368 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS [C] = 0.5(0.5K' - Q)(e -k2Qt - 1) (eq. 12) 1 -- 0.SK' - Q . e_k2Qt 0.SK' + Q Eq. 12 may be rewritten as -k2Qt = ln([C] + 0'5(0'5K' - Q).0'5K' + QQ) [C] + 0.5(0 5K' + Q) 0.5K' - (eq. 13) Since K' and Q (or ICy]) are known, the right hand side of eq. 13 may be plotted as a function of time (t) from the kinetic data. The slope of this straight line is -k2Q. Therefore, the reaction rate constants k 2 and k• can be determined. The values for k• and k 2 for the hair keratin obtained using the least square linear regression are 12.80 and 5.00 hr-•, respectively. Figure 2 shows the formation of mono-DNP-cystine as a function of time for some hydrolysate concentrations. The curves in the figure were calculated from eq. 12. E .3 .2 o o lO 20 TIME (days) Figure 3. Formation of mono-DNP-cystine as a function of time using hydrolysates of hair which had undergone various degrees of bleaching in alkaline hydrogen peroxide solution. The curves were calculated from eq. 12 with K' = 3.33 X 10 -3 , k2 = 5.0 hr -•, and [Cy]s from Table I. Key: ß = untreated ß = 1X bleached • = 3X bleached ß = 5X bleached.

HAIR BIS-DINITROPHENYL CYSTINE INTERCHANGE 369 CYSTINE CONTENT IN OXIDIZED HAIR Figure 3 depicts rates of mono-DNP-cystine production for hair at different levels of peroxide treatment. The amount of mono-DNP-cystine formed is related proportionally to the level of the treatment. This indicates an increase in the disulfide bonds broken as the hair was subjected to more oxidation. The cystine concentration in the oxidized keratin fibers could be calculated from the concentration of mono-DNP-cystine at equilibrium using eq. 5 and the equilibrium constant obtained above. The amounts of hair used, the concentration of mono-DNP-cystine at equilibrium, and the calculated cystine contents are listed in Table I. The rates of mono-DNP-cystine formation as a function of time for the bleached hair are shown in Figure 3. The curves in the figure are calculated from eq. 12 using the same reaction rate constants (k• and k2) as for the virgin fibers. It can be seen that good agreement (r = 0.988, t = 23.14) exists between the experimental data for the oxidized hair and the rates predicted using the constants derived from untreated hair. In the peroxide bleaching process, the perhydroxy anion (HO2-) is the reactive species, and its attack on hair keratin appears to be focused on the disulfide bond (6). As the cystine content decreases, there is a corresponding increase in cysteic acid which is the only established major end product of the oxidative cleavage (7,8). Any other reaction intermediates formed would be unstable under alkaline conditions and would revert to cystine and cysteic acid during hydrolysis. The conversion of the disulfide group to two more hydrophilic cysteic acid groups will increase the liquid retention of the oxidized hair fiber (9). The disulfide concentrations and the corresponding liquid retentions for the peroxide bleached hair fibers are listed in Table II and shown in Figure 4. As expected, the disulfide concentration decreases and the liquid retention increases when the number of treatment increases. CONCLUSION Sanger's (1,2) experience in producing a mixed disulfide from the reaction of two symmetric disulfides was successfully applied to hair keratin disulfide analysis. Using eq. 5 with different amounts of hair in the hydrolysate and the corresponding equilib- rium concentrations of the mixed disulfide formed, the cystine content in hair and the equilibrium constant for the exchange reaction were determined. The forward and the Table I Experimental Results and Calculated Cystine Content* for Bleached Hair Number Amount of Hair Con. of Mono-DNP Cystine of in Hydrolysate at Equilibrium Treatments m (g/l) [C] (m mole/l) Calculated Cystine Content in Hair [Cy] (• mole/g hair) 0 0.20184 0.245 1 0.21216 0.211 3 0. 2086 0. 187 5 0.2204 0. 181 647 553 489 450 * Using eq. 5 with K' = 3.33 X 10 -3.