*3.1.3.2. Pretension*

**Material Number of**

GO (Solutionbased deposition)

Mica (Mechanical exfoliated)

Se.

h-BN (CVD growth)

*3.1.3.1. Young's modulus*

**layers**

**Young's modulus**

228 Two-dimensional Materials - Synthesis, Characterization and Potential Applications

90 ± 6.4 (37 L)

224 ± 18 (2 L) 230 ± 27 (3 L)

269 ± 13 (4 L) 252 ± 15 (5 L) **Pretension (mN/m)**

54 ± 14 (1 L) 32 ± 6 (2 L) 28 ± 4 (3 L)

8.8 ± 1.2 (2 L) 12.8 ± 1.3 (4 L) 15.7 ± 1.5 (5 L)

**Table 1.** Summary of the in-plane mechanical properties of 2D materials measured from experiments.

2–14 202 ± 22 140 ± 80 4–9 2–4.5 Indentation on

Pristine monolayer graphene (prepared by mechanical exfoliation from bulk graphite) is reported to be the stiffest 2D material on earth so far with a Young's modulus of approximately 1 TPa [3, 49, 51], because of the strong in-plane covalent carbon–carbon bonds. For 2D TMDCs––MX2 (M = Mo, W; X = S, Se) with the same crystal structure (chalcogen atoms in two hexagonal planes separated by a plane of transition metal atoms) [11], a smaller Young's modulus of WSe2 has been observed compared with MoS2 and WS2 [42]; due to a decrease in the charge transfer and an increase in the lattice constant, resulting in a weakened binding between the metal and chalcogen [53], as M changes from Mo to W and X changes from S to

Meanwhile, the Young's modulus of some 2D materials (e.g., MoS2, BP, and h-BN) [2, 7, 41, 48] have been found to decrease with an increase in their thickness (number of layers), which is caused mainly by interlayer stacking errors. The occurrence of interlayer sliding in multi‐ layer 2D materials during indentation is also a factor for underestimating the intrinsic Young's modulus [7]. However, the Young's modulus of WSe2 remains unchanged statistically with increasing number of layers, which possibly results from the strong interlayer interaction in WSe2 [42]. As stated earlier, for 2D materials with thickness-dependent Young's modulus, precaution needs to be taken when using model Eq. (5) to derive the Young's modulus. Furthermore, the highly anisotropic atomic structure in 2D materials, such as BP, presents an

In addition, the mechanical properties of 2D materials largely depend on the density of crystal defects and thus are related to the preparation methods. For instance, the larger number of vacancy defects in the GO-reduced graphene and the existence of voids at the grain boundaries, together with wrinkles in polycrystalline graphene prepared by the CVD method, can contribute to the weaker mechanical properties [4, 55]. In addition, the presence of a larger

anisotropic Young's modulus along the different crystal orientations [54].

**Breaking stress (GPa)** **Breaking strain (%)**

N/A N/A Indentation on

~9 2.2 Indentation on

180–1200 >25 >8 Indentation on

**Characterization method**

circular membrane

circular membrane

circular membrane

circular membrane

**Ref.**

[41]

[57]

[60]

[2]

**(GPa)**

17, 37 276 ± 32 (17 L)

1–3 208 ± 23 (1 L)

2, 4, 5 279 ± 20 (2 L)

The factors that can affect the pretension in 2D materials are quite complicated. The pretension not only depends on the intrinsic mechanical properties of 2D materials, but also on the fabrication process of the suspended structure (e.g., the method of transferring 2D material onto the substrates). Therefore, the pretension values of suspended 2D materials in **Table 1** vary greatly. Generally, the dry transfer process with scotch tape or viscoelastic stamp introduces higher pretension compared with wet transfer process such as solution-based deposition [57]. Suspended structures fabricated by etching sacrificial layer (method shown in **Figure 1(c)**) normally possess less pretension than 2D materials transferred directly onto prepatterned substrates (method shown in **Figure 1(a)** and **(b)**). Annealing, as a common method to remove the residue on 2D materials left over by a fabrication process, can introduce thermal stress due to the different thermal expansion coefficients between the substrates and the 2D materials.

### *3.1.3.3. Breaking strength*

As presented in **Table 1**, the 2D materials with higher Young's modulus normally possess higher breaking strength. Many reports have found that the breaking stress of 2D materials can reach the theoretical upper limit (*E*Y/9) [7], due to low disorder and impurities in the characterized 2D materials. The existence of anisotropic breaking strength along armchair and zigzag directions has been found in BP, possibly resulting from its anisotropic Young's modulus [54]. Except for the 2D dielectrics (mica and h-BN), the breaking strain of most 2D materials is above 7%, which is comparable with the common materials used as substrates for flexible electronics, namely polyimide (PI) or polydimethylsiloxane (PDMS) [58], implying that most of the 2D materials are compatible with flexible electronic devices.
