Hydrogen transport on graphene: Competition of mobility and desorption

The results of molecular dynamics (MD) simulations of atomic hydrogen kinetics on graphene are presented. The simulations involve a combination of approaches based on Brenner carbon-hydrogen potential and first-principles force calculations. Both kinds of MD calculations predict very similar qualitative trends and reproduce equally well the features of hydrogen behavior, even such sophisticated modes as long correlated jump chains. Both approaches agree that chemisorbed hydrogen diffusion on graphene is strongly limited by thermal desorption. This limitation rules out long-range diffusion of hydrogen on graphene but does not exclude the short-range hydrogen diffusion contribution to hydrogen cluster nucleation and growth.

Figure 1

Snapshot of an instantaneous system configuration at 1700 K. Carbon atoms and hydrogen atom are shown as dark gray and light gray (yellow in color) spheres, respectively. The simulation box is also outlined.

Figure 2

Hydrogen atom on graphene. (a) Equilibrium configuration at 0 K; (b) an example of instantaneous configuration during dynamic simulation with Brenner potential at high temperatures (here, 1400 K).

Figure 3

The minimum energy paths for H atom on graphene. Included are the 1NN jump barrier profile predicted by CI-NEB (solid line with shaded background) and PES profiles along the lines connecting 1NN, 2NN, and 3NN carbon atoms (solid, dashed, and dotted lines with circle markers, respectively).

Figure 4

The potential energy surface for a H atom on top of a graphene sheet. Carbon network is marked with straight lines. Open circles (or black dots in color version) indicate calculation points. The correspondence between the shades of gray (colors in color version) and hydrogen energies is shown in the scale bar at the right of the figure.

Figure 5

The potential energy increase of the hydrogen atom in the “drag” simulation experiment.

Figure 6

(a) An example of hydrogen atom trajectory corresponding to an 80-ps-long simulation at 2000 K viewed normal to the $x$-$y$ plane. The initial hydrogen position is at the center of the simulation cell. When the hydrogen is attached to the graphene, its trajectory (dark blue in color) remains close to carbon lattice sites (small hollow circles), whereas the freely flying hydrogen moves along thicker straight lines of different shades (in color—red and green), allowing differentiation between the “up” and “down” flight directions. Thin dashed lines connect the trajectory points at the opposite sides of the simulation cell to guide the eye. (b–d) The enlarged trajectory parts demonstrating 1NN jump (b), 2NN jump (c), and a sequence of 1NN and 2NN jumps (d). The trajectory parts associated with different carbon atoms are shown in light gray (in color version—green, light blue, and violet), whereas those corresponding to hydrogen transitions from one atom to another are shown as thick black lines marked with dots identifying hydrogen positions in consecutively saved snapshots (separated by 4 fs). The freely flying H atom trajectories are straight dark gray (in color—red) lines. In (c), the central part of the jump trajectory, shown in lighter shade of gray (blue in color), indicates hydrogen association with the carbon atom on the site marked with an asterisk.

Figure 7

Various carbon and hydrogen parameters vs. time at 1400 K. (a) C${}_1$-H (dash) and C${}_1$-C${}_2$ (solid) bond lengths, $L_b$; (b) $z$ coordinate of C${}_1$; (c) H-C${}_1$-C${}_2$ dihedral angles $\gamma$. Three solid curves in panels (a) and (c) correspond to different C${}_2$ neighbors of C${}_1$; curves for the same neighbors have the same color in both figures (in color version). Horizontal lines in these figures indicate the equilibrium values of corresponding parameters. All results are from MD simulations with Brenner potential.

Figure 8

Distributions of hydrogen lifetimes (a) and hydrogen diffusion jumps per lifetime (b) at different temperatures, as observed in MD simulations with Brenner potential. The mean values in (a) are shown with vertical dash lines.

Figure 9

The temperature dependence of the average hydrogen lifetimes on graphene (solid symbols) and the average hydrogen on-site residence times (open symbols). Circular symbols are from regular runs with the temperature-independent simulation box size. At the lowest two temperatures, the points for the runs in biaxially compressed (triangles down) and expanded (triangles up) simulation cells are added, as marked in the legend and explained in the text. Straight lines are least squares fits through regular data points (circles) only.

Figure 10

The relative frequencies of different jump lengths (the number of C-C bonds traveled during the jump, as indicated in the legend) at different temperatures.

Figure 11

The distributions of on-site residence times as a function of the hydrogen lifetime on the graphene surface for two simulation temperatures (as indicated in figure legends). Because all hydrogen attachment events have different lifetimes, points with the same abscissa are from one and the same event. Shown are only those events in which at least one diffusion jump per lifetime has occurred.

Figure 12

Snapshot of the instantaneous system configuration after development of a sinusoidal vibration instability. $t$$=$1300 K.

Figure 13

Samples of carbon atom trajectory projections onto the $z$-axis at different times during the same simulation run at 1200 K (top row) and the corresponding temporal Fast Fourier Transform (FFT) amplitudes for these trajectories (bottom row). The sampling time ranges for FFT are indicated in the figure legends.

Figure 14

Example of a hydrogen trajectory in one MD-DFT run projected onto the $x$-$y$ plane. Graphene lattice sites are marked by background gray circles. The straight trajectory sections correspond to free hydrogen flights between opposite graphene surfaces.

Figure 15

(a) Kinetic energy loss in several H detachment events (dashed line is the average of Δ$E$ over all events). (b) Histogram of kinetic energy loss in several jump events.

Figure 16

Several consecutive hydrogen atom configurations within the same diffusion jump in MD-DFT simulations.

Figure 17

Dependence of the average number of hydrogen jumps per lifetime, $n_D$, on the inverse temperature, as predicted by MD simulations with the Brenner potential. The dashed line (with slope corresponding to an activation energy of 0.15 eV) is the least squares fit.