This method makes use of AHAB to assess WAB:
WAB = —«abAHab (13)
where f is a free energy to enthalpy conversion factor and nAB the number of acid-base adducts per unit area. AHAB can be evaluated experimentally, e. g., by microcalorimetry [13], infrared spectroscopy [13,15,55], and contact angle measurements [49,50], or evaluated by Drago’s four-parameter equation [31]. Equation (10) can thus be rewritten as
W = 2(yAyB)1/2 — f«AB(EA^B + CaCb) (14)
Equations (3) and (12) were applied to the benzene/water interface, using Drago’s EA and CA constants for water and EB and CB for benzene. Drago’s equation predicts a AHAB value of —5.0kJ/mol. The cross-sectional area of benzene (0.50 nm2) leads to nAB = 3.3 pmol/m2. Applying Eq. (13) yields WAB/f = 16.5 mJ/m2, which compares well with the value determined at 20°C using Eqs. (8) and (12):
wAB = y1+y2 — y 12 — 2(y1 y 2)1/2
= 72.8 + 28.9 — 35 — 2(22 x 28.9)1/2= 16.3mJ/m2 (15)
This implies that f = 1. However, f cannot be set equal to unity as found by Vrbanac and Berg [56] in their study of various neutral, acidic, and basic polymer surfaces. They checked Eq. (13) using a combination of wettability to determine W, conductimetric titrations for the assessment of nAB, flow calorimetry to determine AHAB, and temperature-dependent determination of surface tension and contact angle to estimate f. It was concluded that f (temperature dependent) was significantly below unity in most cases and that even including this effect, Eq. (15) was still not verified quantitatively when the terms were measured independently. Indeed for the DMSO-poly(ethylene-co — acrylic acid 5%) system, WAB = 1.3 and 3mJ/m2 from wetting measurements and independent measurements of the various parameters in Eq. (13), respectively. As this procedure was applied to a single system one cannot claim or conclusively deny the quantitative (dis)agreement between the two ways of estimating WAB.
Liquid |
у |
/ |
AB у |
у+ |
у |
Ref. |
Water |
72.8 |
21.8 |
51 |
25.5 |
25.5 |
10 |
Glycerol |
64 |
34 |
30 |
3.92 |
57.4 |
10 |
Formamide |
58 |
39 |
19 |
2.28 |
39.6 |
10 |
Ethylene glycol |
48 |
29 |
19 |
3 |
30.1 |
57 |
DMSO |
44 |
36 |
8 |
0.5 |
32 |
10 |
a-Bromonaphthalene |
44.4 |
43.5 |
0 |
0 |
0 |
10 |
CH2I2 |
50.8 |
50.8 |
0 |
0 |
0 |
10 |
Silicone oil |
18.8 |
18.8 |
0 |
0 |
0 |
58 |
Tricresyl phosphate |
40.9 |
40.9 |
0 |
0 |
0 |
4 |
DMSO: dimethylsulfoxide. |