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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 [2] and the double-cantilever beam test [3]. 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 [4]. 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) [5]. 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. [2] 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 [8]. 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 [9]. 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.
References
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.
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Comments
Mechanisms dictating graphene adhesion
Thanks, Rui, for this timely discussion.
The importance of understanding the adhesion between graphene and other materials cannot be overstated for achieving more reliable graphene-based applications in electronic devices and nanocomposites. Given the two-dimensional nature of graphene, its adhesion is not only related to graphene's intrinsic properties, but also, more crucially, dictated by extrinsic interactions with the surrounding materials that graphene interfaces. In the past several years, we have investigated the mechanisms that dictate the adhesion of graphene, both freestanding and substrate supported. The following papers summarize the findings:
thanks for your comments
Teng,
Thanks for your comments. I have yet to read your most recent paper on this subject. It is on my list.
RH
Which forces are relevant?
Hi Rui,
Thanks for the nice post. In your discussion, you mentioned many possible forces that can contribute to the interfacial adhesion -- van der Waals, Casimir, electrostatic, capillary, etc. In reference 4, you consider the van der Waals interactions. I am curious if it is generally accepted in the community that van der Waals forces are the most important. I am curious for 2 reasons:
1. What kinds (if any) of qualitatively different phenomena would you observe if some of the other forces were important?
2. In other systems of monolayers on substrates (i.e. materials other than graphene) is it possible that some of these other interactions are more prevalent?
Good questions
Hi Matt,
I cannot answer either of your questions unfortunately. Many people simply attribute interfacial adhesion of graphene to van der Waals forces. However, others in field of adhesion would caution that other forces cannot be easily ruled out. In particular, it is well known that adhesive properties are very sensitive to the presence of even trace amounts of vapors in the environment, due in part to the capillary condensation of water on surface. Some preliminary experiments have observed interfacial forces over a much longer range than typical van der Waals forces (~1 nm), possibly due to the capillary forces.
RH
can we have the graphene and the substrate surface bounded
Dear Rui, Thank you for posting the interesting topic.
As you mentioned, the interfacial adhesion between graphene and substrate
is usually produced by van der Waals forces. In your paper, an equilibrium
separation between graphene and the substrate surface was assumed.
In experiment operation, can we have the graphene
and the substrate surface bounded together(the separation is zero)? I am not
sure whether or not the assumption(no separation between graphene and the
substrate surface) is reasonable to study the mechanics of grapheme-coated structures?
Thanks,
Lianhua
zero separation
Lianhua,
At the atomistic scale, the separation can never be zero. The relevant length scale varies with the bonding mechanism. A chemical bond has a separation in the order of 0.1 nm. The van der Waals forces typically have a scale of 0.3-1 nm (longer range compared to the chemical bond). The Casimir effect is reported to have a range of 10 nm. In experiments, it depends on the resolution of your measurements. If the resolution is no less than 10 nm, a separation of 0.1 nm may be considered zero. For monolayer graphene, the zero separation assumption would be no good since the thickness of graphene (however you define it) is comparable to the interfacial separation. Whether you can assume zero separation may also depend on what problem you are trying to solve.
Regards,
RH