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.*
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
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