Changing the Shape of Hair 176 that the difference is due to more extensive reduction in the outer portion of the fiber. The bending modulus of a fiber is proportional to the square of the cross-sectional area, while the tensile modulus is proportional to the area, so reduction in the outer portion of the fiber will affect bending more than extension. A model in which the elastic modulus of the fiber after reduction varies according to a quadratic equation was shown to give good fit to the data. Undoubtedly, reaction is faster in the outside of the fiber during moving boundary reduction (see Figure 11) and the model gives a logical explanation for why it is easier to set a fiber in bending than in extension. However, under some reaction conditions used by Wortman and Kure the reaction is expected to be pseudo first order and a sharp front of reduction would probably not be expected. Furthermore, much greater set in bending compared to extension is found even in fine wool fibers set in water at 100°C where the treatment effect is almost certainly uniform across the fiber.56 Max Feughelman has given an alternate explanation for the relative ease of setting in bending compared to extension based on his two- phase model of a-keratin structure.1,39,56-59 As described in Chapters 1 and 7 of this text, the two-phase model postulates a strong, water impermeable phase, C, embedded in a more permeable matrix phase, M, whose strength is highly dependent on the presence of disulfide bonds.60,61 When the matrix phase is weakened by reduction, the connection between the rods in phase C is reduced causing loss of shear stress, as illustrated in Figure 14. This mechanism is not available to release stress in extension. To visualize this, think of a bundle of fine wires. The resistance to extension is given by the sum of the tensile strength of the wires and is independent of any connection between them. However, the wire bundle will be much more difficult to bend or twist if the wires are securely fastened together than if they are free to move past one another during bending or twisting. Thus a “treatment” that removes connections between the wires as they are bent or twisted and then reestablishes those connections while the bundle