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Quasiperiodicity and the nanoscopic morphology of some polyurethanes
Author(s) -
Stribeck Norbert,
Li Xuke,
Eling Berend,
Pöselt Elmar,
in 't Veld Pieter J.
Publication year - 2015
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576715000874
Subject(s) - small angle x ray scattering , fibonacci number , nanoscopic scale , materials science , morphology (biology) , quasiperiodicity , scattering , crystallography , polyurethane , chemical physics , quasiperiodic function , physics , chemistry , nanotechnology , optics , composite material , condensed matter physics , mathematics , combinatorics , biology , genetics
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.