. Author manuscript; available in PMC: 2017 Mar 21.

Published in final edited form as: Chem Soc Rev. 2016 Mar 21;45(6):1750–1780. doi: 10.1039/c5cs00914f

Table 3.

Relevant Mechanical Properties of 2D Materials and Biological Structures

	Bending stiffness κ (k_BT)	In-plane Young’s modulus Y^2D /area extension modulus K_A (J/m²)^a	Breaking strength/lysis tension (J/m²)^b	Thickness h (nm)	Poisson ratio ν
Graphene monolayer	56 ^{286, 287}	340 ^{286, 288}	42 ²⁸⁸	0.32 ²⁸⁹	0.17 ^{288, 289} 0.149 ²⁸⁶
h-BN monolayer	37 ²⁹⁰	271 ^{286, 291}; 292 ²⁹²	27.8 ²⁹¹; 71.7 ²⁹²	0.32 ²⁹³	0.211^{286, 291}
MoS₂ monolayer	375 ²⁹⁴	180±60 ^{295, 296}	15±3 ²⁹⁵	0.65 ^{295, 297}	0.3 ²⁹⁶
MoS₂ bilayer	700^c	260±70 ²⁹⁵	28±8 ²⁹⁵	1.3	0.3
Graphyne monolayer	65 ²⁹⁸	166 ^{299, 300}	20.64 ³⁰⁰	0.32 ²⁹⁸	0.42 ^{299, 300}
GO monolayer with carbon-to- oxygen ratio (4:1)	183^d	270 ³⁰¹	17–22 ³⁰¹	0.7 ³⁰²	0.165 ³⁰²
Lipid bilayer membrane^e	10–20 ^{282, 303}	0.25 ^{303, 304}	on the order of 0.001 J/m^{2 305,} ³⁰⁶	4–5 ²⁸²	N/A
Plasma membrane of red blood cell^f	50–100 ^{282, 307}	0.45 ²⁸²	on the order of 0.001 J/m^{2 305,} ³⁰⁶	4–5 ²⁸²	0.33 ³⁰⁸

The in-plane Young’s modulus E^2D of solid 2D materials, representing material resistance against in-plane deformation, is defined as E^2D=E_bh, where E_b is the bulk Young’s modulus of a three-dimensional stack of layers spaced at h.

The lysis tension is the maximum biaxial tension a lipid bilayer membrane can sustain before rupture.

The bending stiffness of MoS₂ bilayer is usually expressed as κ=E^2Dh_s³/[12(1-ν²)] according to the conventional theory of plates and shells, where the in-plane Young’s modulus E^2D is taken to be 260 J/m², Poisson ratio ν=0.3, and thickness h_s=0.62 nm.²⁸⁶

Mechanical properties of a GO monolayer depend on its atomic structure and chemical composition such as carbo-to-oxygen ratio.

Although the bending rigidity of a lipid bilayer falls typically in the range κ=10–20 k_BT, it can vary from 10 k_BT to 150 k_BT depending on the membrane composition.

The plasma membrane of a red blood cell consists of a bilayer of phospholipids, cholesterol molecules, transmembrane proteins and an underlying spectrin network which is attached to the membrane. Poisson ratio of the plasma membrane can be attributed to that of the spectrin network which is typically taken as ν=0.33.