EFFECT OF HAIR COLOR ON LUSTER 431 The second feature we observe from Figure 4 is that the red-colored hair has the greatest luster compared to blue- and green-colored hair for all dyeing times. For a 45-minute dyeing time, red-colored hair had a luster of 28%, whereas for blue- and green-colored hair the corresponding value was 21%. The luster for untreated Piedmont hair is 15 %. Typical GP curves for these samples are shown in Figure 6. The surface roughness of hair is comparable for tresses of all colors, as shown with similar intensities of specular reflectance. Thus, it is reasonable to assume that the specular reflectance measured from GP curves is not affected by the color of the hair (i.e., Isv is constant and I R in equation 3 is diffuse reflectance). The diffuse component of the GP curves is very different for Piedmont and red-colored hair. In the case of blue and green hair, the diffuse reflectance seems to have a constant ratio to the specular component, leading to almost identical luster values for these samples, but slightly lower values compared to red-colored hair. The reflectance at 632 nm (i.e., the wavelength of illumination) for Piedmont hair is 56% and for red-colored hair 25%, whereas it is lower for green- and blue-colored hair, being 18% and 15%, respectively (see Figure 2). Since absorbance is -(I-R), the absor- bances of Piedmont and red-, green-, and blue-colored hair at 632 nm are 44%, 75%, 82% and 85%, respectively. For a colored hair fiber the diffuse reflectance will depend upon the absorption coeffi- cient of the color for the specific wavelength of the radiation used and its depth of penetration. The total absorbance, A, per unit path length of the fiber is given by A = a?l? + a•l• (5) 0.4 0.36 0.3 0.1 0.05 Piedmont (sp Red (sp) (sp) i i i i i i i i i 0 10 20 30 40 $0 60 70 80 90 100 Scattering angle (degrees) Figure 6. Typical goniophotometric curves for bare Piedmont hair and Piedmont hair colored with blue, red, and green semipermanent dyes for 45 minutes. Illumination wavelength is 632 nm.

432 JOURNAL OF COSMETIC SCIENCE Here, ap and ad are the absorbances per unit pathlength of the undyed and dyed parts of the Piedmont hair, respectively, and lp and ld are fractions of the undyed and dyed pathlengths within the fiber, respectively. Since lp = 1-1•t, we obtain the following expression for total absorbance: A - % - 1,•(% - a,•) (6) Since a_v is always smaller than ad, a• - ad 0, and A will increase with an increase in ld (i.e., dye penetration), we note that in the case of undyed Piedmont hair, ld = 0 and A = a•. The diffuse reflectance can be expressed by combining equations 2 and 6 and knowing that IAB -- IoA , as follows: I,e = Io(1 - A) - Isc - Io• T (7) Equation 8 shows the dependence of diffuse reflectance on dye absorbance and the pathlength of the dyed region. AccoMing to equation 8, diffuse reflectance I R will have its highest value if ld and ad are zero (i.e., undyed Piedmont hair). Therefore, for Piedmont hair, luster is low. For colored hair, ld 0 and diffuse reflectance is reduced. Diffuse reflectance is reduced especially by dyes having higher ad, i.e., a higher extinc- tion coefficient, and higher ld, i.e., the capability of penetrating the fiber completely. Such hair colors will increase the luster. Equation 8 can be used to interpret the relative magnitudes of diffuse reflectances observed in Figure 6: examination of cross sections of hair fibers dyed for 45 minutes by microscope reveals the variation in penetration depths for studied semipermanent dyes. In the case of blue and green dyes, ld was significantly smaller compared to the red dye. Therefore, the values of IR are lower compared to Piedmont hair. In the case of red-colored hair, though its absorbance is slightly lower than that dyed with the green and blue colors, ld was higher. This is the reason that red-colored hair gave a lower diffuse reflectance and a higher luster value. Thus, equation 8 demonstrates the importance of both dye absorbance and penetration depth on the amount of diffusely reflected light, and thus on luster. In order to illustrate the importance of dye distribution in the fiber on luster, we conducted the following experiment. We used 1% solutions of pure, single-component dyes, CI acid orange-4, CI acid red-4, and CI acid blue-25, to saturate Piedmont hair fibers by dyeing them under the following conditions: pH = 4.5, T -- 55øC, and t = 30 min. These dyes are ionic anthraquinone dyes consisting of sulfonic acid groups and have a high affinity to protein fibers. Under the given dyeing conditions, strong coloration with homogeneous dye distribution throughout the hair fiber was achieved, as confirmed by examination with an optical microscope. This is in marked contrast to the basic dyes used in commercial semipermanent products. The actual coloration of the Piedmont hair after dyeing with CI acid dyes is shown in Figure 3B. The reflectance spectra for hair tresses colored with CI acid dyes are displayed in Figure 7. Reflectances for red-, orange-, and blue-dyed hair at the illumination wavelength of 632 nm are 63%, 57% and 4%, respectively. For this system a• = 0, and since the fibers are dyed throughout ld = const, equation 8 will reduce to I• = Io(1 - l•za•z ) - Isc- Io• r (9)