Deformation of Wrinkled Graphene

The deformation of monolayer graphene, produced by chemical vapor deposition (CVD), on a polyester film substrate has been investigated through the use of Raman spectroscopy. It has been found that the microstructure of the CVD graphene consists of a hexagonal array of islands of flat monolayer graphene separated by wrinkled material. During deformation, it was found that the rate of shift of the Raman 2D band wavenumber per unit strain was less than 25% of that of flat flakes of mechanically exfoliated graphene, whereas the rate of band broadening per unit strain was about 75% of that of the exfoliated material. This unusual deformation behavior has been modeled in terms of mechanically isolated graphene islands separated by the graphene wrinkles, with the strain distribution in each graphene island determined using shear lag analysis. The effect of the size and position of the Raman laser beam spot has also been incorporated in the model. The predictions fit well with the behavior observed experimentally for the Raman band shifts and broadening of the wrinkled CVD graphene. The effect of wrinkles upon the efficiency of graphene to reinforce nanocomposites is also discussed.


Transfer of the CVD graphene to the PET substrate
The CVD graphene was transferred to PET using the well-known technique of chemical etching of copper in ferric chloride. The graphene/copper had a poly(methyl methacrylate) (PMMA) coating applied to the surface to act as a support during transfer. This was allowed to dry at room temperature. The backside graphene was removed by oxygen plasma. The PMMA/graphene/copper foil was then placed in ferric chloride until all copper was dissolved.
The film was then subsequently transferred to three baths of DI water. The PMMA/graphene film was then fished from the last DI bath with a clean PET film and allowed to dry overnight.
The PMMA/graphene/PET film was then soaked in acetone to remove the PMMA. The graphene/PET film was rinsed in IPA and blown dry with nitrogen as a final cleaning step.

Determination of the lateral dimensions of the graphene islands
The lateral dimension of each graphene island was estimated by averaging the length of two crossed lines across the island, as shown in Figure S1. Over 500 islands were measured in this way to give the statistical distribution in Figure 1(c). A typical example of this measurement is shown in Figure S1

3, The effect of wrinkles upon stress transfer
The AFM height scan in Figure 1(d) in the manuscript clearly shows that the wrinkles stick up above the PET substrate. As shown before for a different system, when the wrinkles form by a similar mechanism, the upper layer stick up and leave a hollowed region between the top and bottom layer. 1 Similarly in our situation, there will be a hollow region within the wrinkles in which there can be no stress transfer giving rise to the mechanically-isolated graphene islands and mechanically-free edges within the wrinkles because of the absence of the interface with the substrate, as shown schematically in Figure S2. Deformation will also lead to straightening of the wrinkles. It should be noted that the diagrams in Figure S2 are not to scale -the size of the islands (1.2 m) is much larger than the height of the wrinkles (20 nm).

Determination of the mean rates of 2D Raman band shift and band broadening
The mean size of the graphene islands was fixed by the process used to produce the CVD graphene/PET material although Figure 1(c) shows that there was a wide distribution of sizes.
Although we were not able to modulate the mean value, we were able to investigate the effect of The Raman spectra of a typical CVD graphene/PET specimen at different strain level are in shown in Figure S4.

The estimation of the laser spot size and the local laser intensity calculation
It can be assumed that the laser intensity I(r) within the spot of a Gaussian laser beam follows the Gaussian distribution: 3 where r is the distance to the laser spot center, and r 0 is the radius of the laser beam, defined as the radius of the plane where I(r) decreases to 1/e 2 of its maximum value. where x 0 is the graphene edge location and A is the amplitude. For regions where the 2D was not resolvable, I was set as zero. By fitting I with eq S2, the radius of the laser beam r 0 is obtained as ~0.7 μm. Thus diameter of the laser spot size is estimated to be 1.4 μm. 5 If the distance between each unit (Figure 4(c)) is then calculated through the unit center, the local laser intensity at unit (L,T), I laser (L,T) is given by modification of eq S1 as: The effect of the exact laser spot position and the ns values to the variation of ω 2D and FWHM 2D are also considered. The laser spot is approximated to a square and Figure S6 shows the situation where the laser spot is centred at the wrinkles. The overlapped region of graphene islands and laser spot contributes to the calculated Raman spectra, and only the region marked by dashed red lines was taken into calculation due to its symmetrical geometry.