Multi-Scale Simulations of the Growth and Assembly of Colloidal

Nanoscale MaterialsKristen A. Fichthorn

Department of Chemical EngineeringDepartment of PhysicsPenn State University

DE-FG0207ER46414

Complex Nanostructures in Colloidal Crystal Growth: How Do They Form?

Ostwald Ripening

Cluster-ClusterAggregation

OrientedAttachment

How Does OA Happen?

Complex Nanostructures in Colloidal Crystal Growth: Oriented Attachment

Oriented Attachment of TiO2:Intrinsic Crystal Forces

Oriented Attachment andthe Mesocrystal State:The Role of Solvent

R. Penn and J. Banfield, Geochim.Cosmochim. Acta 63, 1549 (1999).

M. Alimohammadi and K. Fichthorn, Nano Lett. 9, 4198 (2009).

V. Yuwano, N. Burrows, J. Soltis, and R. Penn, JACS 132, 2163 (2010).

Complex Nanostructures in Colloidal Crystal Growth: Capping Agents

Y. Sun, B. Mayers, T. Herricks, andY. Xia, Nano Lett. 3, 955 (2003).

Polyol ProcessSolvent: Ethylene Glycol

Salt: AgNO3

“Stabilizer”: PVP

What Happensin the Pot?

B. Wiley,…Y. Xia, Chem. Eur. J. 11, 454 (2005).

“One-Pot” Solution-Phase Synthesis of Nanostructured Metal Materials

N,N-DMF ReductionSolvent: N,N-DMF

Salt: AgNO3

“Stabilizer”: PVP

All Kinds ofNano-Shapes

Heat at ~400 K

B. Wiley,…Y. Xia, Chem. Eur. J. 11, 454 (2005).

Reductionof Ag

Nucleation

Growth

Nanostructure Formation:General Aspects

Determined bySalt and…Solvent or PVP? Probably Determined

by PVP…

SeedFormation

Does PVP Prefer Ag(100) Over Ag(111)?

Nanowires from Multiply-Twinned DecahedralSeeds

Nanocubes from Single-Crystal Cubo-OctahedralSeeds

One Possible Role of PVP: Surface-Sensitive Binding

G. Grochola, I. Snook, and S. Russo, J. Chem. Phys. 127, 194707 (2007).

Y. Sun, B. Mayers, T. Herricks, and Y. Xia, Nano Lett. 3, 955 (2003).

Interaction of PVP with Ag(100) and Ag(111):First-Principles Challenges

Direct Bonding +van der Waals (vdW)

vdW

Historically DFT Described Direct Bonds,Including vdW Interactions is New…

S. Grimme, J. Comput. Chem. 27, 1787 (2006).M. Dion,…, D. C. Langreth, B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004).A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009).K. Lee, …, D. C. Langreth, B. I. Lundqvist, Phys. Rev. B 82, 081101 (2010).

L. Delle Site, K. Kremer, Int. J. Quant. Chem. 101, 733 (2005).

nCoarse-Grained

Model

Interaction of PVP with Ag(100) and Ag(111): VASP 5.2.11

• (4×4×14) Super Cell• Slab: 6 layers• Vacuum: 8 layers

• PAW-PBE (GGA) ± DFT-D2 ± TS*• Assess the Influence of

vdW Interactions

• Cut-off: 29.4 Ry

• k-points: (4×4×1)

• Ab-initio Molecular Dynamics

• Static Total-Energy Calculations*Implemented in VASP by Wissam Al-Saidi

van der Waals Interactions in DFT: How Do We Describe Ag??

aS. Grimme, J. Comput. Chem. 27, 1787 (2006).bA. Tkatchenko and M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009) .cE. Zaremba and W. Kohn, Phys. Rev. B 13, 2279 (1976).dS. Eichenlaub, C. Chan, and S. P. Beaudoin, J. Coll. Int. Sci. 248, 389 (2002).eA. Khein, D. J. Singh, and C. J. Umrigar, Phys. Rev. B 51, 4105, (1995).fH. Li, et al., Phys. Rev. B 43, 7305 (1991).gF. R. De Boer, et al., Cohesion in Metals, Amsterdam, (1988).hM. Chelvayohan and C.H.B. Mee, J. Phys. C: Solid State Phys.15, 2305 (1982).

BA AB

ABdampvdW R

CfE

,6

6

)]1(exp[1

1),(

)(

0

0

AB

AB

Rf

RABABdamp dRRf

PBE DFT-D2a TS+ZKb+c Experiment

C6

(J nm6 mol-1)--- 24.67 6.89 6.25d

R0(Å) --- 1.64 1.34 ---

aAg (Å) 4.16 4.15 4.02 4.07e

D12 Ag(100) (%) -2.05 1.3 -1.75 ±1.5f,g

D12 Ag(111) (%) -0.3 1.61 -0.32 0.5 ± 0.8h

Binding Conformations:No vdW Interactions

Experimental IR and XPS:PVP Binds to Ag via the O and/or N Atom.

