282 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS 2 1.5 .3 .2 I0 e ( I+ cos • ) z• (I *cos Oe ) Slopee = - .70 Slope e =-.64 )rce = 20.5 dyn/cm )rce = 23.3 dyn/cm I I I i i I 5 6789100 •'LV {' d yn/cm ) Figure 4. Variation of(1 + cos 0) with %.v for 1 human hair fiber measured m against-scale direction

KERATIN FIBER SURFACE 283 Table II Critical Surface Tension of Hair Fibers Scale Advancing "Equilibrium" direction Slope %,,• ., •.,m Slope Ignored -0.72 +- 0.03 19 4 _-+ 1.0 -0.67 + 0.16 24.8 _+ 3.9 Against scale -0.75 -+ 0.09 20 9 --- 2.4 -0.68 - 0.11 26.0 -+ 6.9 With scale -0.78 -+ 0.10 20.0 --+ 2.0 -0.70 --+ 0.11 24.9 _+ 3.0 Note: Each entry is an interfiber average for 5 fibers reported at 95 per cent confidence level. layer of water molecules, thus reducing the surface free energy of the keratin surface. The values of 3'c• obtained in this work are close to those reported by Alter and Cook [15], i.e., -26 dyn/cm, although the variability is high. The measurement of% using al- cohol-water solutions is known to give a value of -26 dyn/cm irrespective of the solid surface. This is attributed to the adsorption of alcohol molecules on the solid with the hydrocarbon chain oriented towards the liquid, so that all surfaces behave like hydrocarbon surfaces. Thus, the difference between %'a and 3'c• in our work may be due to the replacement of adsorbed water molecules by butanol molecules at the inter- face. The observation that the slopes in Fig. 4 are greater than - 1 (see also average values in Table II) suggests contributions from nondispersion interactions. According to Dann [16], polar interactions make a significant contribution to %,. Therefore, the %. values in Table II cannot represent the total surface free energy of the hair keratin. Alterna- tive methods capable of evaluating both dispersion and nondispersion contributions to the surface free energy have to be used. DISPERSION AND NONDISPERSION CONTRIBUTIONS TO 3',. or HAIR As has been mentioned earlier, such a method is based on the evaluation of cos 0 in 2 different liquids, one polar, i.e., water (%) = 22.0 dyn/cm, %)' = 50.5 dyn/cm), and the other nonpolar, i.e., methylene iodide (%) = 44.1 dyn/cm, 3q. •' = 6.7 dyn/cm). The values of cos 0, %.v, %), and %)' for each liquid is substituted in equation (9), resulting in 2 simultaneous equations with the unknowns, 3,.• • and 3'•"(for details see E1-Shimi and Goddard [13]). The equations can be solved graphically to obtain the values of the unknowns. Such equations were obtained for advancing and "•quilibrium" conditions by using the corresponding values of cos 0. The values of'y•t and 3,• •' obtained for both the above Table III Dispersion and Nondispersion Contributions to 7,. of Hair Fibers (dyn/cm) Scale Advancing "Equilibrium" Direction 7.• '• 3's" 7s '• + 7s" 3's '• 7s" 3's s + 7s •' Against scale 24.8 --+ 2.2 2.6 -+ 1 3 26.8 + 1.4 19.5 --+ 1.9 11.5 -+ 1.7 31.0 --+ 1.6 With scale 23.9 +- 2.2 2.5 -+- 1.5 26.5 -+ 1.0 19.5 --+ 2.4 10.0 +- 2.0 29.6 + 2_2 Note: Each entry is an interfiber average for 10 fibers reported at 95 per cent confidence hmit.