150Åand ethene at 1.33Å bond length) and smallest for triple-bonded carbon (acetylene, 1.20
151Å). On the other hand, the van der Waals (vdW) radius of a carbon atom is given as 1.70152Å . An early measurement of the thickness of the benzene molecule gave 4.70Å, 10 while the 153 thickness of the larger pyrene molecule is 3.53Å, 11 very close to the spacing of the graphene 154 sheets in graphite at 3.35Å.155 These considerations appear to give a clear meaning to the concept of the vdW thickness 156 of graphene, as much as of simpler molecules such as benzene and the higher polycyclic 157 aromatic compounds such as pyrene. It expresses the distance of closest approach of other 158 physisorbed atoms -whether carbon or anything else, because the repulsive interatomic 159 potential deriving from Pauli exclusion is largely independent of the nature of the interacting 160 atoms, and in the absence of a chemical bond, so is the vdW attractive potential. Following 161 Wyckoff, 9 the thickness should be expected to vary with the environment, whether it is a 162 surrounding gas or a substrate, as can be seen in Table I -even quite considerably as the 163 vdW forces, while always weak, can vary by an order of magnitude. 164 B. Graphene elastic stiffness tensor 165 Only in graphite is graphene found in a symmetrical environment (sandwiched between 166 graphene sheets with only a vdW potential binding them) and with a known thickness. We 167 may then define the graphene elastic stiffness constants c ij in this situation as a reference 168 system. To deal with possible variations in thickness in other environments, it makes sense