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).

TORSIONAL PERFORMANCE OF HUMAN HAIR 67 Apart from gaining insights into the mechanics of the hair fi ber and the role of cortex and cuticle, the primary emphasis of the investigation is to account, in a traceable manner, for the systematic fraction of the overall variance in order to improve the discriminative power of the torsional method. Table I shows that the residual variance 2 R s for G′ after the fi t is substantially smaller than the total variance 2 sT . On this basis, a t-test was conducted on the G′-values for samples WB and WBS, in order to assess the signifi cance of the difference between the two sam- ples. The results (t = 1.060) show that this specifi c difference is signifi cant above the 80% level for a one-sided test (p = 0.15) and well below that level for a two-sided test (p = 0.29), when using the raw data. The signifi cance levels increase to close to 95%, (t = 1.953, p = 0.054) when using the residual variance only and for a two-sided test. The signifi cance level exceeds 95%, when a one-sided test is applied (p = 0.027). The ability to separate the random and the systematic component of G′-variance thus leads to a very signifi cant increase of the discriminative power of the torsional test. CONCLUSIONS The torsional storage modulus of hair exhibits, irrespective of pretreatment, a distinct decrease with the moment of inertia. This shows that the modulus is not a material con- stant and that its measurement carries a signifi cant systematic component, which impacts on data variance. The fi t of a morphology-based two-component model, featuring cortex and cuticle, enables to separate the systematic component of data variance. The ability to thus determine the random (residual) component of data variance enables to signifi cantly increase the sensitivity of the torsional method, so that even effects on hair, which would be expected to be very subtle, may be detected. As additional information, specifi c mod- uli data are obtained for cortex and cuticle. Their general changes with cosmetic treat- ments are in line with expectations. Further quantifi cation of the moduli of the morphological components is currently subject to further and detailed analysis. ACKNOWLEDGMENTS The authors are indebted to Mr. J. Karwey, who through his BSc-thesis provided the data basis for our investigations. The thesis was prepared in the context of a collaboration be- tween the University of Applied Sciences of Suedwestfalen (Germany) and Cognis GmbH (now BASF Personal Care and Nutrition GmbH), Duesseldorf (Germany). REFERENCES (1) C. R. Robbins, Chemical and Physical Behavior of Human Hair, 4th Ed. (Springer Verlag, New York, 2002). (2) D. Persaud and Y. K. Kamath, Torsional method for evaluating hair damage and performance of hair care ingredients, J. Cosmet. Sci., 55, S65–S77 (2004). (3) D. L. Harper and Y. K. Kamath, The effect of treatments on the shear modulus of human hair measured by the single fi ber torsion pendulum, J. Cosmet. Sci., 58, 329–337 (2007). (4) J. H. Zar, Biostatistical Analysis (Prentice-Hall Inc., New Jersey, 1996). (5) F. J. Wortmann and S. DeJong, Analysis of the humidity-time superposition for wool fi bers, Tex. Res. J., 55, 750–756 (1985).