Computational Nanotechnology

1. Computational Nanotechnology N. Chandra Department of Mechanical Engineering FAMU-FSU College of Engineering Florida State University Tallahassee, FL 32312

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

3. Smaller and smaller and then some more.. Nanotechnology is the development of products and device at the nanoscale. *From Nanotechnology Magazine (nanozine.com)

4. Revolutionary Aircraft Concepts (30% less mass, 20% less emission, 25% increased range) Multi-Functional Materials High Strength Material (>10 GPa) Reusable Launch Vehicle (20% less mass, 20% less noise) Autonomous Spacecraft (40% less mass) Adaptive Self-Repairing Space Missions Bio-Inspired Materials and Processes Capability of Nanotechnology Source: NASA Ames

5. Library of Congress Library of Congress? Then there are dreams… • 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)

6. Role of Computations in Nanotechnology “...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 • 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 To manipulate things which we cannot see without the unaided eye but indeed understand, we must employ predictive methods: Computational Tools. If you can’t model it, you can’t build it!

7. Carbon Nanotubes Geometric Features Unusual Properties CNT based composites Role of interfaces Experimental Observations

8. 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.

9. Basic Configurations of CNT

10. Carbon Nanotubes • 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.

11. Yielding under tensile stress • MD simulations with high strain rate: • elastic up 30% (Yakobson et al *) • Experimentally feasible strain rate and Temperature 11.5% tensile strained (10,0) T=1600K 9% tensile strained (5,5) T=2400K * Yakobson et al, Comput. Mater. Sci. 8, 341 (1997)

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

13. Stiffness and Plasticity of SW C Nanotubes D. Srivastava, M. Menon and K. Cho, Phys. Rev. Lett. Vol. 83, 2973 (1999)

14. Polymer Composites based on CNTs • 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)

15. SEM images of polymer (polyvinylacohol) ribbon contained CNT fibers & knotted CNT fibers SEM images of epoxy-CNT composite (B. Vigolo et.al., Science, V290 P1331, 2000) (L.S.Schadler et.al., Appl. Phys. Lett. V73 P3842, 1998) Polymer Composites based on CNTs • What are the critical issues? • Structural and thermal properties • Load transfer and mechanical properties

16. Buckling of CNT during Composite Manufacture • Experiment: buckling and collapse of nanotubes embedded in polymer composites. Local collapse or fracture of thin tubes. Buckle, bend and loops of thick tubes..

17. Interface Bonding Issues • Critical length to transfer load1. • Thermally induced residual stresses • Number of bonds between polymer molecules and carbon nanotube Polymer-SWNT interacting 1SJV Frankland, A. Caglar, DW Brenner, M. Griebel, J of Physical Chemistry B, 106, 3046-3048, (2002)

18. Crack nucleation and propagation in MWNT-PS thin films. Failure occurs in low NT densities and propagate along interfaces (2) Buckling of tubes due to residual stresses (1) Load transfer issues in Composites Basic concept in composites • 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)

19. Alignment of fibers is very critical in obtaining desired properties. Distribution of CNTs shown. Extrusion is used in this case (1) Alignment issues in CNT composites CNTs are in nanoscales compared to carbon fibers • 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. • 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. 1.Carole A. Cooper, Dianne Ravich, David Lips, Joerg Mayer, Daniel Wagner, CST, 62, 1105, 1112, (2002)

20. Alignment of Carbon Nanotubes in Polymeric Composites Single-wall nanotubes usually form bundles and webs and are thus strongly entangled rather than aligning straight and in isolation. Schematic view of the orientation of a nanotube-based composite in which the nanotubes are approximately aligned parallel to the shearing direction. . TEM image of a SWNT composite1. 1B. McCarthy et al., Chemical Physics letters, 350, 27-32, (2001)

21. Composites are nothing new…… Early form of Straw Bale brick Straw Bale brick/adobe prototype home under construction in the 1890s Shibam Hadramout, the largest territory in The Republic of Yemen Ghuwaizi Fort In The Republic of Yemen: Built in 1884AD as a guard post

22. CONSTRUCTION OF COMPOSITES 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. 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).

23. TYPES OF FIBER-REINFORCED COMPOSITE PMCs: MMCs: CMCs:

24. DEFINITION AND CLASSIFICATION OF INTERFACE • DEFINITION OF AN INTERFACE An interface is a bounding surface or zone where a discontinuity in physical, mechanical, or chemical characteristics occurs. • 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 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.

