Theory of Liquid Film Growth and Wetting Instabilities on Graphene

We investigate wetting phenomena near graphene within the Dzyaloshinskii-Lifshitz-Pitaevskii theory for light gases of hydrogen, helium, and nitrogen in three different geometries where graphene is either affixed to an insulating substrate, submerged or suspended. We find that the presence of graphene has a significant effect in all configurations. When placed on a substrate, the polarizability of graphene can increase the strength of the total van der Waals force by a factor of 2 near the surface, enhancing the propensity towards wetting. In a suspended geometry unique to two-dimensional materials, where graphene is able to wet on only one side, liquid film growth becomes arrested at a critical thickness, which may trigger surface instabilities and pattern formation analogous to spinodal dewetting. The existence of a mesoscopic critical film with a tunable thickness provides a platform for the study of a continuous wetting transition, as well as the engineering of custom liquid coatings. These phenomena are robust to some mechanical deformations and are also universally present in doped graphene and other two-dimensional materials, such as monolayer dichalcogenides.

Figure 1

Three geometries that are unique to wetting on two-dimensional materials. (Substrate) Graphene with a momentum- and frequency-dependent electronic polarization $\mathrm{\Pi }(\mathit{q},i\omega )$ is placed on top of an insulating substrate with dielectric constant ${ϵ}_3$, and a macroscopic liquid film with ${ϵ}_2$ grows to a thickness $d$ that is in equilibrium with its vapor (${ϵ}_1\approx 1$). (Submerged) Graphene is floated on top of a liquid with dielectric constant ${ϵ}_2$, and a liquid film of the same substance grows on the top side. (Suspended) A liquid film grows on top of a pensile graphene sheet.

Figure 2

Additional liquid film thickness dependence $\mathrm{\Gamma }(d)$ (beyond $1/d^3$) of the van der Waals force between the substrate-liquid and liquid-vapor interfaces due to the insertion of graphene on a ${\mathrm{SiO}}_2$ substrate. The dashed line represents the substrate contribution (in the absence of graphene) and a crossover from $1/d^4$ to $1/d^3$ is observed. Left vertical scale corresponds to helium and the right to nitrogen films.

Figure 3

Thickness dependence of the van der Waals interaction $\mathrm{\Gamma }(d)$ for films formed on submerged and suspended graphene (see Fig. 1) composed of helium, hydrogen, and nitrogen. The dashed line corresponds to films on graphite taken from Cheng and Cole [26]. For submerged graphene, $\mathrm{\Gamma }(d\to \infty )=0$ and in the suspended geometry, there is an instability causing film growth to be arrested where $\mathrm{\Gamma }(d\ge d_c)\le 0$.

Figure 4

Chemical potential of the liquid film (in reference to the bulk) $\mathrm{\Delta }\mu$ as a function of distance $d$ for suspended graphene. An instability corresponding to $\mathrm{\Delta }\mu >0$ is found for helium, hydrogen, and nitrogen at a finite value of $d=d_c$. (Inset) Enlarged region of the main panel showing $d_c$ for He and ${\mathrm{H}}_2$. Values of $d_c$ are reported in Table 1.