TORSIONAL BEHAVIOR OF HAIR 91 0.3 0.2 0.! Logarithmic Decrement (3) ß ß ß ß ß ß ß :// i i ! i i i i i . 65 70 75 80 85 90 95 100 Fiber Diameter 04m) Figure 2. Logarithmic decrement at 65% RH. there is a relevant difference in properties between the cuticular and cortical materials, then this histological inhomogeneity can exert readily discernible effects as seen in the dependence of the supercontraction characteristics of hair on the hair diameter (5). Speakman, in his pioneering study of wool torsion (6), found no obvious relation between the torsional moduli and the fiber diameter over a wide range of humidities. While the data reported by Bogaty (1) did show lower moduli for fine fibers than for coarse ones, the author did not attach much importance to this small difference. Our results of torsional modulus measurements carried out in air at 65% RH (Figure 1) with hair of different racial origin show no apparent dependence of fiber diameter. The values of torsional moduli are within the range of those published by Bogaty (1) and the logarithmic decrement appears constant (Figure 2). Although wetting of the fibers drastically lowers their rigidity (Figure 3), the modulus invariance with the fiber 0.3 0.2 Rigidity Ratio ß ß ß ß ß ß ß ß ß ß ß ß ß ß ß ß I I I I I I I _ 75 80 85 90 95 1OO 105 Fiber Diameter (•m) ( /

92 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS diameter appears to hold. This, however, is not the case with the logarithmic decrement (Figure 4), which increases as the fibers become finer, confirming the original obser- vation of this effect made by Bogaty (1). An increase in the logarithmic decrement (8) reflects an intensification of the damping capacity of the fiber and a corresponding rise of the loss modulus, i.e., the fiber becomes more viscous and less elastic. In this respect the contrast between the dry and wet fibers is striking. For dry fibers the G•/G ratio is diameter-invariant, for wet fibers a diameter decrease from 100 to 70 Ixm brings about well over a 50% increase in the G•/G ratio. By plotting the data of Figure 4 as a function of the cuticle fraction of hair, we obtain a very convincing linear fit (Figure 5), implicating the cuticle as an important factor in the observed rheological changes. The cuticle, in its response to moisture, mimics the behavior of hair matrix however, a progressive increase in 8 suggests that in the case of cuticle, the plasticizing effect of water is even more pronounced than that observed for the hair matrix. This, in turn, leads to the conclusion that the torsion modulus of the cuticle is less than that of the fiber. The regression analysis of the rigidity ratios for fibers in H20 (Figure 3) gave us the best fit (correlation coefficient of 0.83) for a linear function with the slope value of 0.001. The smallness of the latter probably explains the apparent modulus invariance with the fiber diameter, yet it allowed us to make an estimate of the torsional modulus of the cuticle in the wet state. The modulus was computed using the following equation: G-comp R24 - G-cort R41 = R4 _ R4 ............ (V) 0.55 0.50 0 ./45 0.40 0.35 Logarithmic Deeremenk (5) ß ß ß i f 80 85 90 Fiber Diameter (gm) Figure 4. Logarithmic decrementin H20. I i 95 100 105