Electronic structure calculations: methods and applications. George C. Schatz Northwestern University

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1 Electronic structure calculations: methods and applications George C. Schatz Northwestern University

Materials Fracture and Degradation Steven

Schatz Northwestern University Also thanks to:

2 Materials Fracture and Degradation Steven Mielke, Diego Troya, LiPeng Sun, Jeff Paci, Ted Belytschko, Sulin Zhang, Roopam Khare and George C. Schatz Northwestern University Also thanks to: Rod Ruoff, Horacio Espinosa Northwestern Peter Zapol, Orlando Auciello-ANL Roberto Car - Princeton

3 Using Electronic Structure Theory to Model Mechanical Properties of Nanomaterials Nanotubes, rods and other nanomaterials provide the simplest systems for which mechanical properties (stress/strain behavior) can be measured. These materials provide an excellent opportunity to learn about the influence of defects and chemical functionalization. They are sometimes amenable to study using electronic structure theory methods, thus providing a platform for connecting fundamental theory with experiment.

4 Electronic Structure Theory will be used to: Establish shape of stress/strain curves, and their sensitivity to nanotube structure. Interpret experiments, establish theoretical limits. Examine the role of defects and chemical functionalization on fracture behavior. Integrate single nanotube results with bulk results.

5 Using electronic structure theory to describe fracture in nanosystems is a big challenge Minimum size systems to model structure typically contain >100 atoms, and real systems are usually much larger. The quality of theory needs to be carefully considered: bonds are being broken, open-shell effects can be important, both finite cluster and periodic boundary conditions need to be considered. Finite temperature effects might be important, but it is impossible to do useful MD calculations with most electronic structure models. Multiple pathways to fracture are possible.

6 Model Systems Carbon Nanotubes (defects, chemical functionalization) Ultrananocrystalline Diamond Films (grain boundary fracture, doping effects)

7 Electronic structure methods DFT (PBE): SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms): a self-consistent DFT program. Highest accuracy of the methods we have studied, but computational effort is a serious problem. PM3: Semiempirical method which is reasonably close to DFT for carbon-based nanostructures. Largely restricted to finite cluster calculations. MSINDO: Semiempirical method that can be used both for clusters and for periodic boundary conditions. For carbon-based nanostructures it is less accurate than PM3. SCC-DFTB (density functional-based tight-binding with self-consistent charges): an approximate DFT method.

8 Other methods For systems with carbon and hydrogens, can use Tersoff-Brenner (reactive bond-order) potential for MM calculations. Mixed MM/CM studies (and ultimately QM/MM/CM) to extend from a few atoms to a continuum description.

$Carbon nanotube fracture Carbon nanotubes are likely the strongest known materials$ larger tensile loads than reinforced steel) and their lightweight nature (six times

larger tensile loads than reinforced steel) and their lightweight nature (six times

9 Carbon nanotube fracture Carbon nanotubes are likely the strongest known materials Their superior mechanical properties (resisting more than 1 order of magnitude larger tensile loads than reinforced steel) and their lightweight nature (six times less than steel) make them perfect candidates for reinforcement materials in nanocomposites

10 Fracture of Carbon Nanotubes MM calculations with empirical force fields T. Belytschko, S. P. Xiao, G. C. Schatz and R. Ruoff, Phys. Rev. B 65, /1-/8 (2002). (single wall tube results) (Multiwall tubes)

$Carbon nanotube fracture Determination of stress vs strain curve for [5,5]$

11 Carbon nanotube fracture Determination of stress vs strain curve for [5,5] tube with Stone-Wales defect (170 carbon atoms) l/2 l 0 l/2 strain= l/ l 0

$255 (just before fracture) 8 6 E-E 0 / a.u. 4 2 0 0 0.$

12 PM3 results: Strain = (just before fracture) 8 6 E-E 0 / a.u strain

13 Strain = 0.26 (just after fracture) 8 6 E-E 0 / a.u strain

14 Stress-Strain Curves: undefected tubes [5,5] tube [10,0] tube

15 One and Two-Atom Vacancies

16 Fracture for one/two atom vacancies Two-atom vacancy (sym) [5,5] tube One-atom vacancy (asym), [10,0] tube

17 Fracture for Large Hole Defects Hole Defect MM results Slit Defect

18 Undefected CNTs have fracture stress >100 GPa Chem vap dep Arc discharge

Peng, Mark Locascio, Peter Zapol, Shuyou Li, Steven L.

