The Applications of Nano Materials

1. The Applications of Nano Materials Department of Chemical and Materials Engineering San Jose State University Zhen Guo, Ph. D.

2. Fundamentals of • Nano Material Science • Session II: Atomic Structure/Quantum Mechanics • Session III: Bonding / Band Structures • Session IV: Computational Nano Materials Science • Session V: Surface / Interface Properties

3. Session III: Bonding and Band Structure • Bonding • Bonding Type • Band and Electronic Structures

4. Atomic Bonding • Attractive Force: Coulomb Force between atom nucleus and electron in the other atoms. • Repulsive Force: Pauli Exclusion for two electrons • Bonding length at r=r0, F=0 and E is minimum. • Bonding Energy, everything below zero. • Non-symmetric shape. Thermal expansion

5. Theory of Linear Combination of Atomic Orbital (LCAO) • Electrons in molecular occupy Molecular Orbital (MO) which can be expressed as the linear combinations of atomic orbital (Eqn 1) where yi are the AO wave function of the atoms in this n-atom molecular and Ci is the contribution to the specific AO (Eqn 2)

6. Theory of Linear Combination of Atomic Orbital (LCAO) (Con’d) Substitute Eqn 1 into 2 and define: Overlap Integral Coulomb Integral (j=k) Resonance Integral We have: For any arbitrary wave function, we varies Ci to achieve lowest energy state

7. Hückel Assumptions • Assumption 1: The Coulomb Integrals are treated identical • Assumption 2: Resonance Integrals are depending upon bonding for adjacent atoms for other atoms • Assumption 3: The wave functions are orthogonal so overlap integral can be neglected for j=k for other atoms

8. Two-atoms Molecular Assume atom 1 and 2 has their wave function as ψ1 and ψ2 Bonding Molecular Orbital Anti-Bonding Molecular Orbital • a represents the first ionization energy (~-10ev) of atoms, so -13.6ev for H • b represents bonding energy for isolated bond (~-1ev) • Both a and b are negative number so the energy of bonding MO is actually lower than anti-bonding MO

9. Hydrogen Molecular • When two Hydrogen atoms are far enough: no overlap of wave function, still two atoms. • When they are approaching each other, electron cloud or wave function start to overlap, form a covalent bonding. Molecular Orbital is Linear Combination of atomic orbital (LCAO) method • If two hydrogen atoms are in phase, they will form symmetric Bonding Molecular orbital • If two hydrogen atoms are out of phase, they will form antisymmetric anti-bonding Molecular Orbital Courtesy from S. O. Kasap Principle of

10. Linear Combination of Atomic Orbital • Energy of bonding and anti bonding orbital • -- Bonding orbital has energy lower than sum of two isolated H atoms. • -- Anti bonding orbital has energy higher than sum of two • Bonding energy is delta energy between two isolated H atoms and one H molecular. For H atom, two isolated with 2a while two electrons on 1 MO is 2(a+b). So the bonding energy DE is 2b

11. Three-Atom-Molecular • Three Hydrogen atoms, each will contribute one electron but two available states. • Electrons still always starts from the lowest energy and fills bottom up to form spin pairs • Comparing this configuration with two-hydrogen-atom-molecular, it is obvious that the latter are more stable.

12. LCAO theory on Multi-atom System 6 atoms 4 atoms Courtesy from Rainer Waser Nanoelectronics and Information technology

13. LCAO theory on Multi-atom System 24 atoms Chain Courtesy from Rainer Waser Nanoelectronics and Information technology

14. Many-Atom System: Band Structure • N Hydrogen or Lithium atoms, each will contribute one valence electron but two available states. • Electrons still always starts from the lowest energy and fills bottom up to form spin pairs • Because N number is so large (1023), the energy delta between different states are so small that it can be considered as continuous. • In case of Li, N electrons are occupying 2N states so the valence band is only half full

15. Band Structure for metals and semiconductors

16. Band Structure for Nano Materials • Nano Materials does not have infinite number of atoms. • -- A particle of 5nm Nano materials with lattice parameter of 2.5A consists of about 20X20X20 i.e. 8000 atoms. • -- This number is large enough to pose significant challenge for any attempt to accurate calculations of Energy level through computational material science • -- However it is still not enough to be considered as continuum mechanics from any macroscopic point of view • Today’s computational material science can calculate up to hundreds atoms using ab initio or first principle calculations • (Next Session – Computational Nano Material Science)

17. Bonding Type I – Metallic Bonding

18. Bonding Type II – Covalent Bonding

19. Bonding Type III – Ionic Bonding

20. Bonding Type IV – Van De Walls Force from permanent and induced Dipole

21. Summaries

22. Examples • Carbon: 1S22S22P2 Hybridization: SP3 / SP2 • 3-D Structure – Diamond; 2-D Structure – Graphite; 1-D structure – CNT 0-D structure -- Bucky Ball • Different bonding and crystal structure will lead to different band and therefore electronic Properties

23. 3-D Carbon Structure -- Diamond • Diamond structure – SP3 Hybridization. • Bonding and Anti-bonding Molecular Orbitals • Covalent Bonding -- Two neighboring atoms shared one pair of electrons. • Bonding Orbital will form valence band (Full) and anti-bonding orbital will form conduction band (Empty) • Large Band gap => Insulator

24. 2-D Carbon Structure -- Graphite • Graphite Structure – SP2 Hybridization. • 3 in-plane covalent bonding (120 degree with each other) • One weakly bonded electrons between layers • Electronically it is conductor when field is perpendicular with layers. • Mechanically it is good lubricant when shear force applied between layers Courtesy from http://www.phy.mtu.edu /~jaszczak/structure.html

25. Graphite Band Structure • Theoretical calculations showed Bonding and Anti-bonding energy are touching. • Zero Band gap semiconductor between conduction band and valence band. • In reality, there are 40mV overlap between these two band due to interaction between layers Courtesy from Rainer Waser Nanoelectronics and Information technology

26. 1-D Structure – Carbon Nano Tube Chiral Vector: where a1 and a2 are unit vector of hexagonal lattice and (n, m) set up Chiral angle Courtesy from Rainer Waser Nanoelectronics and Information technology

27. Band Structure of SCNT • Arm Chair Structure (3, 3) -- Metallic • Chiral Structure (4, 2) -- Semiconductor Courtesy from Rainer Waser Nanoelectronics and Information technology

28. 0-D Carbon Structure: C60 Ball • 0-D C60 Fullerence • Soccer ball with 5 and 6-atom rings Courtesy from Rainer Waser Nanoelectronics and Information technology