314 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Individual differences in reactivity of dithiol reducing agents also occur as demon- strated by the data in Table III. The average apparent rate constants found for the six individuals studied vary over a five-fold range. These differences are probably due to biological variations in the porosity of hair rather than from chemical damage, as this Table III Individual Variations in Reactivity to Lipoate Standard Individual n K* Deviation M 10 5.1 X 10 -7 4 X 10-8 B 5 5.2 X 10 -7 6 x 10-8 C 4 7.0 X 10 -7 7 X 10-8 J 4 2.0 X 10 -6 2 X 10 -7 P 10 2.3 X 10 -6 3 X 10 -7 0.17 M Sodium Lipoate, pH 9.0, 22øC *The units on K are cm M-' sec-3/2 n = number of hairs per individual. hair was obtained from donors who claimed that they have never permed, straightened, or colored their hair. The total sulfur content and wet Young's Modulus of hair from these individuals were not found to correlate to the reactivity differences seen in Table III (8). CONCLUSIONS The work described in this communication has led us to draw the following conclusions: 1. The SFTK method is useful for basic studies of the interaction of reducing agents with hair. 2. Under some reaction conditions a moving boundary of reducing agent is formed, while under other conditions reaction occurs simultaneously throughout the hair. 3. DTT and lipoate generally react via the moving boundary mechanism, while TG kinetics are pseudo first-order at pH 9 or below, and moving boundary at pH 10 and above. 4. There are significant variations in the susceptibility of hair from different individuals to reductive treatment. While we are confident that a moving boundary is formed when indicated by SFTK curves and that the SFTK rate dependence at early times is correctly described by F(t)/F(O) = exp(--constant x t3/2), we cannot state with certainty that the exact form of the constant term is given by equation 5. The data in Figures 4 and 5 and Table I show reasonable but not exact agreement with the theory. However, equation 5 provides a convenient and fairly precise way to normalize between hairs of different dimensions or across different concentrations of reducing agents. Note that even a factor of two difference in average cross section leads to relatively little difference in SFTK curves with DTT (Figure 3). Even so, all of our concentration, pH, and temperature series were run on different sections of the same hair to minimize the possibility of artifacts due to differences in hair dimensions.

KINETICS OF HAIR REDUCTION 315 It seems possible that the tendency of DTT and lipoate to form moving boundaries at all reaction conditions can be explained by the ability of these compounds to form a dithiolane (5-membered) or dithiane (6-membered) ring structure on oxidation. The ring structure stabilizes the oxidized molecule even though these rings are strained (2,4,6). This stabilization shifts the reduction equilibrium, and the presence of any reducing agent in the hair causes considerable reaction, greatly increasing the permeability of the hair, leading to the formation of the moving boundary. TG is a small molecule and is not an efficient reducing agent much below pH 10. Thus it can diffuse through the hair to a considerable extent before any significant reaction takes place, leading to pseudo first-order kinetics. Sodium bisulfite behaves in a similar fashion (1). At pH 10, TG is a very efficient reducing agent and also forms a moving boundary. The work reported here is of a basic nature, but the SFTK method could be used for more development-oriented studies such as comparing the efficacy of hair waving solutions. By using different sections of the same hair, the efficacy of reducing solutions could be compared by simply determining the per cent of reduction in tensile force at a given time. This method would not require extensive data analysis and does not rely on the assumptions that went into deriving equations 3 and 5. The SFTK method has two important advantages over the recently reported "hair loop test" (7) which is similar in principle. Our method uses much less hair than the hair loop test so different sections of the same hair can be used for comparisons, and information about the reaction mechanism can be inferred from the shape of the SFTK curves. The SFTK method should be applicable to studies of disulfide bond reduction in wool, and could be used to probe changes in the permeability of keratin fibers that may have occurred as a result of other treatments by determining the effect on reduction rates. ACKNOWLEDGEMENTS The strain cycle procedure was suggested and developed by Mr. James Innis. The micrographs shown in Figure 5 were obtained from Dr. Bruce Barman and were taken in the Microscopy Department of the Miami Valley Laboratories by Ms. Janet Van. REFERENCES (1) C. E. Reese and H. Eyring, Mechanical properties and structure of hair, Textile Res. J., 20, 743-750 (1950). (2) W. W. Cleland, Dithiothreitol: A new protective reagent of SH groups, Biochemistry, 3, 480-482 (1960). (3) J. Crank, The Mathematics of Diffusion (Oxford University Press, 2nd Ed., 1975), pp 298-313. (4) H. D. Weigman, Reduction of disulfide bonds in keratin with 1,4 dithiothreitol 1. Kinetic investigations,J. Polymer Sci., A 1:6, 2237-2253 (1968). (5) L.J. Wolfram, Reactivity of disulphide bonds in strained keratin, Nature, 206, 304-305 (1965). (6) U. Schmidt, P. Grafen, and H. W. Goedde, Chemistry and biochemistry of c•-lipoic acid, Angew. Chem. Internat., Edit/Vol. 4, 846-856 (1965). (7) J. Szadurski and G. Erieman, "The hair loop test," Cosmetic Science and Technology, Vol. II (IFSCC 12th International Congress, Paris, 13-17 September 1982), pp 391-405. (8) R. R. Wickett, unpublished results.