A Thermomechanical Framework for the Critical Temperature in Nanotube Structural Transitions

Abstract Thermally induced structural transitions in nanotubes between cylindrical and collapsed states are central to their applications in nanotechnology. Despite extensive research, the explicit determination of the critical temperature governing this phase boundary remains theoretically challenging. Here, we address this by developing a thermomechanical framework quantifying three energetic contributions: adhesion, elasticity, and configurational entropy. The model links geometric parameters (diameter, wall number) to material properties (bending stiffness, interlayer interactions), yielding an analytical formula for the critical temperature. The formula shows that the critical temperature increases steadily with diameter, approaching an asymptote set by the ratio of interlayer adhesion to entropy change and hitting zero at a critical diameter linked to the ratio of bending stiffness to adhesion. Molecular dynamics simulations for carbon nanotubes validate the framework. Our work not only deepens our fundamental understanding of nanotube thermomechanics but also furnishes a powerful predictive tool for tailoring the thermal response of nanodevices.