Effects of functional group mass variance on vibrational properties and thermal transport in graphene

Intrinsic thermal resistivity critically depends on features of phonon dispersions dictated by harmonic interatomic forces and masses. Here we present the effects of functional group mass variance on vibrational properties and thermal conductivity ($\kappa$) of functionalized graphene from first-principles calculations. We use graphane, a buckled graphene backbone with covalently bonded hydrogen atoms on both sides, as the base material and vary the mass of the hydrogen atoms to simulate the effect of mass variance from other functional groups. We find nonmonotonic behavior of $\kappa$ with increasing mass of the functional group and an unusual crossover from acoustic-dominated to optic-dominated thermal transport behavior. We connect this crossover to changes in the phonon dispersion with varying mass which suppress acoustic phonon velocities, but also give unusually high velocity optic modes. Further, we show that out-of-plane acoustic vibrations contribute significantly more to thermal transport than in-plane acoustic modes despite breaking of a reflection-symmetry-based scattering selection rule responsible for their large contributions in graphene. This work demonstrates the potential for manipulation and engineering of thermal transport properties in two-dimensional materials toward targeted applications.

Figure 1

Calculated room temperature $\kappa$ for functionalized graphene versus functional group mass (black-dotted curve). The dashed red curve gives the $\kappa$ contribution from acoustic modes, while the dashed blue curve gives that from optic modes. First-principles calculated $\kappa$ for graphane (purple square) and fluorographene (purple triangle) from Ref. [27] are also given. The inset shows the structure of these systems.

Figure 2

Phonon dispersion of graphane (C-${}^1\mathrm{H}$; solid black curves), C-deuterium (C-${}^2\mathrm{H}$; dashed red curves), and C-tritium (C-${}^3\mathrm{H}$; dotted blue curves) in the $\mathrm{\Gamma }\to M\to K\to \mathrm{\Gamma }$ high-symmetry directions.

Figure 3

Accumulated $\kappa \left(\omega \right)$ versus frequency for C-${}^1\mathrm{H}$ (blue curve), C-${}^3\mathrm{H}$ (black curve), C-${}^5\mathrm{H}$ (red curve), C-${}^{10}\mathrm{H}$ (green curve), C-${}^{30}\mathrm{H}$ (orange curve), and C-${}^{60}\mathrm{H}$ (purple curve). Each curve is scaled by the corresponding calculated total $\kappa$ for each system: 1718, 911, 637, 417, 284, and $376\mathrm{W}/\mathrm{m}\mathrm{K}$, respectively. The maximum acoustic frequency for each system is marked by corresponding colored arrows. Accumulated $\kappa \left(\omega \right)$ is given by $\kappa \left(\omega \right)={\sum }_{\vec{q}j}{C}_{\vec{q}j}{v}_{\vec{q}j\alpha }^2{\tau }_{\vec{q}j\alpha }\theta (\omega -{\omega }_{\vec{q}j})$ where $\theta$ is the Heavyside step function, zero for $\omega -{\omega }_{\vec{q}j}<0$ and 1 for $\omega -{\omega }_{\vec{q}j}>0$. Other terms are defined in the text.

Figure 4

Phonon dispersion of two highly dispersive optic branches and the LA branch in the $\mathrm{\Gamma }\to M$ direction for C-${}^3\mathrm{H}$ (black curves), C-${}^5\mathrm{H}$ (red curves), C-${}^{10}\mathrm{H}$ (green curves), C-${}^{30}\mathrm{H}$ (orange curves), and C-${}^{60}\mathrm{H}$ (purple curves).

Figure 5

Calculated $\kappa$ contributions for in-plane acoustic modes (green curve), out-of-plane acoustic modes (red curve), and optic modes (blue curve) versus functional group mass. Values are scaled by the total $\kappa$ for each system. Also given is the calculated $\kappa$ with phonon-isotope scattering from natural carbon concentrations scaled by $\kappa$ of the isotopically pure systems (black curve).