PERMANENT WAVING AND PERM CHEMISTRY 105 j K - S- S- K 2e 2KS (7) 2RS R - S- S- R 2e j (8) K -S-S- K 2RS 2KS R -S-S-R j ( 9) In a cco rda nce with standard textbook chemistry, the acquisition of electrons represents a reduction reaction, whereas loss of electrons is oxidation. Cleavage of disulfi de bonds within the hair therefore represents a redox reaction: the cystine bonds are reduced and the thiol is the reducing agent which itself becomes oxidized in the process. The two half equations are combined (with cancelation of the electrons) to produce the total ionic equation shown in equation (9). The thermodyn amic driving force for a redox reaction is given by the following equation: % , G nFE (10) where ' G i s th e Gibbs free Energy, n is the number electrons involved, F is the Faraday constant, and E is the difference between the reduction and oxidation potentials of the species involved. Therefore, the driving force for the perm reaction is directly propor- tional to the oxidation potential of the reducing agent. An oxidation po tential of +1.06 volts can be measured for thioglycolate, whereas a value of +0.56 volts results for cysteamine. This shows how thioglycolate is a signifi cantly stronger reducing agent and explains the superior results associated with this active in producing tighter, true to rod-shaped curls. In summary, we learn that cystine disulfi de bonds can theoretically be cleaved by treat- ment with any reducing agent, with the effectiveness being related to the oxidation po- tential of the active. The most common means of achieving this end involves the use of thiols, with the level of activity being further controlled by manipulation of the solution pH. The scientifi c literature describes the use of numerous thiols (and other reducing agents) for cleaving disulfi de bonds in wool and hair. However, virtually none of these have received commercial attention. Clearly, any reagent must be proven to be safe for use on consumers, and such testing is generally costly (and unpopular). One additional benefi t associated with the use of thiols involves an ability to minimize the likelihood of overprocessing hair. The reaction schemes shown previously all represent equi- librium processes, and so a buildup of the oxidized thiol (i.e., R-S-S-R) within the hair would be expected to progressively retard forward progress of equation (2) in a fortuitous manifestation of Le Chatelier’s principle. The work of Salce et al. (10) appears to confi rm this supposition, and consequently, it is relatively common to fi nd dithioglycolate (DTG) being included in thioglycolate-based perms to help control the extent of reaction. The previous di scussion predominantly deals with chemical and thermodynamic aspects of the perm process, but as hinted previously, there is also the need to consider kinetic aspects. A comprehensive discussion of this topic is given in the following section. THE RATE OF DIS ULFIDE BOND CLEAVAGE Early efforts t o follow the rate of the perming process involved chemical analysis of cys- tine content after exposing hair to reagents for differing periods of time (11–13). This is

JOURNAL OF COSMETIC SCIENCE 106 a rather slow and tedious approach, and moreover, yields an overall change in total cystine content (it will be recalled that specifi cally we are interested in cystine contained within the alpha-helical keratin protein that makes up the microfi brils within the hair cortex). An interesting proposition for a potentially more useful method involves monitoring the tensile properties of hair while immersed in the perm solution. The crystalline protein that comprises the microfi brils is responsible for the wet-state tensile strength of hair, and so breakage of cystine bonds in this structure would be expected to produce a progressive decrease in mechanical properties. In short, the change in tensile properties is used as a proxy for the reaction progression. The inception of this idea dates back to the 1950s and the work of Reese and Eyring (14). A similar approach was used by Kubu (15,16) in the textile industry, although the method was subsequently popularized in perm research by the work of Wickett (17–22) during the 1980s and 1990s, who also coined the phrase single-fi ber tensile kinetics (SFTK). There are a number of assumptions that must be made in directly equating changes in tensile properties to the reaction progression, and in actuality, many of these appear dis- tinctly dubious. However, the results shown herein will demonstrate that the method nevertheless yields predicted outcomes in validation studies while producing remarkably reproducible results. However, before discussing these assumptions, there is the need for a brief overview of the relationship between hair structure and the tensile properties. The acquisition of mechanical data necessitates some form of sample perturbation. This is generally performed by one of two different approaches—either one precisely applies a given deformation (i.e., strain) to the test specimen and measures the generated force (i.e., a strain-controlled experiment) or conversely, one applies a force/stress and measures the con- comitant deformation (i.e., a stress-controlled experiment). Figure 4 shows a stress–strain curve that was generated by stretching dry hair at a constant extension rate using a strain- controlled instrument. When viewing these curves, it is convenient to consider the mechanical properties of hair in terms of deforming a spring (i.e., the alpha-helical keratin structure). A spring can be stretched within a given range whereupon removal of the applied deformation allows for complete recovery of the initial structure. This is termed elastic or Hookean behavior and is represented by a linear relationship between the stress and the strain. From Figure 4, it is seen that hair fi bers approximate this behavior up to around 2% extension. The slope of this portion of the curve represents an indication of the spring strength and is termed Young’s modulus. The application of deformations above this point causes the spring-like structure to unfurl, and in doing so, internal forces are dissipated via molecular motion. This threshold condition is termed the yield point, and extension beyond this limit dis- torts the spring to a point where it no longer returns to its original conformation on re- moval of the stimulus. The stress–strain curve remains relatively fl at during extension through the yield region, but ultimately, at still greater extensions, the protein chains themselves become strained and internal forces again build until breakage even- tually occurs. The objective of SFTK experiments is to monitor the tensile properties of hair as a function of time while the test specimen undergoes reaction with a perm solution. Accordingly, it is imperative that experiments be carried out under deformation condi- tions that reside within the linear-like region. That is, under these conditions, the decrease in tensile properties is representative of cleaving strength-supporting disulfi de bonds and