A Twisted Filament and Its Helix Structure Formation

摘要

The relation is investigated between the wave number k_0 of a twisted polypropylene filament and the wave number k_1 of the double helix composed of the filaments. The sum of the wave numbers is zero, illustrating the rule of wave number conservation unless the product t = ka of the wave number k and radius a of the filament is large. The deviation from the rule Δt is proportional to t_0~3 ≡ k_0~3a~3, and the proportionality constant γ is equal to the elasticity/rigidity ratio E/G.