computational nanotechnology

Namas ChandraCSIT-Computational Nanotechnology

Nov 1, 2002Slide-1

Computational Nanotechnology

N. Chandra

Department of Mechanical EngineeringFAMU-FSU College of Engineering

Florida State UniversityTallahassee, FL 32312

N. Chandra

Department of Mechanical EngineeringFAMU-FSU College of Engineering

Florida State UniversityTallahassee, FL 32312


Nov 1, 2002Slide-2

Outline of the talk

• What is nanotechnology?

• Some potential applications•Composites, Electronics, energy storage

• Carbon nanotube and CNT based composites•Geometric features

•CNT based composites

•Role of interfaces in composites

•Experimental observations

• Computational Aspects of Nanotechnology

• Outstanding mechanics Issues


Nov 1, 2002Slide-3

Smaller and smaller and then some more..

*From Nanotechnology Magazine (nanozine.com)

Nanotechnology is the development of products and device at the nanoscale.

Capability of Nanotechnology Capability of Nanotechnology

High StrengthMaterial (>10 GPa)High StrengthMaterial (>10 GPa)

Revolutionary Aircraft Concepts (30% less mass, 20% less emission, 25% increased range)

Revolutionary Aircraft Concepts (30% less mass, 20% less emission, 25% increased range)

Adaptive Self-Repairing Space MissionsAdaptive Self-Repairing Space Missions

Reusable Launch Vehicle (20% less mass, 20% less noise)

Reusable Launch Vehicle (20% less mass, 20% less noise)

Multi-Functional MaterialsMulti-Functional Materials

Autonomous Spacecraft (40% less mass)Autonomous Spacecraft (40% less mass)

Bio-Inspired Materialsand ProcessesBio-Inspired Materialsand Processes

Source: NASA Ames


Nov 1, 2002Slide-5

• Library of Congress inside a sugar cube

• Bottom-up manufacturing

• Materials (100x) stronger but lighter than steel

• Speed and efficiency of computer chips & transistors• Nano contrast agents for cancer cell detection • Contaminant removal from water & air• Double energy efficiency of solar cells

*From Nanotechnology Magazine (nanozine.com)

Then there are dreams…

Library of Congress?Library of

Congress


Nov 1, 2002Slide-6

By nature, humans live, work and play in the macroscale. But they have the unique ability to “think” in the nanoscale.

Control must inherently come from the MACROSCALE because that is the scale where humans reside.

MANY PATHS TO FOLLOW Biochemistry: Custom protein design Chemistry: Molecular recognition Physics: Scanning probe microscopy

Computing: Molecular modeling Engineering: Molecular electronics Engineering: Quantum electronic devices Engineering: Nanocomposites Engineering: Nanomaterials engineering

“...thorough control of the structure of matter at the molecular level. It entails the ability to build molecular systems with atom-by-atom precision, yielding a variety of nanomachines. These capabilities are sometimes referred to as molecular manufacturing.” - K. Eric Drexler, 1989

To manipulate things which we cannot see without the unaided eyebut indeed understand, we must employ predictive methods: Computational Tools.

If you can’t model it, you can’t build it!

Role of Computations in Nanotechnology

Carbon NanotubesCarbon Nanotubes

Geometric Features

Unusual Properties

CNT based composites

Role of interfaces

Experimental Observations

Geometric Features

Unusual Properties

CNT based composites

Role of interfaces

Experimental Observations

Carbon Nanotubes (CNTs)Carbon Nanotubes (CNTs)

CNTs can span 23,000 miles without failing due to its own weight.

CNTs are 100 times stronger than steel.

Many times stiffer than any known material

Conducts heat better than diamond

Can be a conductor or insulator without any doping.

Lighter than feather.


Nov 1, 2002Slide-9

Basic Configurations of CNT2There are three orbitals in CNT.

In plane -bond is extremely strong.

Out-of-plane -bond is weak.Different tubes in MWNT is connected by -bond.

sp

60, 70, 80C C C are fullerens.

Graphene sheets are rolled into tubes,

is based on the angle .

0 ;0 30 ; 30 ;

Properties depend on chirality

r na mb

Chirality

Zig Zag Chiral Armchair


Nov 1, 2002Slide-10

• Carbon nanotubes (CNT) is a tubular form carbon with diameter as small as 1 nm. Length: few nm to microns.

• CNT is configurationally equivalent to a two dimensional graphene sheet rolled into a tube.

• CNT exhibits extraordinary mechanical properties • Young’s modulus over 1 Tera Pascal as stiff as

diamond• tensile strength ~ 200 GPa.

