Phonon transport in graphene has been extensively studied due to its exceptional thermal conductivity and potential applications in thermal management. Experimental techniques such as Raman thermometry and theoretical models have provided insights into phonon behavior, particularly in suspended versus supported graphene configurations. The interaction between graphene and substrates significantly influences phonon transport, with implications for heat dissipation in electronic devices.

Raman thermometry is a widely used experimental method to measure thermal properties of graphene. This technique relies on the temperature-dependent shift of the G-peak in the Raman spectrum. By calibrating the G-peak shift with temperature, researchers can map local temperature distributions and extract thermal conductivity. For suspended graphene, measurements have reported room-temperature thermal conductivity values ranging from 2000 to 5000 W/mK, among the highest of any known material. In contrast, supported graphene exhibits reduced thermal conductivity, typically between 600 and 1000 W/mK, due to phonon scattering at the graphene-substrate interface.

Theoretical models of phonon transport in graphene often employ Boltzmann transport equation (BTE) approaches or molecular dynamics (MD) simulations. BTE-based models account for phonon-phonon scattering (Umklapp and normal processes) and boundary scattering, while MD simulations provide atomistic insights into phonon dispersion and lifetimes. In suspended graphene, phonon transport is dominated by intrinsic scattering mechanisms, with long phonon mean free paths (MFPs) contributing to high thermal conductivity. Optical phonons play a negligible role in heat conduction due to their low group velocities, while acoustic phonons (longitudinal, transverse, and flexural modes) dominate thermal transport.

Substrate coupling introduces additional scattering pathways that degrade thermal conductivity. When graphene is placed on a substrate such as SiO2 or hexagonal boron nitride (hBN), phonons scatter at the interface due to mismatch in vibrational spectra and interfacial roughness. Studies have shown that the thermal conductivity of supported graphene decreases with stronger substrate interactions. For example, graphene on amorphous SiO2 exhibits greater suppression of thermal conductivity compared to graphene on crystalline hBN, where the latter provides a smoother interface with better phonon mode matching.

The flexural (out-of-plane) phonon modes in graphene are particularly sensitive to substrate effects. In suspended graphene, these modes have low frequencies and contribute significantly to thermal transport due to their long MFPs. However, when graphene is supported, substrate interactions suppress flexural phonons, leading to a reduction in thermal conductivity. Measurements and simulations confirm that the suppression of flexural modes accounts for a substantial portion of the thermal conductivity reduction in supported graphene.

Applications in thermal management leverage graphene's high thermal conductivity and tunable interfacial interactions. For instance, graphene-based thermal interface materials (TIMs) can enhance heat dissipation in electronics by minimizing thermal boundary resistance. By optimizing substrate coupling, researchers aim to balance mechanical stability with thermal performance. Suspended graphene is ideal for high-performance thermal applications where minimal phonon scattering is desired, while supported graphene offers practical advantages for integration into devices.

Comparative studies between suspended and supported graphene highlight trade-offs in thermal performance. The table below summarizes key differences:

Thermal Property Suspended Graphene Supported Graphene
Thermal Conductivity 2000-5000 W/mK 600-1000 W/mK
Dominant Scattering Intrinsic phonon-phonon Substrate interface
Phonon MFP Long (microns) Short (nanometers)
Flexural Phonon Role Significant Suppressed

Future research directions include exploring engineered substrates to mitigate phonon scattering and hybrid structures that combine suspended and supported regions for optimized thermal management. Understanding substrate coupling effects at the atomic level will enable precise control over thermal transport in graphene-based devices.

In summary, phonon transport in graphene is highly dependent on its environment, with suspended graphene exhibiting superior thermal conductivity compared to supported configurations. Experimental techniques like Raman thermometry and theoretical models provide valuable insights into phonon-substrate interactions, guiding the development of graphene-based thermal management solutions. Advances in substrate engineering and interfacial design will further enhance the performance of graphene in heat dissipation applications.