Phase Transformation in Helical Structures: Theory and Application

Abstract

A helical structure is a collection of molecules at positions given by the orbit of a helical group acting on the position vectors of the atoms of a single molecule. In this thesis, we systematically study phase transformations from one helical structure to another and search for potential applications. Motivated in part by recent work that relates the presence of compatible interfaces with properties such as the hysteresis and reversibility of a phase transformation, we give necessary and sufficient conditions on the structural parameters of two helical phases such that they are compatible. We show that, locally, four types of compatible interfaces are possible: vertical, horizontal, helical and elliptical. Furthermore, we discuss more complex microstructures in transforming helical structures that mix different types of these interfaces. Similar to crystal case, we conjecture that compatible helical transformations with low hysteresis and fatigue resistance would exhibit an unusual shape memory effect involving both twist and extension. The example we give for the application side is the phase-transforming helical Miura origami (HMO). An HMO is the origami structure generated by applying a helical group on a unit cell. The unit cell here is a partially folded four-fold Miura parallelogram. Here we demonstrate the methodology to construct a closed HMO and study its phase transformation properties. To do this, firstly, we conduct a rigorous analysis of the kinematics of the unit cell. We show that, by choosing discrete Abelian group generators and satisfying special discrete conditions, the HMO is generated to close itself at some isolated folding angle, which also means the structure is rigid. Furthermore, inspired by compatible interfaces we have in helical structures, we show that compatible horizontal and helical interfaces occur between two variants − the two different ways of folding for the same unit cell. By transforming one variant to the other, finally, we achieve overall twist and extension actuation, which can be used to develop novel actuators and artificial muscles.