Shear Failure in Supported Two-Dimensional Nanosheet Van der Waals Thin Films

Abstract

Liquid-phase deposition of exfoliated 2D nanosheets is the basis for emerging technologies that include writable electronic inks, molecular barriers, selective membranes, and protective coatings against fouling or corrosion. These nanosheet thin films have complex internal structures that are discontinuous assemblies of irregularly tiled micron-scale sheets held together by van der Waals (vdW) forces. On stiff substrates, nanosheet vdW films are stable to many common stresses, but can fail by internal delamination under shear stress associated with handling or abrasion. This “re-exfoliation” pathway is an intrinsic feature of stacked vdW films and can limit nanosheet-based technologies. Here we investigate the shear stability of graphene oxide and MoSe₂ nanosheet vdW films through lap shear experiments on polymer-nanosheet-polymer laminates. These sandwich laminate structures fail in mixed cohesive and interfacial mode with critical shear forces from 40 – 140 kPa and fracture energies ranging from 0.2 – 6 J/m². Surprisingly these energies are higher than delamination energies reported for smooth peeling of ordered stacks of continuous 2D sheets, which we propose is due to energy dissipation and chaotic crack motion during nanosheet film disassembly at the crack tip. Experiment results also show that film thickness plays a key role in determining critical shear force (maximum load before failure) and dissipated energy for different nanosheet vdW films. Using a mechanical model with an edge crack in the thin nanosheet film, we propose a shear-to-tensile failure mode transition to explain a maximum in critical shear force for graphene oxide films but not MoSe₂ films. This transition reflects a weakening of the substrate confinement effect and increasing rotational deformation near the film edge as the film thickness increases. For graphene oxide, the critical shear force can be increased by electrostatic cross-linking achieved through interlayer incorporation of metal cations. These results have important implications for the stability of functional devices that employ 2D nanosheet coatings.

1. Introduction

Liquid phase deposition of two-dimensional (2D) nanosheets is used to create films, coatings, or papers with diverse applications that include molecular barriers(1–3), selective membranes(4), wearable sensors(5, 6), electronic devices(5) and protective coatings with anticorrosive, antifouling or antibacterial function(6,12). Nanosheet films are complex structures formed by random tiling and stacking of individual nanosheets of finite size, usually on the micron- or submicron-scale. The resulting films do not possess a continuous 2D lattice, but are van der Waals (vdW) assemblies held together by weak non-covalent forces both in the Z-direction and between adjacent nanosheets in the X-Y film plane.

Nanosheet films are often supported on substrates, most commonly on one-side (as a coating), but sometimes on two-sides in the form of imbedded “sandwich” laminates. In these cases the substrate(s) carry mechanical load and can provide sufficient device stability against most types of mechanical stress during use. One exception where the substrate cannot provide mechanical stability is shear stress, which may be introduced by rubbing or abrasion for one-sided coatings, or shear or peel loadings on laminate architectures. In these cases, 2D nanosheet films may fail internally by cleavage along vdW gaps in a manner analogous to the original synthesis of nanosheets by exfoliation of layered crystals. While much attention has been paid to the mechanical properties of 2D materials(7, 8), this “re-exfoliation” pathway for shear failure of vdW nanosheet films has not been studied to our knowledge.

The limited relevant data in the literature suggest that stacked nanosheet films will be highly shear sensitive. Interlayer adhesion energies in 2D layered crystals are calculated to be of order 50–500 mJ/m² (9–11). Adhesion energies have been measured at 86 mJ/m² for bilayer graphene (10) and 220 mJ/m² for bilayer molybdenum disulfide(12). These energies are much lower than those for polymer adhesives, which are engineered to create trans-interface chain entanglement and/or covalent bonding that increase adhesion energy(13, 14). Where shear failure limits nanosheet film technologies, it may be addressed by addition of polymer, metal or ceramic to form a composite, but some of the characteristic behaviors of the neat 2D films can be lost, especially those behaviors related to the well-defined interlayer regions of interest in nano-fluidics and intercalative energy storage. The interface between the nanosheet film and the substrate can be engineered to prevent interfacial/adhesive failure, but even so the internal cohesive failure of neat vdW films would remain as a fundamental limitation on overall strength.

