Partitioning equilibrium model

Two classes of mathematical models have been developed those which are specific and attempt to describe the transport and degradation of a chemical in a particular situation and those which are general or "evaluative" and attempt to generally classify the behavior of chemicals in a hypothetical environment. The type of modeling discussed here, equilibrium partitioning models, fall into the latter category. Such models attempt, with a minimum of information, to predict expected environmental distribution patterns of a compound and thereby identify which environmental compartments will be of primary concern. 

Like algae, phytoplankton, and macrophytes, an equilibrium partitioning model commonly is used to estimate the chemical concentration in zooplankton (Cz, g chemical/kg organism). Hence, Cz is the product of the freely dissolved chemical concentration in the water (CVVI), g chemical/L water), the lipid content of zooplankton (Lz, kg lipid/kg organism), and the lipid-water partition coefficient (KL, L water/kg lipid), which the octanol-water partition coefficient approximates (Clayton et al. 1977) ... 

Bioaccumulation in Benthic Invertebrates 9.5.5.1 Equilibrium Partitioning Models... 

There is no mechanistic equilibrium-partitioning model for toxic metals available for the soil and sediment compartments. However, the free metal ion concentration in pore water that is considered relevant for uptake in biota (water exposure route) may experimentally or empirically be related to the total metal content of the soil, according to equation 2.1 (above). 

Equilibrium-Partitioning Models for Organic Chemicals in Water... 

Despite these considerations, the first approach in method development for ESl-MS is the formation of preformed ions in solution, i.e., protonation of basic analytes or deprotonation of acidic analytes. Thus, for basic analytes, mixtures of ammonium salts and volatile acids like formic and acetic acid are applied. Alternatively, formic or acetic acid may be added to the mobile phase, just to set a low pH for the generation of preformed ions in solution. The latter approach is successful if sufficient hydrophobic interaction between preformed aiialyte ions and the reversed-phase material remains. The concentration of buffer is kept as low as possible, i.e., at or below 10 nunol/1 in ESl-MS. The buffer concentration is obviously determined by the buffer capacity needed to achieve stable pH conditions upon repetitive injection of the samples. Constantopoulos et al. [99] derived an equilibrium partitioning model to predict the effect of the salt concentration on the analyte response in ESI. If the salt concentration is below 10 moFl, the analyte response is proportional to its concentration. The response is found to decrease with increasing salt concentration. 

Methylmercury partitions strongly into the lipid-rich tissues of fish hence, it becomes highly bioconcentrated. Assume the BCF for fish is 106 liters/kg (i.e., assume an equilibrium partitioning model is an acceptable approximation to the real world). What fraction of the methylmercury in a lake would actually be in fish tissue, if the lake had a volume of 106 m3 and contained a metric ton (1000 kg) of fish ... 

A flowchart for estimating sediment toxicity is presented in Figure 6.2. First, a bulk sediment sample is taken and the PAH concentration and total organic carbon are measured. The equilibrium partitioning model is run to predict the concentration of each PAH in the interstitial water of the sediment. The predicted PAH concentrations are then converted to toxic units (TUs) using the 10-d amphipod LC50 as the toxicity benchmark. The TUs are then added up and processed through the concentration response model. The expected mortality is then converted to nontoxic, uncertain, and toxic predictions. 

For sediment-dwelling organisms, one important factor that determines the degree of exposure to xenobiotics in the sediment phase is the partitioning from the true sediment phase into interstitial water from which the xeno-biotic may then be accumulated by biota. Exposure of sediment biota to xenobiotics is, however, a complex process, since uptake may proceed either via particulate material or via interstitial water, or by both routes. In the equilibrium partition model the concentration of a xenobiotic in the interstitial water (Ciw) is given by the following relation ... 

These results have been confirmed in laboratory experiments on desorption (McGroddy et al. 1996), and underscore the limitations of equilibrium partition models for PAHs — although not apparently for PCBs. 

As discussed by Voutsas et al. [44], despite the empirical nature of the Dow model, it can be considered as a two step equilibrium partitioning model compound from a sorption site on the soil particles -> compound in the soil water compound in the atmospheric air. 

Figure 2.4. Schematic of a droplet with two separate phases, surface excess charge and internal electrically neutral. Analytes (A and B ) compete with electrolyte (E ) for the surface excess charge phase of the droplet. A postulate of the equilibrium partitioning model is that the analytes that are part of the surface excess charge phase are most likely to become gas-phase (analyzable) ions. Those ions that reside in the droplet interior will be paired with counterions and consequently will not be detectable by the mass spectrometer. (Reprinted fiom Ref. 77, with permission.)...

The final postulate of the equihbrium partition theory is that the surface concentration of analyte, [A ], would be related to its appearance in the mass spectrum. This was demonstrated in the paper that originally introduced the equilibrium partitioning model, in which experimental data of Kebarle and Tang using tetraalkyl ammonium salts was lit to Eqs. (2.7) and (2.8). Kebarle later reconciled the equations from the equilibrium partition... 

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