Atomic-Scale Simulations in the Nanoscience of Interfaces

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1 Atomic-Scale Simulations in the Nanoscience of Interfaces Kristen A. Fichthorn Departments of Chemical Engineering and Physics The Pennsylvania State University University Park, PA USA

2 We Care About Including Relevant Atomic-Scale Details into Macroscopic Models (that might be) Relevant for Engineering Design

3 The Challenge: Predicting Assembly from First Principles Well Understood Complexity HELP! Solid-State Systems Energy Dominates DFT Enables Detailed Understanding Rare-Event Dynamics Theory Developed Molecules on Surfaces Entropy Plays a Role DFT Not As Good, Sampling! Rare-Event Dynamics, Hydrodynamics Some Theory Nanoparticles in Solution Entropy Plays a Big Role DFT is Limited, van der Waals, Sampling! Some Rare-Event Dynamics, Hydrodynamics Macroscopic Theories K. Becker and K. Fichthorn, J. Chem. Phys. 125, (2006)

4 Most Problem We Work on Have a Fluid Near a Solid Surface. Two Examples: Forces and Assembly of Colloidal Nanoparticles Y. Qin and K. Fichthorn, J. Chem. Phys. 119, 9745 (2003). Y. Qin and K. Fichthorn, Phys. Rev. E 73, (2006). K. Fichthorn and Y. Qin, I&EC Res. 45, 5477 (2006). Y. Qin and K. Fichthorn, Phys. Rev. E 74, (2006). Nanostructured Interfaces from First Principles R. Miron and K. Fichthorn, J. Chem. Phys. 115, 8742 (2001). R. Miron and K. Fichthorn, J. Chem. Phys. 119, 6210 (2003). R. Pentcheva, K. Fichthorn, M. Scheffler et al., Phys. Rev. Lett. 90, (2003). K. A. Fichthorn and M. Scheffler, Nature 429, 617 (2004). R. Miron and K. Fichthorn, Phys. Rev. Lett. 93, (2004). R. Miron and K. Fichthorn, Phys. Rev. B 72, (2005).

5 Nanostructured Surfaces from First Principles Non-Equilibrium Kinetics + Interactions = Ag/ 2 ML Ag / Pt(111) H. Brune et al., Nature 394, 451 (1998). InAs/GaAs(001) M. Xu et al., Surf. Sci. 580, 30 (2005). Al / Al(110) F. Bautier de Mongeot et al., PRL 91, (2003)..And More!!!

6 Surface Phenomena Involve Multiple Length and Time Scales Bautier de Mongeot et al., Phys. Rev. Lett. 91, (2003). Thin-Film Growth e.g. fcc(110) homoepitaxy Also Crystal Growth, Catalysis at Surfaces and More Atoms Hopping (A, ps) Hut Formation (nm, min) Hut Organization (μm, min) K. Fichthorn and M. Scheffler, Nature 429, 617 (2004).

7 Challenge: Reactor Design from First Principles Example: Growth of GaAs Thin Films Charge-Density Contours for GaAs(001) from Density-Functional Theory (Å) Kinetic Monte Carlo Simulation of Growth of GaAs(001) (nm, s) Continuum Equations for Fluid Flow, Heat Transfer, Mass Transfer, Kinetics in a Rotating Disk Reactor (m,h) Transition-State Theory Kratzer and Scheffler, Comp. Sci. Eng

8 Kinetic Monte Carlo Simulations Edge Diffusion Deposition, F Aggregation Nucleation Terrace Diffusion, D K. Fichthorn and W. Weinberg, J. Chem. Phys. 95, 1090 (1991). K. Fichthorn et al., Appl. Phys. A 75, 17 (2002).

9 Concerted Cluster Diffusion Mechanisms Difficult to Characterize and Include in kmc R. Miron & K. Fichthorn, J. Chem. Phys. 115 (2001).

10 Electronic Pair Interaction on Ag/Pt(111): Still New Frontiers Energy, mev single atom diffusion barrier E 0b = 52 mev K. Fichthorn & M. Scheffler, Phys. Rev. Lett. 84, 5371 (2000). Agrees with Exp t: H. Brune et al., Phys. Rev. B 52 R14380 (1995).

