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By John E. Proctor, Daniel Melendrez Armada, Aravind Vijayaraghavan

"This booklet introduces the reader to the technology of graphene and carbon nanotubes. The reader will achieve the elemental clinical wisdom to seriously overview the claims made within the literature and within the public area concerning the actual homes and power for functions of graphene and carbon nanotubes. additionally, the e-book makes use of those easy platforms as first-class types to illustrate vital thoughts in Read more...

summary: "This publication introduces the reader to the technology of graphene and carbon nanotubes. The reader will achieve the elemental clinical wisdom to seriously overview the claims made within the literature and within the public area in regards to the actual homes and capability for purposes of graphene and carbon nanotubes. moreover, the ebook makes use of those uncomplicated structures as first-class versions to illustrate very important innovations in good kingdom physics and fabrics chemistry to the reader. The ebook is co-authored by means of one of many leaders in public engagement on the nationwide Graphene Institute at Manchester collage, which used to be based in honour of the Nobel Laureate Sir Andre Geim"

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A larger overlap leads to more energy being saved when the bond forms, and hence a stronger bond. g. carbyne or acetylene): Hybridized orbitals are formed from linear combinations of the Ψ(2s) and Ψ(2px) wave functions. g. graphene or benzene): Hybridized orbitals are formed from linear combinations of the Ψ(2s) and Ψ(2px), Ψ(2py) wave functions. g. diamond or methane): Hybridized orbitals are formed from linear combinations of the Ψ(2s) and Ψ(2px), Ψ(2py), Ψ(2pz) wave functions. e. Z protons and one electron), the 2s and 2p orbitals have the same energy.

3, but propagating through the graphene lattice with wavevector k. The wavevector enters the calculation because it determines the phase shift between the values of the electron wave function at adjacent atomic sites. To find the energy we apply the Hamiltonian operaˆ to the function Ψ(π). We then pre-multiply the exprestor H sion by Y *A (2pz ), and integrate over all space. 4) H 36 An Introduction to Graphene and Carbon Nanotubes 1 ˆ Y A ( 2pz ) dt ± 1 Y *A ( 2pz ) H 2 6 ò åòY* ( 2p )Hˆ Y A z Bn ( 2 p z ) dt n E(k) E(k) = Y *A ( 2pz ) Y A ( 2pz ) dt ± 6 2 ò åòY* ( 2p ) Y A z Bn ( 2 p z ) dt n We can separately evaluate each term in this expression.

1 sp hybridization Mathematically, sp hybridization is the simplest case of orbital hybridization in carbon. 5) Y ( sp )b = C3 Y(2s) + C4 Y ( 2px ) The Ψ(sp)a,b wave functions must be orthonormal. 6) 2 2 We have defined C4 as negative here. However, we can see by inspection that whichever coefficient we define as negative, hybridized orbitals in which the electron clouds have the same spatial distribution will result – that is, |Ψ|2 (the only physical observable) will be unaffected. What do the Ψ(sp)a,b hybridized orbitals look like?

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