Thermodynamics-based partition

By combining thermodynamically-based monomer partitioning relationships for saturation [170] and partial swelling [172] with mass balance equations, Noel et al. [174] proposed a model for saturation and a model for partial swelling that could predict the mole fraction of a specific monomer i in the polymer particles. They showed that the batch emulsion copolymerization behavior predicted by the models presented in this article agreed adequately with experimental results for MA-VAc and MA-Inden (Ind) systems. Karlsson et al. [176] studied the monomer swelling kinetics at 80 °C in Interval III of the seeded emulsion polymerization of isoprene with carboxylated PSt latex particles as the seeds. The authors measured the variation of the isoprene sorption rate into the seed polymer particles with the volume fraction of polymer in the latex particles, and discussed the sorption process of isoprene into the seed polymer particles in Interval III in detail from a thermodynamic point of view. 

In thermodynamically based models, it is critical to account for the P- and T-dependence of the partitioning of elements among minerals, as well as the mass balance of reactions among minerals. A set of equations corresponds to each of these requirements. The principles have been detailed elsewhere (Spear, 1993), and so the equations are simply presented here. 

As demonstrated by the chapters in this short course, stable isotope techniques are an important tool in almost every branch of the earth sciences. Central to many of these applications is a quantitative understanding of equilibrium isotope partitioning between substances. Indeed, it was Harold Urey s (1947) thermodynamically based estimate of the temperature-dependence of fractionation between calcium carbonate and water,... 

The cavity model of solvation provides the basis for a number of additional models used to explain retention in reversed-phase chromatography. The main approaches are represented by solvophobic theory [282-286] and lattice theories based on statistical thermodynamics [287-291]. To a lesser extent classical thermodynamics combining partition and displacement models [292] and the phenomenological model of solvent effects [293] have also been used. Compared with the solvation parameter model all these models are mathematically complex, and often require the input of system variables that are either unknown or difficult to calculate, particularly for polar compounds. For this reason, and because of a failure to provide a simple conceptual picture of the retention process in familiar chromatographic terms, these models have largely remained the province of the physical chemist. 

Theory. Liquid-liquid extraction in dilute solution is thermodynamically based on the partition coefficient (15, 16), Gibbs phase rule states that ... 

The pKa of a molecule, a charge-state-related parameter, is a descriptor of an acid-base equilibrium reaction [34,35]. Lipophilicity, often represented by the octanol-water partition coefficient Kp is a descriptor of a two-phase distribution equilibrium reaction [36]. So is solubility [37-39]. These three parameters are thermodynamic constants. On the other hand, permeability Pe is a rate coefficient, a kinetics parameter, most often posed in a first-order distribution reaction [40-42]. 

In its simplest form a partitioning model evaluates the distribution of a chemical between environmental compartments based on the thermodynamics of the system. The chemical will interact with its environment and tend to reach an equilibrium state among compartments. Hamaker(l) first used such an approach in attempting to calculate the percent of a chemical in the soil air in an air, water, solids soil system. The relationships between compartments were chemical equilibrium constants between the water and soil (soil partition coefficient) and between the water and air (Henry s Law constant). This model, as is true with all models of this type, assumes that all compartments are well mixed, at equilibrium, and are homogeneous. At this level the rates of movement between compartments and degradation rates within compartments are not considered. 

Schantz, M.M., Martire, D.E. (1987) Determination of hydrocarbon-water partition coefficients from chromatographic data and based on solution thermodynamics and theory. J. Chromatogr. 391, 35-51. 

It is of interest to mention that, once particular choices are made concerning how the mean-field interactions are incorporated into the model, the corresponding partition function and thermodynamics follow in a straightforward manner. In particular, there exists a method based upon a variational argument, to formulate the best possible corresponding (mean-field) potential fields. We will not go into these details here, but refer to the variational method, as... 

The LFER that results when correlating partitioning in the octanol-water system and the humic substances-water system Implies that the thermodynamics of these two systems are related. Hence, much can be learned about humic substances-water partitioning by first considering partitioning In the simpler octanol-water system. The thermodynamic derivation that follows is based largely on the approach developed by Chlou and coworkers (18-20), Miller et al. (21), and of Karickhoff (J, 22). In the subsequent discussion, we will adopt the pure liquid as the standard state and, therefore, use the Lewls-Randall convention for activity coefficients, l.e., y = 1 if the mole fraction x 1. 

The description of the sorption process is largely based on empirical correlations, without knowledge of the detailed structure of the sediments. No doubt, in the future a greater effort will have to be made to understand sorption behavior in terms of sediment constituents. It will not suffice to consider sorption onto sediments simply in terms of partitioning into a uniform, thermodynamically ideal, stationary organic phase. 

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