Extracting Thermodynamic Properties of Carbyne from Tip-Enhanced Raman Scattering Images

The measurement of thermodynamic properties for nanosystems is essential to comprehend the inherent characteristics of nanomaterials. Traditional spectroscopy measurements, such as Raman or ultraviolet-visible spectroscopies, are limited to offering insights near the Γ point in the Brillouin zone and thus cannot precisely determine the system's thermodynamic properties, for example, heat capacity. Utilizing the intrinsic broad momentum distribution in highly confined plasmonic fields, here we take sp-hybridized carbyne as a proof-of-the-principle example to show that ultrahigh-resolution tip-enhanced Raman scattering (TERS) images have the ability to access all k-points in the phonon Brillouin zone of one-dimensional nanosystems, allowing the comprehensive determination of vibrational features and heat capacity for finite carbon chains. Comparing phonon dispersion spectra and heat capacities under different boundary conditions, i.e., linear carbon chains and cyclic carbon molecules, we find that the heat capacities of linear structures converge more rapidly than the counterparts of cyclic structures to the benchmark of ideal carbyne. We also study the effects of different terminal groups in linear structures as well as the aromaticity in cyclic structures on heat capacity. This study provides a practical method for characterizing the thermodynamic properties of nanosystems, demonstrating the potential applications of TERS imaging in nanomaterial science.