This paper examines the shear stability and failure modes of supported nanosheet vdW films/coatings using graphene oxide (GO) and molybdenum diselenide (MoSe₂) as model materials. Two-sided polymer-nanosheet-polymer laminates are used to create uniform shear loadings and lap shear experiments are adopted as the primary tool for mechanical characterization. The failure modes are identified and the critical shear forces and fracture energies determined as a function of film thickness, and compared to other types of coatings or adhesive films. A mechanical model of the fracture process was developed using finite-element methods. The model predicts a transition between a sliding failure mode and tensile-type failure mode as film thickness increases, and also explains the contrasting behavior of GO and MoSe₂ films based on the large (GO) and small (MoSe₂) lateral dimensions of the constituent nanosheets.

2. Results and Discussion

2.1. Film structures and lap shear experiments

Graphene oxide and MoSe₂ nanosheets were synthesized to serve as model materials with large differences in lateral size and aspect ratio (Fig. 1). Lateral dimensions by SEM image analysis (Fig. 1b) are < 0.4 μm for MoSe₂ and 0.5 – 2 μm for GO. Lateral size (L) distributions by image analysis (see Fig. 1) give volume-weighted average lateral sizes (∑L^2.d.L/ ∑L^2.d = ∑L³/ ∑L²) of 1.0 μm (GO) and 0.36 μm (MoSe₂) and mean aspect ratios of 1430 (GO), 550 (MoSe₂). The significant difference in aspect ratio implies a significant difference in stiffness, with GO being more conformal and sheet-like, while MoSe₂ is more plate-like, as reflected in the film structure (see Fig. S1 and text below).

Figure 1. Nanosheet characterization.

a, SEM images of as-produced GO and MoSe₂ nanosheets on silicon surfaces. Scale bar, 1 μm. b, Distribution of nanosheet lateral dimension from image analysis (imageJ) of SEM micrographs.

Drop casting from aqueous stock suspensions was used to make multilayer nanosheet films of thickness ranging from 0.2 – 5 μm. XRD (Fig. S2) shows clear peak at 0.65 for MoSe₂. The top surfaces of the GO films are smooth with wrinkles, consistent with the conformal nature of GO nanosheets (Fig. S1). The top surface of MoSe₂ films are granular and rough (Fig. S1), consistent with the rigid plate-like nature of the lower-aspect-ratio MoSe₂ nanosheets. For lap shear testing, we created polymer-nanosheet-polymer “sandwich” films by adding a second polymer substrate on the top of the nanosheet film with an overlap (Fig. 2a, Fig. S3) immediately after casting and drying for 48h (Fig. S3). Drying temperatures ranged from 22°C to 70°C, and no significant difference was observed in the critical shear force as a function of drying temperature (Fig. S4).

Figure 2. Experimental behavior of vdW nanosheets films under shear stress.

a, Sketch of the lap shear experiment. l and b are the length and width of the polymer strip substrate, respectively, and F is the applied force. b, Example raw data as force vs travel curves for GO and MoSe₂ films of 0.2 μm thickness. c, Measured critical forces and maximum shear stress for GO and MoSe₂ films of varying thicknesses. Data is presented as mean ± s.e.m. d, Calculated fracture energies using the Kendall equation (17) for GO and MoSe₂ films of varying thicknesses. Data is presented as mean ± s.e.m. All tests were performed at speed of 1 mm/min.

