Anharmonicity and Universal Response of Linear Carbon Chain Mechanical Properties under Hydrostatic Pressure

Isolated linear carbon chains (LCCs) encapsulated by multiwalled carbon nanotubes are studied under hydrostatic pressure (P) via resonance Raman scattering. The LCCs' spectroscopic signature C band around 1850 cm^{-1} softens linearly with increasing P. A simple anharmonic force-constant model not only describes such softening but also shows that the LCCs' Young's modulus (E), Grüneisen parameter (γ), and strain (ϵ) follow universal P^{-1} and P^{2} laws, respectively. In particular, γ also presents a unified behavior for all LCCs. To the best of our knowledge, these are the first results reported on such isolated systems and the first work to explore universal P-dependent responses for LCCs' E, ϵ, and γ.