25. Factors affecting interfacial properties Asperities Interfacial chemistry Mechanical effects Origin:Surface irregularities inherent in the interface Issues: Affects interface fracture process through mechanical loading and friction Approach: 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. Residual stress 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 ) 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. Metal/ ceramic/ polymer Interface CNTs Properties affected Trans. & long. Stiffness/strength Fatigue/Fracture Thermal/electronic/magnetic

26. Mechanics of Interfaces in Composites Formulations Atomic Simulations Interfacial traction-displacement relationship are obtained using molecular dynamics simulation based on EAM functions Interfaces are modeled as cohesive zones using a potential function are work of normal and tangential separation are normal and tangential displacement jump The interfacial tractions are given by Grain boundary interface Reference 1.X.P. Xu and A Needleman, Modelling Simul. Mater. Sci. Eng.I (1993) 111-132 2.N. Chandra and P.Dang, J of Mater. Sci., 34 (1999) 655-666

27. Issues 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

28. Computational Aspects Multi-scale modeling methods Formulations and solution procedures Computational Requirements Some sample simulations Outstanding issues in nanomechanics and nanophysics

29. Hierarchical Modeling of Materials MACRO SCALE Theory Balance Laws (Force,Momentum,Energy) Continuum Mechanics Thermodynamics (Constitutive Equations) Numerical Tools FEM, FDM,BEM Minimize Global Energy FEM mesh for a Superplastic Component Computational Issues Large Scale Computing Adaptive Auto Remeshing Massive Parallel Computing Data Structure for Parallel Adaptive Solution Visualization Applications Structural Design Bulk /Sheet Forming Composite Mechanics Paperless Design of Boeing777

30. Hierarchical Modeling of Materials ATOMIC - SCALE Theory Ab-Initio methods Quantum Mechanics Density Functional Theory EAM Potential Pair Potential Numerics Molecular Statics Molecular Dynamics Monte Carlo Simulations Computational Issues Limited by time (ps) And space (103 to107 atoms) Parallel Molecular Dynamics PMD code developed at Sandia (110) 9 Grain Boundary Red Atoms Show GB Applications Defects,(e.g.Vacancies,Dislocations) Grain boundary sliding Crack tip evolution Phase transformation Nanocrystals, Thin films

31. Multiscale Approaches for Systems Simulations Finite element for homogeneous, Continuum description ~ bulk continuous media Mesoscopic dynamics for non-homogeneous ~ 1000,000,000 atoms or grid Atomistic MD, many-body force fields ~ 1000,000 atoms Semi-empirical, tight-binding MD ~ 1000 atoms ab-initio, structure, energetics ~ 100 atoms Molecular Dynamics Experiments Long time structural KMC, TDMC Hyperdynamics ~ up to 100s of ns ~ up to sec, hours

32. How do we Go Directly from Electrons to Solid Mechanics? Density Functional Theory E=Sk ek -rsc[VH(r)/2 +Vxc(r)] dr + Exc[rsc(r)] O(2) Error, Self-Consistent, Variational, Parameterized Harris Functional E=k ekout -rin[VH(r)/2+Vxc(r)]dr + Exc[rin(r)] O(2) Error,Self-Consistent Variational, Parameterized Tight Binding Methods E = A(r) +kk . O(2) Error, Self-Consistent, Variational,Parameterized Conceptual Framework Materials Applications Large-Scale Atomic Simulation Continuum Mechanics Cauchy- Quasi- Born Continuum Molecular Monte Dynamics Carlo Practical Implementation Analytic Potentials Embedded-AtomMethod: E= F(ri) + ij U(rij) Bond Order Potentials: Ei = ij [Ae-r- z1/2Be-r] O(2) Error, Self-Consistent, Variational,Parameterized Moments Theorem

33. Nanoscale Mechanics – Characteristics • 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

34. Nanoscale Mechanics – Limitations • 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

35. Nanoscale Mechanics – Challenges • 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 • Dislocations (centro-symmetry parameters) • Density • Populations/families NOTE: discrete dislocation simulations focus on defect field interactions rather than lattice per se

36. Nanoscale Mechanics – Challenges • Modeling evolution of microstructure • Defect generation/motion • Coarsening/ageing – phase stability • 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

37. Theoretical and Computional Modeling Issues • 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

38. Theoretical and Computional Modeling Issues-2 • 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, currentlyadded to first principles calculations in an ad hoc manner

39. Theoretical and Computional Modeling Issues-3 • 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

40. 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?