274 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS layers of the cuticle tough and somewhat brittle. Exposure to ultraviolet rays of the sun can degrade the cuticle material, giving rise to hydrophilic groups in the surface. Severe mechanical damage during washing and combing of hair can destroy the cuticle and expose the hydrophilic cortex. It would appear, therefore, that measurement of the water wettability of the fiber surface could provide useful semiquantitative in- formation about the extent of damage undergone by the fiber. Apart from the kinds o'f damage described above, various chemical treatments of hair for aesthetic purposes such as bleaching (oxidation) and waving (reduction) also degrade the cuticle by breaking disulfide bonds and generating hydrophilic groups in the surface. Again, changes in the wettability of the hair surface against water should be a good measure of the extent of oxidation or reduction in the surface regions of the fiber. However, it should be noted that such measurements do not give any informa- tion about the changes occurring within the bulk of the fiber. Knowledge of the surface free energy of the fiber will be useful for the formulatot of hair-care products, which are applied in the form of sprays, and are expected to spread spontaneously on the surface. The critical surface tension would be a useful measure of the surface free energy of the hair fiber surface. It should be noted, however, that the conventional method of Zisman [4] for determining the critical surface tension of solids, is of limited applicability in that it represents only the dispersion contribution to the surface free energy. In the work presented here, an attempt has been made to understand the effect of weathering and mechanical damage on the wettability of the fiber surface against water. The same technique has been used to monitor oxidation and reduction reactions at the fiber surface. The role of dispersion and nondispersion contributions to the surface free energy have been evaluated, and it is hoped that this will lead to a better under- standing of the processes occurring at hair-liquid interfaces. THEORETICAL The spreading of liquids on the surface of a solid is governed by the 3 interfacial ten- sions, Tsv, Ts•., and %.v, where the symbols S, L, and V stand for solid, liquid, and vapor, respectively. The relationship between these tensions when a liquid surface is in equilibrium contact with a solid surface is given by the Young-Dupr• equation: 7t.v cos 0 = 7.sv -- 'Ys•. (1) where 0 is the contact angle. The term %.x cos 0 is often referred to as the wettability W of the surface. Determination of the wettability of a fiber by the Wilhelmy balance principle involves the measurement of the force acting (upward or downward), depending on the contact angle) on a counterbalanced single fiber when contact with the liquid surface is es- tablished. Equations relevant to this situation have been developed by Miller and Young [5]. The vertical force acting on the fiber is given by F,,. = w - F•, (2) where w is the wetting force, F,,. is the electrobalance force reading corrected for force

KERATIN FIBER SURFACE 275 reading in air, and Fb is the buoyancy force on the fiber. The buoyancy force on the fiber is given by Fb = lad (3) where 1 equals immersed length of the fiber, a equals area of the fiber cross section, and d equals density of the liquid. Substituting for Fb in equation (2) leads to equation (4): F,,. = w - lad (4) Therefore, a plot of Fw as a function of immersion depth 1 should give a straight line with slope (-ad) and intercept w. Wettability W, defined as the wetting force per unit length of the wetted perimeter, is given by w/P, where P is the perimeter of the fiber, i.e., W- w _7LvCOS0 (5) P ß The interfacial tension between a solid and a liquid phase in equilibrium is given by 3•s•. = 3•sv + Ylx - A (6) ß where A is the work of adhesion. Substituting eq. (1) in (6) gives A = 3'kv (1 + cos 0) = %.v + W (7) It should be noted that the work of adhesion is physically more meaningful than either W or the contact angle, since it quantifies solid-liquid interactions in such a way that the attraction between a series of liquids and one or more solids can be compared directly. ::i.. Therefore, some results have been expressed in terms of the work of adhesion instead ß ofwettability or contact angle. Equation (7) can be written in logarithmic form , • log (1 + cos 0) = log A - logg'•.v (8) According to Fowkes [6], if only dispersion interactions are involved, a plot of log (1 + cos •9) for a series of liquids on a given solid versus log 9q.v should be linear with a slope ß of -1, and the intercept on the 9'i.v axis at log 2 (cos 0 = 1) should give the so-called ß .. critical surface tension, a measure of the surface free energy of the solid. Conventional Zisman plots have been found to be nonlinear for the solid-liquid systems used in this work, suggesting that there'are contributions from interactions other than dispersion ::: for ce s, • Therefore, dispersion and polar contributions to surface free energy have been evaluated by the method of Wu [7]. This method uses the "reciprocal means" approach for the dispersion and polar contributions to the work of adhesion A in eq. (7), so that we obtain 'YLv COS •9 --'¾LV -t- 4'Ysa'YLa 4'ysP'YLP = 1- (9) 7s a + .yLd .ys P + .y•p By measuring cos •9 (or, in our case, 9'•.v cos •9) for a solid in 2 different liquids, 1 polar and the other nonpolar, 2 simultaneous equations are obtained, which can be solved