We chose to characterize the shear stability and failure of these vdW nanosheet films through the lap shear method (Fig. 2a), which is widely used to test the strength of adhesive bonds(15–18). The overlap region of the polymer substrate strips contains the nanosheet film and its geometry was standardized at 2 cm in length and 0.5 cm in width. Tests were performed at speeds from 0.01 – 1mm/min, and Fig. S5 shows no significant effect of speed within this range. Fig. 2b shows example raw data in the form of a load vs. displacement curve for GO and MoSe₂ films of 0.2 μm thickness. The maximum load force values in such plots were taken as the critical shear force and summarized in Fig. 2c for different material compositions and film thicknesses. It is noteworthy that GO films require generally larger forces than MoSe₂ films for shear failure, and the two materials show opposite trends as film thickness increases.

We used the theory of Kendall (17) to estimate fracture energies from the critical shear forces (see Methods). Fig. 2d summarizes the total fracture energies for GO and MoSe₂ films of various thickness. The two materials show the opposite trend with increasing film thickness, which will become a target for mathematical modelling (vida infra). In addition, the fracture energies are significantly higher than the measured and predicted adhesion energies for few-layer stacks of nanosheets with extended lateral dimension determined by smooth peeling experiments or theory (9, 10, 12). This comparison suggests that the fracture of nanosheet films is not an orderly, near-reversible peeling process, but involves significant energy dissipation in the processing zone within the film as the crack propagates through randomly tiled, overlapping nanosheets. A final interesting feature, is that graphene oxide films show increasing critical shear forces (and energies) with increasing thickness, in contrast to results on the failure of many other lap shear joints(18–20).

2.2. Cohesive vs. interfacial failure modes

Explaining the data features in Fig. 2 will require some understanding of the fracture mechanisms. A first question is the extent to which failure occurs within the nanosheet film (“cohesive failure”) or at one of the interfaces between the imbedded film and the two polymer substrates (“interfacial failure”). Fig. 3a shows digital optical scans (reflected light) of the two strips after separation by the lap shear test, viewed with the cleavage plane facing upward. The images show a chaotic pattern of thick GO residues (dark) interspersed with lighter areas that represent thinner GO residues or bare polymer. It is clear that these imbedded nanosheet films fail by mixed mode (part cohesive, part adhesive) and the cohesive failure does not occur along a single smooth plane as in the peeling of continuous sheets of extended dimension(9, 10). Instead, the local fracture process involves the chaotic pullout of large clusters of nanosheets to produce a rough cleavage surface, and the fracture plane migrates randomly in the Z direction throughout the film and in places reaching the film/polymer interface. These processes involve local material deformation and energy dissipation, which is believed to be the cause of higher fracture energies for these vdW nanosheet films relative to energies for smooth peeling of extended 2D sheets reported in the literature(9–12).

Figure 3. Analysis of failure mode and fracture mechanism.

a, Example digital optical scans (reflected light) of GO-containing polymer substrates after lap shear failure of GO sandwich film (0.2 um thickness) with cleavage plane facing upward (left) and their conversion to binary images (right) that reveal the presence or absence of GO residues at each location. In the combined image areas shaded in black are locations where GO residues appear on both top and bottom substrates, implying cohesive (within film) failure. b, Example graphene oxide fragment in-plane size distribution after lap shear test; c, Box plot of percent cohesive failure for graphene oxide films of varying initial thickness. Grey circles represent individual data points.

Image analysis was used to estimate the fraction of the surface that failed cohesively (leaving GO residues on both sides) and the fraction that failed adhesively (with bare polymer exposed on one side). The optical images were converted to GO thickness values using a calibration curve developed for pure polymer and polymer covered by known thicknesses of GO (Fig. S6). An example thickness distribution is shown in Fig. 3b. Overlaying the top and bottom polymer substrate in the proper registry reveals areas in which GO residues are found on both sides (cohesive failure) or on only one side (interfacial failure) (Fig. S7). Fig. 3c shows a summary of the results, which clearly indicate mixed mode failure.