19 Measurements of near-ultimate strength for multiwalled carbon nanotubes and irradiation-induced crosslinking improvements, Bei Peng, Mark Locascio, Peter Zapol, Shuyou Li, Steven L. Mielke, George C. Schatz and Horacio D. Espinosa, Nature Nanotech, 3, (2008)

$fracture stress in excess of 100$ GPa Calculations shows

20 Stress-strain results show fracture stress in excess of 100 GPa Calculations shows significant load transfer in the cross-linked tube

21 Polymer/Carbon Nanotube Composites Ramanathan, T.; Liu, H.; Brinson, L. C..J. Polymer Sci B (2005), 43(17),

22 Graphite and Graphite Oxide (GO) Graphite Graphite Oxide d = 0.71 nm B. Brodie, 1855 C:O:H is 2:1:0.2

sheets (2600 m 2 /g) Readily dispersed in polymers Retain inherent mechanical,

23 Graphene-Based Composites TEGO - Thermally exfoliated GO: 30% of carbon is lost as CO/CO 2 during heating to 1500K GO TEGO TEGO Properties: Individual sheets (2600 m 2 /g) Readily dispersed in polymers Retain inherent mechanical, thermal, electrical properties of graphene Dramatically improved composite properties

24 TEGO Nanocomposites (Cate Brinson, Northwestern) Thin sheets wrinkled in situ interaction with polymer Remarkable increase in Tg (30 C) with 0.05% loading of TEGO!

$1 GPa, Tg 105 C, (fracture stress) Ultimate strength - 70 MPa Thermal degradation temperature - 295 C Ramanathan, T.; Abdala, A. A.; Stankovich, S.; Dikin, D. A.; Herrera-Alonso, M.; Piner, R. D.; Adamson, D.$

25 TEGO-PMMA Mechanical Properties PMMA/1wt% Nanoinclusion Normalized values TEGO/PMMA a-swnt/pmma PMMA values: E-2.1 GPa, Tg 105 C, (fracture stress) Ultimate strength - 70 MPa Thermal degradation temperature C Ramanathan, T.; Abdala, A. A.; Stankovich, S.; Dikin, D. A.; Herrera-Alonso, M.; Piner, R. D.; Adamson, D. H.; Schniepp, H. C.; Chen, X.; Ruoff, R. S.; Nguyen, S. T.; Aksay, I. A.; Prud'Homme, R. K.; Brinson, L. C.. Functionalized graphene sheets for polymer nanocomposites. Nature Nanotechnology (2008), 3(6),

26 Structure of Graphite Oxide? (1939) (1946) (1969) Dekany and coworkers, Chem. Mater.18, 2740 (2006) (1996) (1998)

27 Lerf, Klinowski (1998) Model Dekany (2006) Model 1. Aliphatic six-membered rings containing epoxides and hydroxides. Ketones and other C=O bonds are on the edges. No 1,3 ethers. 2. Aromatic regions that give rise to a nearly flat carbon grid. 1. Trans linked cyclohexane chairs that is functionalized with tertiary OH, 1,3-ether, ketone, quinone and phenol 2. Ribbons of aromatic rings

28 Basic Questions 1. What is the structure of GO, and how do defects in graphite get propagated into GO? 2. What are the mechanical properties of GO and TEGO? 3. What does this teach us about graphite oxidation?

Add these functional groups to both sides of the basal plane.

