Extracting Thermodynamic\nProperties of Carbyne from\nTip-Enhanced Raman Scattering Images

The measurement of thermodynamic properties for nanosystems\nis\nessential to comprehend the inherent characteristics of nanomaterials.\nTraditional spectroscopy measurements, such as Raman or ultraviolet–visible\nspectroscopies, are limited to offering insights near the Γ\npoint in the Brillouin zone and thus cannot precisely determine the\nsystem’s thermodynamic properties, for example, heat capacity.\nUtilizing the intrinsic broad momentum distribution in highly confined\nplasmonic fields, here we take <i>sp</i>-hybridized carbyne\nas a proof-of-the-principle example to show that ultrahigh-resolution\ntip-enhanced Raman scattering (TERS) images have the ability to access\nall <i>k</i>-points in the phonon Brillouin zone of one-dimensional\nnanosystems, allowing the comprehensive determination of vibrational\nfeatures and heat capacity for finite carbon chains. Comparing phonon\ndispersion spectra and heat capacities under different boundary conditions,\ni.e., linear carbon chains and cyclic carbon molecules, we find that\nthe heat capacities of linear structures converge more rapidly than\nthe counterparts of cyclic structures to the benchmark of ideal carbyne.\nWe also study the effects of different terminal groups in linear structures\nas well as the aromaticity in cyclic structures on heat capacity.\nThis study provides a practical method for characterizing the thermodynamic\nproperties of nanosystems, demonstrating the potential applications\nof TERS imaging in nanomaterial science.