Mechanical Interactions at the Interfaces of Atomically Thin Materials (Graphene)

Transcription

1 Mechanical Interactions at the Interfaces of Atomically Thin Materials (Graphene) Rui Huang Center for Mechanics of Solids, Structures and Materials Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin April 4, 218

2 Acknowledgments Peng Wang (graduate student) Chaochen Xu (visiting graduate student, Tianjin University) Wei Gao (former graduate student, now at UTSA) Prof. Ken Liechti (UT) Prof. Nanshu Lu (UT) Prof. Yong Zhu (NCSU) Funding: National Science Foundation

3 Mechanical properties: elastic and inelastic Electromechanical coupling Interfacial properties: adhesion and friction Applications (synthesis, origami/kirigami, devices)

4 Mechanics of 2D Interfaces: Adhesion and Friction Bunch et al, Egberts et al, 214.

5 Adhesion experiments Micro-blister tests (Bunch et al., ) Large-scale blister tests (Liechti et al., ) DCB tests (Yoon et al., 212; Na et al., ) Nanoindentation experiments (Jiang and Zhu, 215; Suk et al., 216) In addition to the adhesion energy, measurements of the tractionseparation relations for the adhesive interactions provided more information as to the interaction mechanisms.

6 van der Waals Interactions DFT (DFT-D2, vdw-ts, vdw-df) δ.1 Interaction energy (J/m 2 ) UFF Charmm Dreiding DFT (Hydroxylated) DFT (Reconstructed) MD (LJ potential): V ij ( R ij ij ) ij Rij 12 ij Rij Separation (A) Continuum approximation: U vdw 3 ( ) Gao et al., J. Phys. D 47, (214).

7 Traction-Separation Relations vdw du vdw d 9 2h h 4 h 1 vdw capillary experiment vdw (DFT) Capillary Experiments (MD) Strength (MPa) ~1 ~9 ~5 Range (nm) ~1 ~3 1-6 Toughness (J/m 2 ) ~.3 ~.1 ~.3 Low strength Long range

8 Adhesion Energy of Graphene Substrate Si/SiO x Cu film Cu foil Cu transfer Γ (J/m 2 ) ~6. ~.34 The adhesion energy of graphene on Si/SiO x compares closely with the predictions by DFT for van der Waals interactions. More complicated for copper substrates, depending on the surface roughness and Cu grain structures Relatively scarce data for adhesion on polymer substrates (epoxy, PDMS, PET) Other effects: o Effect of surface roughness (across many length scales) o Effect of temperature (thermal rippling) o Effect of moisture (wet adhesion) o Effect of mode mix (normal and shear interactions)

9 Effect of Surface Roughness on Adhesion Long-wave limit: conformal graphene, with the adhesion energy same as the flat surface Short-wave limit: suspended graphene, with effectively lower adhesion energy, depending on the amplitude of surface waviness Gao and Huang, J. Phys. D 44, 4521 (211).

10 Multilayered Graphene Higher bending stiffness less conformal lower adhesion energy 1.46 g / s N = 1 N = 2 N = 3 (J/m 2 ) =.45 J/m 2 =.6 nm s s =.1 nm.2 N = 1.38 s =.2 nm /h N Gao and Huang, J. Phys. D 44, 4521 (211).

11 Thermal Rippling of Graphene on Substrate ( T ) substrate Compared to freestanding graphene, rippling amplitude of a supported graphene is considerably lower and independent of the membrane size. Thermal rippling leads to an entropic repulsion, and hence the equilibrium separation increases (out-of-plane thermal expansion) and effective adhesion energy decreases with increasing temperature. Wang et al., JAP 119, 7435 (216).

12 Biaxially strained graphene Tension reduces rippling amplitude and the entropic repulsion. Compression amplifies rippling amplitude significantly, resembling a buckling instability. Wang et al., JAP 119, 7435 (216).

