TGA-INDUCED STRUCTURAL CHANGES IN HAIR 193 Figure 10 shows the relationship between the wet initial modulus, Ew, observed for the reoxidized hair fi bers, and TGA concentration at different pH values. The curves are very similar to the patterns obtained for the relationships of the shear modulus, G, and the shape factor, κ, with TGA concentration (see Figures 4 and 7). It is suggested from these facts that the extension modulus of the hair fi ber in water is highly depen- dent on the small number of intermolecular SS cross-links located on the surface of the cystine-rich matrix proteins, i.e., 4.6 moles as cross-linking sites on the globular surface (15), which may play a role in the stabilization of the α-helix. In contrast, the type of intermolecular cross-links between IF, amounting to 3 moles of the rod domain and 8 moles of the terminal domain, is unlikely to be affected by the extension modulus, because as described above, the values of [SS]inter in reoxidized hair fi bers are essen- tially the same as that in the unreduced fi ber (untreated hair), except in highly re- duced cases (Figure 5). It has been reported that the extension modulus in water refl ects the mechanical stability against the deformation of the α-crystal and that sta- bility depends on not only the integrity of α-crystallites but also on the cross-link Figure 9. Stress–strain curves in water at 20°C for reoxidized hair fi bers after reduction treatments under different molar concentrations of TGA at (a) pH 8.7 and (b) pH 9.3. (1) untreated, (2) 0.3, (3) 0.5, (4) 0.75, (5) 1.0, and (6) 1.5. Figure 10. Relationships between initial modulus for hair fi bers in water, Ew, and TGA concentration at different pH levels: ( ) 8.7 and ( ) 9.3.

JOURNAL OF COSMETIC SCIENCE 194 density around IF molecules (36). The disulfi de cross-linked structure and the me- chanical property relationship of keratin fi ber remains an important issue to be ad- dressed in the future. CONCLUSIONS Under the conditions for the permanent wave treatment of hair, the reactivities of SS bonds located on IF and KAP molecules with TGA were determined by analyzing the structural parameters calculated by fi tting the theoretically derived equation of state to the stress–strain curves measured for reduced and reoxidized hair fi bers in a concen- trated mixed solution of aqueous LiBr and BC. Similarity in the number, type, and location of SS cross-links between hair and wool IF was inferred, and the total number of SS cross-links was evaluated to be 21 moles (residues) per IF chain, 7 moles in the rod and 14 moles in the terminal domains. Eight moles of IF–IF-type intermolecular SS cross-links are reactive with TGA under strong reducing conditions and 2 moles of IF–KAP- or IF–IF-type intermolecular SS cross-links in the terminals may be reactive with TGA, whereas 3 moles of IF–IF-type cross-links in the rod domain are non- reactive with TGA under usual treatment conditions. Moreover, 2.3 moles of KAP– KAP-type intermolecular links are the most reactive with TGA, whereas 17 moles of intramolecular SS cross-links within a KAP molecule are non-reactive. The volume oc- cupied by KAP was approximately 57% for each hair fi ber containing 627 and 636 μmol/g of SS content, and the percentage ratio of SS cross-links in IF and KAP was estimated to be 13.8:86.2. The percentage ratios of inter- and intramolecular links were 66:34 and 12:88, respectively. The following important conclusions were obtained from the correlation of the pa- rameters for reduced and reoxidized hair fi bers: (i) TGA attacks preferentially the SS bonds between the ellipsoidal KAP domains and between KAP and IF molecules, and as a result, the ellipsoidal shape of the globule changes to a near-spherical form (ii) nearly complete reformation of SS cross-links occurs between IF proteins through oxidation even when a large number of SS bonds break under strong reducing condi- tions (iii) the decrease in the volume of KAP in the reduction step recovers consider- ably after oxidation and (iv) the extension modulus of the hair fi ber in water is highly dependent on the number of intermolecular SS cross-links between KAP molecules around IF. REFERENCES (1) H. Bogaty, Molecular forces in permanent waving, J. Soc. Cosmet. Chem., 11, 333–342 (1960). (2) F.-J. Wortmann and N. Kure, Bending relaxation properties of human hair and permanent waving performance, J. Soc. Cosmet. Chem., 41, 123–139 (1990). (3) M. Feughelman, A note on the permanent setting of human hair, J. Soc. Cosmet. Chem., 41, 209–212 (1990). (4) M. Feughelman, A comment on “Bending relaxation properties of human hair and permanent waving performance,” J. Soc. Cosmet. Chem., 42, 129–131 (1991). (5) M. Okano, H. Oka, T. Hatakeyama, and R. Endo, Effect of thiol structures on reduction of hair, J. Soc. Cosmet. Chem. Jpn., 32, 43–51 (1998). (6) A. Kuzuhara and T. Hori, Reduction mechanism of thioglycolic acid on keratin fi bers using microspec- trophotometry and FT-Raman spectroscopy, Polymer, 44, 7963–7970 (2003).