Spatial confinement model applied to phonons in disordered graphene-based carbons

Analyzing the various bands in Raman spectra, mostly the G (optical carbon-carbon mode) and D (defect-related double resonance process) bands, is powerful at characterizing defects in disordered graphene-based carbons. The crystallite size La could be estimated from the ID/IG (intensity) or AD/AG (area) ratio, but with large uncertainties. Using the spatial confinement model (SCM) of the phonons has fully explained the linewidth variation for the D band, but could not explain the linewidth variation for the G band over the whole La range. Indeed, if the latter for large, Bernal-stacked graphenes is due to the Kohn anomaly and can be explained considering phonon dispersion curves, turbostratically-stacked graphenes with small La generate an additional broadening of the G band not accounted by the phonon-related SCM only. The realistic SCM proposed here explains the way the G band shape is related to La. The model was also validated by successfully duplicating the evolution of the D (mostly related to the electronic band dispersion) and D′ band linewidths with decreasing La down to 5 nm. The work aims to be a guide for future computational works on Raman spectra of graphene-based carbon materials.