Axial compression measurements and failure processes in monolayer graphene sheets embedded in polymer matrices

The mechanical behavior of embedded monolayer graphene in a polymer matrix under axial compression is examined here by monitoring the shifts of the 2D Raman phonons under an incremental applied strain. In order to establish the effect of aspect ratio upon the critical strain to failure a wide range of length-to-width ratios of almost rectangular 1LG flakes were tested up to an external compression strain of approximately -1 %. Care was taken to define the position of zero strain due to the presence-in some cases-of a residual stress and to assess the effect of transfer length upon the efficiency of stress transfer. The obtained critical strain values for first failure- after transfer length correction in short flakes- were found to be independent of flake size with a mean value of - 0.60 + 0.11%. By combining Euler mechanics with a Winkler type of approach, both the modulus of interaction between graphene and polymer, as well as, the buckling wavelength could be established. The results show clearly that unlike buckling in air, the presence of a constraint such as a polymer matrix induces graphene buckling of very short wavelength of the order of 1-2 nm. Finally, by conducting calculations of the interaction between an analogue of monolayer graphene (coronene) and PMMA oligomers within the framework of density functional theory (DFT), the effect of lateral constrain provided by the polymer, upon the out-of-plane buckling of graphene has been assessed.