TGA-INDUCED STRUCTURAL CHANGES IN HAIR 185 as 66:34 (see also Table IV). In Table I, the total number of [SS]inter is 135 (= 112 + 23) and of [SS]intra is 39 μmol/g. The ratio of these values is not similar to the value obtained for hair. Note that when [SS]U was assigned to the intramolecular cross-link, the percent- age ratio of [SS]inter = 135 and [SS]intra = 78 (= 39 + 39, i.e., 63:37) was considerably similar to the value obtained for hair. RESULTS STRESS–STRAIN CURVE FOR SWOLLEN HAIR FIBER Figure 3 shows typical stress–strain curves for the reduction and reoxidation samples. Fitting the experimental data for equation 3 with suitable choices of parameters Mc, ϕd, and κ, we can evaluate the values of these parameters. The results obtained for untreated and treated hair fi bers are shown in Table II. SWELLABILITY OF TREATED HAIR FIBERS As shown in Table II, the values of v2 (an index inversely related to swellability) decreased with increasing TGA concentration and pH for the reduced hair fi bers, and the values were infl uenced more by the latter as compared to the former. The swellability for reoxi- dized hair fi bers was lower than that for the corresponding reduced fi bers. This suggests that the regeneration of intermolecular SS cross-links occurs more or less in the hair fi ber during the oxidation step. SHEAR MODULUS OF SWOLLEN HAIR FIBERS The relationships between shear modulus, G, and TGA concentration at different pH values are shown in Figure 4. The values of G for reduced hair fi bers decrease dramatically with increasing TGA concentration and pH. The value of G at the highest TGA concentration Figure 3. Typical stress–strain curves of swollen hair fi bers: (a) untreated, (b) reduced with 0.75 M TGA at pH 9.3, and (c) reoxidized samples. Lines fi tted to the experimental data by equation 3.

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.