Heat Capacity of Thermally Reduced Graphene Oxide: Compaction and Thermal Annealing Effects

We present a comprehensive investigation of the low-temperature heat capacity of thermally reduced graphene oxide (trGO) as a function of compaction pressure and annealing temperature. Graphene oxide was synthesized using a modified Hummers method and subsequently thermally reduced at 300\,{\deg}C, 500\,{\deg}C, and 700\,{\deg}C under vacuum to systematically vary the oxygen content and structural ordering. The specific heat data in the 2--300\,K range reveal that the thermal response is governed by phonons, including contributions from a Schottky-type anomaly, a defect-related linear term, a Debye term, and a dispersive term with a negative coefficient associated with out-of-plane flexural (ZA) phonons. Increasing compaction pressure alters interlayer coupling and leads to non-monotonic changes in heat capacity, while higher annealing temperatures enhance graphitization, reduce disorder, and modify phonon dispersion. The absence of a boson peak -- similar to that observed in carbon nanotubes -- supports the dominance of two-dimensional vibrational modes. These findings elucidate the relationship between dimensionality, structural disorder, and processing parameters in shaping the phonon dynamics of trGO, providing guidance for tailoring its thermal behavior in advanced carbon-based functional materials.