136 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS tially, and after 16 hours release in water, R16. The decrease of set and hence the increase of recovery with time is indicated by the ratio Ri/R16 with a mean value of 0.8. The ratio Ro/Ri describes the relation between the recovery prediction and the recovery measurement for the various conditions. The predicted recovery is, depending on the conditions, higher than the measured recovery by a factor of 1.4 to 1.7. Figure 7 shows graphically the relation between R i and R0 and the related standard errors. The data suggests a linear relationship that passes through the origin for the three more concentrated solutions. These data are shown as a solid line in Figure 7, with a slope of R0/R i = 1.43. The (Ri,R0) result for 0.3 M TA lies above this line. Though the values for the mea- sured recovery, Ri, are equal for 0.3 M TA and 1 M Cys-HC1, the predicted R 0 is significantly higher for 0.3 M TA (one tail test, 95% confidence level). DISCUSSION Keratin fibers including human hair are essentially two-phase composites (16) con- sisting of continuous, linear, elastic filaments (phase C) embedded in an amorphous matrix (phase M). Appraisal of the components of hair fiber morphology with respect to the specific properties of the two phases of the model leads to the conclusion that phase C represents the or-helical material of the keratin fiber. Short or-helical segments held together in complex aggregates by a variety of primary and secondary bonds (17) form continuous filaments which are the crystalline regions of the microfibrils amounting to about 30% of the fiber material, e.g., for Lincoln wool fibers (18). Phase M comprises all the noncrystalline, supposedly amorphous components of the fiber. Both phases contribute to the overall modulus of a hair fiber. The contribution of phase Table II Bending Recovery Values, Ri, Measured Initially and After 16 Hours Release in Water, R16 Conditions R•, % R•6, % R•/R•6 Ro/R• 0.3 MTA (21) • 37 49 0.76 1.70 SE 2. 2 2. 7 1 MTA (24) • 20 31 SE 1. 7 1. 9 1 M Cys-HCI (103) • 37 47 SE 0.8 1-2 1 M Sulfite (172) • 44 45 SE 1. o 3.• O.64 1.50 0.79 1.46 0.98 1.39 i= 0.8 SE = 0.07 Means and standard errors, number of determinations in parenthesis. Ratios R•/R•6 and Ro/R •, see text.

EXTENSION OF PERMED HAIR 137 M is small in water and relaxes (within feasable experimental time limits) to an extent that the equilibrium modulus is approached (Figures 2-5). This modulus amounts to about 80% to 85% of the initial modulus (Figure 6) and is the contribution of the or-helical filaments to the overall fiber modulus. From an experimental point of view, it follows that the initial difference between the relative static and dynamic forces in water of about 15% is the contribution of phase M to the dynamic modulus. Considering the concept of the dynamic and the static modulus for rubber, as outlined by Tobolsky (4), there are two possible mechanisms that can affect the apparent contri- bution of phase M during reduction, and these processes have opposing effects. First, any back reaction of the reduction will decrease the number of sulfur bonds broken in the hair fiber at any given time and will increase the dynamic compared to the static modulus, and will hence increase the difference between the moduli. Second, the con- tribution of phase M to the static modulus is removed by stress relaxation, so that the difference between the dynamic and the static modulus is the dynamic modulus of phase M. Any effect of sulfur bond fission on the mechanical properties of phase M will decrease its dynamic modulus and therefore decrease the moduli difference. As outlined in Results, no significant change of the difference between static and dy- namic moduli occurs on reduction with 0.3 M TA, 1 M Cys-HC1, and 1 M sulfite. Either the properties of phase M are unchanged by the reduction or the effects of the two mechanisms that can induce a modulus change cancel each other. Assuming the invariance of the phase M properties, it follows that the reduction reactions all occur, as was to be expected, without any substantial back reaction, i.e., without reformation of broken sulfur bonds that contribute only to the dynamic modulus. Basically all sulfur bonds that are broken stay broken in the presence of the reducing agent. For 1 M TA the moduli difference, and hence the modulus of phase M, vanishes on reduction, indi- cating that rather severe conditions are required for the mechanical properties of phase M to be significantly affected. For all cases the main effect of reduction is on the contribution of the crystalline fila- ments, and it is the change of their properties that induces permanent fiber set (6, 14). It is likely that the helices themselves, as crystalline structures, are not affected by reduction (19), but rather the interactions between helices, which also rely on disul- phide bonds, are affected (17). Feughelman's model for the filaments in ot-keratins (20) proposes that the or-helical units are short so that any disruption of their interaction would lead from a contin- uously reinforced material towards a short-fiber composite, with the consequence of a significant decrease of the fiber modulus (21). During reduction a fraction of the sulfur-based interactions between the or-helical units is broken and the static modulus decreases. When the interactions are reformed, fila- ments are generated and their equilibrium state is the deformed shape. These filaments contribute to the modulus Ero that opposes redeformation and, hence, recovery. Ere is a measure of the amount of filaments or of the fraction of the original filament modulus that still supports the original form. On rinsing, the static force level stays constant since any stress-free, reformed sulfur bond in the related reformed filament whose equilibrium state is the deformed state will not contribute to the static force level. The dynamic force rise during rinsing indicates the shift of the equilibrium towards the sulfur bond reformation when the reducing