Linear partitioning sorption model

Figure 4 shows phenanthrene and naphthalene sorption isotherms to kaolinite covered with varying levels of sorbed surfactant these levels of surfactant coverage correspond to the different regions existing in the surfactant sorption isotherms discussed earlier (Fig. 1). The linearity of each isotherm was evaluated using Freundlich and linear sorption models. It is apparent from Fig. 4 and Table 4 that HOC partitioning to kaolinite with and without adsorbed surfactants results in linear or near-linear isotherms. As the amount of surfactant adsorbed on the kaolinite surface increased, the sorption of phenanthrene and naphthalene to the solid phase also increased. However, upon normalizing by the amount of sorbed surfactant present, the sorbed surfactant partition coefficient (Kss) decreased with increasing sorbed surfactant amounts (Table 4).

Tillotson et al. (1980) Nitrification and urea hydrolysis by first-order kinetics NH3 volatilization by first-order kinetics from (NH4)2C03 formed from urea hydrolysis NH sorption by linear partition model NH and NOy plant uptake involving diffusion to roots. 

In some sorption cases 1/n equals 1. When this condition is met, a plot of -SC versus C will produce a straight line with KD as slope (C-type isotherm Fig. 4.16). This type of isotherm best describes soil sorption of hydrophobic organics (e.g., chlorinated hydrocarbons) (Fig. 4.17). The linearity of such data can be explained by the schematic model in Figure 4.18. In this model, (linear partition model), the hydrophobic organic contaminant distributes itself linearly between hydrophobic organic matter adsorbed on an inorganic mineral particle and solution. Linearity... 

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... 

The Linear Partitioning Model. Several conceptual and empirical models have been proposed to quantify sorption of hydrophobic organic contaminants (HOCs) by soils and sediments. The simplest of these is the linear partitioning model, in which the solid-phase solute concentration, is assumed to be directly proportional to the aqueous-phase solute concentration, Q i.e.,... 

The linear partition model has been challenged with respect to its implied mechanistic interpretation of HOC sorption by soils and sediments (5, 6, 77, 14-17, 32), and with respect to its validity for the prediction of such processes (77, 14, 17, 19, 21). 

The slow, nonlinear and apparently hysteretic behavior commonly observed for soils and sediments is phenomenologically and mechanistically incompatible with the linear partition model. The clear dependence of sorption properties on chemical structures and elemental compositions of SOM found by several investigators (77, 14, 19, 21-23, 32-36) confirms that SOM is in most cases neither homogeneous nor completely gel-like in character, as assumed implicitly by the linear partitioning model. 

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)... 

Unfortunately, cation exchange does not lend itself to simple mathematical description as does idealized sorption of hydrophobic organic compounds. For low concentrations of a contaminant ion in a constant background of other ions, however, the ion exchange process often is treated approximately as a linear partitioning process, and use of a simple retardation factor in a transport model may be justified. Distribution coefficients for ionic contaminants in an aquifer are usually determined experimentally. Typically, a batch test is performed in which the ionic concentration on a fixed volume of aquifer solids and the ionic concentration in the associated pore waters are analyzed the distribution coefficient is taken as the ratio of the concentrations. Because sorption by ion exchange is affected by the concentrations of all other ions in the groundwater, the... 

Modified Freundlich sorption models were developed to describe sorption in heterogeneous geosorbents containing both NOM and carbonaceous materials. Composite or distributed reactivity models (DRM) were introduced [28] and applied in a manner which combines the linear partitioning (absorption) part with the nonlinear adsorption part [26, 27, 31, 32]. The overall sorption isotherm can be described in the form of ... 

In addition to the dependence of sorption on the organic fraction of the sorbent, and the KQw of the sorbate, Chiou et al. (13) cite the following observations as support for the hypothesis that the sorptive mechanism is hydrophobic partitioning into the organic (humic) fraction of the sediments (1) the linearity of the isotherms as the concentration approaches solubility, (2) the small effect of temperature on sorption, and (3) the lack of competition between sorbates for the sorbent. These arguments also illustrate the applicability of the approach for modeling sorption on hydro-phobic compounds an approach which has been criticized when used in the context of adsorption of trace metals onto oxides (17). 

Sorption of organic contaminants onto aquifer solids is frequently described as a partitioning process, where the hydrophobic organic compound partitions into natural organic material associated with the aquifer solids [8]. Sorption can be characterized as either an equilibrium or rate-limited phenomenon. Equilibrium sorption can be modeled as either a linear or non-linear process. Equilibrium sorption may be assumed when the flow of groundwater and other processes affecting contaminant transport are slow compared to the rate of sorption. In this event the sorption of the contaminant can be considered instantaneous. If we assume equilibrium sorption, the relationship between sorbed and aqueous contaminant concentrations may be described by a sorption isotherm. 

Adsorption of purely hydrophobic compounds onto soils and sediments has been successfully modeled and predicted by treating the organic matter fraction as a separate phase in equilibrium with the aqueous phase (see Karick-hoff et al., 1979). Morel (1983) succinctly summarizes findings from the considerable amount of work that has been completed in this area (i) within a typical range of concentrations, sorption isotherms are linear, (ii) the extent of partitioning is proportional to the sediment organic C content, and... 

A mainstay of the classical partition model is the experimental observation that the major thermodynamic driving force for sorption is the hydrophobic effect. The hydrophobic effect results from gain in free energy when non- or weakly-polar molecular surface is transferred out of the polar medium of water 2-4), The hydrophobic effect is manifested by a linear free energy relationship (LFER) between the NOM-normalized partition coefficient (A om) and the w-octanol-water partition coefficient K ) [i.e.. In nom a n + b where a and b are regression constants], or the inverse of the compound s liquid (or theoretical subcooled liquid) saturated water solubility CJ) [i.e.. In AT om = -c In + d. ... 

Some basic statistical requirements were also overlooked when quantitative models based on coefficients were developed. The most important assumption underlying the linear regression model is that the dependent variable contains all the errors in each data pair (Maes 1984 Irvin and Quickenden 1983). The range for 1-octanol/water partition coefficients obtained for each molecule clearly demonstrates that this basic assumption is not met. It has been demonstrated (York 1966) that if this basic assumption is violated, the fitted slopes can deviate by as much as 40% from the correct value. Thus, the validity and applicability of published quantitative models describing the relationship between the Kq coefficients and soil sorption coefficients are highly questionable. 

All that which has been said about empirical models based on the 1-octanol/water partition coefficients is also true for models based on the water solubilities (a) the measured water solubility data are of low precision (see TABLE 4), (b) there exists a wide variety of quantitative linear models correlating soil sorption coefficients and water solubility (Wijayaratne and Means 1984 Chiou et al. 1983 Banwart et al. 1982 Means et al. 1982 Briggs 1981 Kenaga and Goring 1980 Karickhoff etal. 1979), and (c) the statistical requirements for linear regression models are violated by the large errors in the experimental water solubility data. That some quantitative models (Wijayaratne and Means 1984 Banwart et al. 1982 Means et al. 1982) use non-molar units ( ig mL ) for water solubility data, further impedes their use. 

Most models that handle the transport of organic contaminants within soil are based on the landmark publication of Jury et al. (1983). This model treats soil as a mixture of air, water, and soil particles with the assumption of uniform soil properties, linear sorption isotherms, and equilibrium partitioning between the solid, gas, and liquid phases of soil. 

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