Impact of density and disorder on the low-temperature heat capacity of carbon–carbon composites

The low-temperature specific heat of expanded graphite (EG) and EG–multiwalled carbon nanotube (MWCNT) composites (1.0, 3.0 wt. % MWCNTs) was investigated over the temperature range of 2–300 K. The results reveal that the heat capacity of pure EG and EG–MWCNT composites is primarily governed by low-frequency out-of-plane phonons with quadratic dispersion, characteristic of two-dimensional layered systems. These flexural phonon modes dominate vibrational behavior at cryogenic temperatures. Compared to bulk crystalline graphite, EG exhibits higher heat capacity at low temperatures due to its increased defect density, structural disorder, and reduced interlayer coherence. X-ray diffraction and Raman spectroscopy measurements of the structure supported by energy-dispersive x-ray spectroscopy analysis confirmed the variations in the stacking order, defect concentration, and impurity levels. Heat capacity was effectively described by a three-term equation: a defect-related linear term (C1T), a Debye phonon term (C3T3), and a dispersive phonon term (C5T5). A strong correlation was observed between the linear coefficient (C1) and EG density, validated by the Raman I2D/IG ratio. The negative C5 coefficient in EG samples confirms the quadratic dispersion of flexural phonons, aligning with the Komatsu–Nagamiya phonon model and emphasizing EG's anisotropic vibrational properties. The absence of a low-temperature hump, typical in disordered solids, further supports the two-dimensional phonon behavior. These findings highlight the impact of MWCNT integration and structural disorder on the vibrational heat capacity of EG-based composites, offering insight into phonon dynamics in anisotropic carbon systems.