Ag(100)

Top

Hollow

BridgeAg(111)

Top

fccHollow

hcpHollow

Bridge

Trial & Error:Bonding with O Atom Down

F. Bonet et al., Bull. Mater. Sci. 23, 165 (2000).Z. Zhang et al., J. Solid State Chem. 121, 105 (1996).H. H. Huang et al., Langmuir 12, 909 (1996).

Binding Energies: No vdW Interactions

Adsorption site Ethane 2-Pyrrolidone(100) Hollow 0.0 0.19

(100) Bridge 0.0 0.22

(100) Top - 0.21

(111) fcc Hollow 0.0 0.19

(111) hcp Hollow - 0.16

(111) Bridge - 0.20

(111) Top - 0.26

Bond Strength (eV)

Predominantly vdW

Ag(100)

Top

Hollow

Bridge

Ag(111)

Top

fccHollow

hcpHollow

Bridge

Preference for Ag(111): Contrary to Expectations

) ( surfacemoleculesurfacemoleculebind EEEE

Ethane Binds:X.-L. Zhou and J. M. White, J. Phys. Chem. 96, 7703 (1992).

)( surfacemoleculesurfacemoleculebind EEEE

vdW Interactions Support Structure-Directing Hypothesis

Site PBE PBEDFT-D2

PBETS+ZK

(100) Hollow 0.19 1.05 0.59

(100) Bridge 0.22 1.34 0.77(100) Top 0.21 1.05 0.60

(111) fcc 0.19 0.61 0.58

(111) hcp 0.16 0.80 0.58

(111) Bridge 0.20 0.70 0.62

(111) Top 0.26 0.79 0.64

Bond Strength (eV)

Why Such Big Differences Between Methods??

DFT-D2: Ag(100) Reconstructs

eV 27.0 )100(

EEE hexhex

Ag(100) Reconstruction has not been Observed Experimentally…

TS+ZK:2-Pyrrolidone on Ag(100)

HollowEbind = 0.59

Bridge Ebind = 0.77

Top Ebind = 0.60

Hollow || Ebind = 0.77Bridge ||

Ebind = 0.81

Top ||Ebind = 0.78

Lots of Options!Binding via O and N

F. Bonet et al., Bull. Mater. Sci. 23 (2000).Z. Zhang et al., J. Solid State Chem. 121 (1996).H. H. Huang et al., Langmuir 12 (1996).

KTkTEP

P400 );/exp(139

)111(

)100(

PVP ~139 Times More Likely to Bind toAg(100) “Sides” than Ag(111) “Ends”

TS+ZK EnergiesTS+ZK Geometries

PBE Energies TS+ZK Geometries D

Site Ebind EPauli+Edirect bond EvdW

(100) Hollow || 0.78 0.36 0.42

(100) Bridge || 0.81 0.32 0.48

(100) Top || 0.77 0.30 0.47

(111) Top ┴ 0.64 0.12 0.51

(111) Bridge ┴ 0.62 0.09 0.53

(111) Bridge || 0.63 -0.19 0.82

TS+ZK Method: Break-Downof Binding Energy

bonddirectPaulivdWbind EEEE

TS+ZK EnergiesTS+ZK Geometries

PBE Energies TS+ZK Geometries D

Site Ebind EPauli+Edirect bond EvdW

(100) Hollow || 0.78 0.36 0.42

(100) Bridge || 0.81 0.32 0.48

(100) Top || 0.77 0.30 0.47

(111) Top ┴ 0.64 0.12 0.51

(111) Bridge ┴ 0.62 0.09 0.53

(111) Bridge || 0.63 -0.19 0.82

TS+ZK Method: Break-Downof Binding Energy

bonddirectPaulivdWbind EEEE

Ag(100): vdW and Direct Bonding Synergize

TS+ZK EnergiesTS+ZK Geometries

PBE Energies TS+ZK Geometries D

Site Ebind EPauli+Edirect bond EvdW

(100) Hollow || 0.78 0.36 0.42

(100) Bridge || 0.81 0.32 0.48

(100) Top|| 0.77 0.30 0.47

(111) Top ┴ 0.64 0.12 0.51

(111) Bridge ┴ 0.62 0.09 0.53

(111) Bridge || 0.63 -0.19 0.82

TS+ZK Method: Break-Downof Binding Energy

bonddirectPaulivdWbind EEEE

Ag(111): vdW is the Dominant Attractive Force

Sometimes the only Attractive Force

• We Observed Stronger Binding to Ag(100) when we Include vdW As Inferred by Experiment

Conclusions• We Studied Surface-Sensitivity of PVP Binding to Ag(111) and Ag(100)

• DFT-D2 Reconstructs Ag(100)

• Ag(100) Preference from Synergy Between vdW Attraction and Direct Bonding

Oriented Attachment in Crystal Growth:Role of Intrinsic Crystal Forces

See Also:M. Niederberger and H. Cölfen, Phys. Chem. Chem. Phys. 8, 3271 (2006). Q. Zhang, S. Liu, and S. Yu, J. Mater. Chem. 19, 191 (2009).

