Viscous peeling of a nanosheet

Combining molecular dynamics (MD) and continuum simulations, we study the dynamics of propagation of a peeling front in a system composed of multilayered graphene nanosheets completely immersed in water. Peeling is induced by lifting one of the nanosheet edges with an assigned pulling velocity normal to the flat substrate. Using MD, we compute the pulling force as a function of the pulling velocity, and quantify the viscous resistance to the advancement of the peeling front. We compare the MD results to a 1D continuum model of a sheet loaded with modelled hydrodynamic loads. Our results show that the viscous dependence of the force on the velocity is negligible below a threshold velocity. Above this threshold, the hydrodynamics is mainly controlled by the viscous resistance associated to the flow near the crack opening, while lubrication forces are negligible owing to the large hydrodynamic slip at the liquid-solid boundary. Two dissipative mechanisms are identified: a drag resistance to the upward motion of the edge, and a resistance to the gap opening associated to the curvature of the flow streamlines near the entrance. Surprisingly, the shape of the sheet was found to be approximately independent of the pulling velocity even for the largest velocities considered.

1 Peeling force vs edge height from the continuum model We use eq.(27) in the main article to calculate the pressure drop at entrance and COMSOL simulations to calculate the edge drag force (see Fig.10a in the main article). The edge drag force is applied as a concentrated force at the left edge.
The increase in F with v is qualitatively similar to that suggested by the MD data. The agreement is not perfect because these continuum estimated of entrance pressure drop and drag force are 1D approximations for small deflections of the sheet.

Molecular dynamics details 2.1 Method
We use the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) force field to model graphene 1 , the TIP4P/2005 model for water 2 and the all-atom Gromos force field for NMP 3 . Carbonwater interaction parameters are calculated using the Lorentz-Berthelot mixing rule. Water molecules are maintained at a constant temperature T = 300 K using a Nosé-Hoover temperature thermostat 4,5 .

Peeling in vacuum
We have carried out simulations of peeling of graphene in vacuum for v = 0 (quasi-steady case) and v = 100 m/s. Fig. S2 shows that there is no difference in F for the two velocities in the case of vacuum. Contrarily, the increase in force is evident for water at v = 100 m/s. We have performed peeling simulations of graphene in N-Methyl-2-pyrrolidone (NMP) for v =1, 10 and 50 m/s. We find that the F vs h 0 shows characteristic similarities to the case of water (Fig.S3). Interestingly, we notice a wavy pattern in the case of NMP. Shih et al. have recently reported that the potential between graphene sheets exhibit an oscillatory pattern in NMP 6 . The large size of NMP molecules can also cause nanofluidic effects, for example, fluid structuring or disjoining pressure 7 .

A COMSOL analysis of the entrance pressure drop for 2D circular entrances with infinite-slip walls
We have carried out COMSOL simulations for a system in which fluid from a reservoir is flowing into a stationary channel of width a through a circular entrance with a constant radius of curvature R, as shown in the inset of Fig. S4. In these simulations, we solve the incompressible Stokes equations with free slip boundary condition at all surfaces. We impose a flux Q at the right end of the channel. The reservoir height and width of the computational domain is 100R × 100R to avoid finite size effect. We measure the pressure difference (∆P ) between the far edge of the reservoir and the channel outlet. We plot ∆P/P 0 as a function of R/a (Fig. S4) where P 0 is the pressure difference given by Hasimoto's formula 8 (Eq.24). We analytically solve for the pressure drop in the converging channel. Using Stokes equation at the Using dimensional arguments, the velocity gradient can be estimated as is the y-averaged fluid velocity below the sheet and δ(x) is the local length scale over which U (x) varies. Thus, a simple model for the horizontal pressure gradient is dp dx . (S1) It is expected that this pressure gradient is a function of the curvature of the channel 9 . The pressure drop corresponding to eq.S1, We know from Hasimoto's result that lim R→0 ∆P −8µQ/πa 2 . This suggests that δ 2 (x) −πhR/8 as h → a for R → 0, thus We compare the results of Eq.S3 with the COMSOL simulations described above in Fig. S4. Both the analytical and numerical results show a plateau for R/a ≤ 1, approximately, and a region for R/a > 1 for which ∆P decays. The decay rate predicted by COMSOL results for large values of R/a is very close to the one found numerically using Eq.S3, i.e., for R/a 1, ∆P/P 0 follows the power-law (R/a) −1/2 . For R/a ≤ 1, the COMSOL results for ∆P/P 0 are a 25 % larger than the numerical prediction as expected 9,10 , i.e., for a costant Q, ∆P predicted by Hasimoto's formula (Eq.24) is nearly 20% lower in magnitude than ∆P predicted using COMSOL.