Computational Domains for Explorations in Nanoscience and Technology

1
Computational Domains for Explorations in
Nanoscience and Technology
Shaoping Xiao, CCAD, College of Engineering,
University of Iowa Deepak Srivastava, NASA Ames
Research Center Meyya Meyyappan, NASA Ames
Research Center Jun Ni, ITS, University of Iowa
2
Outline

• 1. Introduction to nanotechnology
• 2. Computational nanotechnology
• Molecular modeling Quantum mechanics, Monte
  Carlo and molecular dynamics
• Multiscale modeling Hierarchical and concurrent
  multiscale methods
• High-performance computer techniques
• 3. Applications of Computational nanotechnology
• Nanoscale materials nanotubes and nanocomposites
• Nanoscale devices nano-gears and
  nano-oscillators
• 4. Conclusions

3
Nanotechnology

• Nanotechnology is the understanding and control
  of matter at dimensions of roughly 1 to 100
  nanometers, where unique phenomena enable novel
  applications.
• Encompassing nanoscale science, engineering, and
  technology, nanotechnology involves imaging,
  measuring, modeling, and manipulating matter at
  this length scale.

4
Nanotechnology

• National Nanotechnology Initiative (launched in
  2001)
• The vision of the National Nanotechnology
  Initiative is a future in which the ability to
  understand and control matter on the nanoscale
  leads to a revolution in technology and industry
  (NNI, 2004).
• NNI Goals and Plans (NNI 2004)
• Maintain a world-class research and development
  program aimed at realizing the full potential of
  nanotechnology.
• Facilitate transfer of new technologies into
  products for economic growth, jobs, and other
  public benefits.
• Develop educational resources, a skilled
  workforce, and the supporting infrastructure and
  tools to advance nanotechnology.
• Support responsible development of
  nanotechnology.

5
Nanotechnology

• Four generations of nanotechnology applications
  (NNI 2004)
• First generation of products (2001 - ) passive
  nanostructures, illustrated by nanostructured
  coatings, dispersion of nanoparticles, and bulk
  materials such as nanostructured metals, polymers
  and ceramics.
• Second generation (2005 - ) active
  nanostructures, illustrated by transistors,
  amplifiers, targeted drugs and chemicals,
  actuators, and adaptive structures.
• Third generation (2010 - ) three-dimensional
  nanosystems with heterogeneous nanocomponents
  using various syntheses and assembling techniques
  such as bioassembling networking at the
  nanoscale and multiscale architectures. Research
  focus will shift towards heterogeneous
  nanostructures and supramolecular system
  engineering.
• Fourth generation (2015 - ) heterogeneous
  molecular nanosystems, where each molecule in the
  nanosystem has a specific structure and plays a
  different role. Molecules will be used as devices
  and from their engineered structures and
  architectures will emerge fundamentally new
  functions.

6
Computational Nanotechnology

• COMPUTATIONAL NANOTECHNOLOGY
• Modeling and simulation are becoming vital to
  designing and improving nanomaterials and
  nanodevices.
• One of the challenges
• Multi-scale
• Scale plays an important role in science and
  engineering.

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Multiscale

• Biology/Bioengineering challenge (from top to
  bottom)
• Peter Hunter
• University of Auckland

Cell
Tissue
(10-3m)
(10-6m)
Organ
(1m)
(10-9m)
Protein
Organ systems
Atom
(10-12m)
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Multiscale

• Physical scales (from bottom to top)

Microscale (10-6m)
Mesoscale (10-3m)
Nanoscale (10-9m)
Macroscale (1m)
Molecular scale
(10-12m)
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Nano-to-Micro Scale Simulations and Modeling
Few microns
Multi-scale Modeling and Simulations
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Computational Nanotechnology

• Common computational methods
• Quantum mechanical calculations
• First principle calculation
• Ab initio
• Etc.
• Molecular methods
• Molecular dynamics/mechanics
• Monte Carlo methods
• Multiscale methods
• Hierarchical multiscale modeling
• Concurrent multiscale modeling

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Quantum mechanical calculations

• Quantum mechanical calculations
• tight binding method, the method of linear
  combination of atomic orbitals.
• Hatree-Fock approximation
• Density functional theory
• First principle calculations, solving
  Schrodingers equation.
• Etc.
• Computationally Intensive, O(N4)
• Up to 3000 atoms

