# Further insights into the thermodynamics of linear carbon chains for temperatures ranging from 13 to 300 K

## TL;DR

This study explores the thermodynamic behavior of linear carbon chains at low temperatures, extending previous findings and refining key parameters like thermal expansion and specific heat.

## Contribution

The study provides more accurate temperature derivatives and extends thermodynamic analysis of LCC to lower temperatures (13–293 K).

## Key findings

- Thermal properties like Grüneisen parameters are refined with corrected derivatives of C-band frequency.
- Isolated and bundled LCC@MWCNT show similar vibrational and thermodynamic properties.
- Thermodynamic parameters remain stable despite corrected frequency derivatives.

## Abstract

It was recently shown that small bundles of linear carbon chains (LCC) encapsulated by double- and multi-wall carbon nanotubes (LCC@DWCNT and LCC@MWCNT, respectively) behave as Debye’s materials for temperatures as high as 293 K with an estimate that such materials could still withstand such characteristics for even higher temperatures (≈700 K). Using the Debye model, thermodynamic observables (internal energy, coefficient of linear thermal expansion, specific heat, thermal strain, and Grüneisen parameter at constant pressure) were empirically determined for the first time in the range of temperatures 70 < T < 293 K. These observables were all correlated with the C-band frequency (ωLCC) dependence on the temperature (T) and its first and second derivatives with relation to T, dωLCC/dT, and d2ωLCC/dT2. The C-band is a Raman spectroscopic signature for LCC, which is not only temperature-dependent but also dependent on the number of carbon atoms (N) constituting the LCC. In this present study, we extend these findings to temperatures ranging from 13 < T < 293 K, which provide more accurate values for both dωLCC/dT and d2ωLCC/dT2. The corrected values of these derivatives affect the Grüneisen parameters associated with the LCC, even though the other associated thermodynamic parameters remain essentially unchanged. Our measurements were performed in both isolated and small bundles of LCC@MWCNT, which allowed us to demonstrate that small bundles or isolated environments do not seem to influence the vibrational and thermodynamic properties measured.