Drago’s E and C Parameters

Drago proposed a four-parameter equation to predict the heat of acid-base adduct for­mation [31]:

—AHAB — (EaEb + CaCb) (3)

where E and C are the susceptibilities of the acid (A) and the base (B) to undergo an electrostatic interaction (E) and a covalent bond (C), respectively. Drago showed that his equation estimated AHab for almost 1600 adducts with an accuracy of 0.1-0.2kcal/mol (0.4-0.8 kJ/mol). Stable adducts are obtained when the acid and the base have both large E and C constants. Fowkes [6] suggested determining E and C parameters for polymers and other materials by using a set of reference acids and bases of known Drago parameters. However, this is best achieved by choosing a set of reference species of widely differing C/E ratios (where C/E can be considered to be a measure of relative softness). Table 2 displays Drago’s parameters for some frequently used acidic and basic probes.

Fowkes and co-workers have used test acids (e. g., phenol and chloroform) and bases (e. g., pyridine and ethyl acetate) to determine Drago’s parameters for polymers and metal oxides using essentially calorimetric heats and infrared (IR) measurements [13,27,37,38].

Acids

Ca

Ea

Ca/Ea

Iodine

1.00

1.00

1.0

SbCl5

5.13

7.38

0.695

t-BuOH

0.30

2.04

0.147

Pyrrole

0.30

2.54

0.116

CF3CH(OH)CF3

0.62

5.93

0.105

Phenol

0.44

4.33

0.102

Chloroform

0.16

3.02

0.053

H2O

0.26

2.61

0.010

Bases

Cb

Eb

CB/EB

TCHP Sab

9.67

0.61

15.8

Triethylamine

11.1

0.99

11.19

Pyridine

6.40

1.17

5.47

THF

4.27

0.98

4.37

Diethyl ether

3.25

0.96

3.38

1,4-Dioxane

2.38

1.09

2.18

Acetone

2.33

0.98

2.36

Ethyl acetate

1.74

0.98

1.79

Et3P=Oac

2.70

1.64

1.65

E and C in (kcal/mol)1/2 from [31], except: a[36]; btricyclohexyl phosphine oxide; ctriethyl phosphine oxide.

The approach of Fowkes was applied in combination with inverse gas chromatography (IGC) to determine E and C for conventional polymers [39], conducting polymers [40,41], and untreated and silane-treated glass beads [42]. It is also worth noting the potential use of nuclear magnetic resonance (NMR) [13] and x-ray photoelectron spectroscopy (XPS) [15,43] for the assessment of E and C.

Table 3 reports the E and C parameters for various polymers and metal oxides using a variety of techniques. Clearly, several methods can be used to determine E and C. Alternatively, it would perhaps be possible to assess these constants by using contact angles of diiodomethane solutions of specific probes such as phenol. Indeed, the determi­nation of AHAB for probe-surface systems was suggested by Fowkes et al. [49] on the basis of temperature-dependent contact angles and a substitution of the Young equation into the Gibbs equation for solute adsorption from diiodomethane onto the surface under investigation. Such applications include the surfaces of PMMA [49] and chemically mod­ified Teflon [50].

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