• CNT can be metallic or semiconducting, depending on chirality.

Carbon Nanotubes


Nov 1, 2002Slide-11

Yielding under tensile stress

11.5% tensile strained (10,0) T=1600K

9% tensile strained (5,5) T=2400K

- MD simulations with high strain rate:

- elastic up 30% (Yakobson et al *)

- Experimentally feasible strain rate and Temperature

* Yakobson et al, Comput. Mater. Sci. 8, 341 (1997)


Nov 1, 2002Slide-12

Yielding: Strain-rate and Temperature dependence

Tensile strain applied to a 60Å long (10,0) CNT

- yielding: strongly dependent on the strain rate and temperature !

- Linear dependence on the temperature of the of the yielding strain vs strain rate ~ activated process


Nov 1, 2002Slide-13

Stiffness and Plasticity of SW C Nanotubes

D. Srivastava, M. Menon and K. Cho, Phys. Rev. Lett. Vol. 83, 2973 (1999)


Nov 1, 2002Slide-14

To make use of these extra-ordinary properties, CNTs are used as reinforcements in polymer based composites

CNTs can be in the form Single wall nanotubes Multi-wall nanotubes Powders films paste

Matrix can be Polypropylene1 PMMA2

Polycarbonate3

Polystyrene4

poly(3-octylthiophene) (P3OT)5

1 Andrews R, Jacques D, Minot M, Rantell T, Macromolecular Materials And Engineering 287 (6): 395-403 (2002) 2 Cooper CA, Ravich D, Lips D, Mayer J, Wagner HD Composites Science And Technology 62 (7-8): 1105-1112 (2002) 3 Potschke P, Fornes TD, Paul DR Polymer 43 (11): 3247-3255 MAY (2002) 4 Safadi B, Andrews R, Grulke EA Journal Of Applied Polymer Science 84 (14): 2660-2669 (2002) 5 Kymakis E, Alexandou I, Amaratunga GAJ Synthetic Metals 127 (1-3): 59-62 (2002)

Polymer Composites based on CNTs


Nov 1, 2002Slide-15

What are the critical issues? Structural and thermal properties Load transfer and mechanical properties

SEM images of polymer (polyvinylacohol) ribbon contained CNT fibers & knotted CNT fibers

(B. Vigolo et.al., Science, V290 P1331, 2000)

SEM images of epoxy-CNT composite

(L.S.Schadler et.al., Appl. Phys. Lett. V73 P3842, 1998)

Polymer Composites based on CNTs


Nov 1, 2002Slide-16

Buckling of CNT during Composite Manufacture

• Experiment: buckling and collapse of nanotubes embedded in polymer composites.

Buckle, bend andloops of thicktubes..

Local collapse orfracture of thintubes.


Nov 1, 2002Slide-17

o Critical length to transfer load1.

o Thermally induced residual stresses

o Number of bonds between polymer molecules and carbon nanotube

Polymer-SWNT interacting

1 SJV Frankland, A. Caglar, DW Brenner, M. Griebel, J of Physical Chemistry B, 106, 3046-3048, (2002)

Interface Bonding Issues


Nov 1, 2002Slide-18

Composites are engineered material system with a matrix, reinforcement and an interface. Interface is not usually designed but arises naturally.

In CNT reinforced polymer matrix composites, the load and other properties are not transferred properly.

We have never had to deal with interfaces at the atomic scale.

1.Bower, Rosen, Jin, Han and Zhou, APL, 74, 22, 3317-3319 (1999)2.Qian, Dickey, Andrews, Rantell, APL, 76,20,2868-28770 (2000)

Load transfer issues in Composites

Basic concept in composites

Buckling of tubes due to

residual stresses (1)

Crack nucleation and propagation in MWNT-PS thin films. Failure occurs in low NT densities and propagate along interfaces (2)


Nov 1, 2002Slide-19

Carbon fibers ( 4-5 micron) diameter whereas CNTs (10-100nm). Strength of CNTs are two orders higher than carbon fibers. We need desired alignment and they can be achieved during

processing either in the liquid or/and solid state.

1.Carole A. Cooper, Dianne Ravich, David Lips, Joerg Mayer, Daniel Wagner, CST, 62, 1105, 1112, (2002)

Alignment issues in CNT composites

CNTs are in nanoscales compared to carbon fibers

Alignment of fibers is very critical in obtaining desired properties. Distribution of CNTs shown. Extrusion is used in this case (1)

CNTs should be distributed homogeneously throughout the volume.

