Quasiperiodicity and the nanoscopic morphology of some polyurethanes

When straining polyurethane elastomers (PUEs), it is often observed that the long-period peak of the small-angle X-ray scattering (SAXS) does not shift normally. An explanation is indicated for some PUEs in the real-space chord distribution. It exhibits a sequence of constant long-period bands. The band positions form a Fibonacci sequence. This relates to the underlying chemical synthesis by polyaddition of hard and soft modules, indicating a nearly quasiperiodic setup in sequences of stringed hard domains. These sequences appear to be the probes provided by SAXS for the study of morphology evolution in such PUEs. Should a regular-as-possible arrangement of physical crosslinks optimize a property of the material, then in the synthesis the mole fraction n_H of hard modules should be chosen to be n_H = τ/(1 + τ) ≃ 0.62, where τ is the golden ratio.