11 Challenges in Multi-Scale Modeling Accurate Semi-Empirical Potentials Efficient Algorithms for Finding ALL TST Rate Processes Stiff Systems Length and Time Scale of KMC Atomic Continuum Link

12 Challenges in Multi-Scale Modeling Accurate Semi-Empirical Potentials Efficient Algorithms for Finding ALL TST Rate Processes Incorporating TST Rates into KMC Stiff Systems Appropriate Atomic Detail in Continuum Reactor Design

13 Co/Cu Heteroepitaxy Promising for spintronic recording media 1 ML of Co on Cu(001) Pentcheva and Scheffler, Phys. Rev. B 60 (2000). Interesting heteroepitaxial growth modes

14 ab initio kmc of Submonolayer Co/Cu(001) Heteroepitaxy Spin-Polarized, FP-LAPW DFT For Energy Barriers.. Hopping / Exchange of Co & Cu Adatoms Experiment Cu Hopping Away from Exchanged Co Co Grows on Top of Cu Co Trapped at Exchanged Co Co Hopping Away from Exchanged Co Co, Cu Escape from Exchanged Co R. Pentcheva, K. Fichthorn, M. Scheffler, et al., PRL 90, (2003).

15 Tight Binding Potential Fit to DFT Levanov Miron Levanov Miron Based on potential by Levanov et al., Phys. Rev. B 61 (2000). R. Miron and K. Fichthorn, Phys. Rev. B. 72, (2005).

16 = A T B k V A T B k V B A TST k B ) ) / ( exp( ) ) / ( *)exp( (, R R R R δ ν Accelerated Molecular Dynamics (Hyperdynamics) A. Voter, J. Chem. Phys. 106, 11 (1997). Detailed Balance! V (R) * * A B C * * B A C V (R) V (R) V (R) V (R) ) / exp( / ) ( / ) / exp( ) / exp( / ) / ) exp( ( ) ( exp ) ( ) ( / ) / ) ( ) exp( ( ) ( / ) / ) ( ) exp( ( ) ( * * = = = T k W T k T k T k k T k V W W T k V W W T k V W k B B B B B TST B B B B TST R R R R R R R R R R R R R δ ν δ ν

17 Accelerated Molecular Dynamics (Hyperdynamics) A. Voter, J. Chem. Phys. 106, 11 (1997). k TST, A B = k TST,A B / 1/W(R) A * * k TST, A C = k TST,A C / 1/W(R) A k k TST, A B TST, A C = k TST,A B k TST,A C C A B Detailed Balance!

18 Accelerated Molecular Dynamics Challenge: How to Build V(R) On The Fly? A. Voter, J. Chem. Phys. 106, 11 (1997). Monitor Smallest Eigenvalue of Hessian Matrix Expensive! * * Steiner et al., Phys. Rev. B 57, (1998). Monitor Changes in Single-Particle Or Total Potential Energy C A B Can t Easily Define for Many-Body Interactions! Fluctuations in Total Energy! Wang et al., Phys. Rev. B 63, (2001). Monitor Changes in Single-Particle Energy

19 Accelerated Molecular Dynamics The Bond Boost Method R. Miron & K. Fichthorn, J. Chem. Phys. 119, 6210 (2003)

20 Overview of the Bond Boost Method

21 Diffusion on Cu(100): Elementary Processes

22 The Bond-Boost Method: Diffusion on Cu(100) Accelerated MD is 10 5 Times Faster!!

23 Rare Events and the Small Barrier Problem Annoyingly Small Barriers

24 State-Bridging Accelerated MD to Solve the Small-Barrier Problem Fast Motion in a Group of Recurrent States Connected by Small Barriers

25 State-Bridging Accelerated MD to Solve the Small-Barrier Problem Boost Potential Fast Motion in a Group of Recurrent States Connected by Small Barriers: The Maximum Boost is Limited

26 State-Bridging Accelerated MD to Solve the Small-Barrier Problem Bridging Potential Boost Potential Consolidate Groups of Recurrent States Connected by Small Barriers into One Big State Ignore the Dynamics and Achieve a High Boost R. Miron & K. Fichthorn, Phys. Rev. Lett. 93, 2004.