HRTEM: Oriented Attachment of TiO2 NanoparticlesR. Penn and J. Banfield, Geochim. Cosmochim.Acta 63, 1549 (1999).

Dipole-Dipole Interactions May Assemble Nanoparticles

T. Zhang, N. Kotov, and S. Glotzer, Nano Lett. 7, 1670 (2007).

Z. Tang and N. Kotov, Adv. Mater. 17, 951 (2005); Z. Tang, N. Kotov, M. Giersig, Science 297, 237 (2002).

CdTe Nanoparticle Chains

+ - + -

Two WulffNanocrystals

(001) TruncatedNanocrystals

(112) TruncatedNanocrystals

i

iiq rm=35 D

m=0

m=250 D

m=75 D

TiO2 (Anatase) NanocrystalsMatsui-Akaogi Force FieldMol. Sim. 6, 239, 1991.*

Aggregation of Wulff Nanocrystals

Nanocrystal Aggregation:The Hinge Mechanism

Initial Contact of Edges:The “Hinge”

Rotation About the “Hinge”

Nanocrystal Aggregation:Driven by Electrostatic Forces

M. Alimohammadi and K. Fichthorn, Nano Lett. 9, 4198 (2009).

Nanocrystal Aggregation: Driven by Multipoles from Under-CoordinatedSurface Atoms

M. Alimohammadi and K. Fichthorn, Nano Lett. 9, 4198 (2009).

HRTEM Image Showing Oriented Attachment of 5 TiO2 NanoparticlesR. Penn and J. Banfield, Geochim. Cosmochim. Acta 63, 1549 (1999).

Simulation vs. Experiment: Still Have a Way to Go

Aqueous EnvironmentHour (or longer) Times

Vacuum EnvironmentNanosecond Times

Nanocrystal Aggregation is Driven by Local Interactions.

We Should Re-Think the Dipole Idea…

Conclusions

P. Schapotschnikow et al., Nano Lett. 10, 3966 (2010).

Also found this for capped and uncapped PbSe…

1D Nanostructures form via Mesocrystals and Oriented Attachment

M. Giersig, I. Pastoriza-Santos, L. Liz-Marzan,J. Mater. Chem. 14, 607 (2004).

Ag Nanowires

V. Yuwano, …, and R. Penn,JACS 132, 2163 (2010).

Goethite Nanowires

Solvent Ordering and Solvation Forces

Solvent Density Profile

Solvent ordering around solvophilic nanoparticles

Y. Qin and K. A. Fichthorn, J. Chem. Phys. 119, 9745 (2003).

Y. Qin and K. A. Fichthorn, Phys. Rev. E 73, 020401 (2006).

MD: Aggregation of a Small, Isotropic*Crystal with a Larger, Anisotropic Crystal

*Relatively

RectangularCuboid

SquarePlate

2

1

32

1

● Generic Anisotropic fcc Nanoparticles● Solvophilic Nanoparticles● Strong vdW Attraction (Ag)● Isotropic Organic Solvent

Aggregation of Small and Large Nanocrystals: Mesocrystal States

Mesocrystal State 1One Solvent Layer

Mesocrystal State 1One Solvent Layer

Mesocrystal State 2Two Solvent Layers

Mesocrystal States: Free-Energy Minima

Escape-Time Distribution

Aggregation Probability

kTGeR

eRtf/

Rt

~

)(

RA eP 1)(

Aggregation of Small and Large Nanocrystals: Mesocrystal States

Mesocrystal State 1One Solvent Layer

Mesocrystal State 1One Solvent Layer

Mesocrystal State 2Two Solvent Layers

Aggregation:Fastest at End of RectangleSlowest on Face of SquareEven on SidesMesocrystal State 1

Most FrequentMesocrystal State 2Occurs on SquareMesocrystal State 3

DissociationNot Typically FrequentDissociation

Nanocrystal Encounters:Frequency of Outcomes

3

1

2

1

2

Aggregation is the Most FrequentOn the Smallest Facets,Perpetuating 1D Growth

Disruption Solvent Ordering at EdgesLeads to Fast Aggregation on Small Facets

Square Plate

Rectangle

7.26.66.05.44.84.23.63.02.41.81.20.60

/r rb

Rectangle

Conclusions

Solvent Ordering Around Nanocrystal SurfacesPromotes Growth of 1D Nanostructures

Leads to Mesocrystal States

Faster Aggregation on Smaller Facets

Collaborators

FundingNSF DMR-1006452, NIRT CCR-0303976, CBET-0730987DOE DE-FG0207ER46414ACS, EPA, NCSA

Mozhgan AlimohammadiHaijun FengAzar ShahrazJin Pyo HongDr. Ya ZhouDr. Yangzheng Lin

AlumsDr. Yong QinDr. Rajesh SathiyanarayananDr. Leonidas Gergidis

Fritz Haber InstituteAlexander TkatchenkoVictor Gonzalo Ruiz LopezMatthias Scheffler

Univ. of PittsburghDr. Wissam Al-Saidi