Wettability of partially suspended graphene

The dependence of the wettability of graphene on the nature of the underlying substrate remains only partially understood. Here, we systematically investigate the role of liquid-substrate interactions on the wettability of graphene by varying the area fraction of suspended graphene from 0 to 95% by means of nanotextured substrates. We find that completely suspended graphene exhibits the highest water contact angle (85° ± 5°) compared to partially suspended or supported graphene, regardless of the hydrophobicity (hydrophilicity) of the substrate. Further, 80% of the long-range water-substrate interactions are screened by the graphene monolayer, the wettability of which is primarily determined by short-range graphene-liquid interactions. By its well-defined chemical and geometrical properties, supported graphene therefore provides a model system to elucidate the relative contribution of short and long range interactions to the macroscopic contact angle.


SI1: Graphene wrinkles formation
The transfer method used in this study leads to the formation of wrinkled graphene layers.
In order to get insight in the formation of the folds, we observed graphene layers during all steps of the process. The pattern of folds is not correlated to the grain boundaries of the copper foil supporting the graphene layer at the initial stage. Moreover, PMMA-assisted transfer of the same graphene sample did not show the presence of any wrinkle, indicating that the folding occurs latter in the process. Indeed, it was observed that the graphene layer is already folded when lying at the liquid interface (see Fig SI1) showing that folds do not result from the drying of the liquid layer on the substrate. The wrinkling therefore occurs at the liquid interface, due to surface tension effects when the copper foil is etched away. Indeed, the first millimeter in the periphery of the graphene layer is fully crumpled which is useful to visualize the graphene sheet floating at the liquid interface.

SI2: Characterization of suspended graphene layers
The partially supported graphene layers were characterized by SEM and AFM. The patterns of folds present the same characteristics as the ones observed on flat substrates. They are clearly evidenced in the images (see Fig. SI2a, SI2c and SI2d), together with the holes in the layer. The main difference with flat substrates lies in the occasional presence, on patterned substrates, of short cracks that propagate following the paths between posts (see  Micro-Raman spectra were acquired on a Horiba Xplora-MV2000 spectrometer in a 1-m focal spot area exempt of visible wrinkle ( Figure SI3c). Two intense peaks are recorded at 1580 cm -1 and 2670 cm -1 that correspond to the G and 2D bands of graphene respectively.
Two weaker peaks at 1330 cm -1 and 2450 cm -1 are the first order D band and the second order D+D" band, 1,2 which characterize defects in the layer. The areal ratio of the 2D and G bands ( 2~4 − 5) together with the single Lorentzian shape of the 2D band are strong indications of a single monolayer. As expected, micro-Raman spectra measured on wrinkles exhibit a much more intense D band due to a higher density of defects in these regions.

SI4: Protocol for contact angle measurements on supported graphene layers
The contact angle measurements were performed on a Kruss DSA100 goniometer. In order to optimize the protocol to achieve contact angle measurements of water on graphene layers, we transferred on SiO 2 /Si flat samples, graphene layers from three different commercially available graphene sources (two from Graphene Supermarket Inc. USA and one from Graphenea, SP) grown on copper surfaces by chemical vapor deposition (CVD). After transfer the samples were cleaned using the annealing procedure described in the previous section.
Advancing and receding contact angles were measured on several graphene regions, immediately after the reductive annealing and for a few hours afterwards (see Figure SI4) in order to probe the dynamics of airborne contaminants re-adsorption. The results show no influence of the graphene source. Importantly, the measurements on flat substrates reveal an increase of the contact angle with time, in agreement with recent reports. 3,4 In particular, the advancing contact angle increases from 68° ± 1 ° reaching a plateau at 85° ± 2° when exposed to ambient air, in agreement with the results of Li et al.. 3 However, we have found that the wettability change occurs on a time scale of ca. 5 hours rather than 1h, as reported in ref. 2a, provided that the cleaned samples are kept under nitrogen atmosphere at all time. In agreement with recent AFM force measurements, 5 this evolution of the advancing angle is attributed to the decrease in effective surface energy as water and airborne hydrocarbon contaminants adsorb on graphene. For these reasons, all the contact measurements reported here were performed within ten minutes from the end of annealing process. Conversely, the receding contact angle was found not to vary significantly ( rec = 45° ± 2°) after the annealing process, suggesting that this quantity is dominated by pinning of the receding contact line on anchoring defects, 6 which are present after the transfer of graphene but do not evolve in time. The repeatability of the contact angle measurements was checked by performing identical experiments on six different layers transferred on flat Si/SiO 2 surfaces pre-cleaned by sulfuric 9 acid and hydrogen peroxide solution. The results show that the value of the advancing contact angle is highly reproducible (standard deviation < 1°) while receding contact angle values are more spread (s.d. > 9°). This is also consistent with the conclusions of Raj et al. 6 and suggests that the advancing contact angle provides a more reliable measure of the intrinsic wettability of graphene compared to the receding angle, which is more influenced by monolayer defects.
For this reason, we only report advancing contact angles measurements.

SI5: Influence of defects
In order to assess the influence of defects in the graphene layer, we considered a graphene layer with a contact angle assumed independent of the underlying substrate and with a density of defects (holes) Φ . The contact angle of the defective layer can then be calculated using a Cassie-Baxter equation using the substrate contact angle for the defects. It reads On Fig. SI5, the expression given by Eq. (1) is plotted for two different density of defects namely Φ =2% and 8%. As expected the influence of defects increases with defects density.
For Φ = 2% which corresponds to the majority of samples studied, the variation of contact angle is negligible. On sharp textures, the density of defects increases up to Φ = 8% which may explain part of the evolution of contact angle measured experimentally.

SI6: Wettability of multilayer graphene and graphite
In a rough approximation, the wettability of multilayer graphene can be estimated graphically Indeed, the contact angle on n+1 layers can be determined from the contact angle on n layers using the = ( ) relation deduced experimentally. This leads to can then be used to compute ( +2) . This can be simply obtained graphically using the diagonal of the graph as shown on Figure SI6a starting from a suspended single monolayer. The same could be obtained for multilayer graphene floating on water, starting from = 1, or from any situation. In Figure SI6b are reported the contact angles as a function of the number of layers in both situations. It shows that both values converges rapidly towards a value which corresponds to the contact angle on HOPG i.e the stack of an infinite number of graphene layers. This convergence is rather fast since the contact angle value for a 3-layers (4-layers) configuration approaches the one of HOPG value within 0,7° (0,14°), respectively.