27 Overview of State-Bridging Accelerated MD Commence With a Low Boost Raise the Boost After A Waiting Time Miron & Fichthorn, J. Chem. Phys. 115, Detect Barriers When Transitions Occur, Compare To Threshold Memorize and Consolidate Pairs of States Connected by Low Barriers R. Miron & K. Fichthorn, Phys. Rev. Lett. 93, 2004.

28 Benefits of State Bridging State-Bridging Accelerated MD Regular Accelerated MD

29 Thin Film Growth at 250 K, F = 0.1 ML/s Note Cluster Mobility

30 Island Density vs. Coverage from Accelerated MD

31 Cluster Mobility Reduces Island Density Pentcheva et al., PRL 90 (2003). J. Villain et al., J. Phys. I France 2 (1992).

32 Growth Approaching Multi-Layers: Monolayer or Bilayer? Kief et al., Phys. Rev. B 47 (1993). F = 0.03 ML/s Bilayer for T = K Fassbender et al., Surf. Sci. 383 (1997). T = 330 K Monolayer for F = ML/s Bilayer for F = 0.3 ML/s Monolayer: Low F / Medium T Bilayer: High F / Low T?

33 State-Bridging Accelerated MD of Co/Cu(001) Heteroepitaxy: T = 250 K, F = 0.1 ML/s, Θ = 0.54 ML MD Simulations were run for 5.4 s R. Miron and K. Fichthorn, Phys. Rev. B 72, (2005). Mechanism of Bilayer Island Formation

34 Bilayer Formation Mechanisms When an atom is pulled up, it stays there!

35 Flux Dependence of Bilayer Formation Small, Irregular Islands Grow Bilayer Large, Smooth Islands Grow Monolayer

36 Conclusions Simple and Efficient Accelerated MD With the Bond-Boost Method Accelerated MD Lets Us Find Complex Kinetic Mechanisms AND Simulate Experiments Cluster Diffusion Influences Island Density Origins of Monolayer vs. Bilayer Island Growth in Co/Cu(001) Epitaxy

37 Nanoparticles: Potential Building Blocks For New and Existing Materials Catalysts Optical Materials Structural Materials Electronic Materials Nano-Electronics: Replace Lithography by Self-Assembly? C. Keating, Penn State Chemistry but Difficult to Assemble or Disperse Nanoparticles. Nanoparticle Forces are POORLY UNDERSTOOD!

38 Colloidal Forces from Molecular Dynamics Simulations van der Waals and Electrostatic Forces: DLVO theory Solvation Forces: Solvent Ordering Depletion Forces: Entropic How Do These Work for Colloidal Nanoparticles?

39 Parallel Molecular Dynamics Simulation Solid Nanoparticles in Liquid Solvent ( ~ 10 5 Atoms) : Lennard-Jones: ρ* = 0.7, T* = 1.0 n-decane: ρ= g/ml, T = K n n n 4 n intra U () r = U b ( θi ) + U t ( φi ) + ULJ ( rij ) i= 3 i= 4 i= 1 j= i+ 4 1 U b i k 2 ( θ ) ( θ θ ) 2 = b i 0 C i-1 θ i φ i C i U t 5 ( ) = a ( cos φ ) i l = 0 l i l φ C i-3 C i-2 Solvophilic Nanoparticles: (ε fs = 3.0, 5.0ε ff ) Solvophobic Nanoparticles: (ε fs = 0.2ε ff )

40 Model Nanoparticles Probing the Size and Shape Dependence of Forces Small Sphere d = 4.9σ 64 atoms ~1.7 nm Large Sphere d = 17.6σ 2048 atoms ~6 nm Icosahedron d = 4.0σ 55 atoms ~1.4 nm Cube d = 13.2σ 2744 atoms ~4.5 nm

41 Solvation and van der Waals Forces Solvation Force ) ( δ ) = r F F solv F AB A, S i B, Si i i Free-Energy Change ΔA ij = δ δ j i F solv (δ ) dδ F van der Waals Force vdw ij ( δ ) = rˆ AB i A j B du dr ij

42 F σ/kt F σ/kt Solvation Forces in Lennard-Jones Liquid Small Sphere δ/σ Solvophilic Solvophobic van der Waals δ/σ Cube van der Waals Solvophilic F σ/kt Large Sphere Oscillatory solvophilic forces are comparable to van der Waals forces, as seen in SFA, AFM [e.g.,israelachvili, Surf. Sci. Rep. 14, 109 (1992); Gao, Luedtke, and Landman, J. Chem. Phys. 106, 4309 (1997)] δ/σ Solvophilic Solvophobic van der Waals Y. Qin and K. Fichthorn, J. Chem. Phys. 119, 9745 (2003).