A noteworthy feature of the data is the contrasting behavior of GO and MoSe₂ with GO showing higher fracture energies and an increase in energy with increase in film thickness (Fig. 2c). Failure of nanosheet films may involve contributions for sliding (shear), with high frictional energy dissipation, or tensile-type failure depending on the geometry of the nanosheets and the film confinement. We hypothesize that the higher energies for GO film failure relate to the much larger lateral dimension of the GO nanosheets (and thus larger aspect ratio and flexibility) that favor the sliding (shear) failure mode.

2.3. Fracture mechanics modelling

To investigate and better understand the sliding (shear) failure behavior of nanosheet vdW films, a two-dimensional single-lap model was built with a pre-existing edge crack in the thin film (Fig. 4a). Since vdW films are layered structures assembled from irregularly shaped, randomly stacked nanosheets, they contain numerous defects including voids and wrinkles (21, 22), which act as microcracks and can propagate under loading. In the mechanical model, therefore, the edge crack was used to simulate a critical defect (near the location of maximum local stress) in a vdW film which is thought to be responsible for the initiation of failure. Under lap shear loading conditions, regions of stress concentration occur in a thin film near the corners attached to the middle part of substrate (denoted by red circles in Fig. 4a, as opposed to the corners attached to the edge of substrate). The edge crack was thus placed in the left half of the thin film on the consideration that cracks usually start to develop first in high stress regions. The distance from edge crack to the nearest film-substrate interface was kept constant based on the assumptions that microcracks are uniformly distributed and crack density is the same for vdW films of different thicknesses. The latter assumption is made because all the samples in the experiments were prepared with the same method and in the same environment. Only one edge of the thin film needs to be considered since the structure (excluding the edge crack) and boundary conditions are centrosymmetric about the film center. The structural deformation in width direction can be ignored (i.e., the model is assumed in plane-strain state), because the width of the structure is much larger than the thicknesses of thin film and substrates.

Figure 4. Mechanical model and intrinsic mechanisms for lap shear experiment.

a, Schematic illustration of the mechanical model and boundary conditions. Stress is concentrated in regions near the film corners marked by red circles. In the magnified diagram of the film edge, the most dangerous crack (solid line) to the stability of film is focused, while the effect of other defects (dashed lines) is smeared into the effective anisotropic surrounding medium. The inset shows different forms of defects in the vdW film. b, Energy release rates (ERRs) at the crack tip for films of different thicknesses. $\stackrel{-}{{\mathrm{E}}_{\mathrm{p}}}$ and $\stackrel{-}{{\mathrm{E}}_{\mathrm{n}}}$ denote elastic moduli of the film in the directions parallel and normal to the film basal plane, respectively. c. Ratios of mode-I and mode-II stress intensities of crack tip for films of different thicknesses. b-c, In all cases, $\stackrel{-}{{\mathrm{E}}_{\mathrm{p}}}$ was chosen as 2.28 GPa (27) and the crack size as $\stackrel{-}{\mathrm{a}}=1.0$. d, Edge crack openings $\stackrel{-}{\mathrm{\zeta }}$ for films of different thicknesses. The colors indicate von Mises stress distribution in the film. e. Effect of crack size on the crack tip ERR and the shear-to-tensile failure mode transition. The film material with $\stackrel{-}{{\mathrm{E}}_{\mathrm{p}}}/\stackrel{-}{{\mathrm{E}}_{\mathrm{n}}}=100$ was used. f, Crack propagation direction in the film under lap shear loading conditions. The arrows indicate the directions of maximum opening stress in front of the crack tip.