29 Monte Carlo-based simulations of graphite oxide formation: Introduction Add OH and epoxide groups to graphene. Add these functional groups to both sides of the basal plane. Build sheets with experimentally-observed stoichiometry (C 10 O 5 H 2 ). Use cluster- and PBCmodels. SCC-DFTB, PBE(DZP) Harris(DZP), simulations. A graphene sheet.

30 The algorithm 1) Add two OH and three epoxide groups to the basal plane composed of, e.g., 128 carbon atoms with PBCs. Locations chosen at random. 2) Geometry-optimize structure, calculate energy, using Metropolis MC to accept or reject structures for further functionalization. Steps 1) and 2) are repeated N times. Result is N sheets of partiallyoxidized GO. A partially-oxidized sheet of GO. Paci, Jeffrey T.; Belytschko, Ted; Schatz, George C. Journal of Physical Chemistry C (2007), 111(49),

31 Final results: C 2 OH 0.2 stoichiometry undefected graphene Defect = line of epoxides

32 Some aromaticity remains for low oxygen/carbon ratio Requirements: Planar, cyclic, one p- orbital/atom perpendicular to the plane of the ring. 4n+2 pi electrons, where n is an integer. Shown here: A carbon to oxygen ratio of 2:0.77. Aromatic carbons are shaded purple.

33 Final results 1. Interplanar spacing: 5.8Å (calc) 6.0Å (expt) (vs. graphite = 3.4Å) 2. Chemical species (out of 64 oxygens): O Found at edges Unimportant Unimportant 3. Hole formation: Does not occur in pristine graphene. Previously existing holes can expand during growth. Paci, Jeffrey T.; Belytschko, Ted; Schatz, George C. Journal of Physical Chemistry C (2007), 111(49),

34 Heating GO to 1323K leads to gaseous CO, as well as a mechanism for making holes OH O O O O OH + CO O

35 Fracture studies: Notched graphene sheet Energy (E h ) Strain

erode in low Earth orbit (LEO) (~200-700

36 Polymer degradation in LEO Spacecraft surfaces made of polymeric hydrocarbons erode in low Earth orbit (LEO) (~ km). J. W. Connell, High Perform Polym 12, 43 (2000)

37 Most abundant species in atmosphere as function of altitude Minton, in Chemical Dynamics in Extreme Environments, (World Scientific, Singapore, 2001), pp 420. Roble, in The Upper Mesosphere and Lower Thermosphere: A Review of Experiment and Theory, Geophysical Monograph 87, pp 1 21, 1995.

38 Materials erosion in low earth orbit Materials (polymers) on the RAM surfaces of satellites in low earth orbit are degraded by 5eV O( 3 P) as well as other neutrals, ions, UV, electrons and dust. Many mechanisms for erosion have been discussed including intersystem crossing, collision induced dissociation and ion-surface reactions.

39 O + graphite J. Zhang, T. K. Minton, High Performance Polymers (2001), 13(3), S467-S481. K. T. Nicholson, T. K. Minton, S. J. Sibener, J Phys Chem B (2005), 109(17), CO CO 200 N(t) / arb. units CO Time of Flight / s

40 Configuration-biased Monte Carlo studies of graphite oxide Jeffrey T. Paci, Ted Belytschko, George C. Schatz, J. Phys. Chem. C, 111, (2007)

41 O + graphite simulations Paci, Jeffrey T.; Upadhyaya, Hari P.; Zhang, Jianming; Schatz, George C.; Minton, Timothy K. Theoretical and Experimental Studies of the Reactions between Hyperthermal O(3P) and Graphite: Graphene-Based Direct Dynamics and Beam-Surface Scattering Approaches. Journal of Physical Chemistry A (2009), 113(16),

42 Summary Molecular dynamics (molecular mechanics) with quantum forces provides the most accurate approach for describing structures and bond breaking. System size (few hundred atoms) and time scales (<10 ps) are the primary limitations. Fracture properties of carbon nanotubes and other nanomaterials. Structure of graphite oxide. Degradation of graphite in LEO.