Probing elastic properties of graphene and heat conduction in graphene bubbles above 1000∘C

Abstract

The elastic and thermal properties of graphene were investigated by illuminating graphen bubbles with a laser spot. Tempertures above $1000{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ were obtained in large ($>10\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{m}$) graphene bubbles. The formation of standing optical waves lead to laser heating depending on the height of the garphene bubble, which results in Raman band oscillations when scanning the laser spot across the bubble. The profile of the bubble under laser illumination can be deduced from the Raman G band oscillations. A distinct swelling at the center of the bubble is observed which is attributed to the strong softening of graphene above $1000{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$. From the size and height of the swelling it is deduced that the elastic modulus is reduced by at least $40%$ at $1000{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$. On solving the heat equation for the heat dissipation through the graphene only, analytical expressions are obtained for the isotherms on the bubble for both symmetrical and asymmetrical positions of the laser spot. It was found that a large fraction of the absorbed heat dissipates through the gas in the bubble using the finite volume method. Analytical expressions for the temperature distribution in the bubble are deduced from the numerical results. Heat conduction through the gas in the bubble influences the temperature distribution and needs to be taken into account in the heat dissipation in graphene bubbles.