Linear partitioning model

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... 

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. 

Several methods have been developed for the quantitative description of such systems. The partition function of the polymer is computed with the help of statistical thermodynamics which finally permits the computation of the degree of conversion 0. In the simplest case, it corresponds to the linear Ising model according to which only the nearest segments interact cooperatively149. The second possibility is to start from already known equilibrium relations and thus to compute the relevant degree of conversion 0. 

Almost all widely used, reliable prediction models for logarithmic partition coefficients, and especially for the octanol-water partition coefficient log P w, are linear regression models with respect to fragment counts, atom types, bond types or... 

A problem of all such linear QSPR models is the fact that, by definition, they cannot account for the nonlinear behavior of a property. Therefore, they are much less successful for log S as they are for all kinds of logarithmic partition coefficients. 

For the linear isotherm model, the parameter (Kd) that relates both sorbate and solute is called the partition coefficient. A number of studies have developed empirical relationships for partition coefficients in natural solid phases and several of these studies are summarized in Table 1.Various theoretical-based methods of partition coefficient estimations also exist (Table 1, Eqs. a- f). 

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).

Fig. 2.26. Organic carbon-normalized partitioning coefficients (log K

VLEACH Unsaturated zone VLEACH is a one-dimensional, finite difference model developed to simulate the transport of contaminants displaying linear partitioning behavior through the vadose zone to the water table by aqeuous advection and diffusion. 

Soil Organic Matter. A variety of soils and sediments sorb organic compounds in patterns that can be approximated by linear isotherm models, at least over relatively narrow (e.g., 1 decade) concentration ranges. Such isotherms are generally, although often imprecisely, expressed in terms of a partitioning coefficient, fy such that... 

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... 

Based on the EPI generated values for solubility (log Sol), octanol-water partitioning (log Kow), vapour pressure (log VP) and Henry s Law constants (log HLC) new linear QSAR models are build by estimating the relationships between the EPI generated data and available experimental data for up to 65 organophosphor insecticides, the general formula for the descriptors, Du to be used being... 

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. ... 

The effect of sample concentration on the chromatographic behaviour of ionic solutes on Sephadex G-10 can be qualitatively described by means of the partition isotherms derived on the basis of the ion partition model proposed by Shibukawa et al. [ref. 69] (see Sec. 2.2.1). The overall partition isotherms are anticipated to be represented as shown in Fig. 9 from the analogy with typical ion-exchange isotherms [ref. 70], if the partition isotherm of process (A) is linear. It is thus predicted that, in the system where the contribution of the steric exclusion effect can be neglected, the difference in the affinity for the internal gel phase between sample ion, s , and coion Y , that is, the equilibrium constant of ion-exahange process (B), K, determines the sample concentration dependence of the elution behaviour of sample ion in the following manner. When > 1, the elution volume or the distribution coefficient of sample ion decreases and the elution profile is more skewed with sharp leading... 

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