Jyväskylä Summer School

Course description:

Carbon is the key to an enormous number of organic substances, without which Life on Earth is unthinkable. Even in its elemental form, carbon forms a large variety of allotropes, ranging from diamond and graphite to graphene, nanotubes, fullerenes, onions, cones, chains and rings. Carbon also plays the key role in the evolving interdisciplinary field of Nanoscale Science and Technology, often called Nanotechnology.

In this short self-contained course, I will offer an introduction to what makes fullerenes, nanotubes, graphene and other carbon nanostructures so special. I will focus on promoting the basic understanding of the physical phenomena found in carbon nanostructures. To achieve this, I will utilize computer graphics and animations, while keeping the formal treatment at a minimum. I also wish to use brain-teasers as a fun way to promote independent thinking and an active communication among participants.

Lecture plan:

• Introduction to Carbon Nanosctructures
  • How It All Began: Synthesis of carbon buckyballs
  • List of stable carbon allotropes extended:
    diamond, graphite, graphene, fullerenes, metallofullerenes, solid C₆₀, bucky onions, nanotubes, nanocones
  • Challenging problems:
    
    • Dynamics of formation and destruction of nanocarbons
    • Static stability of carbon nanostructures
    • Stability of fullerenes under static pressure
    • Stability of fullerenes in collisions
    • Stability of fullerenes at high temperatures
    • Superconductivity of doped solid C₆₀
    • Static polarizability of fullerenes
    • Optical properties of fullerenes
  • Fullerene structures: From Leonardo da Vinci to the Geodesic Dome
  • Euler's Theorem and its application to fullerenes
  • Basic facts about graphite as building motif of fullerenes
• Theoretical Tools
  • Molecular dynamics for different thermodynamic ensembles
  • Basics of electronic structure and total energy calculations
  • Continuum elasticity theory: Fullerenes as deformed graphite
  • Density functional theory: The Limping Rolls-Royce
  • Parametrized Linear Combination of Atomic Orbitals (LCAO) approach: Strengths and Limitations
• Finite carbon structures: From chains to fullerenes
• Equilibrium geometry of carbon clusters
  • Small carbon clusters: Chains, rings, fullerenes
  • Entropy and finite temperature effects on structures
  • Stability of solid C₆₀ under compression
  • Relative stability of fullerenes: Deformation of graphite
  • Multi-wall fullerenes: Transition to graphite
  • Genealogy of fullerenes
• Atoms in a Cage: Endohedral fullerene complexes
  • Stability of donor and acceptor complexes
  • Dynamics of endohedral fullerenes: Roll, rattle and shake
• Collision dynamics of fullerenes
  • C₆₀-C₂₄₀ collisions at various energies ( movies)
  • Slow equilibration in nanostructures: A surprise that should not be one
• Melting transition in fullerenes
  • Do fullerenes undergo a melting phase transition?
  • Signatures of different "phases"
• Conductivity and superconductivity of the doped C₆₀ solid
  • C₆₀ as a molecular solid
  • Jahn-Teller effect and electron-phonon coupling
  • Electronic versus phonon coupling mechanism: The One-Hat-Fits-All theory and its breakdown
• Giant static polarizability of fullerenes: Fact or artifact?
• Dynamic polarizability of fullerenes
  • Collective dipole excitations in C₆₀
  • Dynamic multipole excitations in fullerenes
  • Inelastic electron scattering: No selection rules
• What have we learned about fullerenes?
  • Nothing new since graphite?
  • Exciting prospects: Use of fullerenes in hybrid structures
• Infinite carbon structures: From graphene to nanotubes
  • Introduction to Nanotubes
    • Nanotubes: From an overlooked by-product of fullerenes to a super-star
    • Tubular carbon allotropes: single-wall nanotubes, multi-wall nanotubes, ropes=bundled nanotubes
    • Challenging problems:
      
      • Isomer selectivity during synthesis
      • Equilibrium structures
      • Stability of nanotubes under extreme conditions:
  • Morphology of Graphene and Nanotubes
    • From a graphene sheet to a nanotube
    • Achiral and chiral nanotubes; single-wall, multi-wall, and bundled nanotubes; zigzag and armchair nanotubes
    • Euler's Theorem in cylindrical and defective nanotubes
  • Production Techniques of Nanotubes
    • Carbon arc bulk synthesis in presence and absence of catalysts
    • High-purity material (bucky paper) production using Pulsed Laser Vaporization (PLV) of pure and doped graphite
    • High-pressure CO conversion (HIPCO) nanotube synthesis based on Boudoir reaction
    • Chemical Vapor Deposition (CVD) synthesisof aligned nanotube films
  • Growth of Single-Wall Nanotubes
    • Experimental puzzles: high yield, universality of diameter, role of metal catalyst
    • Key question: shape of baby-tube?
    • Application of continuum elasticity theory to nanotubes
    • Tube diameter optimization in a finite system
    • Continuous growth by addition of carbon an the open edge
    • Role of metal catalyst: scooter or policeman?
    • Termination of growth
  • Growth of Multi-Wall Nanotubes
    • Experimental puzzles: aspect ratio, perfection, chemical inertness
    • Key question: independent or concerted growth?
    • Consequences of the lip-lip interaction
    • Equilibrium structure of double-wall nanotubes
    • Structure stability at the growing edge
    • Termination by a multi-walled dome
  • Genealogy of Fullerenes and Nanotubes Revisited
  • Nanotube stability and decay at high temperatures
    • Thermal stability/melting point similar to fullerenes and graphite
    • Decay at high temperatures: Transition to 1D structures at the edge ( movie).
  • Nanotube stability and decay under high mechanical stress
    • Unusually high Young's modulus
    • Simulated cutting of a nanotube (movie).
  • Nanotube stability and decay in strong electric fields
    • Experimental puzzles: high stability, large emission current, discrete fluctuations in the emission current
    • Key question: Microscopic structure at the tip?
    • Decay by unraveling atomic wires
• Structural and Electronic Properties of Graphene, Fullerenes and Nanotubes
• Interplay between geometry and electronic structure
  • Electronic structure of graphene and graphite as building block of nanotubes
  • Structural changes in free-standing and interacting nanotubes: Librations, rotations, twistons
  • Effect of inter-tube interactions on the electronic structure
• Structure and dynamics of interacting tubes
• Equilibrium structure of nanotube ropes
• Inter-tube interactions and orientational ordering
• Orientational dislocations in frustrated twisted, interacting tubes
• Mapping on a lattice gas of twistons
• Orientational melting of tubes
• Electronic structure of nanotubes
• Ignoring atomic positions: The layered jellium model
• Effect of chirality and discrete atoms: Conducting versus insulating nanotubes
• Band structure of metallic carbon nanotubes: dominant contribution of two pp-pi bands at E_F
• Band structure of interacting metallic nanotubes: The fatal touch that opens a gap
• Density of states of isolated and interacting metallic nanotubes: Van Hove singularities and pseudogaps
• Effect of doping on conductivity
• Dipole response of nanotubes: no surprises since fullerenes and graphite
• Application of Carbon Nanotubes
• Harnessing field enhancement: Flat-panel displays
• Harnessing tensile strength: Nano-velcro
• Controversy about Hydrogen Storage
• Summary and Conclusions
• Nanotubes as a unique self-assembling system
• Unusual properties: stability, thermal, electric conductance

Course Coordinator: Prof. Hannu Häkkinen (hannu.hakkinen@phys.jyu.fi)