Use of Thermodynamic Transfer Functions

Approaching solvent effects from the viewpoint of thermodynamic transfer functions allows one to examine in a systematic manner the outcome of medium change, from a protic to a dipolar aprotic reaction medium, in terms of structure and charge distribution in reactants, transition states, and products (Buncel and Wilson, 1979,1980). 

The free energy of activation for a reaction in a particular standard solvent O, and in a solvent S, may be expressed by Equations 6.2 and 6.3 where T refers to the 

From Equation 6.6 it is apparent that SG can be evaluated from calculated values of the transfer free energies of stable solute species, SG, in conjunction with the measured kinetic activation parameters, SAG. The required transfer free energies SG can readily be obtained from activity coefficient measurements using Equation 6.7 in which / refers to solute activity coefficients in the different solvents (y and are referred to the same standard state in solvents 

or any other medium). Methods used to obtain these activity coefficients have included vapor pressure, solubility, and distribution coefficient measurements. 

By analogy it is apparent that for the equilibrium situation the transfer free energy relationship will be given by Equation 6.8 where SGl the transfer energy of the 

---

Perron, G., DeLisi, R., Davidson, L, Genereux, S., Desnoyers, J.E. On the use of thermodynamic transfer functions for the study of the effect of additives on micellization volumes and heat capacities of solutions of sodium octanoate systems. J. Colloid Interface Sci. 1981, 79(2), 432-442. 

Thermodynamic data never give us any direct information on the molecular nature of the solute-solute or solute-solvent interactions. It is only through a comparison with other systems and through models and theories that the relative importance of the various types of interactions can be established. This comparative approach will therefore be used with the transfer functions. 

In particularly thorough examples of the traditional physical organic approach, Parker (1969) and Abraham (1974) interpreted solvent effects on Walden inversion reactions by using thermodynamic transfer functions. However, in order to explain the reaction rate decrease upon solvation from a microscopic point of view, quantum mechanical electronic structure calculations must be carried out. Micro-solvated Sn-2 reactions were initially studied in this way, with the CNDO/2 semiempirical molecular orbital (MO) method, by using the supermolecule... 

The first section, under the heading solute-solvent interactions, considers the origin of the medium effect which is exhibited for reactions on changing from a hydroxylic solvent to a dipolar aprotic medium such as DMSO. This section is subdivided into two parts, the first concentrating on medium effects on rate processes, the second on equilibria of the acid-base variety. The section includes discussion of the methods used in obtaining and analysing kinetic and thermodynamic transfer functions. There follows a discussion of proton transfers. The methods and principles used in such studies have a rather unique character within the context of this work and have been deemed worthy of elaboration. The balance of the article is devoted to consideration of a variety of mechanistic studies featuring DMSO many of the principles developed in earlier sections will be utilized here. 

Additionally, examination of pKa values in DMSO and mixtures of DMSO with hydroxylic solvents, as obtained by different methods, has revealed considerable variation. This is illustrated in Table 6 for two compounds frequently used as anchors for acidity function scales. If one is to correlate pATa values with thermodynamic transfer functions [eqn (6)], rationalize varying orders of acidity in different solvents (Table 6), or use them inBr nsted relationships (Section 3),... 

DMSO has been used in a multitude of mechanistic investigations. In the present section we have chosen to highlight certain studies which illustrate the principles and methods discussed in earlier sections of this article. This will be done by reference to several contrasting situations. The systems chosen illustrate rate phenomena, both retardation and acceleration, resulting from use of DMSO. Various techniques for analysing these effects are presented, including the use of acidity functions and thermodynamic transfer functions, and their value as a guide to mechanisms demonstrated. 

Most thermometry using the KTTS direcdy requites a thermodynamic instmment for interpolation. The vapor pressure of an ideal gas is a thermodynamic function, and a common device for reali2ing the KTTS is the helium gas thermometer. The transfer function of this thermometer may be chosen as the change in pressure with change in temperature at constant volume, or the change in volume with change in temperature at constant pressure. It is easier to measure pressure accurately than volume thus, constant volume gas thermometry is the usual choice (see Pressure measurement). 

The thermodynamic properties of the refrigerant determine the suitability for a given condition of operation, particularly when compared with the same requirements or other refrigerants. The quantity of refrigerant needed for a particular level of evaporation is a function of its latent heat, except when using steam jet refrigeration, because the use of its chilled water involves only sensible heat transfer to process fluids. 

To better understand the complexity of situation, it is useful to apply some thermodynamic considerations. The separation process is governed by the change of the Gibbs function due to transfer of solute molecules between the mobile and the stationary phase. One can write... 

Medium-chain alcohols such as 2-butoxyethanol (BE) exist as microaggregates in water which in many respects resemble micellar systems. Mixed micelles can be formed between such alcohols and surfactants. The thermodynamics of the system BE-sodlum decanoate (Na-Dec)-water was studied through direct measurements of volumes (flow denslmetry), enthalpies and heat capacities (flow microcalorimetry). Data are reported as transfer functions. The observed trends are analyzed with a recently published chemical equilibrium model (J. Solution Chem. 13,1,1984). By adjusting the distribution constant and the thermodynamic property of the solute In the mixed micelle. It Is possible to fit nearly quantitatively the transfer of BE from water to aqueous NaDec. The model Is not as successful for the transfert of NaDec from water to aqueous BE at low BE concentrations Indicating self-association of NaDec Induced by BE. The model can be used to evaluate the thermodynamic properties of both components of the mixed micelle. 

We shall discuss now the variation of the three main thermodynamic functions with solvent composition for the case of n-Bu4NBr-water-acetone system and shall extend this discussion to the n-Bu4NBr-water-THF system. Figure 4 and Table IV present the results obtained. The figure was constructed as follows first the standard enthalpy of transfer AH°t, obtained by Ahluwalia and co-workers (12) from pure water to Z2 = 0.30, was used in order to get the standard entropy of transfer function from the relation ... 

Similar transfer functions can be defined for other thermodynamic state functions, e.g. H. However, if these functions are to be combined to yield other state functions, e.g. S, then care must be exercised to ensure that, as in the use of equation (15), the same standard state is always used. 

---