302 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS We have used the SFTK method to investigate the effects of pH, temperature, and reactant concentration with a monothiol reducing agent, sodium thioglycolate (TG), and with two dithiol reducing agents, dithiothreitol (DTT) (Cleland's reagent) (2) and sodium dihydrolipoate (6-8 dithioctanoate). Evidence from light microscopy in support of our kinetic models is presented. SFTK results showing differences between the reactivity of hair from different individuals are also discussed. MATERIALS AND EQUIPMENT Human head hair obtained from the Joseph Fleischer Co., N.Y., N.Y., was used for all the work described in this report. Each bundle of hair was from a single donor who had never subjected her hair to chemical treatment. The hair was given a double lathering with Prell © shampoo and was thoroughly rinsed prior to use. Tensile measurements were made on an Instron © tensile tester interfaced to a Hewlett Packard © 9825A microcomputer. Measurements of hair diameters were made on an optical diameter gauging system made by the Diffracto © Corporation. Temperature was controlled by a Lauda © circulating water bath. Reducing agents were purchased from the Sigma © Chemical Company. THE SFTK METHOD When a hair is extended in water by less than 2% of its original length, stress relaxation is complete in about half an hour. The process may be speeded up greatly by using the following strain cycling procedure. The hair is first extended to 2% strain in buffer of the same pH and temperature as the reducing solution. After extension the hair is allowed to stress relax for twenty seconds. Next the strain is reduced to 1% for twenty seconds, increased to 1.75% for twenty seconds, reduced to 1.25% for twenty seconds, increased to 1.68% for twenty seconds, and then reduced to 1.5%. A constant level of stress is reached within thirty seconds to one minute after completion of the final cycling to 1.5%, reducing the total time required for stress relaxation to about three minutes. In an experiment directly comparing variables such as pH, concentration, or temperature, different sections of the same hair are used and approximately the same level of stress is reached for each section at each part of the cycle. Following the stress relaxation procedure, the buffer solution is rapidly replaced with the reducing solution, and tensile data are collected to monitor the stress relaxation that occurs due to breaking of the disulfide bonds by the reducing agent. The data are displayed graphically as the normalized tensile stress (F(t)/F(0)), the stress at the time t, after addition of reducing agent, F(t), divided by the stress at the time of addition of reducing agent, F(0), versus time. RESULTS AND DISCUSSION KINETIC MODELS FOR HAIR REDUCTION SFTK curves f. or hair treated with sodium thioglycolate (TG) and dithiothreitol (DTT) at 0.30 M molar thiol concentration, pH 9.0 and 25øC are shown in Figure 1. The rate of

KINETICS OF HAIR REDUCTION 303 1.0 0.8 I I I I I I Time (minuoees) Figure 1. SFTK curves for thioglycolate (TG) and 1-4 dithiothreitol, 0.3 M thiol, pH 9.0, 25øC. tensile stress loss is much faster with DTT than with TG, and the curves have very different shapes. The DTT curve starts out slowly and then accelerates before tailing off, while the TG curve is typical of single exponential decay. In order to derive mathematical models for the kinetic processes, we assume that each labile, stress supporting, disulfide bond supports the same percentage of the tensile stress and has the same intrinsic rate of cleavage by a given reducing agent. The additional assumptions required depend upon the nature of the proposed model. Two models have been derived: a pseudo first-order model for reaction conditions producing SFTK curves similar to the TG curve in Figure 1, and a moving boundary model to describe curves similar to the DTT curve. To obtain the pseudo first-order model we assume that the diffusion of the reducing agent through the hair is fast compared to the rate of reduction and that the reducing agent is present in large excess. The rate of bond breaking is: 1. d(S-S)/dt = kCo(S-S), where Co is the concentration of reducing agent, and (S-S) is the instantaneous concentration of intact disulfide bonds. The back reaction is negligible because of the presence of a large excess of reducing agent. The tensile stress at any time, F(t), is assumed to be directly proportional to (S-S) and the solution of the SFTK rate equation is: 2. F(t)= F(0)exp(--kC0t).