## Introduction

Graphene and 2D materials exhibit interesting morphologies which have been classified as wrinkles, ripples and/or crumples1,2,3 depending on their physical dimensions, topology and order. Such corrugations are of paramount importance for the potential applications of graphene since they can modify the electronic structure and carrier transport, alter surface properties, create electron/hole puddle and induce pseudomagnetic field in bilayers4. The formation of wrinkles, ripples and crumples has been attributed to several physical causes, such as (a) the thermal vibration of the 2D lattice5, (b) edge instabilities, defects/ dislocations6, (c) the mismatch between the thermal expansion of the 2D material and its host substrate7,8,9 (d) the evaporation/removal of solvent and its surface tension4,10, and (e) the relaxation of pre-strained substrate and its surface potential11,12,13. Recently, it has been demonstrated that wrinkles in the form of delaminated folds in supported graphenes can be formed either by uniaxial compression or uniaxial tension beyond a certain critical load, depending on the mode of loading. In the first case, the wrinkling direction is perpendicular to the compression axis whereas in tension, wrinkles of the same pattern originate parallel to the loading direction due to Poisson’s contraction exerted laterally by the underlying polymer substrate14.

Herein we demonstrate that in-situ uniaxial tensile testing combined with Atomic Force Microscopy (AFM) can be employed to highlight the formation of complex morphologies in graphene flakes, such as the creation of mosaic patterns similar to those observed in CVD graphenes upon cooling from high temperatures (~1000 °C).

## Results and discussion

In the present study we used a 1-mm-thick sheet of poly-methylmethacrylate (PMMA) as substrate to simply support monolayer (1LG) and bilayer (2LG) graphene flakes that were prepared by mechanical cleavage from HOPG (High Order Pyrolitic Graphite) with the scotch tape method15. Appropriate flakes deposited directly on the PMMA were located using the optical microscope and the exact thickness of each flake was identified by the corresponding Raman line of the 2D spectra.

Optical images of the examined monolayer and bilayer graphene flake supported on PMMA are shown in Fig. 1a, b. The dimensions of the approximately rectangular 2LG flake were ~35 μm (length) and ~60 μm (width), and those of the 1LG flake are 30 μm (length) and ~35 μm (width), which were large enough to ensure efficient load transfer at all strains16 in both the loading and the transverse directions. At rest the flakes appear to be quite flat having only a small and smooth fluctuation of ±0.5 nm in the out-of-plane direction which corresponds to the surface roughness of the polymer substrate, in agreement with measurements conducted previously14 (Fig. 1d). The exact nature of the flakes was identified by the corresponding Raman spectra of the 2D peak (Fig. 1c). The position frequency of the 2D peak at the unstressed state of the 2LG is 2604 cm−1 and of the 1LG is 2598 cm−1, which are close to the wavenumber at 0% strain for the excitation line of 785 nm, hence, the flakes have no residual stress.

It is interesting to note that, upon unloading, the lateral wrinkles previously created upon tension are still present since they have been detached from the substrate and due to the interface slippage, the system does not fully recover. In addition, the formation of new wrinkles now perpendicular to the loading direction is observed (Fig. 3a–f). The coexistence of lateral wrinkles originated by transverse strains (Poisson’s effect) and longitudinal wrinkles originated by axial compression upon unloading result in the formation of a mosaic morphology, which is depicted clearly in Fig. 3a, b. It is worth adding that the mosaic morphologies are very similar for both monolayer and bilayer graphene, with wrinkles of comparable height but with different FWHM (which is higher for 2LG). Furthermore, another substantial difference is the lateral dimension of the islands delimited by the wrinkles, which is 1.37 ± 0.39 μm for 2LG and 0.74 ± 0.28 μm for 1LG.

The formed wrinkles are in fact isolated folds which have been detached from the underlying substrate and control tests reveal that do not come from any undulations of the surface of the substrate (Supplementary Fig. 1). This is evident primarily in as-supported flakes under compression20,21 and has also been simulated by computational modelling14,21. It constitutes a unique form of failure initiation which is the main characteristic of compression (lateral or longitudinal) of such systems. On the contrary flakes fully embedded in a matrix have been found to exhibit the expected Eulerian sinusoidal mode of compression failure22 due to the presence of constraints for fold creation by the surrounding matrix.

