PERMANENT WAVING AND PERM CHEMISTRY 103 different individuals can respond very differently to a given perm treatment. One hypothesis to explain this occurrence involves diffusion rates representing a rate-limiting step. REDOX CHEMISTRY OF THE PERM PROCESS The most common chemical species used for attacking cystine disulfi de bonds in the perm process are organic thiols, which are characterized by the presence of a sulfhydryl functional group. The cleaving of keratin disulfi de bonds by a thiol is typically repre- sented by the reaction scheme given as follows : j K -S-S- K+RSH K -S-S-R+HS- K, ( 1) that is, the thiol (RSH) attacks cystine disulfi de bonds within the keratin (K-S-S-K) and itself becomes attached to form a mixed disulfi de (K-S-S-R) and cysteine (sometimes called ½ cystine, HS-K). In addition, it is also possible for continued reaction of the thiol with the mixed disulfi de (Reaction 2) with the production of another mole of cysteine and the dimer of the original thiol (R-S-S-R). j K -S-S-R+RSH 2K - SH+RSSR (2) In actuality, it is widely acknowledged that the active species in the perm reaction is the thiolate ion, as opposed to the thiol itself. Therefore, the fi rst step in the previous reaction scheme involves deprotonation of the thiol, as illustrated in step 3. As will be shown momentarily, the presence of a proton in this equilibrium represents the origin of the pH dependence in the perm reaction. j RSH RS H ( 3) The equilibrium constant for any reaction is given as the concentration of products di- vided by the concentration of reactants, that is: ¯ ¯ ¡ ¡ ± ± RS K RSH (4 ) T aki ng negative log10 of each side of the equation leads to the following equation: ¯ ¡ ± ¯ ¡ ± 10 10 10 RS log K log H log RSH (5) It is recognized that -log10 [H+] is the pH, whereas -log10 K is the pKa. Therefore, equa- tion (5) can be rearranged to give the following equation: ¯ ¡ ± 10 RS pH pK log RSH a (6) In sh ort , equation (6) shows how knowledge of pKa for a given thiol allows for calculat- ing the relative proportions of the active thiolate ion, [RS-] versus the inactive fully protonated species [RSH] as a function of pH. By means of illustration, Figure 3 shows

JOURNAL OF COSMETIC SCIENCE 104 the result of performing this exercise for two commonly used perm actives, cysteamine and ammonium thioglycolate (ATG). That is, the concentration of the active thiolate ion [RS-] is seen to increase dramatically when the pH is raised through the pKa. It is common practice to formulate chemical treatments, such as bleaches or permanent color products, at elevated pH because these conditions cause increased swelling and facilitate penetration into the hair. The same is likely true for permanent wave actives, but at the same time, Figure 3 shows that there is also a more fundamental chemical reason for us- ing an elevated pH in these formulations. It is recalled that depilatory products also use this same underlying chemistry, but these products are formulated at considerably higher pH. These conditions produce still higher concentrations of the active thiolate ion, which compromise the hair structure to the point of disintegration. Figure 3 a lso illustrates why cysteamine-based perms can be formulated at lower pH than traditional thioglycolate formulas, namely, a lower pKa means that the pH does not need to be raised to such high levels to produce a suitable quantity of the thiolate ion. Returning to the chemical equations for cleaving the cystine disulfi de bond, it now be- comes evident that there is the need to also balance electronic charge in addition to the atoms. It is necessary to add electrons to the left-hand side of the equation for disulfi de bond cleavage equation (7) and to the right-hand side for the conversion of the thiol to its dimer equation (8). Figure 3. Calculations for the relative abundance of thiolate ion as a function of pH for two common perm actives.