Table Of ContentLecture Notes in Applied and Computational
Mechanics
Volume 99
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· ·
Akarsh Verma Sanjay Mavinkere Rangappa
·
Shigenobu Ogata Suchart Siengchin
Editors
Forcefields
for Atomistic-Scale
Simulations: Materials
and Applications
Editors
Akarsh Verma Sanjay Mavinkere Rangappa
Department of Mechanical Engineering Department of Materials and Production
University of Petroleum and Energy Studies Engineering
Dehradun, India KMUTNB
Bangkok, Thailand
Shigenobu Ogata
Department of Mechanical Science Suchart Siengchin
and Bioengineering Department of Materials and Production
Osaka University Engineering
Osaka, Japan KMUTNB
Bangkok, Thailand
ISSN 1613-7736 ISSN 1860-0816 (electronic)
Lecture Notes in Applied and Computational Mechanics
ISBN 978-981-19-3091-1 ISBN 978-981-19-3092-8 (eBook)
https://doi.org/10.1007/978-981-19-3092-8
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
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Contents
Introduction to Molecular Dynamics Simulations ..................... 1
Gaurav Kumar, Radha Raman Mishra, and Akarsh Verma
Introduction to Interatomic Potentials/Forcefields .................... 21
Aditya Kataria, Akarsh Verma, Sushanta Kumar Sethi,
and Shigenobu Ogata
Current Perspective on Atomistic Force Fields of Polymers ............ 51
Kiranmai Yellam, Ratna S. Katiyar, and Prateek K. Jha
Forcefields and Modeling of Polymer Coatings and Nanocomposites .... 81
Uday Shankar, Sushanta K. Sethi, and Akarsh Verma
Development, Availability, and Applications of EAM Potentials
for Characterization of Complex HCP Materials ..................... 99
Divya Singh
EAM Potentials for Characterisation of HCP Nuclear Materials ....... 123
Divya Singh
EAM Inter-Atomic Potential—Its Implication on Nickel, Copper,
and Aluminum (and Their Alloys) .................................. 133
Swati Chaturvedi, Akarsh Verma, Sandeep Kumar Singh,
and Shigenobu Ogata
Defect Energy Calculations of Nickel, Copper and Aluminium
(and Their Alloys): Molecular Dynamics Approach ................... 157
Swati Chaturvedi, Akarsh Verma, Sushanta Kumar Sethi,
and Shigenobu Ogata
Tersoff and REBO Potentials ....................................... 187
Rajesh Kumar and Jashveer Singh
v
vi Contents
Reactive Forcefield (ReaxFF): Application to Predict 2D
Nanomaterials Synthesis ........................................... 205
Rajesh Kumar
Reinforcing Potential of 2D Nanofiller in Polyethylene: A Molecular
Dynamics Approach ............................................... 217
Ankur Chaurasia, Sandeep Kumar Singh, and Avinash Parashar
Atomistic Simulations to Study Thermal Effects and Strain Rate
on Mechanical and Fracture Properties of Graphene like BC3 ......... 237
Akarsh Verma and Sachin Sharma
Computational Modelling of Deformation and Failure of Bone
at Molecular Scale ................................................. 253
Akarsh Verma and Shigenobu Ogata
A Review on the Deformation Mechanism of Soft Tissue Collagen
Molecules: An Atomistic Scale Experimental and Simulation
Approaches ....................................................... 269
Ravinder Jhorar and Chhatar Singh Lamba
Introduction to Materials Studio Software for the Atomistic-Scale
Simulations ....................................................... 299
Uday Shankar, Rupam Gogoi, Sushanta K. Sethi, and Akarsh Verma
Data-Driven Phase Selection, Property Prediction and Force-Field
Development in Multi-Principal Element Alloys ...................... 315
Dishant Beniwal, Jhalak, and Pratik K. Ray
Effect of Geometrical Parameters on Branched Cracks: A Finite
Element Method-Based Computational Approach .................... 349
Neeraj Bisht, Harshit Kumar, Virendra Singh, and Sakshi Chauhan
Introduction to Molecular Dynamics
Simulations
Gaurav Kumar, Radha Raman Mishra, and Akarsh Verma
Abstract The invention of novel functional materials and their investigation at
the molecular level are vital in today’s nanotechnology era. Atomistic modelling
approaches are cost-effective and time-consuming alternatives to expensive and time-
consuming experimental methods, and they are precise enough to predict the mechan-
ical characteristics of materials. The current chapter goes through the many steps
involved in a molecular dynamic’s investigation. The various types of interatomic
potentials and their applicability to various materials have been thoroughly examined.
