Multi-Scale Simulations of the
Growth and Assembly of Colloidal
Nanoscale Materials
Kristen A. Fichthorn
Department of Chemical Engineering
Department of Physics
Penn State University
DE-FG0207ER46414
Complex Nanostructures in Colloidal
Crystal Growth: How Do They Form?
Ostwald Ripening
Cluster-Cluster
Aggregation
Oriented
Attachment
How Does OA Happen?
Complex Nanostructures in Colloidal
Crystal Growth: Oriented Attachment
Oriented Attachment of TiO2:
Intrinsic Crystal Forces
R. Penn and J. Banfield, Geochim.
Cosmochim. Acta 63, 1549 (1999).
M. Alimohammadi and K. Fichthorn,
Nano Lett. 9, 4198 (2009).
Oriented Attachment and
the Mesocrystal State:
The Role of Solvent
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, and
Y. Xia, Nano Lett. 3, 955 (2003).
“One-Pot” Solution-Phase Synthesis
of Nanostructured Metal Materials
Polyol Process
Solvent: Ethylene Glycol
Salt: AgNO3
“Stabilizer”: PVP
N,N-DMF Reduction
Solvent: N,N-DMF
Salt: AgNO3
“Stabilizer”: PVP
All Kinds of
Nano-Shapes
Heat at ~400 K
B. Wiley,…Y. Xia, Chem. Eur. J. 11, 454 (2005).
What Happens
in the Pot?
Nanostructure Formation:
General Aspects
Seed
Formation
Reduction
of Ag
Growth
Nucleation
Determined by
Salt and…
Solvent or PVP?
B. Wiley,…Y. Xia, Chem. Eur. J. 11,
454 (2005).
Probably Determined
by PVP…
One Possible Role of PVP:
Surface-Sensitive Binding
Y. Sun, B. Mayers, T. Herricks, and Y. Xia,
Nano Lett. 3, 955 (2003).
Nanocubes from SingleCrystal Cubo-Octahedral
Seeds
G. Grochola, I. Snook, and S. Russo, J.
Chem. Phys. 127, 194707 (2007).
Nanowires from MultiplyTwinned Decahedral
Seeds
Does PVP Prefer Ag(100) Over Ag(111)?
Interaction of PVP with Ag(100) and
Ag(111):First-Principles Challenges
L. Delle Site, K. Kremer, Int. J.
Quant. Chem. 101, 733 (2005).
vdW
Direct Bonding +
van der Waals (vdW)
n
Coarse-Grained
Model
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).
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??
EvdW   
A, B
aS.
f dampC6 AB
0
f damp ( RAB , RAB
)
6
RAB
1
1  exp[  d ( f (RRAB0 )  1)]
AB
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
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).
Binding Conformations:
No vdW Interactions
Trial & Error:
Bonding with O Atom Down
Top
Bridge
fcc
Hollow
Ag(111)
Top
Hollow
hcp
Hollow
Ag(100)
Bridge
Experimental IR and XPS:
PVP Binds to Ag via the O
and/or N Atom.
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
Ebind  ( Emolecule surface  Emolecule  Esurface )
Adsorption site
(100) Hollow
Bond Strength (eV)
Ethane 2-Pyrrolidone
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
Top
Hollow
Ag(100)
Top
Bridge
Bridge
fcc
Hollow
Ag(111)
hcp
Hollow
Predominantly vdW
Ethane Binds:
X.-L. Zhou and J. M. White,
J. Phys. Chem. 96, 7703 (1992).
Preference for Ag(111):
Contrary to Expectations
vdW Interactions Support
Structure-Directing Hypothesis
Ebind  ( Emolecule surface  Emolecule  Esurface)
Bond Strength (eV)
0.19
PBE
DFT-D2
1.05
PBE
TS+ZK
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
0.26
0.70
0.62
0.79
0.64
Site
PBE
(100) Hollow
(111) Top
Why Such Big Differences Between Methods??