They should be oriented in directions dictated by design

Orientations will be directed (for specific properties) or random for isotropic strengthening.


Nov 1, 2002Slide-20

TEM image of a SWNT composite1.

Carbon nanotubes indifferent orientation

Visco-elastic medium

Schematic view of the orientation of a nanotube-based composite in which the nanotubes are approximately aligned parallel to the shearing direction..

Single-wall nanotubes usually form bundles and webs and are thus strongly

entangled rather than aligning straight and in isolation.

1B. McCarthy et al., Chemical Physics letters, 350, 27-32, (2001)

Alignment of Carbon Nanotubes in Polymeric Composites

Composites are nothing new……Composites are nothing new……

Shibam Hadramout, the largest territory in The Republic of Yemen

Ghuwaizi Fort In The Republic of Yemen: Built in 1884AD as a guard post

Early form of Straw Bale brick Straw Bale brick/adobe prototype home under construction in the 1890s

CONSTRUCTION OF COMPOSITES CONSTRUCTION OF COMPOSITES

Why Composites

• High strength to density.• High stiffness to density.• Formable to complex shapes.• Electrically and thermally non- conductive & conductive.• Corrosion resistance.• Wear resistance.• Fatigue resistance.• Creep & stress-rupture resistance.• Low coefficient of thermal expansion.• Tailorable mechanical and physical properties.• Low cost (In some cases).

Why Composites

• High strength to density.• High stiffness to density.• Formable to complex shapes.• Electrically and thermally non- conductive & conductive.• Corrosion resistance.• Wear resistance.• Fatigue resistance.• Creep & stress-rupture resistance.• Low coefficient of thermal expansion.• Tailorable mechanical and physical properties.• Low cost (In some cases).

The Family of Structural Materials

The family of structural materials includes ceramics, polymers and metals. Reinforcenments added to these materials produce MMCs, CMCs and PMCs.

The Family of Structural Materials

The family of structural materials includes ceramics, polymers and metals. Reinforcenments added to these materials produce MMCs, CMCs and PMCs.

Ceramics

Metals

Polymers

MMCs

Reinforcements

TYPES OF FIBER-REINFORCED COMPOSITETYPES OF FIBER-REINFORCED COMPOSITE

PMCs:

MMCs:

CMCs:


Nov 1, 2002Slide-24

DEFINITION AND CLASSIFICATION OF INTERFACEDEFINITION AND CLASSIFICATION OF INTERFACE

An interface is a bounding surface or zone where a discontinuity in physical, mechanical, or chemical characteristics occurs.

An interface is a bounding surface or zone where a discontinuity in physical, mechanical, or chemical characteristics occurs.

DEFINITION OF AN INTERFACE

CLASSIFICATION OF INTERFACE

Based on the materials of constituents, the interface can be classified as:

Metal/Ceramic Interface, e.g., Al/Al2O3, Ti/SiC.

Ceramic/Ceramic Interface, e.g., SiC/SiC. Polymer/Metal Interface, e.g., epoxy/steel. Polymer/Ceramic Interface, e.g.,

epoxy/glass.

Based on the materials of constituents, the interface can be classified as:

Metal/Ceramic Interface, e.g., Al/Al2O3, Ti/SiC.

Ceramic/Ceramic Interface, e.g., SiC/SiC. Polymer/Metal Interface, e.g., epoxy/steel. Polymer/Ceramic Interface, e.g.,

epoxy/glass.

Based on the chemical reaction of interface, there are three classes proposed as:

Class I, fiber and matrix mutually nonreactive and insoluble.

Class II, fiber and matrix mutually nonreactive but Soluble.

Class III, fiber and matrix reactive to form compound(s) at interface.

Based on the chemical reaction of interface, there are three classes proposed as:

Class I, fiber and matrix mutually nonreactive and insoluble.

Class II, fiber and matrix mutually nonreactive but Soluble.

Class III, fiber and matrix reactive to form compound(s) at interface.

Inte

rfac

e

Properties affected

Fatigue/Fracture Thermal/electronic/magnetic

Factors affecting interfacial properties

Trans. & long.Stiffness/strength

Interfacial chemistry

Mechanical effects

Origin: Chemical reaction during thermal-mechanical Processing and service conditions, e.g. Aging, Coatings, Exposures at high temp..

Issues: Chemistry and architecture effects on mechanical properties.

Approach: Analyze the effect of size of reaction zone and chemical bond strength (e.g. SCS-6/Ti matrix and SCS-6/Ti matrix )

Residual stress

Origin: CTE mismatch between fiber and matrix.