The catastrophic failure of the imbedded nanosheet vdW film is determined by the condition under which cracks in the film start to propagate. In the mechanical model, this condition was assumed to be the failure criterion for brittle materials: $\stackrel{-}{G}=\stackrel{-}{G_{\mathrm{c}}}$ (23, 24) where $\stackrel{-}{G}$ and $\stackrel{-}{G_{\mathrm{c}}}$ are the energy release rate (ERR) and critical ERR of edge crack tip, respectively. Here and in other parts, $\stackrel{-}{\left(\bullet \right)}$ stands for a dimensionless variable (Supplementary Information section “Mechanical Modeling”). The assumption of the ERR-based failure criterion is reasonable in light of the experimental results that show the typical features of brittle failure (Fig. 2b). Finite element method (FEM) was used to calculate ERR for the edge crack (Methods and Supplementary section “Mechanical Modeling”). Anisotropic materials are considered for the thin film in FEM calculations since 2D nanosheet vdW films generally have a smaller elastic modulus in the normal direction $\stackrel{-}{E_{\mathrm{n}}}$ compared to that in the parallel direction $\stackrel{-}{E_{\mathrm{p}}}$ (25, 26). Different modulus ratios of $\stackrel{-}{E_{\mathrm{p}}}/\stackrel{-}{E_{\mathrm{n}}}$ are considered (Fig. 4b, c), and in particular, $\stackrel{-}{E_{\mathrm{p}}}/\stackrel{-}{E_{\mathrm{n}}}=1$ represents the case of isotropic film material as reference. The calculated ERRs in all cases in Fig. 4b decrease with film thickness when the film is relatively thin, while then turn to increase for thicker films. This implies that the critical shear force at sliding (shear) failure of vdW film first increases and then decreases with film thickness, which is consistent with our experiment results for GO vdW films (Fig. S12). The ERR simulation results also show that compared to the isotropic film, responses of anisotropic thin films are more sensitive to film thickness.

The upturn trend of the ERR curves in Fig. 4b, or the downturn trend of the critical shear force curves for GO films in Fig. S12, can be explained by a shear-to-tensile failure mode transition. The ratio of stress intensities $\stackrel{-}{K_{\mathrm{I}}}/\stackrel{-}{K_{\mathrm{I}\mathrm{I}}}$ (Fig. 4c) reflects the relative proportion of two driving force components (i.e., mode-I and mode-II ERRs) for the crack propagation, from which we can identify the dominant failure mode in the thin film failure process. The simulation results show that shear failure mode dominates in small film thickness regime, while tensile failure mode becomes more significant when the films are thicker. This failure mode transition can be identified in all cases of anisotropic film materials, however, is not obvious for isotropic film material ($\stackrel{-}{K_{\mathrm{I}}}/\stackrel{-}{K_{\mathrm{I}\mathrm{I}}}$ being always greater than 1). Besides, compared with the isotropic film, anisotropic films have a smaller proportion of tensile failure mode, probably due to weaker load-bearing capability in the normal direction.

The modelling identifies two major contributions to the shear-to-tensile failure mode transition as film thickness increases: (i) the decreasing substrate confinement effect on the edge crack and (ii) the increasing rotational deformation near the film edge. For the first contribution, the two substrates confine the film inhibiting deformation in the normal direction while facilitating its shear deformation in the parallel direction. The calculated crack opening profiles (Fig. 4d) show that the substrate confinement on the edge crack is weakening as the film thickness increases. Therefore, for very thin films (i.e., film thickness smaller than the typical crack size), the substrate confinement effect is very strong, and the crack fails mainly in shear mode. For thick films (greater than the typical crack size), however, the substrate confinement effect is reduced, and the crack increasingly fails in tensile mode. To better demonstrate the substrate confinement effect, the lap shear model was reconsidered under the same conditions except the two substrates are set as rigid. In this scenario, we can exclude the influence of substrate elastic deformation and focus attention on how the thin film is constrained by the substrates. As Fig. S9 shows, the driving force for crack tip formation under rigid substrate $\stackrel{-}{G_{\mathrm{r}\mathrm{i}\mathrm{g}\mathrm{i}\mathrm{d}}}$ is very high when film thickness is small, implying that the crack opening is strictly confined. As film thickness increases, however, the driving force decreases dramatically and becomes flat gradually, which clearly characterizes the relaxation of the substrate confinement effect on the edge crack. Regarding the second contribution, the shear force is created in the film by the two substrates applying tensile force in opposite directions, which produces rotational deformation of the joint part. The rotational deformation increases with film thickness, resulting in larger load component projected in the normal direction and improved proportion of tensile failure mode.

