JOURNAL OF COSMETIC SCIENCE 62 were taken as basis for the determination of the moment of inertia of a fi ber according to Equation 3. No corrections were applied for the limited changes of cross-sectional shape at the conditions of torsional measurement (22 ± 2°C, 22 ± 2% RH). HAIR TREATMENTS Hair tresses were taken from the collective of virgin hair, to be referred to as V in what fol- lows, and submitted to a permanent waving treatment with 7% thioglycolic acid at pH 9.5, adjusted with ammonia. The solution was applied in excess to the tresses for 30 min. This was followed by extensive rinsing and reoxidation with 2.2% hydrogen peroxide solution, adjusted to pH 4.0 with citric acid for 30 min. Finally, the tresses were again extensively rinsed and then dried with a hair drier at ambient temperature. To further sensitize the hair, it was subsequently subjected to a strong bleaching treatment with an 8% hydrogen peroxide/persulfate combination at pH 9.4 for 30 min. Subsequently, the hairs were extensively rinsed and dried with a hair drier at ambient temperature. In what follows, hair from tresses, which have undergone this treatment sequence will be referred to as WB (permanently waved and bleached). To further refl ect the general context of hair cosmetic treatments as well as to target more subtle changes of hair, a commercial shampoo was applied, which claims to be able to repair the hair surface. The shampoo was applied on WB-type hair fi bers already fi tted with crimps and thus ready for torsional testing. The hairs were wetted and then covered with the shampoo for 30 min. Subsequently, the shampoo was rinsed off for 1 min and then the hair dried with an air drier for 15 min at ambient temperature. The long contact time was chosen to maximize the potential effect of the shampoo as well as to refl ect the effects of repeated applications. In what follows hairs, which have un- dergone all treatments will be referred to as WBS (permanently waved, bleached, and shampoo treated). THE CORE/SHELL MODEL FOR HAIR To analyze the dependence of G′ on the moment of inertia, as documented for all samples in Figure 1, a core/shell model for hair is applied. For an individual human hair, the cor- tex is surrounded by a layer of cuticle cells, which are arranged in a tile-like fashion with each cuticle cell being in contact with the cortex as well as being visible on the fi ber sur- face (13). The resulting tilt angle away from the fi ber surface is 2–3° (14,15). In the cross section of a hair fi ber, this arrangement presents itself as a sequence of concentric layers of cuticle cells around the cortex. The thickness of each layer is that of an individual cuticle cell and for human hair generally determined as approximately 0.5 μ m. The total number of cuticle layers for undamaged hair near the scalp is expected to be 6–10, leading to an initial cross-sectional thickness of the cuticle layer of 3–5 μm (13). For the hair fi ber collective used for these investigations, the overall cuticle thickness was found microscopically in cross sections to be largely independent of diameter and about 3 μm, equivalent to six layers. In view of the relatively short length of a sample fi ber (3 cm effective length) and its probable origin with respect to the scalp (approximately 10 cm for

TORSIONAL PERFORMANCE OF HUMAN HAIR 63 commercial hair), this value is assumed to be constant along the fi ber, in good agreement with observations of cuticle-wear patterns by Garcia et al. (16). Implementing the ring/core-structure of cuticle and cortex, Equation 1 yields: ′ ′ ′ ( co co cu cu G I G I) G I (4) with the total moment of inertia of a fi ber given by: co cu I I I (5) where subscripts co and cu relate to cortex and cuticle, respectively. Treating the cuticle, based on the argument made above and for the current hair sample, as a hollow shaft with a constant wall thickness of 3 μm, Icu is calculated by a suitably modifi ed version of Equation 3 (17). Given the principal objectives of the investigation, no correction was applied at this stage to correct for potential changes of cuticle thickness through cosmetic processing. Figure 1. G′-values for individual fi bers from samples of virgin (V), perm-waved and bleached (WB), plus shampoo-treated (WBS) hair at 22°C and 22% RH. The values are plotted against moments of inertia (Equation 3). The solid lines through the data are fi ts according to Equation 4 with the parameter values given in Table I.