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Quantum mechanical calculations
Electron Density Profiles
Electronic Transport Y-junction CNTs
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Molecular Dynamics

• Molecular Dynamics
• Based on the Newtonian classical dynamics
• Atoms are viewed as mass points
• Equations of motion can be derived from classical
  Lagrangian or Hamiltonian mechanics
• Method has received widespread attention since
  the 1970
• Liquids
• Defects in crystals
• Fracture
• Surface
• Friction
• others

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Molecular Dynamics
Atomistic Simulation

• Molecular dynamics

(without consideration of external forces)
Periodic Boundary Condition

• Molecular mechanics

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Molecular Dynamics

• Molecular mechanics potential

i
j
k
j and k are no-bonded
16
Molecular Dynamics

• Molecular dynamics simulation

(NSF summer institute, Northwestern Unviersity,
2004)
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Molecular Dynamics

• Macroscopic properties
• Can be evaluated based on atomic positions and
  velocities

• Temperature

• Internal energy

• Cauchy Stress

18
Molecular Dynamics

• Temperature regulation
• Velocity scaling
• Langevin dynamics
• Berendsen thermostat
• Nose-Hoover thermostat

19
Molecular Dynamics

• MD simulations are very important
• nano-to-mesoscale characterization
• of materials
• Typical 10-100,000 atoms
• 10- Groups few million atoms
• 1 group billion atom simulations
• Issues Mechanics,
• Thermal, Chemical,
• Reactivity, Phase diagrams,
• Thermal and Mechanical response
• Vibrations, placement, fatigue
• Plasticity etc

Carbon Nanotube Mechanics
Si Nanowire Mechanics
20
Molecular Dynamics

• Why molecular dynamics?
• It is consistent all results are derived from a
  classical interatomic potential with a few
  parameters
• It is predictive equilibrium structures,
  reaction transition states, and dynamical
  averages are obtained
• It is cheap up to billions of atoms for nano
  seconds can be simulated
• Its downsides
• Quantum bonding and reactive response are hard to
  build in
• Poorly chosen input potentials produce garbage
  outputs
• Time step is essentially locked to molecular
  vibrations

21
Monte Carlo Method

• Monte Carlo Method
• A simple example Evaluation of

the number of total sampling the number of hits
in the shaded area
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Monte Carlo Method

• Monte Carlo Method
• Importance sampling
• Partition function
• Distribution function
• Metropolis method
• Set up a Markov chain with transition matrix
• Transition matrix consists of the probability of
  transition from one state to another state
• Using the transition matrix to control the flow
  of the simulations

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Monte Carlo Method

• Monte Carlo simulation in a canonical ensemble
• Constant parameters atom number( ),
• Volume( ), and temperature( )
• Atom displacement
• Randomly select an atom
• Randomly choose a position for the selected atom
• Compute the potential energy change due to
  moving the atom to the new position
• Accepting criterion

24
Monte Carlo Method

• Why Monte Carl method?
• It is consistent all results are derived from a
  classical interatomic potential with a few
  parameters
• It is predictive equilibrium structures,
  reaction transition states, and dynamical
  averages are obtained
• It is cheap
• Random process simulations crystal interface
  growth, chemical gradients
• Its downsides
• Quantum bonding and reactive response are hard to
  build in
• Poorly chosen input potentials produce garbage
  outputs
• Effective importance sampling required

25
Monte Carlo Method

• Monte Carlo method versus molecular dynamics
• For some systems in equilibrium state, such as
  system in canonical ensemble, both molecular
  dynamics and Monte Carlo method can work well
• Grand canonical ensemble simulation is easier to
  implement with Monte Carlo method than molecular
  dynamics
• Molecular dynamics allows studying the
  time-dependent phenomena

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Kinetic Monte Carlo Method

• Kinetic Monte Carlo method
• The Monte Carlo method, implemented with the
  standard Metropolis method, which is powerful for
  phase-space explorations, fails to represent the
  time evolution of the system. Therefore, it is
  mainly used for equilibrium description
• The Kinetic Monte Carlo method provides a tool to
  simulate a stochastic process with unambiguous
  time relationship between Monte Carlo steps and
  real-time steps.

