Fugacity model application

Application of Fugacity Models to the Estimation of Chemical Distribution and Persistence in the Environment... 

Mackay D, Diamond M (1989) Application of the QWASI (quantitative water air sediment interaction) fugacity model to the dynamics of organic and inorganic chemicals in lakes. Chemosphere 18 1343-1365... 

Mackay D, Paterson S, Joy M (1983) Application of fugacity models to the estimation of chemical distribution and persistence in the environment. In Swann Eschenroeder (eds) Fate of chemicals in the environment. American Chemical Society Symposium Series 225 175-196... 

Mackay, D., Paterson, S. (1990) Fugacity models. In Practical Applications of Quantitative Structure-Activity Relationships (QSAR) in Environmental Chemistry and Toxicology. Karcher, W., Devillers, J., Eds., pp. 433 -60, Kluwer Academic Publishers, Dordrecht, The Netherlands. 

A valuable overview of the global dissemination of persistent organic compounds has been given (Wania and Mackay 1996), and application of fugacity models to the distribution of PAHs (Mackay and Callcott 1998). Attention should also be directed to the different physiology and biochemistry of the organisms as well as to their trophic level important details of food chains are, however, noted only tangentially in this account. 

The Chao-Seader and the Grayson-Streed methods are very similar in that they both use the same mathematical models for each phase. For the vapor, the Redlich-Kwong equation of state is used. This two-parameter generalized pressure-volume-temperature (P-V-T) expression is very convenient because only the critical constants of the mixture components are required for applications. For the liquid phase, both methods used the regular solution theory of Scatchard and Hildebrand (26) for the activity coefficient plus an empirical relationship for the reference liquid fugacity coefficient. Chao-Seader and Grayson-Streed derived different constants for these two liquid equations, however. 

Mention has already been made of mathematical models which simulate partitioning in the environment. This has been facilitated by the introduction of fugacity principles to environmental modelling, which simplifies the linking of complex partition and rate constants in many of the current multimedia environmental models. A detailed explanation of the ideas involved, and their application, has recently been published by Mackay.39... 

There is at least one major area of activity pertaining directly to the environment for which the reader will seek in vain. The complexity of environmental problems and the availability of personal computers have led to extensive studies on models of varying sophistication. A discussion and evaluation of these lie well beyond the competence of an old-fashioned experimentalist this gap is left for others to fill but attention is drawn to a review that covers recent developments in the application of models to the risk assessment of xenobiotics (Barnthouse 1992), a book (Mackay 1991) that is devoted to the problem of partition in terms of fugacity — a useful term taken over from classical thermodynamics — and a chapter in the book by Schwarzenbach et al. (1993). Some superficial comments are, however, presented in Section 3.5.5 in an attempt to provide an overview of the dissemination of xenobiotics in natural ecosystems. It should also be noted that pharmacokinetic models have a valuable place in assessing the dynamics of uptake and elimination of xenobiotics in biota, and a single example (Clark et al. 1987) is noted parenthetically in another context in Section 3.1.1. In similar vein, statistical procedures for assessing community effects are only superficially noted in Section 7.4. Examples of the application of cluster analysis to analyze bacterial populations of interest in the bioremediation of contaminated sites are given in Section 8.2.6.2. 

It will have become apparent from the preceding discussions that xenobiotics after discharge from a point source may enter any of the various environmental compartments aquatic systems including biota and sediment, the atmosphere, terrestrial systems including soils, biota, and in the long run possibly the ultimate predator — humans. Considerable effort has therefore been devoted to the development and application of models to evaluate this dissemination in quantitiative terms. These involve the concept of fugacity, and it seems appropriate at the beginning to examine this concept briefly. 

More simple models, requiring only an approximate description of the main driving forces as input data, produce less precise results but their versatility allows their application to relatively non-homogeneous areas and, therefore, on a larger scale. Simple runoff models derived from the original fugacity approach , were developed at the University of Toronto by Mackay and co-workers, but too technical to be described here. (Mackay,... 

From the historical point of view and also from the number of applications in the literature, the common method is to use activity coefficients for the liquid phase, i.e., the polymer solution, and a separate equation-of-state for the solvent vapor phase, in many cases the truncated virial equation of state as for the data reduction of experimental measurements explained above. To this group of theories and models also free-volume models and lattice-fluid models will be added in this paper because they are usually applied within this approach. The approach where fugacity coefficients are calculated from one equation of state for both phases was applied to polymer solutions more recently, but it is the more promising method if one has to extrapolate over larger temperature and pressure ranges. 

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