PHYSICAL PROPERTIES OF ALPHA-KERATIN FIBERS 389 The medulla present axially in coarser oz-keratin fibers may be continuous, discontin- uous, or fragmented. Its essential physical characteristic is the presence of large amount of space, which does improve the thermal insulation and economy in weight and material with little loss in the bending characteristics for the fiber. It has a major effect on the optical appearance in particular in low pigmented fiber such as wool. The presence of the medulla causes an increased amount of light scatter especially at the blue end of the optical spectrum, making fibers such as wool with a natural yellowish color appear white. However, in terms of the mechanical properties of an oz-keratin fiber its role is that of empty space, and in this review discussion of the medulla will be largely omitted. LONGITUDINAL MECHANICAL PROPERTIES Speakman (3,14) first showed that the longitudinal mechanical properties of oz-keratin fibers vary markedly with temperature, humidity, and time. The stress-strain behavior of these fibers, he demonstrated, can be considered in terms of three distinct regions of strain. If a fiber is progressively extended under constant temperature and humidity conditions once it is straightened (which depends on the fiber under test, and in the case of a highly crimped Merino wool fiber represents a considerable strain), the stress-strain curve up to a few percent strain has a mechnically stiff, nearly linear region referred to by Speakman as the "ookean" region (Figure 2). This nomenclature is 40 D 30 c I 'n' B A 2 Z, 6 STRESS x 10 -Sdynes/cm2 Figure 2. The stress-strain behavior of a keratin fiber (African porcupine quill) in water at 20øC in: (i) the direction perpendicular to growth, (ii) the direction parallel to growth. In the latter case AB corresponds to the "Hookean" region, BC the Yield region, and CD the Post-Yield region.

390 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS somewhat misleading as this region of strain is far from spring-like in its mechanical properties. Bendit (15), who has published a discussion of this problem, prefers the term "pre-yield" region. However, due to common usage now for some fifty years in the literature, to prevent confusion the term "Hookean" will be applied in this review. With further extension of the fiber for strains beyond the "Hookean" region, increase of strain occurs with little increase of stress up to about 25-30% strain. This region of low stress increase with strain is referred to as the Yield region. For further extension of the fiber beyond the Yield region the stress increases more rapidly with increase of strain. This region of increase in fiber stiffness is referred to as the Post-Yield region. Although there are variations in the mechanical properties of c•-keratin fibers with variation of both the fiber environment and the type of fiber, all fibers in longitudinal extension have a qualitatively similar stress-stain relationship with the three distinct regions of the "Hookean," Yield, and Post-Yield. These three regions are most distinctly defined for a fiber of uniform cross-section in water (10). In these circumstances the ratio of the moduli of the linear portions of the three regions are approximately 100:1:10. The mechanical behavior of c•-keratin fibers in each of the three regions of strain level reflects the state of structure of the fiber and is next discussed in these terms. THE "HOOKEAN" REGION MECHANICAL The linear portion of the Hookean region for c•-keratin fibers at room temperature extends up to about 1% strain with the deviation from linearity becoming large as a strain of about 2% is approached. The Young's Modulus for fibers in water at 20øC corresonding to the linear region depends on the rate of straining (16). Typical results quoted for wool fibers at a rate of strain of 0.01% per minute are 1.7 x 109 pascals and at 10% per minute 2.0 x 109 pascals. Up to the strain level of about 1% the behavior of the fibers approximates to linear viscoelasticity, as indicated by the stress-relaxation and creep data (17,18). Progressively as c•-keratin fibers are placed in drier environments, that is, as their water content is reduced, the stiffness of the fibers increases. In completely dried fibers (• 0% relative humidity environment) the Young's Modulus of the fibers is increased by a factor of about 2.7 relative to the same fiber's modulus in water, the reference cross-section area in both cases being the value for the wet fiber (19). However, this apparent increase in fiber stiffness with the removal of water is completely time dependent. The equilibrium stiffness of the fibers is independent of the moisture content of a fiber, and corresponds to a value of Young's Modulus of 1.4 x 109 pascals in the wet cross-sectional area of the fiber used in all cases as the reference (20). The whole behavior of the fiber corresponds to a fixed Hookean spring contributing 1.4 x 109 pascals to the Young's modulus in parallel with a spring and viscous dashpot in series (10). The viscosity of the dashpot is moisture-dependent and is related to the mobility of the molecular segments, main chains, and side-chains affected by the presence of water. Measurements of Young's Modulus and stress-relaxation data (22) for fibers in water at various temperatures show a progressive reduction of Young's Modulus to a stationary value and disappearance of stress-relaxation between 40 ø and 50øC. This stationary value of Young's Modulus corresponds to temperature at which the time-related phenomena in the structure are short-lived compared with the experimental time. Hence as expected, the value of Young's modulus of about 1.4 x