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Monte Carlo Method

• Kinetic Monte Carlo (KMC) method
• Advantages
• KMC simulates dynamics of the system in and out
  of equilibrium with a firm correspondence to real
  time
• At each time step, the system can be recreated.
  This allows KMC to model dynamics on large time
  scales
• Time scale can change automatically
• Disadvantages
• KMC gives a coarse-grained picture of time
  evolution
• Calculating rates are independent of KMC method
• Need most efficient data structures for each
  specific problem

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Computational Nanotechnology

• Limitations of Atomistic (MD) simulation
• Limitations in length scale
• Computationally intensive, limited to small
  systems
• Rigid/periodic conditions lead to nonphysical
  behavior
• Cause unrealistic wave reflections (iron
  deposition)
• Present unrealistic constraints to dislocation
  nucleation and movement (nanoindentation)
• Artificially dissipate system energy to maintain
  constant temperature
• Limitations in time scale
• Incapable of simulating material behavior at two
  different time scales simultaneously
• Incapable of simulating material properties over
  large time scales

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Multiscale Methods

• Multiscale methods
• Hierarchical multiscale modeling
• Ortiz and Philips of Caltech
• Klein of Sandia National Laboratory
• Etc.
• Concurrent multiscale modeling
• MAAD, Abraham and co-workers at IBM
• Bridging scale, Liu and co-workers, Northwestern
  University
• Bridging domain coupling method
• Belytschko (Northwestern University) and Xiao (U
  of Iowa)
• Etc.

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Hierarchical Multiscale Methods

• Hierarchical Modeling
• The continuum approximation is used to model a
  large group of atoms
• (Cauchy-Born rule)
• The major drawback is that it is only static
  without temperature effect

Arroyo and Belytschko (2002)
Tadmor et al. (1996)
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Concurrent Multiscale Methods

• Concurrent Modeling
• An appropriate model is solved at each length
  scale simultaneously while smooth coupling is
  implemented between different scales
• continuum mechanics for macro elastic media
• molecular dynamics for large groups of atoms
• quantum mechanics for bonds breaking
• The major drawback is the spurious wave
  reflection at the interface of two domains with
  different dispersive characteristics, as well as
  the need in handshake regions of scaling the
  computational mesh down to atomistic scales.

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Concurrent Multiscale Methods

• MAAD (Macroscopic, Atomistic and Ab initio
  Dynamics)
• Quantum mechanics semiempirical tight binding
  (TB)
• Atomistic statistical mechanics molecular
  dynamics (MD)
• Continuum mechanics finite element method (FE)

F. F. Abraham et al. Spanning the Length Scales
in Dynamic Simulation Computers in Physics 1998
2538-546
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Concurrent Multiscale Methods

• MAAD 1D MD/FEM coupling

nonphysical spurious wave reflection
34
Concurrent Multiscale Methods

• Multiscale issues
• numerical issues
• the finite elements are meshed down to the
  atomistic scale in handshake regions.
• Time step is governed by the smallest element in
  the mesh. Time step will be too small for
  continuum region and many time steps will be
  wasted.
• physical issue
• Pathological wave reflection. The wavelength
  emitted by MD region is considerably smaller than
  that which can be captured by the continuum FE
  region. Wave reflection occurs at the interface
  between the MD and FE regions.

35
Concurrent Multiscale Methods

• Bridging domain coupling method

Total Hamiltonian
Constraints
S. P. Xiao and T. Belytschko A bridging domain
method for coupling continuum with molecular
dynamics, Computer Methods in Applied Mechanics
and Engineering, 2004 1931645-1669
36
Concurrent Multiscale Methods

• Bridging domain coupling method

Bridging domain coupling method can almost
eliminate the high frequency wave reflection
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Computational Nanotechnology

• Bridging domain coupling method multiple time
  steps

continuum model
molecular model

38
Concurrent Multiscale Methods

• Bridging domain coupling method
• Crack branching

39
High-performance computing

• High-performance computing
• Molecular dynamics with high-performance
  computing
• Billions of atoms can be simulated
• Still has limitations on length and time scales
• A cubic volume of 10-3 µm3 contains billions of
  atoms
• A nano second needs millions of time steps

