Partitioning also Behavioral

Surfactants have also been of interest for their ability to support reactions in normally inhospitable environments. Reactions such as hydrolysis, aminolysis, solvolysis, and, in inorganic chemistry, of aquation of complex ions, may be retarded, accelerated, or differently sensitive to catalysts relative to the behavior in ordinary solutions (see Refs. 205 and 206 for reviews). The acid-base chemistry in micellar solutions has been investigated by Drummond and co-workers [207]. A useful model has been the pseudophase model [206-209] in which reactants are either in solution or solubilized in micelles and partition between the two as though two distinct phases were involved. In inverse micelles in nonpolar media, water is concentrated in the micellar core and reactions in the micelle may be greatly accelerated [206, 210]. The confining environment of a solubilized reactant may lead to stereochemical consequences as in photodimerization reactions in micelles [211] or vesicles [212] or in the generation of radical pairs [213]. 

Whereas this two-parameter equation states the same conclusion as the van der Waals equation, this derivation extends the theory beyond just PVT behavior. Because the partition function, can also be used to derive aH the thermodynamic functions, the functional form, E, can be changed to describe this data as weH. Corresponding states equations are typicaHy written with respect to temperature and pressure because of the ambiguities of measuring volume at the critical point. 

We make no attempt to discuss the partitioning behavior of U-series elements between aqueous fluids and minerals at ambient conditions. Examples where this behavior is important include uptake of U-series elements by cal cite in speleothems or by bone apatite. Also we do not consider U-series behavior in hydrothermal solutions at high temperatures, such as during dehydration of subducted crust. In both cases complexation behavior in the fluid may play an important role, and at low temperatures kinetic controls may dominate. These are fruitful areas for future experimental study. 

The approach taken here is to use the lattice strain model to derive the partition coefficient of a U-series element (such as Ra) from the partition coefficient of its proxy (such as Ba) under the appropriate conditions. Clearly the proxy needs to be an element that forms ions of the same charge and similar ionic radius to the U-series element of interest, so that the pair are not significantly fractionated from each other by changes in phase composition, pressure or temperature. Also the partitioning behavior of the proxy must be reasonably well constrained under the conditions of interest. Having established a suitable partition coefficient for the proxy, the partition coefficient for the U-series element can then be obtained via rearrangement of Equation (2) (Blundy and Wood 1994) ... 

Figure 8. Partition coefficients (Kd) for Th and Pa and the fractionation factor (F) between Th and Pa plotted as a function of the opal and calcium carbonate percentage in settling particulate material. Note the tendency for the Kd for Th to increase with increasing carbonate fraction and decrease with increasing opal fraction. Pa shows the opposite behavior so that F increases with low opal fraction or high carbonate fraction. This plot is modified from Chase et al. (in press-b) but excludes the continental margin data also shown in that study and instead focuses exclusively on open-ocean sites.

The initial retention of metals in all fractions was linearly dependent upon the loading levels (Figs. 6.1-6.4). This constant partition behavior was also maintained after one year of incubation, but the distribution among fractions had shifted. This behavior indicates that there is no saturation... 

The observed linearity of adsorption isotherms in various data sets in the literature and the absence of competitive effects are not evidence for partitioning alone, because such behavior can also be consistent with a physical adsorption model. 

In the case of porous HDC, as Indicated, one needs to account for both HDC, pore partitioning, and hindered diffusion processes. A model should also have as asymptotes the mean residence time behavior given by Equations 1 to 3 for a nonporous system and Equation 4 for a purely flow-through porous system. 

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