Equilibrium partition theory

Ma, W.-C., A. Van Kleunen, J. Immerzeel, and P.G.-J. De Maagd. 1998. Bioaccumulation of polycyclic aromatic hydrocarbons by earthworms assessment of equilibrium partitioning theory in situ studies and water experiments. Environ. Toxicol. Chem. 17 1730-1737. 

Terrestrial BMOs have also been widely used for monitoring environmental contaminants. In particular, the lipid-like waxy cuticle layer of various types of plant leaves has been used to monitor residues of HOCs in the atmosphere. However, some of the problems associated with aquatic BMOs apply to terrestrial BMOs as well. For example, Bohme et al. (1999) found that the concentrations of HOCs with log KoaS < 9 (i.e., those compounds that should have attained equilibrium) varied by as much as 37-fold in plant species, after normalization of residue concentrations to levels in ryegrass (Lolium spp.). These authors suggested that differences in cuticular wax composition (quality) were responsible for this deviation from equilibrium partition theory. Other characteristics of plant leaves may affect the amount of kinetically-limited and particle-bound HOCs sampled by plant leaves but to a lesser extent (i.e., <4-fold), these include age, surface area, topography of the surface, and leaf orientation. 

Bioavailability of organic chemicals is strongly dependent on aqueous solubility. The equilibrium partitioning theory has been applied to sediment toxicity studies, and it was concluded that uptake from sediment as well as from (pore) water is possible at the same time however, the exposure route in equilibrium is not necessarily important. For substances with log /< W < 5, the equilibrium partitioning theory is considered acceptable to assess the risk. For substances with log Kov/ > 5, a safety factor of 10 is applied, in order to include the additional uptake by sediment ingestion (Loonen et al. 1997). 

To be truly consistent with partitioning theory, particles must also shrink upon dilution, much like POA described above. Different experiments have confirmed that ot-pinene + ozone SOA particles do evaporate upon dilution, but not in the minute or so suggested by the volatility distribution in Fig. 5 and the timescales in Fig. 3. Rather, particles relax back to equilibrium after dilution over hours [31,108], though they do eventually reach the size predicted from equilibrium partitioning theory [108]. This delay is consistent with some phenomenon slowing evaporation by at least a factor of 100. Potential causes for this delay include dissociation of weakly bound oligomers [108] or slowed diffusion in the particles themselves... 

Landrum PF, Dupuis WS, Kukkonen J (1994) Toxicokinetics and toxicity of sediment-associated pyrene and phenanthrene in Diporeia spp. examination of equilibrium-partitioning theory and residue-based effects for assessing hazard. Environ Toxicol Chem 13 1769-1780. 

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

In order to extend the above theory, we have to make use of the equilibrium partition concepts described in Part II. Here we generally define the equilibrium partition function between any phase B and A by ... 

Martin and Synge (3) introduced the important concept of theoretical plates into chromatography. Their concept was derived from partition theory and random statistics, and was related to similar ideas developed for extraction and fractional distillation. They supposed that the column could be divided into a number of sections called theoretical plates, and that solutes (dissolved compounds) could be expected to achieve equilibrium between the two phases (mobile and stationary) that exist within each plate. The chromatographic process, like an extraction process, can be visualized to occur when mobile phase (solvent) is transferred to the next plate, where a new equilibrium is established. Theoretical plate numbers of 1000 or more are common for HPLC columns, which means that 1000 separate equilibria must be established to obtain the same degree of separation by solvent... 

In order to evaluate the solute diffusion coefficient in the stationary phase, Ds, and the equilibrium partition coefficient, Keq, a model for the pore is required. A simple model where the pore is considered to be an infinitely long cylinder and the solute is a rigid sphere has been shown to be adequate in describing the elution process (25). The intrapore diffusivity, Ds, was estimated from the hydrodynamic theory of hindered diffusion for spherical solutes in cylindric pores (19) ... 

The complicated nature of the LLPTC reaction system is attributed to two mass transfer steps and two reaction steps in the organic and aqueous phases. The equilibrium partition of the catalysts between the two phases also affects the reaction rate. On the basis of the above factors and the steady-state two-film theory [60,63,64,68], a phase-plane model to describe the dynamics of a liquid-liquid PTC reaction has been derived. This model offers physically meaningful parameters that demonstrate the complicated reactive character of a liquid-liquid PT-catalyzed reaction. However, when the concentration of aqueous solution is dilute or the reactivity of aqueous reactant is weak, the onium cation has to exist in the aqueous phase. The mathematical model cannot describe this completely. When the onium cation exists in the aqueous phase, several important phenomena involved in the liquid-liquid reaction need to be analyzed and discussed. 

Pankow (1987) consolidated, and subsequently refined early approaches (Pankow and Bidleman 1991, 1992) to describe the equilibrium partitioning between gas and particles based on adsorption theory (Junge 1977 Yamasaki et al. 1982). Much attention has also been paid to the effect of relative humidity (RH) (Thibodeaux et al. 1991 Pankow et al. 1993 Storey et al. 1995) and nonexchangeable matter (Pankow 1988). Pankow (1988) defined the gas-particle partitioning coefficient, Kp (m pg ), which can be related to measured fractions/ concentrations of gas (Ca,g— retained by adsorbent) and particulate phase concentrations (Ca,p— retained by the filter) and the total suspended particle concentration (TSP), in pg m ... 

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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