Conventional partition coefficient

Although this equation reduces to an identity whenever solute-solvent interactions are embodied in the definition of the Henry s law standard state (cf section 10.2), it must be noted that K[ is the molar ratio of trace element i in the two phases and not the weight concentration ratio usually adopted in trace element geochemistry. As we will see later in this section, this double conversion (from activity ratio to molar ratio, and from molar ratio to weight concentration ratio) complicates the interpretation of natural evidence in some cases. To avoid ambiguity, we define here as conventional partition coefficients (with the same symbol K ) all mass concentration ratios, to distinguish them from molar ratios and equilibrium constants. 

In this case, trace element and carrier occupy the same structural position both in the solid phase and in the melt and are subject to the same compositional effects in both phases (i.e., extension of the cation matrix in the melt and amount of anorthite component in the solid). Figure 10.9A shows the effect of normalization the conventional partition coefficient of Sr between plagioclase and liquid varies by about one order of magnitude under equal P-T conditions, with increasing anorthite component in solid solution, whereas normalized distribution coefficient D is virtually unaffected. Figure 10.9B shows the same effect for the Ba-Ca couple. 

Figure 10.10 Arrhenius plot of conventional partition coefficient (A) and thermodynamic constant (B) for clinopyroxene/liquid distribution of Ni.

The behavior described above is exemplified in figure 10.11, where Arrhenius plots of solid/liquid conventional partition coefficients for transition elements reveal more or less linear trends, with some dispersion of points ascribable to compositional effects. 

Figure 10.13 Effect of oxygen fugacity on conventional partition coefficient of Cr. (A) Olivine/liquid partitioning experimental data of Bird (1971), Weill and McKay (1975), Huebner et al. (1976), Lindstrom (1976), and McKay and Weill (1976). (B) Subcalcic py-roxene/liquid partitioning experimental data of Schreiber (1976). Reprinted from A.J. Irving, Geochimica et Cosmochimica Acta, 42, 743-770, copyright 1978, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

The ratio between equations 10.91 and 10.90 gives the relationship between apparent partition coefficient and conventional partition coefficient at interface K (i.e., the integrated form of eq. 10.84) ... 

Equation 10.93 clearly shows that, if apparent partition coefficient is adopted instead of conventional partition coefficient K actually valid at the solid/liquid interface to model Rayleigh s crystallization, errors arise whose magnitudes increase the more K differs from 1 and the longer the process advances. This is clearly shown in figure 10.15, in which fractional differences — K )IK are plotted as functions of T for various values of K . 

Conventional partition coefficient K is replaced by bulk solid/liquid mass distribution coefficient D n, corresponding to the weighted mean of the conventional partition coefficients for each solid/liquid pair ... 

By convention, partition coefficients are usually given relative to the concentration in water as above, since the water phase is usually the easiest to reliably sample (it is well mixed compared with, say. the soil, and the concentrations are higher than in. the air). However, if we wanted a numerical value for the air-biota partition coefficient of the species, ATab.i. we could easily compute it from ii Aw.i and as follows ... 

Both liquid and vapor phases are totally miscible. Conventional vapor/liqiiid eqiiilihriiim. Neither phase is pure. Separation factors are moderate and decrease as purity increases. Ultrahigh purity is difficult to achieve. No theoretical limit on recovery. Liquid phases are totally miscible solid phases are not. Eutectic system. Sohd phase is pure, except at eutectic point. Partition coefficients are very high (theoretically, they can be infinite). Ultrahigh purity is easy to achieve. Recovery is hmited by eutectic composition. 

If both addition and fragmentation arc irreversible the kinetics differ little from conventional chain transfer. In the more general case, the rate constant for chain transfer is defined in terms of the rate constant for addition and a partition coefficient which defines how the adduct is partitioned between products and starting materials (eq. 19). 

Lipophilicity is a molecular property expressing the relative affinity of solutes for an aqueous phase and an organic, water-immiscible solvent. As such, lipophilicity encodes most of the intermolecular forces that can take place between a solute and a solvent, and represents the affinity of a molecule for a lipophilic environment. This parameter is commonly measured by its distribution behavior in a biphasic system, described by the partition coefficient of the species X, P. Thermodynamically, is defined as a constant relating the activity of a solute in two immiscible phases at equilibrium [111,112]. By convention, P is given with the organic phase as numerator, so that a positive value for log P reflects a preference for the lipid phase ... 

In PAMPA measurements each well is usually a one-point-in-time (single-timepoint) sample. By contrast, in the conventional multitimepoint Caco-2 assay, the acceptor solution is frequently replaced with fresh buffer solution so that the solution in contact with the membrane contains no more than a few percent of the total sample concentration at any time. This condition can be called a physically maintained sink. Under pseudo-steady state (when a practically linear solute concentration gradient is established in the membrane phase see Chapter 2), lipophilic molecules will distribute into the cell monolayer in accordance with the effective membrane-buffer partition coefficient, even when the acceptor solution contains nearly zero sample concentration (due to the physical sink). If the physical sink is maintained indefinitely, then eventually, all of the sample will be depleted from both the donor and membrane compartments, as the flux approaches zero (Chapter 2). In conventional Caco-2 data analysis, a very simple equation [Eq. (7.10) or (7.11)] is used to calculate the permeability coefficient. But when combinatorial (i.e., lipophilic) compounds are screened, this equation is often invalid, since a considerable portion of the molecules partitions into the membrane phase during the multitimepoint measurements. 

In conventional analyses of transport based on Fick s laws, the fundamental parameters that define the transport process are the solute diffusion coefficient in the polymer film, DM, and the partition coefficient, KP. Essentially, the diffusion coefficient defines how fast a solute molecule moves, and the partition coefficient... 

Most conventional organic contaminants are fairly hydrophobic and thus exhibit a low but measurable solubility in water. Solubility is often used to estimate the air-water partition coefficient or Henry s law constant, but this is not possible for miscible chemicals indeed the method is suspect for chemicals of appreciable solubility in water, i.e., exceeding 1 g/100 g. Direct measurement of the Henry s law constant is thus required. 

Figure 10.11 Effects of temperature on conventional solid/liquid partition coefficients of various transition elements. Sources of data are also listed.

Figure 10,18 Conventional trace element partition coefficient as a function of factor Reprinted from Treuil et al. (1979), Bullettin Mineralogique, 102, 402-409, with permission from Masson S.A., Paris, France.

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