JOURNAL OF COSMETIC SCIENCE 186 at pH 9.3 is reduced to only approximately 7% of the value for the untreated hair fi ber, while for the corresponding reoxidized hair fi ber, G is restored to the original by only about one-third. This suggests that a large number of SS cross-links disconnected by reduc- tion have remained unrecovered to form intermolecular cross-links. The shear modulus, G, is a function of Mc, ϕd, and κ, as shown by equation 4. In this paper, the number of intermolecular SS cross-links, [SS]inter, in IF proteins is represented as 106/2Mc in μmol/g on the basis of the functionality of the SS bridge. Table II Structural Parameters for SS Cross-Links in Untreated and Permanent-Treated Hair Fibers Treatment Reduction conditions 10-6G (N/m2) v2 κ ϕd Ic d Mc [TGA] (M) pH Untreated — — 11.35 0.599 1.65 0.339 0.566 Id0c 3600 Reduced 0.3 8.7 8.07 0.558 1.47 0.294 0.527 3400 0.5 8.7 6.71 0.559 1.37 0.280 0.501 3500 0.75 8.7 4.82 0.433 1.40 0.219 0.506 3300 1.0 8.7 3.05 0.458 1.15 0.209 0.456 3700 1.5 8.7 2.36 0.435 1.10 0.167 0.384 3700 0.3 9.3 6.84 0.542 1.37 0.286 0.528 3400 0.5 9.3 4.24 0.487 1.23 0.218 0.448 3500 0.75 9.3 1.86 0.387 1.20 0.178 0.460 4300 1.0 9.3 1.02 0.370 1.15 0.151 0.408 5300 1.5 9.3 0.74 0.333 1.20 0.132 0.396 5900 Reoxidized 0.3 8.7 10.32 0.615 1.40 0.356 0.579 3500 0.5 8.7 7.66 0.512 1.50 0.284 0.555 3400 0.75 8.7 6.61 0.551 1.40 0.305 0.554 3700 1.0 8.7 6.13 0.521 1.40 0.271 0.520 3500 1.5 8.7 5.30 0.502 1.40 0.259 0.516 3600 0.3 9.3 6.55 0.565 1.30 0.318 0.563 3700 0.5 9.3 5.06 0.434 1.50 0.261 0.601 3700 0.75 9.3 4.52 0.530 1.20 0.285 0.538 3900 1.0 9.3 3.94 0.541 1.10 0.258 0.477 3700 1.5 9.3 3.20 0.509 1.20 0.229 0.450 3900 Figure 4. The relationships between shear modulus, G, and TGA concentration at different pH levels: ( ) reduced, 8.7 ( ) reduced, 9.3 ( ) reoxidized, 8.7 ( ) reoxidized, 9.3.

TGA-INDUCED STRUCTURAL CHANGES IN HAIR 187 MOLECULAR WEIGHT BETWEEN SS CROSS-LINKS IN IF The value of Mc evaluated for the untreated hair fi ber is 3600 (Table II). This suggests that the number of intermolecular cross-links in the network of IF proteins is 139 μmol/g (= 106/2Mc) on the basis of IF proteins. The value found from the structural parameter appears to be reasonable because mechanically ineffective intramolecular SS links are in- volved in hair keratin (15,16) and the distribution of SS cross-links is not random (30) and occurs in sites too close to play a role as different intermolecular cross-links. Note that [SS]inter for hair and wool are approximately equal, i.e., 139 and 135 μmol/g (= 112 + 23), respectively (Table I). This corresponds to about 63% and 61%, respectively, of the total number of SS cross-links (inter + intramolecular) obtained by the sequenced data of Fraser et al. (30), i.e., 220 μmol/g in the IF proteins (Table I). Figure 5 shows the relationship between the number of intermolecular SS cross-links in IF chains, [SS]inter in μmol/g, and TGA concentration. Here usual permanent wave treatment conditions are used with the TGA concentration in the range 0.2–0.7 M, pH in the range 8.5–9.5, and temperatures between 20° and 30°C. The values of [SS]inter are essentially the same as those for the unreduced condition (untreated hair) except for higher reduction above 0.75 M TGA at pH 9.3. This suggests that almost no SS bond scission occurs on the IF chains forming α-crystals, and that the SS bond in the SS-rich segments of the terminal region is highly inaccessible to the reducing agent. It is further noted that a complete reformation of SS bonds occurs without any change in the type of cross-links from the bonds broken in highly reduced conditions. This phenomenon may be related to the ease of the reformation of the SS cross-link on the segment directly linked with a stable rod- like α-helical chain at a sterically favored position of SH groups produced by reduction. VOLUME FRACTION OF MATRIX DOMAINS IN HAIR With respect to ϕd, which is based on the swollen volume of fi ber, it is of interest to dis- cuss the basis of the unswollen fi ber. By defi nition, the volume fraction of domains in dry hair, Ic d , can be calculated by equation 6: Q c I I . d d 2 (6) The volume fraction, c, Id represents the volume ratio of the globular matrix proteins, KAP, to the total hair proteins, i.e., IF and KAP. Accordingly, the percentage ratio in the volumes of IF and KAP in untreated hair fi bers can be shown by c I Ic 1 d0 d0 , i.e., Figure 5. The relationships between number of intermolecular SS cross-links in IF chains, [SS]inter, and TGA concentration at different pH levels: ( ) reduced, 8.7 ( ) reduced, 9.3 ( ) reoxidized, 8.7 ( ) reoxidized, 9.3.