Revealing Strain Effects on the Graphene-Water Contact Angle Using a Machine Learning Potential

Abstract

Understanding how water wets graphene is critical for predicting and controlling its behavior in nanofluidic, sensing, and energy applications. A key measure of wetting is the contact angle made by a liquid droplet against the surface, yet experimental measurements for graphene span a wide range, and no consensus has emerged for free-standing graphene. Here, we use a machine learning potential with approaching ab initio accuracy to perform nanosecond-scale molecular dynamics and provide an atomistic first-principles benchmark for this unsolved problem. We find the contact angle of water on free-standing graphene, after finite-size correction, to be $72.1 \pm 1.5 °$. We also show that the three-phase contact line of a nanoscale water droplet couples strongly to the intrinsic thermal ripples of free-standing graphene, and that graphene's wetting properties are highly sensitive to mechanical strain. Tensile strain makes graphene significantly more hydrophobic, while compressive strain induces coherent ripples that the droplet "surfs", resulting in pronounced anisotropic wetting and contact angle hysteresis. Our results demonstrate that graphene's wetting properties are governed not only by its chemistry but also by its dynamic morphology, offering an additional explanation for the variability of experimental measurements. Furthermore, mechanical strain may be a practical route to controlling wetting in graphene-based technologies, with promising consequences for nanofluidic and nano-filtration applications.

Figures (3)

• Figure 1: Finite-size corrected contact angle for water on free-standing graphene.(a) Cross-section of a snapshot of a spherical droplet of 4,680 water molecules on a free-standing, fully-dynamical graphene sheet, with the droplet's time-averaged interface overlaid in blue. The contact angle is determined as described in the \ref{['sec:methods']} section and schematically illustrated here in green. (b) The microscopic contact angle for droplets of varying size from different models, plotted against the radius of the three-phase contact line $a$. The dashed lines indicate the best-fit corrections following \ref{['eq:finite-size-correction']}, whose extrapolation yields the finite-size corrected macroscopic contact angles. The plotted points for the Ma et al. potential (green) were extracted from Ref. Ma2016/10.1038/nmat4449, while the points for the Carlson et al. potential (pink) were obtained through our own simulations on spatially frozen graphene.
• Figure 2: Effects of a water nanodroplet on graphene's rippling dynamics under tensile strain.(a) A representative snapshot of a droplet of 1,000 molecules, which was simulated under varying tensile strain conditions applied biaxially to the graphene sheet. The translucent green plane indicates the cross-section, which panels (c) and (d) pertain to. (b) The dynamics of the graphene rippling were studied via the local inclination angle $\theta_{\text{GS}}$ relative to the $z$-axis, and its normalized temporal autocorrelation function $\mathcal{C}_{\text{GS}}(\tau)$ as defined in \ref{['eq:long_time_incl_corr']}; this is further elaborated in \ref{['sec:methods']}. The graph shows two examples of $\mathcal{C}_{\text{GS}}(\tau)$ plotted against $\tau$ for two locations on the free-standing graphene sheet. In general, the autocorrelation functions decay exponentially from unity to some well-defined long-time limit, but this limiting value is affected by both location relative to the droplet edge and strain. (c) The time-averaged $z$-coordinate of the graphene sheet along the cross-section for each strain condition, with the time-averaged droplet interface for the free-standing case overlaid. The graph is plotted with a 5:1 aspect ratio to highlight the distortion of the sheet. (d) The long-time inclination correlation $\mathcal{C}_{\text{GS}}(\tau\to\infty)$ along the cross-section for each strain condition. The density of the first water contact layer for the free-standing case is overlaid in the background, to illustrate the location of the droplet edge.
• Figure 3: Effects of mechanical strain, from compressive (negative) to tensile (positive), on graphene's wetting properties.(a) The microscopic contact angle for a droplet of 1,000 water molecules is affected by the biaxial strain applied upon the graphene sheet. When unstrained, or placed under tensile strain (right side of vertical divider), the graphene sheet ripples randomly due to thermal fluctuations, and increasing tensile strain suppresses these ripples and also increases the contact angle (dashed blue line is a guide to the eye). On the other hand, compressive strains greater than or equal to approximately $-0.2\%$ (left side of vertical divider) cause the graphene sheet to form a long-ranged coherent ripple wave which the droplet "surfs"; as such the droplet exhibits a distribution of anisotropic contact angles, shown here as a violin plot with maximum and minimum values marked. (b--d) Representative snapshots of the graphene sheet and time-averaged droplet interface illustrated in blue under (b) $-2.0\%$ compressive strain, (c) free-standing conditions, and (d) $+2.0\%$ tensile strain, with the carbon atoms color-coded according to their instantaneous $z$-coordinate. Snapshots (c) and (d) share the same color scale, while snapshot (b) is shown with a different color scale as the displacements are an order of magnitude larger. The coherent rippling of the graphene sheet, and "surfing" position of the anisotropic droplet, under compressive strain is seen in snapshot (b).