(a) Dependences of strength and toughness of the two representative crosslink types (coordinative bonds, CB and hydrogen bonds between epoxy and hydroxyl groups, HB1) and graphite. (b) The dependence of tensile strength and toughness on interlayer shear modulus G and graphene sheet size l.
Graphene-based papers attract particular interests recently owing to their outstanding properties, the key of which is their layer-by-layer hierarchical structures similar to the biomaterials such as bone, teeth and nacre, combining intralayer strong sp2 bonds and interlayer crosslinks for efficient load transfer. Here we firstly study the mechanical properties of various interlayer and intralayer crosslinks via first-principles calculations and then perform continuum model analysis for the overall mechanical properties of graphene-based papers. A deformable tension-shear (DTS) model is presented by considering the elastic deformation of the graphene sheets and the interlayer and intralayer crosslinks. The DTS is then applied to predict the mechanics of graphene-based paper materials under tensile loading. According to the results we thus obtain, optimal design strategies are provided for designing graphene papers with ultrahigh stiffness, strength and toughness.
A graphene paper sample. Picture by Lisa Aloisio
* for all the structures, the toughness of graphene paper maximizes for the graphene size at l ~ 23 nm.
* by increasing the graphene sheet size and crosslink strength, the strength and toughness of the materials will be enhanced cooperatively.
* the strength can be changed from 10 MPa to 10 GPa and toughness changes from 3 MPa to 400 MPa.
Graphene-based paper, and in general nanocomposites, are projected for various applications requiring ultrastrong, lightweight and multifunctional features. One additional benefit from interlayer crosslinks is that as they are introduced, the interlayer distance is expanded. In comparison to metals such as aluminum with a mass density 2.7 g/cm3, the density of graphite, 2.25 g/cm3, is already lower. For the coordinative bonds as an example, the expansion due to coordinative bond will further lower the density approximately by half.
So cross-linked graphene can have a density of 1.1 g//cm3 and have optimal cross linking for a strength of 10 GPa.
Material Ultimate tensile strength Density g/cm3 Graphene 130 GPa 1.0 Colossal carbon tube 7 GPa 0.116 Carbon nanotube 11-63 GPa 0.037-1.34 first carbon nanotube ropes 3.6 GPa 1.3 Best Carbon Paper 10 GPa 1.1
By substituting all the mechanical parameters obtained from first-principles calculations to the equations, we plot the strength and toughness of three representative crosslink types in Figure 6(a). For graphite, where the interlayer distance between graphene sheets is h0 = 0.335 nm, interlayer shear modulus G = 2.548 GPa and maximum shear strain γcr = 0.144, the maximal strength and toughness are 6.3 GPa and 38 MPa respectively. With the enhancement from Mg-centered coordinative bonds, G = 970 MPa, h0 = 0.71 nm and γcr = 0.76, thus we have the shear strength approaching 14 GPa, and toughness of 400 MPa. While with the Hbond networks formed between epoxy and hydroxyl groups, where G = 763 MPa, h0 = 0.545 nm and γcr = 0.135, the shear strength and toughness are 2.5 GPa and 10 MPa. It is also noticeable that for all the structures, the toughness maximizes for the graphene size at l ~ 23 nm. Furthermore we vary the shear modulus from 970 MPa to 97 and 9.7 MPa, and graphene sheet size from 100 nm to 1 nm to track their impacts on mechanical properties of the graphene papers. The graphe at the start shows the strength changes from 10 MPa to 10 GPa and toughness changes from 3 MPa to 400 MPa. Thus by increasing the graphene sheet size and crosslink strength, the strength and toughness of the materials will be enhanced cooperatively.