The experimentally observed difference in critical shear force curves for GO and MoSe₂ (Fig. 2c) can be explained by the shear-to-tensile failure mode transition. The FEM results in Fig. 4e show the effect of edge crack size on the ERR of crack tip. For a smaller crack size, the critical point of the ERR curve moves to the left, implying that the film thickness regime dominated by shear failure mode becomes smaller. This is because small edge cracks (compared with film thickness) cannot be confined by the substrate as strictly as larger ones (Fig. S10) and thus prefer tensile failure. Since we assume that edge crack size is proportional to the feature size of 2D nanosheet in vdW film (Fig. 4a), the disparity between lateral dimensions of MoSe₂ (0.36μm) and GO (1 μm) nanosheets (Fig. 1 and Methods) means that the crack size in MoSe₂ films should be much smaller than that in GO film. Therefore, compared to the crack size in MoSe₂ film, the MoSe₂ film thicknesses used in the experiments are not small enough to induce a strong substrate confinement effect. In other words, the failure in MoSe₂ films is always dominated by tensile failure mode, and the measured critical shear force always decreases with film thickness within the experimentally studied regime.

The shear-to-tensile failure mode transition implies that, for a given the nanosheet size (lateral dimension), there exist a theoretical optimum film thickness for the (maximum) shear stability of vdW films. For vdW films composed of small 2D nanosheets, the optimum film thickness is quite small and possibly not easily observed experimentally; whereas for those composed of relatively large nanosheets, the optimum thickness may be observable by lap shear experiments (Fig S12). This optimal shear stability has potential applications in fields, such as flexible electronics and wearable devices, where 2D nanosheet vdW films act as adhesive or bridging part between substrates and mainly bear shear forces. One should also note that the present model cannot make quantitative predictions on the shear stability for various kinds of 2D nanosheet vdW films, because many other factors, such as intrinsic properties of 2D nanosheet, functional groups, water content (28) and surface roughness (29), can have complex effects that are difficult to consider in the present model.

The mechanical model with an edge crack in the thin film contains features of cohesive failure observed in experiment, while the post analysis on crack propagation can further demonstrate the phenomenon of interfacial failure (Fig. 4f). Since the edge crack is under a mixed mode (mode-I and mode-II) loading, the maximum opening stress direction in front of the crack tip is deflected clockwise from the normal direction, and the crack will propagate toward the film-substrate interface. The subsequent propagation path, however, depends on the sophisticated structural environment around the crack tip, as there will be many new defects created in the film or on the film-substrate interface under loading (30). Without interference of other defects or impurities the edge crack front will reach the interface and continue to propagate along the interface, forming interfacial failure of the thin film; otherwise the crack may propagate along other paths within the film if defects and weak nanosheet linkages are dense around the crack tip, forming cohesive failure of the thin film.

2.4. Improving shear strength by interlayer cross linking

A common approach for modifying the properties of GO films is interlayer cross-linking involving polymeric (31, 32), cationic (33), or bi-functional organic (34) crosslinkers. We hypothesized that shear stability could be improved by interlayer cross-linking, but shear effects have not been addressed in the literature to our knowledge. We chose to co-deposit our GO nanosheets with metal-based cations from dissolution of FeCl₃ and Al(NO₃)₃ salts. Graphene oxide is reported to bind strongly to multivalent cations(35, 36), which can neutralize the native negative charge on GO and increase film cohesion by decreasing the repulsive electrostatic component of inter-nanosheet forces. Fig. 5 shows the critical shear forces and fracture energies for both the Fe- and Al-based cross-linked GO nanosheet films. Adding metal ions increases the critical force by a factor of three and the total fracture energy by about one order of magnitude. The cross-linked films appear to be more brittle, however, based on increased cracking seen by SEM imaging of the fracture surface (Fig. S13).

