Ripple edge engineering of graphene nanoribbons

It is now possible to produce graphene nanoribbons (GNRs) with atomically defined widths. GNRs offer many opportunities for electronic devices and composites, if it is possible to establish the link between edge structure and functionalization, and resultant GNR properties. Switching hydrogen edge termination to larger more complex functional groups such as hydroxyls or thiols induces strain at the ribbon edge. However, we show that this strain is then relieved via the formation of static out-of-plane ripples. The resultant ribbons have a significantly reduced Young’s modulus, which varies as a function of ribbon width, modified band gaps as well as heterogeneous chemical reactivity along the edge. Rather than being the exception, such static edge ripples are likely on the majority of functionalized graphene ribbon edges.

Figure 1

H-terminated AGNR, unit cells shown by dotted frames, definition of armchair ribbon width shown by numbers[24] with width six. C atoms are shown grey and H atoms are white.

Figure 2

(a)–(c) Three OH-terminated armchair edge structures: A (metastable base symmetric structure), B (metastable with hydrogen bonding), and C (stable ground state structure with static rippling). (d)–(e) Stable OH-terminated AGNR of type C (width six), (d) perspective view of ribbon and (e) side view with clearly visible rippled edge. Dotted lines are a guide to the eye for the GNR. $u$ stands for “up” and $d$ for “down” for the rippled edge. C atoms are in grey, O atoms are in red, and H atoms are white (same for Figs. 4, 5, and 7).

Figure 3

(a) Energy difference $\Delta U$ between structure A (black) and structure B (green), referring to structure C (blue), vs ribbon width from 4 to 20. (b) Strain along the ribbon ($x$ axis, see Fig. 1), strain is referenced to a perfect flat graphene sheet ($\epsilon =0$%), H termination (red), A (black), B (green), and C (blue). Fits with $\epsilon \left(x\right)=\frac{a}{x^2}+\frac{b}{x}+c$ (the fit parameters are given in Supplemental Material.[25]) The top scale of (a) and (b) in Å  is taken from perfect flat graphene with C-C bond lengths of $d_{c-c}=1.41$ Å  as guide for the eye (also for Fig. 6).

Figure 4

Front view of -OH terminated AGNRs (stable structure C) with (a) width 6, (b) width 12, and (c) width 18.

Figure 5

Pd atom addition to a -OH terminated AGNR (width 10). (a) “Ridge top” site and (b) “valley” site, which is $\Delta U=-0.4$ eV more stable.

Figure 6

(a) Energy gap vs width for different terminated AGNRs. H-terminated AGNR (red), structure B (green), and structure C (blue). (b) Young’s modulus $E$ along the AGNRs (in case of graphene, along the armchair direction). $E$ fitted with $E=\frac{a}{x}+\frac{b}{x^2}+c$ as guide for the eye (fit parameter in Supplemental Material.[25])

Figure 7

Chiral -OH terminated GNR; (a) perspective view, (b) side view, and (c) front view.

Figure 8

AGNR (width 7) -SH terminated; (a) perspective view, (b) side view, and (c) front view. In grey, C atoms are pictured, H atoms are in white, and S atoms are yellow. $u$ stands for “up” and $d$ for “down” for the rippled edge.