One of solutions Multiscale methods with
high-performance computing techniques
40
High-performance computing

• High-performance computing
• The bridging domain coupling method is one of the
  best candidates which can be extended as a
  high-performance computing enhanced multiscale
  method

molecular
A bridging domain coupling model
continuum
At each time step, equations of motion are solved
separately in each domain for nodal/atomic
velocities
molecular
continuum
Then, nodal/atomic velocities in the bridging
domain are corrected
41
High-performance computing

• Grid-based bridging domain multiscale method
• Multiple-length-scale model

Macroscale Linear finite element
methods Microscale Meshfree particle
methods Nanoscale Molecular dynamics
42
High-performance computing

• Grid-based bridging domain multiscale method
• Multiple-time-scale model

43
High-performance computing

• Grid-based bridging domain multiscale method
• Domain Decomposition

44
High-performance computing

• Grid-based bridging domain multiscale method
• Domain Communication

45
High-performance computing

• Grid-based bridging domain multiscale method
• Nano-middleware

46
Computational Nanotechnology

• Grid-based bridging domain multiscale method
• Flow chart

47
Computational Nanotechnology

• Applications of computational nanotechnology
• Nanoscale materials
• Carbon nanotubes
• Nanotube reinforced nanocomposites
• Nanoscale devices
• Nanoscale oscillator

48
Computational Nanotechnology

• Carbon nanotube

Iijima et. al. (1996)
Iijima, S. et.al. Nature (1991)
Yakobson et. al. (1996)
Poncharal et. al. (1999)
49
Nanoscale Materials

• Carbon nanotube

10,10 armchair nanotube
Graphene sheet
R
zigzag nanotube n,0
armchair nanotube n,n
chiral nanotube m,n
50
Nanoscale Materials

• Potential functions for carbon-carbon bonds

1. Second-generation Reactive empirical bond
order (Proposed by Brenner et al.)
2. Modified Morse (Proposed by Belytschko and
Xiao)
3. Full Periodic Table Force Field(Proposed by
Rappe et al.)
51
Nanoscale Materials

• Mechanical properties of carbon nanotube

force
stress
strain
Youngs modulus
Poissons ratio
52
Nanoscale Materials

• Mechanical properties of carbon nanotube

53
Nanoscale Materials

• Mechanical properties of carbon nanotube

(a) Youngs modulus (b) Poissons
ratio Size-dependent mechanical properties of
SWNTs
54
Nanoscale Materials

• Experiments of carbon nanotube fracture

Yu et. al. Strength and Breaking Mechanism of
Multiwalled Carbon Nanotubes Under Tensile Load,
Science, 2000
55
Nanoscale Materials

• Fracture of carbon nanotube
• (Belytschko, Ruoff, Schatz and Xiao)
• Fracture of nanotubes is of great interest
  because
• A nanotube was considered a perfect molecule --
  an opportunity to study fracture in an idealized
  setting
• Nanotubes were first predicted to have very high
  strength which is 300 GPa (Yakobson et al. 1997)
• The low strength is obtained from the experiments
  and it is in range of 11 to 63 GPa (Yu et al.
  2000)

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Nanoscale Materials

• Fracture of carbon nanotube

20,0 zigzag nanotube
57
Nanoscale Materials

• Fracture of carbon nanotube

Failure strength is dependent on chirality
16,8 chiral nanotube
16,4 chiral nanotube
58
Nanoscale Materials

• Fracture of carbon nanotube

Failure strain
Failure stress
30
300GPa
Theoretical studies (Brenner) Yakobson et
al.(1997)
170GPa
Kinetic theory study Samsonidze et al.(2002)
17
15.7
93.5GPa
Numerical simulations Belytschko and Xiao (2002)
213
1163GPa
Experimental results Yu et al.(2000)
59
Nanoscale Materials

• Fracture of carbon nanotube

Frequency of occurrence in the experiments (Yu et
al, 2000)
(We do not believe that the scatter is due to
experimental error)
(GPa)
Nanotube fracture is governed by defects
60
Nanoscale Materials

• Fracture of carbon nanotube
• Defects in the nanotubes
• Chemical Defects
• Oxidization (Mawhinney et al, 2000)
• Chemical vapor deposition (CVD) (Hafner et al,
  1998)
• Topological Defects
• Stone-wales defects (5/7/7/5 dislocation)
  (Yakobson, 1998)
• Vacancy Defects
• Irradiation effects (impacted by high energy
  electrons) such as in SEM environment. (Banhart,
  1999)
• Vacancies in the original nanotube shell.