13 T = 3 K Rippling to Buckling Transition Beyond a critical compressive strain, localized buckling is observed, with possible delamination. Wang et al., JAP 119, 7435 (216).

14 Wet Adhesion: Graphene/water separation 1nm Continuous water film Water cavitation Water bridging Gao et al., EML 3, (215).

15 Traction-separation relations 1 nm 4 nm Three stages of separation. Cavitation at the water/graphene interface sets the critical tension, which is considerably lower than that for bulk water (~14 MPa). Subsequent transitions of water morphology (cavitation to ridges to islands) depend on water thickness. Gao et al., EML 3, (215).

16 Adhesion hysteresis.2.15 Traction (GPa) Separation d (nm) The snap transitions of cavitation leads to adhesion hysteresis. Wang et al., unpublished.

17 Effect of graphene/water contact angle.25.2 = 1 = 9 = 6 = t w = 4.19 nm t w = 3.11 nm t w = 2.6 nm Traction (GPa).15.1 h w = 2 nm Traction (GPa) t w = 1.1 nm θ g = 6⁰ Separation d (nm) Separation d (nm) The traction-separation relation depends on the water contact angle of graphene and the water thickness. Stronger graphene-water interactions lead to lower contact angle and stronger wet adhesion. Thinner water leads to higher initial stiffness and strength.

18 Ultrathin water (< 1 nm) Bilayer of water molecules (~.6 nm) Monolayer water (~.3 nm) Traction (GPa) wg = 1 wg = 9 wg = 6 wg = 3 Traction (GPa) gw wg = 1 wg = 9 wg = 6 wg = Separation (nm) gs Separation (nm) Wang et al., unpublished.

19 Double-peak traction-separation relation Traction (GPa) Separation (nm) First peak: graphene interacting with a water monolayer Second peak: graphene interacting with two half-monolayers Only one peak for weak graphene/water interactions as water remains a monolayer Wang et al., unpublished.

20 Wet adhesion of graphene (summary) S gs g = 1 g = 9 Adhesion (J/m 2 ).15.1 g = 1 g = 9 g = 6 g = 3 Strength S (GPa) g = 6 g = 3.5 gs t (nm) t w (nm) Both the adhesion energy and strength depend on the water contact angle and water thickness. Discrete water layers at sub-nm thickness lead to higher adhesion energy and strength (but shorter ranged). Wang et al., unpublished.

21 Water-filled graphene blisters.25 Modified weak shear.2 Weak shear h/a.15 Strong shear A continuum model predicts the aspect ratio as a function of the adhesion energy, independent of the number of water molecules. Sanchez et al., in review.

22 However, the continuum model breaks down when the adhesion is too weak or the number of water molecules is too small N = 3, =.1 J/m 2 N = 27, =.1 J/m 2 N = 27, =.5 J/m 2 N = 27, =.24 J/m 2 N = 27, =.5 J/m 2.4 ww.2 ws + wg - gs -.2 gs x (nm) Sanchez et al., in review.

23 Shear interactions: sliding friction and stress transfer Graphene strain (%) Why? L Applied strain m (%) Sample #3 Sample #4 c p c ~.5 MPa 2E2D Jiang et al., 214. c ~.3.4 MPa Xu et al., 216.

24 Interlayer shear interactions of bilayer graphene Sliding before delamination Wang et al., PRL 119, 3611 (217).

25 Graphene sliding on a wavy surface Calculate the shear force on each carbon atom:, Γ Xu et al., unpublished.

26 Relation between Adhesion and Shear (Friction) 7. Γ 8.2 ~ Γ Γ Take ~1 nm and ~.5 nm Xu et al., unpublished.

27 Summary Despite extensive effort in experiments and modeling, understanding the mechanical interactions of atomically thin materials (graphene and others) remains a great challenge due to complex physics, chemistry and mechanics. Wolfgang Pauli: God made the bulk; surfaces (interfaces) were invented by the devil. and as we all know, the devil is in the details.