BENDING OF HAIR AND PERMANENT WAVING 127 1,0 0,8 0,6 0,4 0,2 I ß % ß H20 reducfion eeede e ß ß ß ß ß e j I I I I I I I rinse reoxid(]fion rinse TGA H20 H202 H20 i i i i i i i i 0 20 /+0 60 80 100 "- Bro/Bo '"- Br•/Bo f[min] Figure 2. The change of the relative bending stiffness during the five steps of the treatment sequence with 0.3 M TGA at pH 9.0. The experimental definitions for the normalized values of Bre and Bro are indicated (see text). where dc is the diameter of the cylinder the fiber was set on and d the mean diameter of the circles defined by the partially opened loops. The superscript "e" denotes "experi- mentally determined." When S e • 0.5, the loop length 1 covers less than half the circumference of the circle it defines, so that d is unmeasurable. In this case the linear distance between the fiber ends is taken as string of length a of an arc of length 1, that is part of the circle with the unknown diameter d, where 1 is given by the dimensions of the setting cylinder as: 1 = •rdc (5) From geometrical considerations it follows that a = dsin(1 X 180ø/(•r x d)) (6) So that with Equations 5 and 4: a = ddS e sin (S e X 180 ø) (7) On the basis of Equation 7 tables were generated from which values for S e and hence for R e could be taken by interpolation with better than 1% absolute accuracy for any experimental value of a.

128 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS ANALYTICAL CONSIDERATIONS AND RESULTS The application of linear viscoelastic theory to the set of keratin fibers was originally achieved by Chapman (e.g. 7), who confirmed that the cohesive set of wool is governed by the principles of generalized, linear viscoelasticity. Cohesive set is caused by the breaking and reforming of hydrogen bonds, while permanent set is produced by cleaving and recombining some of the sulfur cross-links in keratin. Although the or- igins of both types of set are different, the mechanistic similarity, involving exchange reactions of either secondary or covalent bonds, lends plausibility to the application of similar theoretical approaches for permanent as well as cohesive set. The application of this theory to the permanent set of human hair has been attempted and described in a previous paper (4). Though a reasonable correlation was found be- tween the theoretical sets calculated from the Young's moduli of reduced and reoxidized fibers and the actually observed sets, the calculated values were systematically lower than the actual values. This means that the actually observed fiber set was greater than would have been expected from the change of the Young's modulus of a fiber during reduction. Denby (8) derived a simple formula for the time-dependent cohesive set of wool fibers that in analogy may be applied to permanent set. Since only the initial set at the moment of release is studied, Denby's equation for fiber recovery, eliminating the time-dependent factor, is given by (4): R c = Bre/Bro (8) giving the calculated value for fiber bending set as S c= 1 - B•e/Bro (9) where the subscript "c" stands for "calculated." Equations 8 and 9 are consistent with the experimental observation that the residual fiber bending stiffness or extensional force, also termed "force of retraction" (3), under a given set of conditions is related to the set the fiber receives (9- 11). To correlate the experimental values of set determined on fiber loops and those calcu- lated on the basis of Equation 9, the knowledge of the value of Bro is required for every single experiment. From the experimental point of view, the determination of the new bending stiffness of the released fiber Bro is quite difficult because the bending deformation acquired by the fiber during reduction and subsequent reoxidation prevents a further application of the balanced fiber method. One possibility to determine Bro is to treat an undeformed fiber and measure its bending stiffness afterwards. To follow this approach would have required, beside the measurement of bending relaxation and set, a third, parallel experiment that in the view of the scope of the investigation excluded itself from systematic application. It was thus only applied to verify the validity of the theoretical approach to the problem described below. During the permanent waving treatment, the value of the bending stiffness is decreased by the reducing treatment and is then restored to a value close to the initial value (4)