HAIR MECHANICAL ANISOTROPY 309 As defi ned by equatio n (8), the index of anisotropy is greater than 1 it equals unity only for the isotropic material, i.e., for keratin fi bers having either no rods (xROD = 0), only rods (xROD = 1), or equal values for Young’s modulus of the rods and of the matrix (Y = 1). The defi nition of index of anisotropy, as a ratio of AFM nanoindentation measurements, along and transverse to fi ber axis has the particular advantage of avoiding any supposition on the Poisson ratio for fi bers required by equation (2) for calculating the absolute value of the measured Young’s modulus. Indeed, from equation (2): ¸ V2 ¸ x ¸ V2 * * tip Transverse tip Axial Axial * * Transverse Transverse Transverse tip Axial tip – 1– = , – 1– E E* E E EAxial E E E* E E (9) where EAxial, * Transve rse are the AFM-measured Young’s moduli along the two directions and the value of Young’s modulus of the tip, Etip, is much larger than that of the soft material (hair). As per equation (9), the index of anisotropy can be extracted directly from AFM nanoindentation measurements performed on cross sections and on longitudinal sections (the ratio of the two acquired Young’s moduli). Equations (8) and (9) relate the measured axial and transverse moduli to the amount of rods of the composite material and to the ratio of rod-to-matrix Young’s moduli. The theoretical dependence of the index of anisotropy on the percentage of rods is shown in Figure 2A. The graph of Figure 2B takes into account that the percentage of rods (KIFs) of the hair fi ber is below 50% (20) and that this percentage decreases with increasing moisture absorption (increasing relative humidity). For the sake of simplicity, we neglect several factors, which may affect slightly the anisot- ropy, namely the following: the angle of KIFs, taken in the present work as 0° any tilting of KIFs with increasing moisture absorption the contribution of the interphase, the region of links between KIFs and Matrix (21) and of other subcomponents of keratin fi bers (22). RESULTS AND DISCUSSION AFM nanoindentation measurements were performed on several areas of the hair, both on cross-sectional and on longitudinal section, for cortex, exo- and endocuticle. The relative Figure 2. (A) Theoretical evolution of the index of anisotropy equation (8) with percentage of rods of the composite material. (B) Theoretical evolution of the index of anisotropy of Hair fi ber with increasing Relative Humidity. The horizontal line at one is the ‘isotropic line’ for an isotropic material.

JOURNAL OF COSMETIC SCIENCE 310 humidity, RH, during each indentation experiment was adjusted and controlled, to cover the range between 8% and 92%. The values calculated, from equation (8), for the index of anisotropy of cortex (Figure 4A) do not appear to follow the shape suggested in Figure 2B, for moisture infl uencing only the percentage of rods (KIFs) of the cortex. This led us to consider that moisture, being absorbed only by matrix, affects the Young’s modulus by breaking of hydrogen bonds and, in this way, affecting the rods-to-matrix moduli ratio, Y equation (7). The dotted line in Figure 4A plots the theoretical values of the model developed to account for the hydrogen bonds participation to the Young’s modulus of the matrix (23): 1/3 Matrix = 1– cortex moisture content +0.2 E k (10) Figure 4B illustrates a striking result namely that the exocuticle deviates from isotropic behavior (from IA = 1 line), when relative humidity goes beyond 60%–70% and the effect of relative humidity (dotted line) appears to match fairly well the experimental data. In other words, Figure 4B indicates that the exocuticle exhibits an internal composite structure when enough absorbed moisture allows its release from the otherwise isotropic, heavily cross-linked, environment. Moreover, the values for the indices of anisotropy of exocuticle fall below one, which is at odds with our defi nition in equation (8) requiring the ratio of axial to transverse moduli to be greater than one. We interpret this behavior by assuming that in the case of exocu- ticle the orientation of its presumptive rods is perpendicular to the fi ber growing axis and, likewise, to those of the KIFs of cortex. The experimental results acquired for endocuticle (see Figure 4B), on the other hand, suggest a fair isotropic behavior of this layer over the range of relative humidity. This is in line with the knowledge of the low cross-linked structure of endocuticle (9). Summing up the mechanical results, we hypothesize that exocuticle behave as a heavily cross-linked composite layer, keeping the rods in an isotropic tight arrangement until moisture content of the Cuticle is high enough (RH greater than 60%…70%) to allow the manifestation of the rods. The rods of the exocuticle appear to lie perpendicularly to the KIFs of cortex, i.e., perpendicularly to the growing axis of the fi ber, very much similar Figure 3. The evolution of axial (A) and trans verse (B) Young’s moduli for cortex, exo- and endocuticle with relative humidity. The dotted lines are for eye guidance.