Following that, the integration algorithm for solving a set of Newton’s equations, as
well as the radius cut-off distance and temperature control, was addressed. After-
wards, many types of ensembles and boundary conditions were addressed, which
helped in simulating real-world experimental settings. The approaches for mini-
mizing energy have also been briefly explored. Finally, the limitations of molecular
dynamics have been examined, as well as their applicability.
· · ·
Keywords Molecular dynamics Interatomic potential Temperature control
·
Energy minimization Ensemble
B
G. Kumar ( )
Department of Mechanical Engineering, National Institute of Technology, Uttarakhand, Srinagar
246174, India
e-mail: [email protected]; [email protected]
R. R. Mishra
Department of Mechanical Engineering, Birla Institute of Technology and Science, Pilani 333031,
Rajasthan, India
A. Verma
Department of Mechanical Engineering, University of Petroleum and Energy Studies, Dehradun
248007, Uttarakhand, India
Department of Mechanical Science and Bioengineering, Osaka University, Osaka 560-8531,
Japan
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 1
A. Verma et al. (eds.), Forcefields for Atomistic-Scale Simulations: Materials
and Applications, Lecture Notes in Applied and Computational Mechanics 99,
https://doi.org/10.1007/978-981-19-3092-8_1
2 G.Kumaretal.
1 Introduction
Molecular dynamics (MD) simulation integrates Newton’s equations of motion over
time to obtain the motion of the atoms/molecules in a system (Fig. 1) and, subse-
quently, quantitative and qualitative information about macroscopic behaviour of the
system at the atomistic level [1]. Various properties like thermal expansion coeffi-
cient, melting point, heat capacity, thermal conductivity, radial distribution function,
structural properties, etc. can be determined directly or with the help of statistical
analysis of the data containing atomic positions, momenta, energies, forces, etc. over
each timesteps during and after equilibration. Further, raw data can also be used
to describe processes and phenomena such as crack growth and fast fracture, ion
bombardment, sputtering, vapour deposition, etc. [1].
Three steps are involved in a typical molecular dynamic’s simulation: (1) estima-
tion of forces and evaluation of potential energy based on present atomic locations and
velocities; (2) updating atomic coordinates and velocities as per the integrator algo-
rithm and (3) post-processing and visualization from the raw data of the simulation
[2].
Fig. 1 Interaction of atom 1 with other nine atoms in a particular MD simulation
IntroductiontoMolecularDynamicsSimulations 3
2 Interatomic Potential or Force Field
In classical molecular dynamics, a single point with a finite mass replaces an atom as a
three-dimensional structure (Fig. 1). The balance between attraction and repulsion is
established by the so-called interatomic potential or force field when atoms are close
enough to feel each other [1]. The atoms/molecules in the system have potential
energy due to interaction and bonding with other atoms/molecules in the system,
which may be expressed mathematically by Eq. 1:
(cid:2) (cid:3)
−→ −→ −→ −→
U = U r , r , r ,.....r (1)
1 2 3 n
With the provided interatomic potential, U and the initial positions, r of
i
the particle, i having a mass, m in the system, the force experienced by each
i
atom/molecule is calculated in Eq. 2:
(cid:4) (cid:5)
−→
−→ −→ d−→v d2−→R d−→p −→ (cid:4)−→(cid:5) dU Ri
F = m a = m i = m i = i =−∇ U R =− (2)
i i i i dt i dt2 dt i dr
Using above equations, trajectories and motion of the atoms are determined in a
small timestep ofΔt over transition to lower energy states, i.e. state of equilibrium
from higher energy state (Fig. 1). Forces on atoms can be calculated, and subsequently
the above equation for the system’s temporal evolution can be solved if a system’s
potential as a function of interatomic distance is known. Interatomic potentials are
commonly calculated empirically, either via DFT or by fitting experimental data.
Several potentials having varying degrees of precision had been reported, each
with its own set of advantages and drawbacks. The force fields used to define the
bonded and non-bonded interatomic interaction are critical to any atomistic simula-
tion. The thermo-mechanical properties of the material under investigation should
be accurately reproduced by the interatomic potential. Majority of the forcefield
used in molecular dynamic modelling of materials like nanocomposites, metals,
and nanofillers were developed empirically and tested against experimental data or
high-fidelity simulation data [3]. The choice of potential is significantly influenced
by the application as well as the material. Semiempirical or empirical methods are
preferred alternatives for modelling mechanical properties of materials because they
can frequently simulate huge systems with tens of thousands to billions of atoms. But,
dealing with diverse facets of a material’s mechanical behaviour frequently involves
the use of multiple simulation approaches [4].
Pair potentials are the simplest and computationally efficient way to describe
the particle interactions because interatomic distance solely determines the potential
energy, and the system’s total energy is calculated by adding the all-atomic bond’s
energy over all N particles in the system. The overall energy of the system can be
expressed in Eq. 3 [4]:
