to late Miocene. Hence, compared to soils or recent sediment POM, the organic matter present in this aquitard material can be assumed to be fairly mature and/or contain char particles from prehistoric fires. A nonlinear isotherm was found for TeCB (fitting Eq. 9-2) and the following Freundlich parameters were reported XreCBF = 128(mg g 1)(mg mL 1) "T CBand "TeCB = 0.80. For partitioning of TeCB to this material (linear part of the isotherm at higher concentrations), the authors found a Kioc value of 4.2 x 104 L kg oc. 

Wilson, J. N. First theoretical paper on chromatography. Assumed complete equilibration and linear sorption isotherms. Qualitatively defined diffusion, rate of adsorption and isotherm nonlinearity. 

Sorption coefficients generally are determined from an isotherm, a diagram that depicts the distribution of the test chemical between a solid sorbent and the solution in equilibrium with it over a range of concentrations at constant temperature. These isotherms can be linear or nonlinear, depending on the properties of the test chemical and solid and on the aqueous phase concentration of the chemical. In many cases, sorption isotherms are linear at low concentration but tend to become nonlinear (sorption tends to decrease) as the concentration of chemical in the aqueous phase increases, especially for polar or ionizable... 

Sorption isotherms of less chlorinated ethylenes, trans- and cis-dichloroethylenes, are also nonlinear, but the sorbed amounts are much less than those of TCE and PCE (Alien-King et al., 1997). Vinyl chloride is the least chlorinated one in this series, thus its sorption onto ZVI is also the least (Burris et al., 1998 Deng et al., 1999). 

PAHs in soil may partition into soil organic matter (SOM) or adsorb on soil minerals. The sorptive properties of SOM fractions for organic contaminants in soil play an important role on the transportation of PAHs in soil. Xiao et al. (2004) has reported that soil/sediment organic matter can be fractionated into four fractions with a combined wet chemical procedure and that kerogen and black carbon (BC) are major SOM components in soil/sediment samples collected from the industrialized suburban areas of Guangzhou, China. Phenanthrene and naphthalene were used as the sorbates to study PAH s sorption isotherms on four original and four Soxhlet-extracted soil/sediment samples, 15 isolated SOM fractions, and a char as the sorbents. The sorption isotherms of phenanthrene and naphthalene on all the sorbents were variously nonlinear. The particulate kerogen and black carbon (KB) fractions... 

For reversible interactions, the linear dynamic range is determined by that portion of the coating-analyte sorption isotherm (discussed in Section 5.4) that lies between the LOD and the saturation limit. For irreversible interactions, the LDR will depend on the sorption/reaction kinetics and the coating capacity. For practical reasons, it is desirable to have the widest LDR possible, although inexpensive microprocessors and associated memory make correction for minor nonlinearities straightforward. For an example of a wide linear dynamic range, refer to Figure 5.13. 

The ion-exchange kinetics accompanied by association-dissociation in this model differ, on the one hand, fiom nonlinear sorption processes where the isotherm shape is responsible for the concentration profiles in the bead and for the kinetic rate [63] and, on the other, from conventional ion exchange where the kinetic rate and concentration profiles Cb, Ca are governed by the diffusivity factor D, /Db [16]. In the model both the selectivity (Kb /K b) and the diffusivity (Df/D factors play a role in the IE process. 

However, the sorption of a number of pesticide compounds to some soils has been found to be more accurately described by the nonlinear Freundlich isotherm (e.g., Hamaker and Thompson, 1972 Widmer and Spalding, 1996), i.e.. 

For ideal systems (usually as in elastomers), the solubility wiU be independent of concentration and the sorption curve will follow Henry s law (Equation 4.6), i.e., gas concentration within the polymer is proportional to the applied pressure. For nonideal systems (usually as in glassy polymers), the sorption isotherm is generally curved and highly nonlinear. Such behavior can be described by free-volume models and Flory-Huggins thermodynamics—comprehensive discussions on this may be found elsewhere [1,25,26]. 

A nonlinear local isotherm model is clearly required for description of sorption reactions between the TCB and the shale isolate. A variety of conceptual and empirical models for representing nonlinear sorption equilibria, exists (2). The Langmuir model is one of the ideal limiting-condition-type models cited earlier. It is predicated on a uniform surface affinity for the solute and prescribes a nonlinear asymptotic approach to some maximum sorption capacity. 

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... 

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. 

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. 

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