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: Pνμ(z) and Qνμ(z)
• 2.9 Chebyshev Polynomials: Tn(x) and Un(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

Modelling and Mechanics of Carbon-based Nanostructured Materials sets out the principles of applied mathematical modeling in the topical area of nanotechnology. It is purposely designed to be self-contained, giving readers all the necessary modeling principles required for working with nanostructures.

The unique physical properties observed at the nanoscale are often counterintuitive, sometimes astounding researchers and thus driving numerous investigations into their special properties and potential applications. Typically, existing research has been conducted through experimental studies and molecular dynamics simulations. This book goes beyond that to provide new avenues for study and review.

• Explores how modeling and mechanical principles are applied to better understand the behavior of carbon nanomaterials
• Clearly explains important models, such as the Lennard-Jones potential, in a carbon nanomaterials context
• Includes worked examples and exercises to help readers reinforce what they have read

Early career scientists, advanced graduate students, professional engineers and R&D researchers working in the areas of materials science and nanoscience who are seeking to gain a better understanding of mechanical and modelling principles as they relate to carbon nanomaterials