LIGHT SCATTERING FROM ETHNIC HAIR FIBERS 59 0.4 Pressure 2 Pressure 1 0.3 ::::, ca � 0.2 "iii Nylon/ 0.1 / P1 0.0 20 40 60 80 Scattering angle (degrees) Figure 6. Nylon fiber ellipticity effect on GP intensity scan under white light illumination. Intensities are normalized. Cylindrical I fiber diameter I Minor axis of �� ttened fiber --------�---!-�--.... -- ,' ..... I I I I 1 GP curves ' .... - - -- -- ,, Figure 7. The effect of ellipticity on GP intensity scan. Simplified model for light reflection from cylin­ drical nylon fiber (dotted lines) and flattened nylon fiber (solid lines). either a curlier or a straighter form. When the curvature is large, it dominates many physical fiber properties like fiber friction, flyaway hair, luster, combing ease, manage­ ability, and hair body (19 ,20). Generally, the low luster of curly hair is related to poor fiber alignment. The ethnic hair of African origin used in this study has a natural distinctive and unique configuration, with twists along the fiber leading to a curly structure. As mentioned in the Experimental section, the African-American hair fibers were pulled straight in order to record the GP spectra. Therefore, twists and kinks are more important than a curly structure with large coils. In order to demonstrate the effect of the fiber twist on luster, the goniophotometric intensity curves were recorded first for the nylon fiber with a high ellipticity index and then for the same fiber twisted repeatedly over its longitudinal axis. The result is presented in Figure 8. The following features are observed: shift of the position of the specular peak towards the higher angles, increased W 112 , and increased diffuse reflectance. The reason is that upon illumination of the surface of a twisted fiber, there are number of planes of incidence, i.e., the light reflection occurs at various angles of incidence. Thus, along the fiber, luster is reduced

60 JOURNAL OF COSMETIC SCIENCE 0.16 0.14 0.12 0.10 ta -:i 0.08 · C 0.06 - C \ 0.04 0.02 0.00 20 40 60 80 Scattering angle (degrees) Figure 8. GP intensity scan from nylon fiber with increased ellipticity index and when twisted over its longitudinal axis. at the locations where the fiber twists. From the GP curves the specular peak for African-American hair compared to other hair appeared shifted indeed to higher angles (as shown in Figure 5). LUSTER CALCULATIONS REVISED Although luster used to be calculated at TRI using equation 1, the realization that broadening of the specular peak is detrimental to luster necessitates its revision. Based on the work of Reich and Robbins (1), we have incorporated the width of the specular peak at half height into the luster equation, as shown in equation 3: s L= - --­ (S + D) · W112 (3) Since luster obtained from equation 3 is not dimensionless, we have further refined it by incorporating peak width at half height of a standard specular reflector. This gives equation 4: S w, tandard L =---. 112 (S + D) \V,ample · 1/2 (4) Here the first term of the equation takes into account the contributions from the specular and diffuse reflectance, whereas the second term represents the peak broadening. The second term represents a normalization factor, obtained by dividing the peak width at half height of a standard specular reflector into the width at half height of the specular peak obtained from the fiber of interest. As a standard we used the black mirror provided by Hunter Lab as a black reflection standard. The GP curve of a black mirror under He-Ne laser illumination is given in Figure 9. It has no diffuse reflectance and, therefore, has a luster of 1, or 100%. The reflection profile of a single carbon fiber from the tape shown in Figure 4 is similar to that of Figure 9.