Modelling and Mechanics of Carbon-based Nanostructured Materials

Chapter 1: Geometry and Mechanics of Carbon Nanostructures

• Abstract
• 1.1 Background
• 1.2 Carbon Nanostructures
• 1.3 Interaction Between Molecular Structures
• 1.4 Book Overview
• Exercises

Chapter 2: Mathematical Preliminaries

• Abstract
• 2.1 Introduction
• 2.2 Dirac Delta Function: δ(x)
• 2.3 Heaviside Function: H(x)
• 2.4 Gamma Function: Γ(z)
• 2.5 Beta Function: B(x, y)
• 2.6 Hypergeometric Function: F(a,b;c;z)
• 2.7 Appell’s Hypergeometric Function: F₁(a;b,b’;c;x,y)
• 2.8 Associated Legendre Functions: P_ν^μ(z) and Q_ν^μ(z)
• 2.9 Chebyshev Polynomials: T_n(x) and U_n(x)
• 2.10 Elliptic Integrals: F(ϕ, k) and E(ϕ, k)
• Exercises

Chapter 3: Evaluation of Lennard-Jones Potential Fields

• Abstract
• 3.1 Introduction
• 3.2 Interaction of Linear Objects
• 3.3 Interaction of a Spherical Surface
• 3.4 Interaction of a Cylindrical Surface

Chapter 4: Nested Carbon Nanostructures

• Abstract
• 4.1 Introduction
• 4.2 Atom@Fullerene—Endohedral Fullerene
• 4.3 Fullerene@Fullerene—Carbon Onion
• 4.4 Fullerene@Carbon Nanotube
• 4.5 Carbon Onion@Carbon Nanotube
• 4.6 Carbon Nanotube@Carbon Nanotube—Double-Walled Carbon Nanotube
• 4.7 Nanotube Bundles
• 4.8 Carbon Nanotube@Nanotube Bundle
• 4.9 Fullerene@Nanotube Bundle
• Exercises

Chapter 5: Acceptance Condition and Suction Energy

• Abstract
• 5.1 Introduction
• 5.2 C₆₀ Fullerene Inside a Carbon Nanotube
• 5.3 Double-Walled Carbon Nanotubes
• 5.4 Nanotube Bundle
• Exercises

Chapter 6: Nano-oscillators

• Abstract
• 6.1 Introduction
• 6.2 Oscillation of a Fullerene C₆₀ Inside a Single-Walled Carbon Nanotube
• 6.3 Oscillation of Double-Walled Carbon Nanotubes
• An alternative approach
• 6.4 Oscillation of Nanotubes in Bundles
• Exercises

Chapter 7: Mechanics of More Complicated Structures: Nanopeapods and Spheroidal Fullerenes

• Abstract
• 7.1 Introduction
• 7.2 Nanopeapods
• 7.3 Spheroidal Fullerenes
• Exercises

Chapter 8: Nanotubes as Drug Delivery Vehicles

• Abstract
• 8.1 Introduction
• 8.2 Underlying Mathematics
• 8.3 Encapsulation of Cisplatin Into a Carbon Nanotube
• 8.4 Alternative Nanotube Materials
• Exercises

Chapter 9: New Formulae for the Geometric Parameters of Carbon Nanotubes

• Abstract
• 9.1 Introduction
• 9.2 Conventional ‘Rolled-Up’ Model
• 9.3 New ‘Polyhedral’ Model
• 9.4 Details of the Polyhedral Model
• 9.5 Results
• 9.6 Conclusion
• Exercises

Chapter 10: Two Discrete Approaches for Joining Carbon Nanostructures

• Abstract
• 10.1 Introduction
• 10.2 Nanotori
• 10.3 Joining Carbon Nanotubes and Flat Graphene Sheets
• 10.4 Nanobuds
• Exercises

Chapter 11: Continuous Approach for Joining Carbon Nanostructures

• Abstract
• 11.1 Introduction
• 11.2 Calculus of Variations
• 11.3 Joining Carbon Nanotubes and Flat Graphene Sheets
• 11.4 Nanobuds
• 11.5 Nanopeanuts
• Exercises

Hints and Solutions

• Chapter 1
• Chapter 2
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11