61
Nanoscale Materials

• Fracture of carbon nanotube Vacancy defects

62
Nanoscale Materials

• Fracture of carbon nanotube Vacancy defects in
  320,0 nanotubes

Failure strain()
Failure stress (GPa)
N-atom defect
15.7
93.5
0
8.00
64.1
2
6.00
50.3
4
4.95
42.1
6
4.35
36.9
8
3.20
27.7
16
2.30
20.2
32
63
Nanoscale Materials

• Fracture of carbon nanotube

64
Nanoscale Materials

• Multiscale modeling for nanotube fracture

65
Nanoscale Materials

• Nanocomposites
• Extraordinary properties
• High stiffness High strength Low density.
• Inclusions
• Nanotubes Nanoplates Nanoclay Nanoparticles
  Etc.
• Matrix
• Polymer Ceramics Metals.
• Key issues
• Dispersion of CNTs Alignment of CNTs Load
  transfer.

66
Nanoscale Materials

• carbon nanotube reinforced aluminum composites

Carbon Nanotube E 1000GPa Aluminum
E 70GPa
T. Kuzumaki et al. (1998) Experiment Tensile
test pieces L 15 mm ,D 3 mm Tensile strength
was increased by 100 TEM observations have
shown (i ) The composites are not damaged during
the composite preparation (ii) No reaction
products at the nanotube/Al interface are visible
67
Nanoscale Materials

• carbon nanotube reinforced aluminum composites

Infinite Domain
O
O

RVE 1
Both cases implement periodic boundary
conditions on x,y,z
68
Nanoscale Materials

• carbon nanotube reinforced aluminum composites

Strain
It shows that the discontinuous CNT can not
improve the strength of composites. Therefore,
the following study mainly focus on the
continuous CNT.
69
Nanoscale Materials

• carbon nanotube reinforced aluminum composites

Axial load 001
70
Nanoscale Materials

• carbon nanotube reinforced aluminum composites

Volume Change Schema Tension on Z direction
x
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Nanoscale Devices

• Nanoscale devices
• Nanoelectronics
• Molecular wires
• Diodes
• Field-effect transistor
• Etc.
• Nanotube-based devices
• Nanotweezers
• Nanocantilever
• Nanogears
• Etc.

72
Nanoscale Materials

• Nanotube-based devices

73
Nanoscale Materials

• Nanotube-based oscillators
• High frequency up to 100 GHz

74
Nanoscale Materials

• Nanotube-based oscillators

Frequency prediction
75
Nanoscale Materials

• Nanotube-based oscillators

76
Nanoscale Materials

• Nanotube-based oscillators temperature effects

Effecitve interlayer friction 100K, 0.0158 pN
per atom 300K, 0.0398 pN per atom
1000K, 0.1008 pN per atom
77
Nanoscale Materials

• Nanotube-based oscillators a NanoElectroMechanica
  l System(NEMS)

10 GHz
25 GHz
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Computational Nanotechnology

• Conclusions
• Computational nanotechnology plays an important
  role during the development of nanotechnology
• Although molecular methods are powerful in
  illustrating complex physical phenomena, they
  have limitations on length and time scales
• Currently, multiscale modeling and simulation is
  a key research area in computational
  nanotechnology
• The combination of multiscale methods and
  high-performance computing technique, such as
  Grid computing, will have potential in
  nanotechnology

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Nanotechnology at The University of Iowa
80
NanoEngineering_at_Iowa
81
Nanotechnology at NASA Moors Law
82
Nanotechnology at NASA Miniaturization
Advanced miniaturization, a key thrust area to
enable new science and exploration
missions - Ultrasmall sensors, power sources,
communication, navigation, and propulsion
systems with very low mass, volume and
power consumption are needed Revolutions
in electronics and computing will allow
reconfigurable, autonomous, thinking
spacecraft Nanotechnology presents a whole new
spectrum of opportunities to build device
components and systems for entirely new space
architectures
Micromachines Microrovers Micromanufacturing