On polymeric materials containing fibrils with a phase transition. I. General discussion of mechanics applied particularly to wool fibers

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Abstract
Wool and other a-keratin fibers are known to consist mainly of aligned crystalline fibrils embedded in a less ordered matrix. The fibrils contain a large proportion of protein chains folded in the a-helical configuration. Under an external stress the fibril is capable of transforming to a second thermodynamic phase in which the protein chains are nearly fully extended into the pleated-sheet crystalline structure of β-keratin. This transformation involves local extensions in the fibril of the order of 100%. A constant stress, known as the equilibrium stress, is necessary to maintain the thermodynamic equilibrium between the two phases in the one fibril and this stress is independent of the relative quantities of each phase present. However, the concept is developed that a stress greater than the equilibrium stress is required to nucleate the extended β form from the folded a-form. In the composite fibril-matrix system undergoing extension, the matrix surrounding portions of the fibril which have transformed to the extended phase will be subjected to large complex strains. The resultant behavior of the system is studied by analyzing a simple mathematical model. With reasonable values of the parameters inserted, forward and reverse stress-strain curves have been obtained which compare qualitatively with the stressstrain behavior of wet wool fibers. The theory developed, by suitable adjustment of the parameters, can be applied to other composite systems consisting of aligned fibrils in a matrix.

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