The threshold of fold formation in the lateral direction seems to be accompanied by interfacial failure or slippage of the whole flake giving rise to the formation of folds in the longitudinal direction (Fig. 4a–d) upon unloading as mentioned above. Here it seems that beyond a certain critical tensile strain $$\varepsilon _{\mathrm{p}}$$,which is the maximum strain that can be transferred from substrate to graphene, the graphene flakes cannot be strained any further and gradually relax by slippage23 (see Fig. 4e). Hence, if the maximum deformation applied to the substrate is higher than this value ($$\varepsilon _{\mathrm{m}} > \varepsilon _{\mathrm{p}}$$), no further strain can be transmitted to graphene due to interfacial slippage. Upon unloading at a certain critical point, ε0 (ε0 = εm − εp) the graphene flake will be subjected to compressive strain, which can be of sufficient magnitude to induce longitudinal wrinkling, if exceeds the critical strain for wrinkling $$\varepsilon _{{\rm{cr}}}^{{\rm{comp}}}$$. In particular, it can thus be easily postulated (see Supplementary Discussion for details) that the applied strain level $$\varepsilon _{{\mathrm{onset}}}^{{\mathrm{mosaic}}}$$at which mosaic originates is

$$\varepsilon _{{\rm{onset}}}^{{\rm{mosaic}}} = \varepsilon _m - (\varepsilon _p + \left| {\varepsilon _{{\rm{cr}}}^{{\rm{comp}}}} \right|)$$
(1)

In light of the above equation, the minimum strain to be applied to the substrate in order to obtain mosaic morphology upon loading/unloading is evidently $$\varepsilon _{\mathrm{p}} + \left| {\varepsilon _{{\mathrm{cr}}}^{{\mathrm{comp}}}} \right|$$. For monolayer graphene supported on PMMA, the critical strain for slippage has been found ~1.5% (Fig. 4b) and, as stated before, $${\mathrm{\varepsilon }}_{{\mathrm{cr}}}^{{\mathrm{comp}}}$$ has been experimentally and theoretically found equal to ~ −0.3%21; hence, it is possible to give an estimation of the minimum strain to apply to the substrate in order to create the mosaic morphology for the system at hand, which is approximately 1.8%. The proposed mechanism has been verified by independent mechanical experiments combined with Raman spectroscopy (Fig. 4f), which highlight also the gradual release of compressive strain after mosaic formation. Moreover, it is important to note here that the maximum deformation εm that the graphene/polymer system can withstand is limited by the failure behaviour of the polymeric substrate (Supplementary Figs. 2 and 3) and, also, by the poor interfacial adhesion in graphene/polymer systems in the absence of covalent bonding or additional non-covalent binding interactions such as π–π interactions or hydrogen bonding.

The mechanically self-assembled mosaic pattern formed here is very similar to the island-like morphology of CVD graphene grown on a copper substrate16. In that case the high thermal peripheral (biaxial) stresses induced due to the mismatch of the thermal expansion coefficients between copper and graphene result in a compressive biaxial strain of 2–3% in the graphene at room temperature. Such residual strain is far higher than the critical strain required for graphene wrinkling (buckling) thus giving rise to a network of large out-of-plane wrinkles or folds8. It is interesting to note that the peripheral equi-biaxial strain creates circular mosaic morphologies in contrast to the square patterns obtained here. In our case, the final lateral size in the mosaic morphology is essentially determined by the density of wrinkles developed during the loading and the unloading stages. The higher dimensions of the domains developed in the 2LG flake is compatible to a lower wrinkles density, compared to 1LG, in agreement with theoretical predictions14. These features are strongly dependent on levels of adhesion between graphene and the underlying polymer; hence, the use of different substrates can be thus exploited to tailor the final morphology of the mosaic.

