PERMANENT WAVING: POST-YIELD SLOPE 693 TabIe III Comparison of Degree of Cleavage of Disulfide by Post-Yield Slope Analysis with Data of Haefele and Broge (6) pH of Mercaptan Standardized Solution Slope Degree of Cleavage Slope Haefele and Broge 1. 2.0 0.89 0.03 0.03 2. 5.0 0.63 0.22 0.10 3. 6.5 0.65 0.20 0.14 4. 8.0 0.46 0.34 0.31 5. 9.8 0.27 0.48 0.42 Conditions: 0.55 N Thioglycolic Acid 30:1 Solution to Hair Ratio 10 Minutes Immersion Room Temperature acidities utilizing a heterogeneous iodine/thiosulfate titration of the hair samples. While blank values by this technique can be as high as 3.0% cysteine, it is useful for comparison purposes. The conditions of their experiment were repeated and the post- yield slopes determined. The degree of cleavage by standardized post-yield slope analysis is compared to the values extrapolated from the data of Haefele and Broge in Table Ill. These values assume that (kssk)0 = 0.79m mol/g based on 5.05% sulfur in the hair. In general the post-yield slope gives slightly higher cleavage values than the titration technique, though agreement is good with the exception of the value for pH 5.0. Considering the number of assumptions that are made in this comparison, the agreement is very good indeed. Since the assumption that disulfide cleavage could be estimated by comparison against a standard slope vs. cleavage plot seemed valid, the technique was applied to patrons having waves in the salon. Random hair lengths were obtained before perming, and the average post-yield slope determined. The same procedure was followed at the time the operator judged the test curl sufficient. An averaged standardized slope was obtained by dividing the average perm slope value by that prior to treatment. The degree of cleavage could then be estimated from the previously determined correlation. These data are presented in Table IV. The average degree ofdisulfide cleavage for this wave under salon conditions was 28 m 9% as estimated by post-yield slope analysis. The range of the cleavage values is 13- 41%. This can be compared with the data of Gumprecht et al. (12), who determined the per cent reduction for salon waving by tagging the cysteine generated by cleavage and analyzing the hair by amino acid analysis. Both radioactive and "cold" tags were used. Cysteine was assayed as C•4mcarboxymethyl cysteine utilizing labeled iodoacetic acid as the hot tag, and as S-aminoethyl-cysteine utilizing ethyleneimine as the cold tag. The values by the hot tag method for the degree of cleavage were 22-45%, and 20- 36% by the cold tag methods. The post-yield slope determination yields cleavage values that compare well to those obtained by the more laborious tagging techniques and can be used to estimate the degree of cleavage of disulfide under actual waving conditions.

694 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Table IV The Degree of Cleavage of Disulfide by a Commercial Acid Wave Under Salon Waving Conditions Patron No. Standardized Slope Degree of Cleavage 1 O.54 O.28 2 O.39 O.39 3 O.4O O.38 4 0.54 0.28 5 O.53 O.29 6 0.39 0.39 7 0.64 0.21 8 0.60 0.24 9 0.75 0.13 10 0.69 0.17 11 0.50 0.31 12 0.41 0.38 13 0.37 0.41 14 0.59 0.25 15 0.75 0.13 16 0.64 0.21 Average 0.55 -+ 0.13 0.28 + 0,09 THE EFFECT OF MERCAPTAN CONCENTRATION Since we were convinced that the analysis of the post-yield slope could be used to assess waving parameters, we turned our attention to formulation variables. The equi- librium cleavage of disulfide by mercaptan has been theoretically treated by Wolfram and Underwood (9). The degree cleavage of disulfide by mercaptans depends upon the total concentration (C) of mercatan plus mercaptide anion and varies with C •/2 or C 2/a depending whether eq 1 or eq 2 is dominant. kSSk + RS- --' kSSR + kS- (1) kSSk + 2RS- .• 2kS- + RSSR (2) This concentration dependence assumes that the degree of cleavage is small and that the system is at equilibrium. While such conditions may be approached for alkaline thioglycolate preparations which rapidly penetrate the fiber (8), equilibrium cleavage values are more slowly attained under acid conditions. In practice, the formulating chemist attempts to maximize curl formation while minimizing the processing time and the cost. Our data suggested that the time at which the post-yield slope reached a minimum value correlated with the time of test curl formation. Accordingly, the time of processing could be preselected and the effect of concentration on the post-yield slope investigated by preparing a series of solutions, applying them to hair wrapped on small mandrels and determining the post-yield slope values. Such a technique can give a great deal of information about the formulation without the need for curl evaluation of many separate trial formulas. The results of a typical experiment are presented in Figure 6. In this case the mer- captan was glyceryl monothioglycolate (glyceryl thioglycolate) (16), the pH 6.5, the temperature 50øC and the time of treatment was preselected to be 20 min. The shape of this curve is typical of others that we have investigated. The degree of cleavage increases (or the post-yield slope decreases) with increasing mercaptan concentration