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Modelling and Mechanics of Carbon-based Nanostructured Materials - 1st Edition - ISBN: 9780128124635, 9780128124642

Modelling and Mechanics of Carbon-based Nanostructured Materials

1st Edition

Authors: Duangkamon Baowan Barry Cox Tamsyn Hilder James Hill Ngamta Thamwattana
eBook ISBN: 9780128124642
Paperback ISBN: 9780128124635
Imprint: William Andrew
Published Date: 18th January 2017
Page Count: 386
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Table of Contents

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.

Key Features

  • 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


No. of pages:
© William Andrew 2017
18th January 2017
William Andrew
eBook ISBN:
Paperback ISBN:

Ratings and Reviews

About the Authors

Duangkamon Baowan

Duangkamon Baowan is Associate Professor of Applied Mathematics at Mahilodi University, Thailand, having previously worked at the University of Wollongong, Australia. Her research is focused on the mechanics of nanoscaled materials

Affiliations and Expertise

Associate Professor of Applied Mathematics, Mahilodi University, Thailand

Barry Cox

Barry J. Cox is Senior Lecturer in Applied Mathematics at the University of Adelaide, Australia. His research interests include nanoscaled oscillating systems, modelling nanoscale devices using continuum mechanics and predicting properties of nanomaterials using analytical techniques. He is a member of several professional bodies, including the Australian Nanotechnology Network.

Affiliations and Expertise

Senior Lecturer in Applied Mathematics, University of Adelaide, Australia

Tamsyn Hilder

Tamsyn Hilder is a Lecturer in Computational Chemistry at Victoria University of Wellington, New Zealand. Her research focuses on computational biophysics of membrane proteins and nanomaterials, and the interaction between nano and biological materials.

Affiliations and Expertise

Lecturer in Computational Chemistry, Victoria University of Wellington, New Zealand

James Hill

James M. Hill is Professor of Theoretical Mechanics and Group Director of the Nanomechanics Group at the University of Adelaide, Australia. He has previously written five books and published over 300 research publications in peer-reviewed journals.

Affiliations and Expertise

Professor of Theoretical Mechanics and Group Director of the Nanomechanics Group, University of Adelaide, Australia

Ngamta Thamwattana

Ngamta Thamwattana is Associate Professor at the School of Mathematics and Applied Statistics at the University of Wollongong, Australia. Her research focuses on mathematical modelling in nanotechnology.

Affiliations and Expertise

Associate Professor, School of Mathematics and Applied Statistics, University of Wollongong, Australia