Theory on quench-induced pattern formation: Application to the isotropic to smectic-A phase transitions

TL;DR

This paper develops a theoretical framework to understand pattern formation during rapid phase transitions, specifically applying it to the isotropic to smectic-A transition and matching experimental observations.

Contribution

It introduces a general mechanism based on heat transfer and energy conversion competition, applied to analyze buckling patterns in smectic-A filaments during quench-induced phase transitions.

Findings

Analytical forms for buckling patterns match experimental data

Rapid cooling induces molecular-level structural transitions

Estimated force of pattern formation is around 0.1 piconewtons

Abstract

During catastrophic processes of environmental variations of a thermodynamic system, such as rapid temperature decreasing, many novel and complex patterns often form. To understand such phenomena, a general mechanism is proposed based on the competition between heat transfer and conversion of heat to other energy forms. We apply it to the smectic-A filament growth process during quench-induced isotropic to smectic-A phase transition. Analytical forms for the buckling patterns are derived and we find good agreement with experimental observation [Phys. Rev. {\bf E55} (1997) 1655]. The present work strongly indicates that rapid cooling will lead to structural transitions in the smectic-A filament at the molecular level to optimize heat conversion. The force associated with this pattern formation process is estimated to be in the order of $10^{-1}$ piconewton.