43 Fluid Ordering: Origin of Solvation Forces Solvent Density Profile Solvent ordering around solvophilic nanoparticles

44 Solvation Forces in Lennard-Jones Liquid F σ/kt Small Sphere Solvophilic Solvophobic van der Waals δ/σ F σ/kt Large Sphere Solvophilic Solvophobic van der Waals δ/σ F σ/kt Cube van der Waals Solvophilic δ/σ Forces Depend on Particle Size And Shape

45 Derjaguin Approximation for Shape Dependence: Influenced by Surface Roughness ( ) Solv F ( δ ) ΔA δ = 2 2 2A ρ π C C DρS Solvophilic Solvophobic ΔA/(2Acρc 2 ) or F Solv /(πdρs 2 ) (ktσ 4 ) Small Sphere Large Sphere Cube ΔA/(2Acρc 2 ) or F Solv /(πdρs 2 ) (ktσ 4 ) Small Sphere Large Sphere Cube δ/σ δ/σ Derjaguin Approximation Describes the Envelope Derjaguin Approximation Works

46 Influence of Surface Roughness on Solvation Forces: LJ Liquid Force (kt/σ) Separation (σ) Left Center Right Interestingly, Roughness Destroys Solvation Forces For Macroscopic Surfaces Particles will Rotate in Solution for a Minimum Free-Energy Approach

47 Influence of Rotation on Solvation Forces Solvophilic Nanoparticles Rotate About Fixed Center of Mass Without Rotation F σ/kt Solvophobic fixed rotation With Rotation δ/σ

48 Minimum-Energy Path for Approach of Nanocrystals Y. Qin and K. Fichthorn, Phys. Rev. E 73, (2006). Vertex to Vertex Edge Face Face to Face Vertex Solvation Forces can Control Alignment in Assembly

49 Nanoparticle Rotation Driven by Solvent Ordering Initial Final Initial Final Nanoparticles Rotate to Reduce Solvent Density in the Gap ρ /ρ bulk

50 Applications: Aligned Nanoparticle Assemblies Cubic Pt Nanoparticles Nanocrystalline Au Arrays T. Ahmadi et al., Chem. Mater. 8, 1161 (1996). R. Whetten et al., Adv. Mater. 8, 428 (1996).

51 Solvation Forces Could Cause Oriented Attachment in Crystal Growth HRTEM Image Showing Oriented Attachment of 5 TiO 2 Nanoparticles R. Penn and J. Banfield, Geochim. Cosmochim. Acta 63, 1549 (1999). See Also: R. L. Penn et al., J. Phys. Chem. B 105, 2177 (2001). J. F. Banfield et al., Science 289, 751 (2000). M. Niederberger and H. Cölfen, Phys. Chem. Chem. Phys. 8, 3271 (2006).

52 Conclusions Solvation Forces can be Important! Solvation Forces Depend on: particle/solvent size particle shape particle-solvent interactions vs. Solvation Forces Can Cause Nanoparticle Alignment in Assembly/Crystal Growth Nanoparticle Suspensions can be Engineered

53 Collaborators Kelly Becker Mozhgan Alimohammadi Maria Mignogna Derek Triplett Yogesh Tiwary Dr. Vishal Kopardé Josh Howe Ryan Muthard David Condon Dr. Hye-Young Kim Funding Alumni Mike Merrick Dr. Yong Qin Dr. Radu Alex Miron Dr. Jee-Ching Wang Dr. Som Pal Dr. Weiwei Luo Fritz-Haber-Institut Dr. Matthias Scheffler Dr. Rossitza Pentcheva PSU NIRT Dr. Theresa Mayer Dr. Chris Keating Dr. Darrell Velegol NSF ECC , DMR , IGERT DGE , DMR , NIRT CCR ACS PRF, EPA, Alexander von Humboldt Foundation