Mechanical Properties of Nanostructured Materials: Quantum Mechanics and Molecular Dynamics Insights

By Abdolhossein Fereidoon, Masuod Darvish Ganji, Farzaneh Memarian and Maziar Dehghan

Nowadays, with the improved abilities of computers, molecular modeling has become a powerful technique in computational chemistry with ever-increasing practical interests. At the moment, using effective algorithms along with powerful processors enables us to simulate systems, including thousands of atoms up to several microseconds. However, finding a balance between the computational costs and reliable results still remains a challenge. Two general approaches help us to reveal the behavior of these systems: quantum chemical calculations and molecular mechanics calculations. Quantum mechanics deals with physical phenomena as well as atoms behavior during chemical bonding and falls in the category of modern physics. In this book, two of the most practical quantum mechanics approaches are investigated: density functional theory (DFT) and density-functional tight-binding (DFTB).

• Language: English
• Publisher: Xlibris US
• Release date: Sep 26, 2016
• ISBN: 9781524544119

Abdolhossein Fereidoon

A. Fereidoon is a professor of applied mechanics in the faculty of mechanical engineering at Semnan University in Semnan, Iran, where he serves as editor in chief of Mechanic of Composite Materials journal and director of the Journal of Modeling in Engineering. His research interests are nanomaterial, polymer nanocomposites, nano modeling, nanodevices, nanomechanics, micromechanics, finite element analysis, and FGM material.

Book preview

Copyright © 2016 by Maziar Dehghan.

ISBN:       eBook       978-1-5245-4411-9

All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner.

Any people depicted in stock imagery provided by Thinkstock are models, and such images are being used for illustrative purposes only.

Certain stock imagery © Thinkstock.

Rev. date: 09/23/2016

Xlibris

1-888-795-4274

www.Xlibris.com

750023

CONTENTS

Preface

1) Mechanical Properties of Multi-Walled Carbon Nanotubes: a case study of SCC-DFTB

1-1) Abstract

1-2) Introduction

1-3) Computational procedure

1-4) Results and discussions

1-5) Conclusions

1-6) References

2) Mechanical properties of Capped Carbon Nanotubes: SCC-DFTB study

2-1) Abstract

2-2) Introduction

2-3) Computational procedure

2-4) Results and discussions

i) Young’s modulus

ii) Shear modulus

2-5) Conclusions

2-6) References

3) Elastic properties of Single Walled CNTs with curved morphology: SCC-DFTB study

3-1) Abstract

3-2) Introduction

3-3) Materials and methods

3-4) Computational method

3-5) Results and discussions

3-6) Conclusions

3-7) References

4) Graphene Young’s modulus: MD and DFT treatments

4-1) Abstract

4-2) Introduction

4-3) Computational methods

4-4) Results and discussions

4-5) Conclusions

4-6) References

5) Atomistic simulation study of mechanical properties of periodic graphene nanobuds

5-1) Abstract

5-2) Introduction

5-3) Atomistic modeling of graphene nanobud

5-4) Results and Discussions

i) Young’s modulus and stress strain evolution

ii) Temperature dependence

5-5) Conclusions

5-6) References

6) Mechanical and electronic properties of carbon nanobuds: First-principles study

6-1) Abstract

6-2) Introduction

6-3) Computational method

6-4) Results and discussions

6-5) Conclusions

6-6) References

7) Mechanical properties of Boron Nitride Nanotubes: a case study of MD

7-1) Abstract

7-2) Introduction

7-3) Atomistic modeling of BNNT

7-4) Results and discussions

7-5) Conclusions

7-6) References

8) Mechanical properties of Silicon Carbide Nanotubes: a case study of MD

8-1) Abstract

8-2) Introduction

8-3) Atomistic modeling of SiCNTs

8-4) Results and discussions

8-5) Conclusions

8-6) References

Preface

Nowadays, by improving the abilities of computers molecular modeling has become a powerful technique in computational chemistry with ever-increasing practical interests. At the moment, using effective algorithms along with powerful processors enables us to simulate systems including thousands atoms up to several microseconds. However, finding a balance between the computational costs and reliable results still remains a challenge. Two general approaches help us to reveal the behavior of these systems: Quantum chemical calculations and molecular mechanics calculations. Quantum mechanics deals with physical phenomena as well as atoms’ behavior during chemical bonding and falls in the category of modern physics. In this book, two of the most practical quantum mechanics approaches are investigated: Density functional theory (DFT) and Density-functional tight-binding (DFTB).

Density functional theory (DFT) has become the most used theoretical techniques in computational chemistry. Since DFT derives the energy from the electron probability density instead of the molecular wave function, the dimension of the problem decreases dramatically. It has been popular in solid state physics since the 1970s due to its agreement with experimental data along with increasing the usage of computational machines. In the 1990s, the DFT simulation results became more accurate by refining the approximations used in the theory that results in a better modeling of exchanges of interactions. Now, DFT is the leading method in chemistry and solid state physics for calculations of electronic structures.

The emergence of the generalized gradient approximation (GGA) for the exchange-correlation functional improved the DFT accuracy. Hence, the predicted molecular structures, relative energies and frequencies are close to the second order Møller-Plesset perturbation theory (MP2) method, with remarkable success to treat transition metal complexes.

Density-functional tight-binding (DFTB) method is a new generation of the DFT, and hence, its advantages and disadvantages are inherited from DFT. DFTB requires small amounts of empirical parameters compared to DFT. The required parameters are obtained from DFT simulations of a few molecules per pair of atom types. DFTB is based on the non-orthogonal tight-binding methods parameterized from DFT and its accuracy is improved by the self-consistent charge extension of DFTB (SCC-DFTB). In addition, DFTB is a quick and efficient quantum mechanical simulation method since its simulation can be improved by using all DFT extensions like treatment of relativistic effects or London dispersion. So, in comparison with DFT, DFTB is faster and more efficient quantum mechanical method.