Figure 5.

Critical lap shear/delamination forces and fracture energies of ionically cross-linked GO films. Left axis (triangle marker): Measured critical force from lap shear testing for metal cation crosslinked graphene oxide films. The samples were prepared following an atomic metal/carbon ratio of 1/5. Right axis (square marker): Fractured energies calculated using the Kendall(17) equation for metal cation crosslinked graphene oxide films. All tests performed on samples of 0.5 μm thickness at travel speed of 1 mm/min. Data is presented as mean ± s.e.m.

3. Conclusions

This work shows that supported, neat (matrix free) nanosheet films are sensitive to shear forces and can fail by either delamination from the substrate or internal delamination. The latter failure mode is a type of “mechanical re-exfoliation” with similarities to the original synthesis of the constituent nanosheets from bulk layered crystals, and is an intrinsic limitation of these vdW assemblies. Mechanical modelling predicts the nanosheet films fail internally by either a sliding or tensile-type fracture process with a transition from sliding to tensile-type with increasing film thickness. During the review process, we noticed a recently published work (37) that applies the lap shear test to soft hydrogel materials to study the strength and toughness of interfacial adhesion. Their results from experiments also show the dependence of critical shear force on film thickness and the presence of a transition stage, in spite of the different materials of interest, length scales of samples and interfacial failure patterns.

Fig. 6 attempts to put the present findings on the cleavage / fracture energies of vdW nanosheet films in perspective by comparison with those for layered crystals or polymeric adhesives. Interlayer adhesion energies in crystalline layered materials can be calculated or measured in some cases through orderly peeling processes and lie in a cluster between 0.05 and 0.5 J/m². This regime represents the energies required to reversibly (or nearly reversibly) overcome vdW forces between closely packed but non-bonded sheets. Interestingly, the defect-rich nanosheet vdW films with their lower packing density and lacking in long-range in-plane order (lateral dimensions < 1 um) have higher shear fracture energies, by about an order of magnitude (~0.5 – 5.0 J/m²). Analyses in this study suggest that these values also represent vdW forces, but are elevated by the complex processes of nanosheet pullout, sliding, and roughness enlarged fracture planes associated with chaotic crack motion. These complex processes involve energy dissipation and produce an overall higher surface energy through the geometric effect of roughness. Finally, it is interesting that fracture energies for vdW nanosheet films are closer in magnitude to those for polymer adhesion (Fig. 6), where chain entanglement at the interface may play an analogous role to irregular nanosheet stacking in increasing overall adhesion energy relative to the behavior of smooth hard surfaces.

Figure 6: Cleavage energies for various layered material architectures.

Entries in blue are experimental and theoretical interlayer energies for layered crystals or multilayer stacks of extended 2D monolayers from the literature. Entries in black are measured cleavage (fracture) energies for nanosheet vdW films in the present study. Entries in red are peel forces (red triangles) or adhesion energies (red bars) for chain polymer films and adhesives, included for reference. Literature key: (a)⁽⁹⁾, (b)⁽¹⁰⁾, (c)⁽¹¹⁾, (d)⁽¹³⁾, (e)⁽³⁸⁾, (f)⁽¹⁴⁾, (g)⁽¹²⁾.

Overall, neat vdW film coatings are expected to be sufficiently robust for some applications, but may not withstand surface abrasion or laminate peel stresses relevant to many other applications. Graphene oxide films can be strengthened modestly by simple interlayer ionic cross linking. Higher strengths may be achieved by covalent cross-linking or introduction of a matrix material, but such measures may comprise some of the novel and characteristic properties of neat nanosheet vdW films.

4. Methods

Materials.

Materials. Iron Chloride, Aluminum Nitrate and Sodium Tetraborate Decahydrate were purchased from Sigma-Aldrich. Laboratory nitrile gloves were purchased from Kimberly-Clark Professional. Clear polyester substrates were purchased from Coveme. All water was deionized (18.2 MΩ, mill-Q pore). All reagents were used as received without further purification.

Nanosheet synthesis and film formation.

GO suspensions were prepared by a modified Hummer’s method as described previously [Yang et al, 2014](39) with nanosheet lateral size of approximately 1 μm and thickness of approximately 1 nm. The GO concentration in the suspensions ranged from 3.5 to 10 mg mL⁻¹. MoSe₂ suspensions were prepared by organolithium chemical exfoliation as described previously [Wang et al, 2016](40) with nanosheet lateral size on the order of 100 nm and stock suspension concentrations of about 1.2 mg mL⁻¹. Polymer substrates were cut into 5 cm × 0.5 cm rectangles and treated with pure oxygen plasma (Harrick Plasma PDC-001 System) to facilitate wetting. Plasma was generated at 100% power (50 W) for 30 minutes in 0.13 mbar of air followed by slow venting of the chamber. Nanosheet suspensions were drop-cast onto substrates (e.g. 18 μl of GO to obtain 1 μm thick film and 0.588 μl of MoSe₂ to obtain 1 μm thick film) and a second substrate strip was placed on the top (Fig. S3). Low temperature drying (20 – 70 C) was used to create the final “sandwich” films (polymer/nanosheet-film/polymer) for lap shear testing. A glove box was used for MoSe₂ films to prevent air oxidation during drying.

Fabrication of metal ion crosslinked graphene oxide films.

Suspensions of Al(NO₃)₃ / graphene-oxide and FeCl₃ / graphene-oxide were prepared using an metal/carbon atomic ratio of 1:5. Next, 16.8 μl of suspension was drop-casted onto plasma treated polyester substrates (Fig. S3) to obtain a 0.5 μm thick film and a second substrate strip was placed on top and air dried at 48h at (22°C) to create sandwich structures (Fig. S3).

Nanosheet film characterization.

Morphologies of GO and MoSe₂ nanosheets and their vdW films were investigated by field emission scanning electron microscopy (SEM) (LEO 1530 VP) operating at 3.5 – 10 kV for low-, medium- and high-resolution imaging and atomic force microscopy (AFM) (Asylum MFP-3D Origin) operating in contact mode. SEM samples were pre-coated with AuPd (~2 nm). The interlayer spacings of the GO and MoSe₂ films were measured by X-ray diffractometry (Bruker AXS D8 Advance) with Cu KR radiation (λ = 1.5418 Å).

Lap shear testing.

Lap shear tests were performed using an Instron 5940 Mechanical Test System equipped with a 500N load cell. The tests were carried out with travel rate of 0.01 mm/min, 0.1 mm/min and 1mm/min. Full force-displacement curves were generated, and the maximum load force extracted from each curve as the critical shear force for film failure. The total fracture energy was calculated using a published relation from Kendall (17) for lap joints, $W={\left(\frac{F}{b}\right)}^2\frac{1}{4Ed}$. Where W is the total fracture energy (J/m²), F is the critical load force (N), b is the substrate width (m), E is the Young’s Modulus of the substrate and d is the substrate thickness (m).

Image analysis.

See Supplementary Information “Optical analysis of graphene oxide samples”.

Finite element simulations.

Finite element simulations were implemented through the commercial computer-aided engineering software ABAQUS (Dassault Systemes Simulia Corp., Providence, RI). The lap shear model was built as a 2D model in plane-strain state. The film was attached to the substrate surfaces by tie constraints. The value of energy release rate was obtained with the J-integral method (41, 42) and averaged over values calculated on four integration contours around the crack tip. Both the film and substrates were meshed by 4-node bilinear quadrilaterial, reduced integration, solid elements (CPE4R). The post analysis on crack propagation was implemented using the extended Finite Element Method (XFEM) (43, 44). See Supplementary Information “Mechanical Modeling” for more details.