### Mosaic morphology as self-assembled wrinkle networks for fluid administration

In the mosaic morphology, when the newly formed wrinkles interact with the existing lateral wrinkles form different types of junctions. High-resolution AFM images acquired at those points reveal that the most evident features are T-, X- and Y-junctions (Fig. 3g), as also predicted by Zhang et al.24. These typical features of the mosaic could be of paramount importance since it may broaden graphene application in the areas of electronics, photonics, nano-fluidics and bio-engineering4. For instance, the strong coupling between localized deformation and the electronic structure that is expected at the junctions could be exploited by strain engineering. Furthermore, constructive use of the self-assembled wrinkle networks could be harnessed as surface texturing agent to direct cell alignment and morphology in tissue engineering25 or for the creation of nano-channels in nano-fluidic devices transporting liquids. In light of possible application, the stability of the wrinkles to cyclic loading, which is particularly important for the off/on controlled applications of the mosaic, has been also verified (Supplementary Fig. 4). It is known that graphene is impermeable to most gases and liquids26,27 and thus the as-presented wrinkle networks obtained via mechanical deformation could be seen, in principle, as interconnected channels where fluid could flow or be stored at the nano-scale. In this regard, we have investigated herein the feasibility of mosaic morphology as described above for the development of mechanically self-assembled nano-fluidic devices. This has been carried out in combination with methods suitable for the encapsulation of liquids in the area between graphene and its support28. More specifically, after the formation of mosaic morphology via mechanical deformation, the supported graphene bilayer has been exposed to a high humidity environment (RH = 90%) for several days. The selection of bilayer mosaic for this feasibility study has been encouraged by recent results of a molecular dynamics study of pressure-driven water transport through graphene bilayers which suggests that, as the channel width increases, the water flow rate increases monotonically and also the increase of channel thickness leads to weaker water-graphene interaction and thus higher water molecule mobility29. The AFM images acquired immediately after the exposure reveal that triangular and polygonal blisters nucleate at most junctions (Fig. 5), in agreement with theoretical models assessing the stability of wrinkle networks to interstitial pressure24. These blisters are likely induced by water molecules trapped in the interstitial space between supported graphene and the polymeric substrate, as also postulated earlier28, and are connected through the network of wrinkles previously formed via mechanical deformation. It is interesting to note that control experiments reveal that, blisters shrink to their initial configuration of junctions as shown in Fig. 5, after the removal of the system from the high humidity environment at RT. In light of these preliminary observations, the mosaic morphology of graphenes presented herein could be seen as a network of nano-reservoirs interconnected by nano-channels.

Fluid release from blisters/nano-reservoirs could be triggered in different ways, depending on desired application; for instance, it has been shown that graphene blisters can be controlled by an external electric field30. Furthermore, it is interesting to note that the small dimensions of the channels can pose challenges to nano-fluidic devices transporting liquids, as recently demonstrated by Xie et al.31. In particular, it has been shown that if the graphene channel diameter is small enough, water diffusing into the interstitial space underneath can freeze at room temperature due to the strong geometric confinement and, if the space inside graphene wrinkles is large enough, water becomes liquid again and can flow under certain conditions28.

## Methods

### Sample preparation and flakes localization

Graphene flakes were prepared by mechanical exfoliation of graphite using the scotch tape method and deposited directly on a PMMA/SU- 8 substrate. The SU-8 (SU-8 2000.5 Micro-Chem) is a photoresist polymer and was spin coated on the top surface of a PMMA film at 2000 rpm creating a layer of 300 nm thickness. The samples were characterized by means of AFM (see below) and Raman spectroscopy, by InVia (Renishaw) microspectrometer with 2400 grooves/mm grating for the 785 nm laser excitation; Raman spectra were measured at and the laser power was kept at 1.2 mW on the sample to avoid laser-induced local heating. A ×100 objective with numerical aperture of 0.95 was used in all cases. Experimental data were fitted by using Lorentzian functions, one for the monolayer and four for the bilayer graphene.

### Combined uniaxial tensile test and atomic force microscopy

The tensile experiments were conducted using a micro-tensile tester (Deben MT 200) that could be adjusted under AFM for simultaneously applying strain and acquiring images under AFM. The increment step of strain was 0.1% for all cases. The AFM images were obtained using Dimension Icon microscope (Bruker) operating in Peak Force Tapping mode using ScanAsyst-Air probes (stiffness 0.2−0.8 N/m, frequency 80 kHz). No data treatment apart from line subtraction (retrace) to remove the tilt has been performed. Wrinkle amplitudes and half wavelengths were measured from line profiles manually for each wrinkle. Medians of the thus obtained parameters were then used to characterize the wrinkles in each profile. Also, lateral size of the islands delimited by the wrinkles has been estimated by averaging the length of two crossed lines across the island measured manually from line profiles.

### Combined uniaxial tensile test and Raman spectroscopy

Tensile experiments have been performed using the same set-up under the Raman microscope (InVia Renishaw microspectrometer) by using the 785 nm laser excitation. At each deformation step, several Raman spectra were acquired in different location of the 1LG flake under investigation (near the geometric centre) and experimental data were fitted by using one Lorentzian function.

### High humidity exposure experiments

High humidity exposure experiments were performed at 90% RH and at RT in a custom-made climate chamber32.