EXTENSION OF PERMED HAIR 131 DETERMINATION OF FIBER SET Treating hairs as loops on a cylindrical roller and then cutting the loops to measure the fiber set by observing how much of the initial loop form is retained is a convenient measure of the efficiency of a treatment and has close proximity to the practical situa- tion. Since the loops are formed as virtually two-dimensional structures, it is readily shown (neglecting the fiber diameter) that the bending recovery, R, acquired by the fiber at any point along the loop and the diameter of the circle enclosing the partially opened loop are related by: R = 1 - dc/d (17) dc = diameter of the cylinder. d - diameter of the circle enclosed by the partially opened loop. R i is the initial recovery measured within 1 min after cutting the fiber loops. To determine the increase of the recovery with time, the fibers were remeasured after 16 hours of release in water. The related recovery was termed R16. From the principles outlined above, recovery is expected to be independent of the fiber as well as of the roller diameter, in agreement with Mitchell and Feughelman's (11) observations. This result does not contradict the practical experience that the quality of a wave depends on the fiber and on the curler diameter (2) since the shape and the mechanical properties of the helix formed by the fiber released from the curler after the treatment depend on both fiber and curler diameter (12, 13) for various mechanical fiber properties. One further consequence of equation 6 is that the experimental procedure of extensional testing only indirectly applies to bending recovery via equation 4, while it directly relates to extensional recovery and extensional set. The extensional,set, i.e., the length set S L observed in the experiments, that should agree with the prediction according to equation 6 and equation 2, is defined as: S r = [(ll - 10)/10]/½ s (18) 10 is the initial length of the fiber, and 1• the length of the fiber after the treatment (Fig. 1). ½s is the initial static strain imposed. RESULTS Figures 2 to 5 show typical results for the change of the normalized static force F(t)/F 0 and of the normalized dynamic force AF(t)/AF 0 as continuous curves. The individual points are shown in Figure 2 to give the range of scatter and were omitted subsequently for reasons of clarity. Figure 6 summarizes the relative force data (95% confidence limits) from the static and the dynamic part of the experiment at the end of the various treatment steps. In all cases the static stress decreases during reduction and remains essentially constant during subsequent treatments, though a tendency for a 'further decrease is observed. This result supports Tobolsky's view (4) that the static stress reflects the performance of

132 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS w w REOXIDATION J REDUCTION 0 2o 2o 0 I TREATMENT 0 20 0 25 0 H20 RINSE I TIMES [mini RINSE Figure 2. Typical curve for the change of the normalized static force F(t)/F 0 and the normalized dynamic force AF(t)/AF 0 during reduction/reoxidation with 0.3 M thioglycolic acid at pH 9 for 20 minutes (0.3 M TA). the sulfur bonds that come under stress during fiber deformation, part of which are broken during treatment. The remaining bonds support a constant residual stress that is virtually invariant during further treatment. Bonds that are reformed during oxidation are unstrained in the deformed state. The relative static force at the end of the reduction F(t2)/F 0 is lowest for 1 M TA and similar for the three other conditions. The overall reformation of sulfur bonds is given by the final dynamic modulus Ergo . The modulus attained for all treatments after reoxidation and rinsing is about 90% of the initial, dynamic modulus Eg and remained unchanged for the time of further observa- tion (approx. 5-10 rain). The value of 90% agrees well with the change in the 20% index recovery observed by Gershon et al. (2) under similar conditions. The dependence of the residual static modulus on treatment conditions and the invari- ance of the final dynamic modulus combine in equation 6 to explain Munakata's (14) observation that there is a proportionality between the stress decrease in a fiber during a treatment and the set achieved. The decrease of both the static and the dynamic forces increases for reduction by thio- glycolic acid with increasing concentration. Only for reduction with 1 M TA does the level of the dynamic force reach the level of the static force. The drop of the static as well as the dynamic stress in 1 M TA is considerably larger than the decrease in the 20% index however, an "infinite bath" was used here vs a 2:1 liquor/hair ratio to obtain the 20% index data (15).