686 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS D E 20% INDEX --.. STRAIN, % Figure 1. Typical stress-strain curve ofuntreated and permanent waved hair. are known to involve bond breakage within the keratin structure, such as permanent waving, bleaching and straightening. A commonly reported parameter is the so-called 20% Index, or I20, which is a measure of the ratio of the work required to stretch the fiber to 20% extension after a treatment to that before the treatment was given (5). If this ratio is 1.0, then the fiber was unaffected by the process the lower the value of the ratio, the more effect the process has had on the fiber properties. For example, a typical alkaline permanent wave will reduce this value to about 0.8 (6), which is a reduction in the toughness of the fiber by about 20%. The lower stress-strain curve of Figure 1 is typical for a hair fiber which has been permanent waved, as compared to the normal curve. The shaded area in Figure 1 represents the difference in work of extension between the treated and untreated hair. While such measurements are valuable to the chemist to assess the overall effect of a given process on the toughness of the fiber, they are "after-the-fact." It would be valu- able to be able to correlate such changes to variations between cosmetic formulations themselves with the goal of optimizing the formulation from a performance and eco- nomic point of view while maintaining the hair's initial mechanical vroperties. Hamburger and Morgan (7), in 1952, were the first workers to note the decrease in post-yield slope (PYS) as hair fibers remained in contact with typical permanent wave solutions. While no attempt was made to study various formulation variables, nor did the conditions of the experiments simulate the conditions of permanent waving, they demonstrated that the post-yield slope could be linearly correlated with the time of im- mersion of the hair in the waving solution. Subsequent investigations by Herrmann (8) showed that the rate-limiting step in the reaction between hair keratin and alkaline thioglycolate was diffusion of the mercaptan into the hair fiber. The time of diffusion was strongly dependent upon pH and temperature, and varied for different mer- captans. The coupling of these observations led us to investigate the effect of typical permanent wave formulation variables on the slope of the post-yield region. The formulating

PERMANENT WAVING: POST-YIELD SLOPE 687 chemist is concerned with the variables of mercaptan concentration, pH, temperature and additives. At the same time, the ultimate user wants efficient and rapid processing. The post-yield slope can be used to assess the effect of formulation variables under actual waving conditions and can be correlated to molecular changes within the fiber, such as the degree of disulfide bond cleavage. The results of these investigations are reported herein. EXPERIMENTAL Hair samples were obtained from individual heads of known cosmetic history, or purchased as virgin European hair from DeMeo Brothers, New York, NY 10003. These samples were washed with a mild anionic commercial shampoo (Redken Labora- tories, Inc., Canoga Park, CA 91303) and thoroughly rinsed with tap water. For most experiments, 10 hair fibers were wrapped on single plastic mandrels (diameter 8 ram), saturated with the waving solutions, placed in plastic bags and treated for the desired length of time. For the reaction of hair keratin with sulfite, the procedures of Wolfram and Underwood (9) were duplicated. For the reaction of hair keratin with mercaptans to determine the degree of cleavage, the conditions of Haefele and Broge (6) were repeated. Mercaptan compounds of known purity were commercially available and obtained as samples from either Halby Division, Argus Chemical Co., New Castle, DE 19720, or Evans Chemetics, Inc., Darien, CT 06820. Solution concentrations throughout are based on the weight percent of active mer- captan species. All other chemicals were reagent grade. Stress-strain curves for individual fibers were obtained at ambient temperature (20- 25øC) and humidity (40-60% R.H.) utilizing the instrumentation described by Tyson and Curtis (10). • Post-yield slopes were obtained from the stress-strain curves by graphical interpolation. Reported slopes generally represent the average of 10 fiber de- terminations for each set of experimental conditions. In general the standard deviation was _+ 10% of the determined value. Penetration studies utilized the iodine decolorization technique as described by Herrmann (8). DISCUSSION AND RESULTS In order for the post-yield slope to be valuable in the assessment of formulation vari- ables in permanent waving it must be sensitive to these variables under actual permanent waving conditions. The data of Hamburger and Morgan (7) had been ob- tained by immersing the hair fibers in containers of the waving lotion, which represents very high solution to fiber ratios. The treated hairs were rinsed and subjected to analysis. In permanent waving practice, the weight ratio of solution to fiber is typically between 0.6 and 1.2, with a value of 1.0 being most representative. • A single hair fiber is horizontally suspended between a set of clamps. Force is applied by a constant speed motor which elongates the fiber at the rate of 1.5%/sec. Stress is monitored on the other end by a strain gauge transducer, while the stress-versus-strain graphs are plotted on an XY Recorder (Hewlett-Packard, Inc., ?alo Alto, CA 94303).