Mechanical properties, such as malleability and ductility, do not apply to single atoms of any element because mechanical properties arise when atoms bond. The type, strength and orientation of these resulting bonds determines the mechanical properties of matter.
The covalent carbon-carbon bond between two carbon atoms involves the participation of one, two or three electrons from each atom. Single carbon-carbon bonds most commonly result when two carbon atoms each hybridize and share their sp3 orbitals. Single bonds between carbon atoms can also result from other, less common orbital hybridizations, such as sp2 hybridization. The approximate energy of a single carbon-carbon bond is 80 kilocaries per mole.
Two carbon atoms can also double bond through two hybridized sp2 orbitals and two unhybridized p orbitals. The average energy of the resulting bond is 140 kilocaries per mole.
These values are exceptionally high in comparison with other elemental bond energies, such as 38.4 kilocaries per mole for nitrogen-nitrogen bonds and 35 kilocaries per mole for oxygen-oxygen bonds. Carbon is also capable of catenation, the formation of long, continuous chains of its own atoms. The high interatomic bond strength and catenation ability of carbon give it different forms of exceptional mechanical properties. Carbon nanotubes have a theoretical Young’s modulus of 1 tetrapascal and tensile strengths between 11 and 63 gigapascals. The covalent nature and directionality of carbon-carbon bonds limit the malleability and ductility of carbon allotropes.