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

PHYSICAL PROPERTIES OF ALPHA-KERATIN FIBERS 391 109 pascals as the stationary value agrees well with the equilibrium Young's Modulus with which it should correspond. At the temperature of liquid nitrogen (-196øC) no segmental mobility exists in the keratin fiber structure (23), and any mechanical distortion of the structure results in bond deformation only. The Young's Modulus of c•-keratin fibers under these conditions is 9.6 x 109 pascals which is a value close to that of ice, indicating the correspondence to the expected stiffness of a hydrogen bonded network (24). Similar values of longitudinal mechanical stiffness were obtained in experiments in which the strain was of very short duration (-10 microseconds), under which circumstances segmental mobility was again eliminated (25). The values of Young's Modulus quoted for keratin fibers in water correspond to an aqueous medium at a pH around neutrality. If an c•-keratin fiber is tested in aqueous media of varying pH at 20øC it is found that the mechanical stiffness of the fiber (26) remains unchanged from neutrality down to pH 3. Below pH 3 the Young's Modulus decreases by about 40% until a plateau is reached at pH 1. This phenomenon is reversible and indicates the reversible breakdown of Coulombic interactions (salt links) from pH 3 to pH 1 as the increased hydrogen ion concentration neutralizes the side chain carboyxlic acid groups (-COO- ---• -- COOH), resulting in a loss of interaction with positively charged groups in the side-chains of the polypeptides in the keratin structure. About 6-7 x 108 pascals of the equilibrium Young's Modulus values of 1.4 X 109 pascals are due to Coulomibic interactions (27,22). Although Coulomibic interactions are present throughout the keratin structure, only those shielded from water molecules, that is not interacting to any degree with water molecules, are involved in opposition to mechanical distortion. These are the interactions producing the stiffness which makes such a major contribution to the Young's Modulus of the fiber (28). X-RAY DIFFRACTION AND THE o•-HELIX Astbury (29) demonstrated that with extension of an c•-keratin fibre in the "Hookean" region the folded molecular structure corresponding to the material responsible for the high angle X-ray diffraction pattern changes by the equivalent amount corresponding to the overall strain of the fiber. This folded structure in c•-keratin has been shown by Pauling (30) to correspond to the helical structure designated as the c•-helix present in a large proportion of proteins. The mechanical opposition to extension of c•-helices has been demonstrated to be due mainly to hydrogen bonds present between the turns of the helices (31). X-ray evidence suggests that water sorbtion in an c•-keratin fiber is mainly confined to the non-crystalline regions (32). While the crystalline o•-helical structures are intact the stiffness of the c•-keratin fibers in water corresponds to a Young's Modulus of the order of 109 pascals. However, if the c•-helices are randomized (33) (as discussed below) in aqueous solutions of lithium bromide at concentrations greater than 6.4M, the Young's Modulus drops to the value of a material in an elastomeric state (of the order of 10 y pascals). OPTICAL BIREFRINGENCE In keratin fibers the optical birefringence of the fiber is mainly a measure of crystallinity (34). Fibers placed in aqueous solutions of lithium bromide (33) of a progressively increased molarity from pure water to a concentration of 5M, experience a relatively