TORSIONAL PERFORMANCE OF HUMAN HAIR 65 treatment makes the hair fi ber overall stiffer, at least at this low humidity. Effects at higher humidities may be quite different and even reverse (3). The decrease of G′ with the subsequent shampoo treatment (WBS), which may be attributed to a positive action of the product in terms of “softening,” is in this context not signifi cant on the 95% confi - dence level (p = 0.29). The latter observation corroborates the observation that data sets for samples WB and WBS in Figure 1 would strongly overlap, if plotted together. This seems to indicate that the discriminative power of the torsion method may thus be satis- factory for harsh hair treatments, but may not be adequate for more subtle ones, in appar- ent agreement with previous observations on a comparable set of samples (3). The values for G′ as such, as given in Table I, are in good general agreement with previous observa- tions by Bogaty (24) and Harper and Kamath (3) for virgin as well as cosmetically pro- cessed hair. ESTIMATING THE TORSIONAL STORAGE MODULI OF CORTEX AND CUTICLE The errors signifi ed by the boxes and whiskers in Figure 2 are implicitly assumed to be random. Figure 1 shows for all samples, however, that the errors, e.g., given by the total variances 2 T s (see Table I), contain in fact a signifi cant systematic component, namely the drop of G′ with the moment of inertia. Fitting Equation 4 to the data sets in Figure 1, this drop of G′ is used to separate the torsional storage moduli of cortex (G′co) and cuticle (G′cu). These two moduli values are given in Table I, together with the coeffi cient of de- termination (r2) of each fi t. The fi ts account in each case for a major fraction of the overall data variance. Figure 3 gives a graphical presentation of the data in Table I. It emphasizes that G′cu is much larger than G′co, supporting the view that the torsional properties of a hair fi ber, similar as in bending (25), are controlled to a signifi cant extent by cuticle properties (2). The large difference between the moduli values for the two morphological components is in agreement with observations by Parbhu et al. (23) and with a priori expectations, re- garding the high degree of cross-linking, namely, in the exo-region of the cuticle (13). The storage modulus of the cortex G′co drops from 0.61 GPa for virgin hair by about 1/3 to 0.40 GPa with permanent waving and bleaching. The relative drop as such is largely Table I. Arithmetic means of the storage modulus G′ for samples V, WB, WBS (see text) at 22°C and 22% RH. N is the number of fi bers tested in each case. 2 T s is the total variance of the data and 2 R s the residual variance after subtracting the amount accounted for by the fi t of the data using Equation 4. G′co and G′cu are the storage moduli for cortex and cuticle determined on the basis of those fi ts. The goodness of fi t is characterized by the coeffi cient of determination r2, giving the fraction of data variance explained by the fi tted regression lines (Equation 7). Fits are conducted on the assumption of a diameter-invariant thickness of the cuticle of 3 μm, thus assuming six layers of cuticle cells (see text). All values are based on the cross-sectional dimensions of the fi bers at 22°C and 55% RH. Sample (N) G′, GPa 2 T s × 102 2 R s × 102 G′co, GPa G′cu, GPa r2 V (69) 1.58 3.81 2.07 0.61 3.60 0.457 WB (56) 1.81 4.47 1.39 0.40 4.84 0.689 WBS (23) 1.76 3.65 0.88 0.37 4.63 0.758

JOURNAL OF COSMETIC SCIENCE 66 consistent with the changes observed for fi laments and matrix in the cortex by differ- ential scanning calorimetry (26) of hair in water after reduction (27) and oxidation (28). Since the shampoo treatment will affect the surface only, the cortex properties stay largely unchanged, accordingly. Since G′co is determined by extrapolation to I→∞, the absolute values in Table I have to be considered with some care and are subject to further investigations. The cuticle modulus increases with the reduction/oxidation treatment (see Table I). This can be expected to lead to increased stiffness of the hair surface structures, in agreement with frictional measurements (29) and also general observations by consumers of “dry” hair after such harsh cosmetic processing. The slight drop of cuticle modulus with the shampoo treatment may be associated with a trend towards cuticle “softening”, possibly through the surface deposition of a relatively soft layer of polymer. However, apart from these general considerations, no attempt is made at this stage to as- sess the quantitative quality of the moduli of cuticle and cortex, thus determined. This would require to take into account the complex composite structure of cuticle and cortex as well as the relationship between moduli from different types of testing geometries and is thus well beyond the scope of these investigations. Figure 2. Graphical summary of the G′-data for the three samples, giving the mean (▲), the standard error (S.E., as box), and the limits of the 95% confi dence range (±1.96 × S.E., as whisker). Figure 3. Torsional storage moduli for the whole fi ber (G′) and separately for cortex (G′co) and cuticle (G′cu) for the various samples (see Table I).