Issues: Significantly affects the state of stress at interface and hence fracture process

Approach: Isolate the effects of residual stress state by plastic straining of specimen; and validate with numerical models.

Asperities

Origin: Surface irregularities inherent in the interfaceIssues: Affects interface fracture process through mechanical loading and frictionApproach: Incorporate roughness effects in the interface model; Study effect of generating surface roughness using: Sinusoidal functions and fractal approach; Use push-back test data and measured roughness profile of push-out fibers for the model.

Metal/ceramic/polymer

CNTs


Nov 1, 2002Slide-26

T

T

Interfaces are modeled as cohesive zones using a potential function

( , ) ( , , , )n t n t n tf ,n t are work of normal and

tangential separation

are normal and tangential displacement jump ,n t

The interfacial tractions aregiven by

,n tn t

n t

T T

Interfacial traction-displacement relationship are obtained using molecular dynamics simulation based on EAM functions

1.X.P. Xu and A Needleman, Modelling Simul. Mater. Sci. Eng.I (1993) 111-1322.N. Chandra and P.Dang, J of Mater. Sci., 34 (1999) 655-666

Grain boundaryinterface

Mechanics of Interfaces in Composites

Atomic Simulations

Reference

Formulations

Issues in CNT based compositesIssues in CNT based composites

Expected Properties of Composites are not realized. Some issues include

Controlling alignment during processing Homogeneous distribution (spatial)

Orientation control (directional)

Processing induced residual stresses

Interface boding (at atomic level) Load transfer

Fracture/load shedding

Expected Properties of Composites are not realized. Some issues include

Controlling alignment during processing Homogeneous distribution (spatial)

Orientation control (directional)

Processing induced residual stresses

Interface boding (at atomic level) Load transfer

Fracture/load shedding

Computational AspectsComputational Aspects

Multi-scale modeling methods

Formulations and solution procedures

Computational Requirements

Some sample simulations

Outstanding issues in nanomechanics and nanophysics

Multi-scale modeling methods

Formulations and solution procedures

Computational Requirements

Some sample simulations

Outstanding issues in nanomechanics and nanophysics


Nov 1, 2002Slide-29

Hierarchical Modeling of MaterialsHierarchical Modeling of Materials

Balance Laws(Force,Momentum,Energy)Continuum MechanicsThermodynamics(Constitutive Equations)

FEM, FDM,BEMMinimize Global Energy

Large Scale ComputingAdaptive Auto RemeshingMassive Parallel ComputingData Structure for Parallel Adaptive SolutionVisualization

Structural DesignBulk /Sheet FormingComposite Mechanics

MACRO SCALETheory

Numerical Tools

Computational Issues

Applications

1m

10-3 m

10-6 m

10-9 m

FEM mesh for a Superplastic Component

Paperless Design of Boeing777


Nov 1, 2002Slide-30

Ab-Initio methodsQuantum MechanicsDensity Functional TheoryEAM PotentialPair Potential

Molecular StaticsMolecular DynamicsMonte Carlo Simulations

Limited by time (ps)And space (103 to107 atoms)Parallel Molecular DynamicsPMD code developed at Sandia

Defects,(e.g.Vacancies,Dislocations)Grain boundary slidingCrack tip evolutionPhase transformationNanocrystals, Thin films

Theory

Numerics

Computational Issues

Applications

ATOMIC - SCALE Hierarchical Modeling of MaterialsHierarchical Modeling of Materials1m

10-3 m

10-6 m

10-9 m

(110) 9 Grain BoundaryRed Atoms Show GB


Nov 1, 2002Slide-31

Multiscale Approaches for Systems Simulations

Finite element for homogeneous, Continuum description

Mesoscopic dynamics for non-homogeneous

Atomistic MD, many-body force fields

Semi-empirical, tight-binding MD

ab-initio, structure, energetics~ 100 atoms

~ 1000 atoms

~ 1000,000 atoms

~ 1000,000,000 atoms or grid

~ bulk continuous media

Molecular Dynamics

~ up to 100s of ns

Experiments

~ up to sec, hours

Long time structuralKMC, TDMC

Hyperdynamics


Nov 1, 2002Slide-32

Materials Applications

Practical Implementation

Conceptual Framework

Analytic Potentials

Embedded-AtomMethod:E= F(i) + i j U(rij)

Bond Order Potentials: Ei = i j [Ae-r

- z1/2Be-r]O(2) Error, Self-Consistent, Variational, Parameterized

Density Functional Theory

E=k k -sc[VH(r)/2 +Vxc(r)] dr + Exc[sc(r)]

O(2) Error, Self-Consistent, Variational, Parameterized

Harris Functional

E=k kout -in[VH(r)/2+Vxc(r)]dr +

Exc[in(r)]

O(2) Error, Self-ConsistentVariational, Parameterized

Tight Binding Methods

E = A(r) +k k.

