Measuring Interlayer Shear Stress in Bilayer Graphene

Monolayer two-dimensional (2D) crystals exhibit a host of intriguing properties, but the most exciting applications may come from stacking them into multilayer structures. Interlayer and interfacial shear interactions could play a crucial role in the performance and reliability of these applications, but little is known about the key parameters controlling shear deformation across the layers and interfaces between 2D materials. Herein, we report the first measurement of the interlayer shear stress of bilayer graphene based on pressurized microscale bubble loading devices. We demonstrate continuous growth of an interlayer shear zone outside the bubble edge and extract an interlayer shear stress of 40 kPa based on a membrane analysis for bilayer graphene bubbles. Meanwhile, a much higher interfacial shear stress of 1.64 MPa was determined for monolayer graphene on a silicon oxide substrate. Our results not only provide insights into the interfacial shear responses of the thinnest structures possible, but also establish an experimental method for characterizing the fundamental interlayer shear properties of the emerging 2D materials for potential applications in multilayer systems.

Figure 1

(a) Schematic diagram of a bilayer graphene bulging device and characterizations. The left inset shows profiles of a graphene bubble with increasing pressures. The right inset shows Raman spectra of a graphene $G$ band stacked vertically in the direction of a line scan. (b) Optical and (c) SEM images of exfoliated graphene sheets on the prepatterned ${\mathrm{SiO}}_2$ substrate.

Figure 2

Schematic diagrams of bulged (a) monolayer and (b) bilayer graphene samples. Raman contour maps of $G$-band frequency in one quadrant revealed the strain distributions in (c)—(e) monolayer and (f)—(h) bilayer graphene samples in both suspended and supported regions at different pressures. The cross sections of Raman contour maps are shown for (i) monolayer and (j) bilayer graphene. The insets show the variation of the $G$-band frequency near the edges of the hole. Solid vertical lines are positioned at the edges of the hole, and the dashed horizontal lines indicate the frequency of the $G$ band at zero strain.

Figure 3

(a) Spatial distribution of the interfacial binding energy between bottom-layer graphene and the silica substrate. (b) Decomposed in-plane displacement $u_r$ in the top-layer graphene calculated from the MD simulation results. (c,d) The interlayer shear behaviors of bottom-layer and top-layer graphene, resolved by the atomic displacement under specific pressure difference.

Figure 4

The growth of the (a) interfacial and (b) interlayer shear zone versus $\mathrm{\Delta }p$ for monolayer and bilayer graphene bubbles. The lines are predicted by the membrane analysis with different interfacial shear stresses. Normalized center deflection versus $\mathrm{\Delta }p$ for (c) monolayer and (d) bilayer graphene bubbles. Solid lines are predicted by the membrane analysis with $Et=390\mathrm{N}/\mathrm{m}$ and ${\tau }_1=1.64\mathrm{MPa}$ for monolayer and ${\tau }_2=0.04\mathrm{MPa}$ for bilayer. Dashed lines are predictions without considering interfacial or interlayer shear deformations in the supported regions.

Figure 5

Measured shear stresses for graphene-${\mathrm{SiO}}_2$ and graphene-graphene interfaces. Dashed lines correspond to the average values of 1.64 MPa and 0.04 MPa.