The other branch mentioned earlier is Molecular dynamics (MD). It studies the motion of a set of interacting atoms, molecules or particles. MD can extract experimental observables from the dynamics of the system by investigating the system motion. Alder and Wainwright initiated the MD while studying the interactions of hard spheres in 1950s at Lawrence Radiation Laboratory in the US. The first MD simulation with a continuous potential based on the finite difference method was done in 1961 by Gibson et al. and it was followed by Stillinger & Rahman in 1974 to simulate a realistic system. Today, MD becomes a powerful technique in physics, materials science, and mechanical engineering.

This book aims at using the above-mentioned methods to calculate mechanical properties of some nano-scale structures such as carbon nanotubes (CNTs), Graphene, Graphene nanobuds (GNBs), Carbon nanobuds (CNBs), and Boron Nitride Nanotubes (BNNTs).

In nano-scale modeling there are two general approaches: (1) the use of highly advanced many-body quantum mechanical methods, such as density functional theory (DFT) of atoms and molecules, for an ab initio investigation of nano-systems composed of several ten to several hundred atoms; and (2) the use of highly advanced classical statistical mechanics methods, such as molecular dynamics (MD) simulation methods, for modeling nano-scale structures and processes composed of several thousand to several million atoms. It should be noted that DFT simulation results are more accurate compared to classical MD methods since DFT accounts more details about electrons and ions and, hence, it can consider more interactions such as electron-electron, electron–ion and ion–ion interactions while the classical MD does not consider so.

The chapters are as follows:

1. Mechanical Properties of Multi-Walled Carbon Nanotubes: a case study of SCC-DFTB

In this chapter, a SCC-DFTB computational procedure was performed to investigate the Young’s and shear moduli of metallic and semi-conducting single walled (SWCNTs) as well as double-walled (DWCNTs) and triple-walled carbon nanotubes (TWCNTs). Also, the effect of separation wall distances of DWCNTs on the Young’s modulus of the nanotubes was investigated. Furthermore, to elucidate the crucial effects of interlayer interactions between the walls of the MWCNTs, the dispersion corrections for the long-range van der Waals (vdW) interaction was also considered.

2. Mechanical properties of Capped Carbon Nanotubes: SCC-DFTB study

In the second chapter, the SCC-DFTB method was employed to calculate the Young’s modulus of (6, 6) SWCNTs with different lengths of tube and compared these values with those for capped SWCNTs. Moreover, an incremental torsion angle was imposed on both ends of the tube to obtain the shear modulus of SWCNTs.

3. Elastic properties of Single Walled CNTs with curved morphology: SCC-DFTB study

The third chapter examines the effect of curvature of CNTs on the Young’s modulus based on experimental observations by SCC-DFTB calculations. Furthermore, the effects of curvature and diameter of the CNTs on the Young’s modulus of curved nanotubes was considered.

4. Graphene Young’s modulus: MD and DFT treatments

In chapter four, the Young’s modulus of single layer graphene sheet has been investigated by using comprehensive classic as well as quantum mechanics (QM) calculations. Molecular mechanics (MM) approach with various well-defined force-fields such as AIREBO, Tresoff, and EDIP potentials have been considered. In QM category, several conventional methods (DFTB and DFT-LDA/GGA) have been employed. In this section in order to find the best method among the most known classic and QM methods, it is tried to use all methods on the same system and compare them with each other, in terms of computational cost and accuracy.

5. Atomistic simulation study of mechanical properties of periodic graphene nanobuds

Among the graphene-based hybrid nanostructures, graphene nanobuds (GNBs); a hybrid of graphene/ fullerene architecture, are one of the most interesting nanostructured materials. In this chapter, we have investigated the mechanical properties of graphene nanobud through molecular dynamic simulations. The effects of temperature, size of graphene sheet and also neck’s length on the mechanical properties of this novel material were investigated, for the first time.

6. Mechanical and electronic properties of carbon nanobuds: First-principles study

Carbon nanobuds (CNBs), a novel carbon nanostructure, can be engineered by attaching C60 (buckyballs) onto the sidewall of a single-walled carbon nanotube (SWCNT). In chapter 6, Density functional theory (DFT) calculations are used to investigate the structural, electronic and mechanical properties of armchair (6, 6) and zigzag (10, 0) CNBs.

7. Mechanical properties of Boron Nitride Nanotubes: a case study of MD

In chapter 7, the molecular dynamics simulation is used to calculate the mechanical properties of single, double and triple walled boron nitride nanotubes (SWBNNT, DWBNNT and TWBNNT). The effects of diameter, chirality, interlayer distance and temperature on the mechanical properties of respected systems have been investigated.

8. Mechanical properties of Silicon Carbide Nanotubes: a case study of MD

In chapter 8, molecular dynamics (MD) simulations are employed to investigate effects of diameter, interlayer distance, chairality and temperature on mechanical properties of single/double-walled silicon carbide nanotubes (SiCNTs). Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) and Visual Molecular Dynamics (VMD) visualizer are used to study the mechanical properties of SiCNTs.

September 2016

A. Fereidoon (Semnan University)

M.D. Ganji (Islamic Azad University of Pharmaceutical Science)

F. Memarian (Semnan University)

M. Dehghan (Semnan University)

1

Mechanical Properties of Multi-Walled Carbon Nanotubes: