Drago E and C Parameters

The surface reactivity of solids is, to a large extent, a function of site concentration and the acidic or basic strength of sites, properties nore easily determinable by a variety of wet chemical techniques than by vacuum instrumentation. The determination of the Drago E and C parameters of surface sites appears to offer more predictability of surface reactivity than other techniques. 

Figure 3.1 Determination of the Drago E and C parameters for the surface SiOH sites of silica, using heats of adsorption of test bases determined by isothermal...

It is tempting to correlate these E and C parameters with the concept of hard and soft acids and bases (see Section 8.1). This is difficult, however. The idea of hardness implies a single-parameter scale (although no satisfactory numerical scale of hardness/softness has yet been established) while the Drago approach requires two parameters for each acid or base (acceptor or donor). 

Table 2-6. Some E and C parameters expressing Lewis acid/base strength according to Drago [217] ) cf Eq. (2-12).

Jensen [9] indicated that there is no evidence that Drago s parameters reflect the relative electrostatic and covalent contributions to the bonding in resulting adducts. They were not correlated with either a physical property (dipole moment, ionization potential) or with a quantum-mechanically calculated index. Drago s approach is a purely empirical method of calculating enthalpy of formation for molecular adducts. Fowkes applied the Lewis E C equation [19] and has attempted to determine E and C parameters for both polymers and surfaces. However, Jensen [9] indicated the potential problem connected... 

Table 3 Drago s E and C Parameters (kcal mol for Some Polymers and Fillers... 

Drago, R. S., Wong, N., Bilgrien, C., Vogel, C. (1987). E and C parameters from Hammett substituent constants and use of E and C to understand cobalt-carbon bond energies. Inorg. Chem. 26, 9-14. 

It has been pointed out by Chehimi [117], on the basis of XPS analyses by Burger and Pluck [118], that there is an excellent correlation between XPS chemical shifts and -A//ab for a series of quick-frozen solutions of SbCis with a series of Lewis bases in dichloroethane. As Drago s E and C parameters were... 

Fowkes and Maruchi tested Drago s hypothesis applied to the interaction of liquids with a solid surface by measuring the contact angles of various acidic and basic liquids (which had been characterized by Drago in terms of their E and C parameters) on different acidic and basic surfaces. Fowkes calculated and for the liquid and solid and examined the difference between these two quantities, which according to the preceding equations is given by... 

Drago and co-workers Introduced an empirical correlation to calculate the enthalpy of adduct formation of Lewis acids and bases ( 5). In 1971, he and his co-workers expanded the concept to a computer-fitted set of parameters that accurately correlated over 200 enthalpies of adduct formation ( ). These parameters were then used to predict over 1200 enthalpies of interaction. The parameters E and C are loosely Interpreted to relate to the degree of electrostatic and covalent nature of the Interaction between the acids and bases. This model was used to generalize the observations involved in the Pearson hard-soft acid-base model and render it more quantitatively accurate. 

At present the dye techniques are very useful and economical but are somewhat approximate. Advances in use of indicator dyes for measuring surface acidity and basicity may be expected to include a two-parameter measure of acid or base strength similar to the E and C equation of Drago, and the use of fluorescent indicators for colored solids. 

Conversely, the AN seale ean be viewed as a scale of hardness for adds since EtsPO is a hard reference base. Nevertheless, the merit of Gutmann s approach Kes in the fact that his scales provide both addic and basic parameters for amphoteric species, which is not the case with Drago s E and C classifications. 

When all of these limitations are taken into account, it should be emphasized that the parameters E and C introduced by Drago, in general, faithfully reflect the sequence of acceptor and donor strengths for both acids and bases. The E and C data relating to some of the more important systems are presented in Tables 4.11 and 4.12. These data are conventionally expressed relative to elemental iodine, for which, therefore, E = 1.00 and = 1.00. This means that the absolute values of... 

An alternative set of factors to HSAB theory that takes into account both electrostatic and covalent contributions is the Drago-Wayland parameters. The enthalpy of formation for the generic acid-base reaction in Equation (14.18) can be calculated from Equation (14.19) using the empirical E and C factors listed in Table 14.9. The subscripts A and B refer to acid and base, respectively ... 

A self-consistent set of E and C values is now available for 33 acids and48 bases, allowing AH prediction for over 1584 adducts. It is assumed that the conditions under which measurements are made (gas phase or poorly coordinating solvents) give rather constant entropy contribution and that most of adducts are of one-to-one stoichiometry. Table 10.2.2 gathers Drago s parameters, given in (kcaEmol) of some common solvents. 

Drago has proposed a "unified scale of solvent polarities" based on an extension of the E and C acid and base parameters discussed above. Each solvent is characterized by a parameter S and the change in some property, A%, of a probe system is given hy Ax = PS + W, where P and W are constants for Ae probe. If the probe is an acceptor (Lewis acid) in a donor solvent, then... 

Several individuals have worked to quantify these trends, making scales of Lewis acidity and basicity. Gutmann has created a series of donor numbers (DN) and acceptor numbers (AN) for various solvents, while Drago and Wayland have assigned parameters E and C, which measure electrostatic interactions and covalent bonding potential, respectively. Lastly, Pearson treats each Lewis acid and base with two parameters, relating what is called the strength of the acid/base and the softness/hardness of the acid/base. In fact, the HSAB trend discussed above is primarily a concept developed by Pearson. 

Acid parameters E and alkaline parameters C can be used to show the acid and alkaline values of the surface of materials. To measure the E and C values of material surfaces, R. S. Drago proposed the famous Formula 2.2 ... 

A and B indicate acid and base while E and C are susceptibilities to undergoing electrostatic and covalent interactions, respectively. The other parameters in Equation 15.9 are a conversion factor (/) and is the number of acid-base interaction sites on the surface. Drago et al (1965) have provided E and C values for about 30-40 acids and bases. In the case of benzene-water, the enthalpy of interaction is -5 kJ mol which incidentally is about Vi of heat of vaporization of benzene. This enthalpy of interaction corresponds to 16.5 mN m (assuming 50 as the area per molecule for benzene) and/= 1 both assumptions have been, however, criticized, see Douillard, 1997. Using such a value the improved Fowkes equation is, as shown by Fowkes et al. (1990), in excellent agreement with the experimental interfacial tension for water-benzene (35 mN m ) ... 

Number of heats used to determine the parameters for the specified base. The solvent recommended for getting enthalpies for comparison is indicated in parenthesis H stands for cyclohexane, hexane or gas phase and C, carbon tetrachloride or gas phase. See M. S. Nozari and R. S. Drago J. Am. Chem. Soc. 94, 6877 (1972). i>) Tentative value calculated from data limited to acids with similar C/E ratios. 

---