Polarity empirical parameters

The next two chapters are concerned with wetting and capillarity. Wetting phenomena are still poorly understood contact angles, for example, are simply an empirical parameter to quantify wettability. Chapter 6 reviews the use of scanning polarization force... 

Many approaches have been used to correlate solvent effects. The approach used most often is based on the electrostatic theory, the theoretical development of which has been described in detail by Amis [114]. The reaction rate is correlated with some bulk parameter of the solvent, such as the dielectric constant or its various algebraic functions. The search for empirical parameters of solvent polarity and their applications in multiparameter equations has recently been intensified, and this approach is described in the book by Reich-ardt [115] and more recently in the chapter on medium effects in Connor s text on chemical kinetics [110]. 

The solvatochromic phenolbetaine Reichardt s Dye (RD) allows to calculate a single parameter that indicates the overall polarity of the polymer. It is obtained by dissolving the dye in the polymer and measuring the absorbance maximum. The molar transition energy (Ex(30)) of RD is an empirical parameter to scale solvent polarity and is obtained by calculating18 Et(30) - hcvmaxNA OT 2.859vmaX R >. 

The expression holds for e < while poi,j = 0 for 8 > e ax, the limiting field, is an adjustable empirical parameter in the formulation. The total polarization energy at a molecule is the sum of polarization energies at each of its electron density pixels, poi = S poi,j. 

The authors of this work proposed a semi-empirical scheme for the calculation of 13C chemical shift tensors based on the bond polarization theory (5). This method can reproduce 13C chemical shift tensors with deviations from experiment comparable to the errors of the ab initio methods. One major advantage is that the calculations can be performed for large molecular systems with hundreds of atoms even on a PC computer. In contrast to the ab initio method a set of empirical parameters is needed for the calculations. In the case of the bond polarization theory these parameters can be estimated directly from experimental chemical shifts solving a set of linear equations. 

Once the semi-empirical parameters are determined, the bond polarization method can calculate the chemical shift values very quickly. In this work we compare... 

Group-symmetry considerations show that for y-pyrones (C2v symmetry) the AT ->1 transition is allowed and polarized in the direction of the symmetry axis. Irrespective of the empirical parameters of... 

The failure of the solvent relative permittivity to represent solute/solvent interactions has led to the definition of polarity in terms of empirical parameters. Such attempts at obtaining better parameters of solvent polarity by choosing a solvent-dependent standard system and looking at the changes in parameters of that system when the solvent is changed e.g. rate constants of solvent-dependent reactions or spectral shifts of solvatochromic dyes) are treated in Chapter 7. 

FA of data matrices containing 35 physicochemical constants and empirical parameters of solvent polarity (c/ Chapter 7) for 85 solvents has been carried out by Svoboda et al. [140]. An orthogonal set of four parameters was extracted from these data, which could be correlated to solvent polarity as expressed by the Kirkwood function (fir — l)/(2fir + 1), to solvent polarizability as expressed by the refractive index function (rfi — + ), as well as to the solvent Lewis acidity and basicity. Thus,... 

Another problem that has been tackled by multivariate statistical methods is the characterization of the solvation capability of organic solvents based on empirical parameters of solvent polarity (see Chapter 7). Since such empirical parameters of solvent polarity are derived from carefully selected, strongly solvent-dependent reference processes, they are molecular-microscopic parameters. The polarity of solvents thus defined cannot be described by macroscopic, bulk solvent characteristics such as relative permittivities, refractive indices, etc., or functions thereof. For the quantitative correlation of solvent-dependent processes with solvent polarities, a large variety of empirical parameters of solvent polarity have been introduced (see Chapter 7). While some solvent polarity parameters are defined to describe an individual, more specific solute/solvent interaetion, others do not separate specific solute/solvent interactions and are referred to as general solvent polarity scales. Consequently, single- and multi-parameter correlation equations have been developed for the description of all kinds of solvent effects, and the question arises as to how many empirical parameters are really necessary for the correlation analysis of solvent-dependent processes such as chemical equilibria, reaction rates, or absorption spectra. 

A quantitative description of the influence of the solvent on the position of chemical equilibria by means of physical or empirical parameters of solvent polarity is only possible in favourable and simple cases due to the complexity of intermolecular solute/solvent interactions. However, much progress has recently been made in theoretical calculations of solvation enthalpies of solutes that can participate as reaction partners in chemical equilibria see the end of Section 2.3 and references [355-364] to Chapter 2. If the solvation enthalpies of all participants in a chemical equilibrium reaction carried out in solvents of different polarity are known, then the solvent influence on this equilibrium can be quantifled. A compilation of about a hundred examples of the application of continuum solvation models to acid/base, tautomeric, conformational, and other equilibria can be found in reference [231]. 

A linear correlation has been found between the solvent-dependent AG° values and the empirical parameter of solvent polarity, t(30) (see Section 7.4). Thus, the host/guest binding strength increases steadily on going from nonpolar solvents to water, thus shifting the complexation equilibrium more and more to the right-hand side with increasing solvent polarity. 

In conclusion, it can be said that the electrostatic theory of solvent effects is a most useful tool for explaining and predicting many reaction patterns in solution. However, in spite of some improvements, it still does not take into account a whole series of other solute/solvent interactions such as the mutual polarization of ions or dipoles, the specific solvation etc., and the fact that the microscopic relative permittivity around the reactants may be different to the macroscopic relative permittivity of the bulk solvent. The deviations between observations and theory, and the fact that the relative permittivity cannot be considered as the only parameter responsible for the changes in reaction rates in solution, has led to the creation of different semiempirical correlation equations, which correlate the kinetic parameters to empirical parameters of solvent polarity (see Chapter 7). 

According to Lutskii, even for quite simple molecules, acceptably precise ealeula-tions of Av/v° still present insuperable difficulties. This explains the growing praetiee of eorrelating Av/v° with empirieal parameters of solvent polarity within the framework of linear Gibbs energy relationships. Some of these empirical parameters are even derived from solvent-dependent IR absorptions as reference processes as, for example, the G-values of Sehleyer et al. [154] cf. Section 7.4. 

At best, this approach provides a quantitative index to solvent polarity, from which absolute or relative values of rate or equilibrium constants for many reactions, as well as absorption maxima in various solvents, can be derived. Since they reflect the complete picture of all the intermolecular forces acting in solution, these empirical parameters constitute a more comprehensive measure of the polarity of a solvent than any other single physical constant. In applying these solvent polarity parameters, however, it is tacitly assumed that the contribution of intermolecular forces in the interaction between the solvent and the standard substrate is the same as in the interaction between the solvent and the substrate of interest. This is obviously true only for closely related solvent-sensitive processes. Therefore, an empirical solvent scale based on a particular reference process is not expected to be universal and useful for all kinds of reactions and absorptions. Any comparison of the effect of solvent on a process of interest with a solvent polarity parameter is, in fact, a comparison with a reference process. 

Empirical Parameters of Solvent Polarity from Equilibrium Measurements... 

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