O(2) Error, Self-Consistent, Variational, Parameterized

Moments Theorem

Large-Scale Atomic Simulation

Continuum Mechanics

Cauchy- Quasi- Born Continuum

Molecular Monte Dynamics Carlo

How do we Go Directly from Electrons to Solid Mechanics?


Nov 1, 2002Slide-33

Discrete nature of matter – dynamical state of particle system is captured

Intrinsically nonlocal behavior Small devices often have significant influence of surfaces

(high specific surface area) Charge distribution may be important for evolution of

microstructure, damage and fracture QM, QMM Even micron scale devices are huge MD problems (especially

in 3D) Potentials are largely phenomenological, but can be adjusted to

fit various physical observations/desired outcomes

Nanoscale Mechanics – Characteristics


Nov 1, 2002Slide-34

Potentials are often unknown for MD or MS for solid solutions,

impurities and interfaces between phases

Dynamical calculations can cover only very limited time

duration and are therefore conducted at very high rate; velocity

scaling is often used to maintain isothermal conditions, but

kinetics are altered Molecular statics can assess sequence of thermodynamic

equilibrium states with presumably non-equilibrium transit, but kinetics must be assigned

Nanoscale Mechanics – Limitations


Nov 1, 2002Slide-35

Calculation of defect field information from many body atomistic solutions needs to be further developed

Vacancies/Porosity (coordination number for lattice) on atom-by-atom or collective basis; pore size and shape distribution an open issue

o Dislocations (centro-symmetry parameters)• Density• Populations/families

NOTE: discrete dislocation simulations focus on defect field interactions rather than lattice per se

Nanoscale Mechanics – Challenges


Nov 1, 2002Slide-36

Modeling evolution of microstructureo Defect generation/motiono Coarsening/ageing – phase stabilityo Recrystallization

MD – timeframe too short with current computing capability & kinetics unrealistic with current implementations MS – sequence of equilibrium states in both cases, kinetics is a “bottleneck” for MS, there is a question of whether representative

non- equilibrium structures can be described

Nanoscale Mechanics – Challenges


Nov 1, 2002Slide-37

• All physics, all the time• multi-physics• at this scale, mechanical, electrical, chemical issues are not seperable

• Must retain some level of continuum description to truly do multi-physics, but

• nucleation & other stochastic events

• non-locality

• Failure tolerant design • massive redundancy

• self-assembly?

• Sub-”physics”• lots of open questions

Theoretical and Computional Modeling Issues


Nov 1, 2002Slide-38

• Scales• length scales are OK for atomistic simulations using empirical or semi-empirical

potentials, but still too big in most cases for first principles descriptions• time scales are disparate - ps to ms to years

• atomistics - hyper MD, parallel replica, temperature scaling, kMC, quasi-static, ensembles…

• response theory• defect dynamics, but…

• Descriptions of atomic interactions• empirical or semi-empirical still needed for “large scale” (>250 atoms) and “long-

time” (> 10 picoseconds)• first principles calculations necessary • van der Waals bonds important, currently added to first principles calculations in an

ad hoc manner

Theoretical and Computional Modeling Issues-2


Nov 1, 2002Slide-39

• Continuum models• properties become boundary value problems non-locality• still required to do multiphysics• still required at the end of the day

• atomistics to find out what is important• continuum to do “real problems” - design

Theoretical and Computional Modeling Issues-3

Where are we headed? Where are we headed?

While continuum mechanics attempts to solve pde’s, molecular dynamics uses multi body dynamics (similar to the earliest planetary mechanics). Energy of the system is the common denominator in both the approaches.

Are continuum concepts valid at atomic scales? If so, how do we define them.

How do we formulate, implement and solve in large scale computing environments nano-meso-macro systems?

While continuum mechanics attempts to solve pde’s, molecular dynamics uses multi body dynamics (similar to the earliest planetary mechanics). Energy of the system is the common denominator in both the approaches.

Are continuum concepts valid at atomic scales? If so, how do we define them.

How do we formulate, implement and solve in large scale computing environments nano-meso-macro systems?

computational nanotechnology

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