Journal Club Theme of March 2013: Interfacial Adhesion of Graphene - Measurements and Analysis
Several recent papers have reported measurements of adhesion energy between graphene and other materials (e.g., Si/SiOx and copper) [1-3]. Like thin films, many experimental methods may be adopted to measure the interfacial properties of graphene, such as the pressurized blister test  and the double-cantilever beam test . The challenges lie in the handling of atomically thin membranes and analysis/interpretation of the data.
Theoretically, several potential mechanisms may contribute to the interfacial adhesion between graphene and other materials, including van der Waals forces, electrostatic forces, Casimir effect, and capillary force. A simple analytical model was developed for the van der Waals forces between a monolayer graphene and an amorphous substrate . In addition to the adhesion energy, an equilibrium separation between graphene and the substrate surface was assumed (~0.4 nm). With the two parameters, a complete traction-separation relation was derived for the graphene/substrate interface, which can be used to analyze the process of interfacial bonding/debonding in the spirit of nonlinear fracture mechanics (e.g., cohesive zone modeling). The same model was later used to study the effect of surface roughness on adhesion of graphene membranes (monolayer and few layers) . Similar traction-separation relations for other interfacial forces may be developed to further understand the mechanisms of interfacial adhesion for graphene. Of particular interests are the effects of surface roughness and environment (e.g., humidity).
Inspired by the pressurized blister test of graphene by Koenig et al.  as well as observations of graphene micro/nano-bubbles by others [6, 7], we recently carried out some analyses based on both membrane and nonlinear plate models of graphene . It was found that, for relatively large graphene bubbles (height > 10 nm), the membrane analysis is sufficient, based on which the interfacial adhesion energy can be determined directly from measurements of the bubble size (diameter and height) by an analytical solution. However, it is cautioned that the simple analytical solution may underestimate the adhesion energy by up to 13%, compared to a more accurate analysis (Hencky’s membrane solution). On the other hand, for graphene nanobubbles (height < 10 nm), the effect of bending stiffness may have to be considered by using the nonlinear plate model, which requires a numerical method for accurate solutions . In this case, the effect of van der Waals force has to be considered as well due to the proximity of the graphene to the substrate. Further studies on graphene nanobubbles would combine the numerical analysis with experimental measurements to determine the adhesion energy and the impact on the graphene morphology.
1. Z. Zong, C.-L. Chen, M.R. Dokmeci, K.-T. Wan, Direct measurement of graphene adhesion on silicon surface by intercalation of nanoparticles. J. Appl. Phys. 107, 026104 (2010).
2. S.P. Koenig, N.G. Boddeti, M.L. Dunn, J.S. Bunch, Ultrastrong adhesion of graphene membranes. Nature Nanotechnology 6, 543-546 (2011).
3. T. Yoon, W.C. Shin, T.Y. Kim, J.H. Mun, T.-S. Kim, B.J. Cho, Direct measurement of adhesion energy of monolayer graphene as-grown on copper and its application to renewable transfer process. Nano Lett. 12, 1448-1452 (2012).
4. Z.H. Aitken and R. Huang, Effects of mismatch strain and substrate surface corrugation on morphology of supported monolayer graphene. J. Appl. Phys. 107, 123531 (2010).
5. W. Gao and R. Huang, Effect of surface roughness on adhesion of graphene membranes. J. Phys. D: Appl. Phys. 44, 452001 (2011).
6. E. Stolyarova, et al., Observation of graphene bubbles and effective mass transport under graphene films. Nano Lett. 9, 332-337 (2009).
7. T. Georgiou, et al., Graphene bubbles with controllable curvature. Appl. Phys. Lett. 99, 093103 (2011).
8. K. Yue, W. Gao, R. Huang, K.M. Liechti, Analytical methods for the mechanics of graphene bubbles. J. Appl. Phys. 112, 083512 (2012).
9. P. Wang, W. Gao, Z. Cao, K.M. Liechti, R. Huang, Numerical analysis of circular graphene bubbles. Journal of Applied Mechanics, accepted for publication, February 2013.