Partitioning Molecular Interactions and Thermodynamics

2 Molecular Interactions Determining the Partitioning of Organic Compounds Between Different Phases 

1 Classification of Organic Compounds According to Their Ability to Undergo Particular Molecular Interactions Relative Strengths of Dispersive Energies Between Partitioning Partners A First Glance at Equilibrium Partition Constants Examples of Absorption from the Gas Phase 

Example 1 Vapor Pressure and Molecular Interactions in the Pure Liquid Compound Example 2 Air-Solvent Partitioning Examples of Adsorption from the Gas Phase Example 3 Air-Solid Surface Partitioning 

3 Using Thermodynamic Functions to Quantify Molecular Energies 

Excess Free Energy, Excess Enthalpy, and Excess Entropy 

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Schrodinger equation. When the molecule is too large and difficult for quantum mechanical calculations, or the molecule interacts with many other molecules or an external field, we turn to the methods of molecular mechanics with empirical force fields. We compute and obtain numerical values of the partition functions, instead of precise formulas. The computation of thermodynamic properties proceeds by using a number of techniques, of which the most prominent are the molecular dynamics and the Monte Carlo methods. 

With these first insights into the molecular interactions that govern the partitioning of organic compounds between different phases in the environment, we are now prepared to tackle some thermodynamic formalisms. We will need these parameters and their interrelationships for quantitative treatments of the various phase transfer processes discussed in the following chapters. 

In terms of the characterization of the thermodynamic behavior, the phase diagram and the variation of response functions - for example specific heat and the membrane-water partition coefficients seen in crossing the phase diagram - are important indicators of the molecular interactions [49],... 

To relate these thermodynamic quantities to molecular properties and interactions, we need to consider the statistical thermodynamics of ideal gases and ideal solutions. A detailed discussion is beyond the scope of this review. We note for completeness, however, that a full treatment of the free energy of solvation should include the changes in the rotational and vibrational partition functions for the solute as it passes from the gas phase into solution, AGjnt. ... 

In this chapter, we introduce a novel system coefficient approach developed in our research center. The system coefficient approach uses a set of probe compoimds to measure the molecular interaction strengths of a skin/chemical mixture system. A linear free-energy relationship (LEER, a thermodynamic principle) is used to dissect the complicated molecular interactions in the absorption system into basic molecular interaction forces, which can be parameterized and used to predict a free-energy-related property of the system, such as partition coefficients or permeability. In the system coefficient approach, a chemical mixture is treated as a medium composed of the major components and other minor or trace components. A set of system coefficients represents the relative molecular interaction strengths of the chemical mixture, and a set of solute descriptors represents the molecular interaction strengths of a chemical. A free-energy-related specific property is interactively correlated to the system coefficients of the chemical mixture and the solute descriptors of the chemicals, which can be used to provide quantitative predictions... 

As already mentioned, one of the merits of the virial equation is that it has a firm foundation in statistical thermodynamics and molecular theory. The theoretical derivation of the series has been described in numerous texts and will not be discussed in detail here. The most complete derivation for a mixture containing an arbitrary number of components is made by means of an expansion of the grand partition function. This leads to expressions for the virial coelficients in terms of cluster integrals involving two molecules for B, three molecules for C etc. These expressions are completely general and involve no restrictive assumptions about the nature of molecular interactions. Nevertheless, to simplify the expressions for the virial coefficients, a number of assumptions are often made as follows ... 

This process ean be easily followed by titration calorimetry, as described below. In particular, the partition coefficients and the boundaries of the coexistence region can be determined. In addition, the thermodynamic quantities obtained from these calorimetric experiments provide new insight into the molecular interactions in these systems. 

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

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