j. Cosmet. Sci., 51, 37-38 (January/February 2000) Letter to the Editor TO THE EDITOR: The cuticle controls bending stiffness of hair Perceptions of the coarseness or fineness of human hair, aside from the uncertainty of being able to observe actual direct differences in diameter, are markedly influenced by the bending behavior of the individual fibers. Accordingly, the hair is more commonly judged by tactile sensation, observation of the amount of "stand-off" from the scalp, and observation of dynamic motion in the hair array, in all of which fiber bending plays a dominant role. A theoretical study has been made of the mechanics of bending of human hair (1) in which this author suggested the cuticle might make a substantial contribution to bending resistance, even despite the relative thinness of this layer at the hair's surface. In the absence of a value for the elastic modulus for the cuticle, assumptions were made that this modulus was the same as for the hair's cortex. On this basis, a freshly emergent hair of circular section, of 70-1•m overall diameter and with a cuticle of 5-1•m thickness, was estimated to have a cuticle contributing perhaps as much as 46% to the fiber's total bending resistance. In a recent most elegant paper Parbhu et al. (2) describe nano-mechanical studies of sections of wool fibers with the aid of an atomic force microscope (AFM). By this means they obtained not only realistic measures for the elastic modulus of the fiber cortex but also elastic moduli for the subcomponent layers of each cuticle cell (exocuticle and endocuticle). These moduli confirm earlier speculations on the physical properties of the major subcomponents of the human hair cuticle based upon their chemical analysis (3). It seems opportune now to extend my earlier studies (1) in the light of these definitive measurements. We will use two principal equations: Bending resistance of a solid rod -- Eq'rr4/4 (1) where r is the rod radius and E is the Young's modulus, and Bending resistance of a cylindrical shell = Eq'r(ro 4 - ri4)/4 (2) where r o and r i are, respectively, the outer and inner radii of the shell. We will consider the bending resistance of a freshly emergent human hair of circular section and 70-pm overall diameter. According to common microscopic wisdom we will consider this hair to possess a cuticle of 5-pm overall thickness, consisting of ten cell 37

38 JOURNAL OF COSMETIC SCIENCE layers (each shell of 0.5-pm thickness), and that each layer contains an exocuticle sub-lamina of 0.3-prn thickness. For the purposes of this calculation we will ignore the cuticle cell membrane complex and the A-layer subcomponent of the exocuticle and assume that the 0.2-pm remaining thickness of each cuticle cell sheet behaves as endo- cuticle. We also make the reasonable assumption that the cortex and the subcomponents of the cuticle of human hair possess the same mechanical properties as wool. Parbhu et al.'s values for the Young's modulii of cortex, exocuticle, and endocuticle, were 4.0, 19.8, and 3.0 GPa, respectively. By summing bending resistances according to equations 1 and 2 for all the components of our target hair (i.e., cortex and ten alternating layers of exocuticle and endocuticle), we can derive an estimate of its overall bending resistance. What we find is that the cuticle as a whole contributes 74% to the total bending resistance (66% from the exocuticle and 8% from the endocuticle). The result of the present theoretical calculations must await confirmation by direct physical measurement of the bending in hairs. Nevertheless, in conjunction with the earlier study (1), there can be no denying the enormous influence the cuticle has upon the hair's bending resistance and a significant influence upon subjective perceptions of the coarseness and fineness of hair. The present results can be extended to provide yet further predictive opportunities for the cosmetic processing of hair. Thus if one's wish were to make fine hair perceptually thicker, this might be accomplished by stiffening the hair's endocuticle and, conversely, making coarse hair appear finer by degrading the stiffness of the exocuticle. Of course, it may be that existing toiletry products unknow- ingly operate by these routes. REFERENCES (1) J. A. Swift, Some simple theoretical considerations on the bending stiffness of human hair. Int. J. Cosmet Sci., 17, 245-253 (1995). (2) A. N. Parbhu, W. G. Bryson, and R. Lal, Disulphide bonds in the outer layer of keratin fibres confer higher mechanical rigidity: Correlative nano-indentation and elasticity measurements with an AFM, Biochemistry, 38, 11755-11761 (1999). (3) J. A. Swift and B. Bews, The chemistry of human hair cuticle. Part 3. The isolation and amino acid analysis of various subfractions of the cuticle obtained by pronase and trypsin digestion,J. Soc. Cosmet. Chem., 27, 289-300 (1976). j. A. Swift Department of Fetal and Infant Toxico-Pathology University of Liverpool Liverpool L69 7ZA, U.K. e-maih jaswift@ gayton. u-net. corn