DFT-D2: Ag(100) Reconstructs
Ag(100) Reconstruction has not
been Observed Experimentally…
DEhex  Ehex  E (100)
 0.27 eV
TS+ZK:2-Pyrrolidone on Ag(100)
Top
Ebind = 0.60
Bridge
Ebind = 0.77
Hollow
Ebind = 0.59
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).
Bridge ||
Ebind = 0.81
Hollow || Ebind = 0.77
PVP ~139 Times More Likely to Bind to
Ag(100) “Sides” than Ag(111) “Ends”
P(100)
P(111)
 139  exp( DE / kT ); T  400 K
TS+ZK Method: Break-Down
of Binding Energy
Ebind  EvdW  EPauli  Edirect bond
TS+ZK Energies
TS+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-Down
of Binding Energy
Ebind  EvdW  EPauli  Edirect bond
TS+ZK Energies
TS+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
Ag(100): vdW and Direct Bonding Synergize
TS+ZK Method: Break-Down
of Binding Energy
Ebind  EvdW  EPauli  Edirect bond
TS+ZK Energies
TS+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
Ag(111): vdW is the Dominant Attractive Force
Sometimes the only Attractive Force
Conclusions
• We Studied Surface-Sensitivity of
PVP Binding to Ag(111) and Ag(100)
• We Observed Stronger Binding to
Ag(100) when we Include vdW
As Inferred by Experiment
• 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
HRTEM: Oriented Attachment of TiO2
Nanoparticles
R. Penn and J. Banfield, Geochim. Cosmochim.
Acta 63, 1549 (1999).
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).
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
TiO2 (Anatase) Nanocrystals
*
=250 D
Matsui-Akaogi Force Field
Mol. Sim. 6, 239, 1991.
(112) Truncated
Nanocrystals
=75 D
=0
Two Wulff
Nanocrystals
   qir i
i
=35 D
(001) Truncated
Nanocrystals
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-Coordinated
Surface Atoms
M. Alimohammadi and K. Fichthorn,
Nano Lett. 9, 4198 (2009).
Simulation vs. Experiment:
Still Have a Way to Go
HRTEM Image Showing Oriented Attachment of 5 TiO2 Nanoparticles
R. Penn and J. Banfield, Geochim. Cosmochim. Acta 63, 1549 (1999).
Aqueous Environment
Hour (or longer) Times
Vacuum Environment
Nanosecond Times
Conclusions
Nanocrystal Aggregation is Driven by Local
Interactions.
We Should Re-Think the Dipole Idea…
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
Goethite Nanowires
V. Yuwano, …, and R. Penn,
JACS 132, 2163 (2010).
Ag Nanowires
M. Giersig, I. Pastoriza-Santos, L. Liz-Marzan,
J. Mater. Chem. 14, 607 (2004).
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
1
1
2
2
3
Rectangular
Cuboid
*Relatively
Square
Plate
● Generic Anisotropic fcc Nanoparticles
● Solvophilic Nanoparticles
● Strong vdW Attraction (Ag)
● Isotropic Organic Solvent
Aggregation of Small and Large
Nanocrystals: Mesocrystal States
Mesocrystal State 1
One Solvent Layer
Mesocrystal State 2
Two Solvent Layers
Mesocrystal State 1
One Solvent Layer
Aggregation of Small and Large
Nanocrystals: Mesocrystal States
Mesocrystal States: Free-Energy Minima
Escape-Time Distribution
f (t )  R e  Rt
R ~ e  DG / kT
Aggregation Probability
PA ( )  1  e R
Mesocrystal State 2
Two Solvent Layers
Mesocrystal State 1
One Solvent Layer
Mesocrystal State 1
One Solvent Layer
Nanocrystal Encounters:
Frequency of Outcomes
1
2
1
2
3
Aggregation:
Aggregation
is the Most Frequent
Fastest at End of Rectangle
On the
Smallest
Facets,
Slowest
on Face
of Square
State 1
Even onMesocrystal
Sides
Perpetuating
1D Growth
Most Frequent
Mesocrystal State 3
Dissociation
Dissociation
Not Typically Frequent
Mesocrystal State 2
Occurs on Square
Disruption Solvent Ordering at Edges
Leads to Fast Aggregation on Small Facets
r/rb
7.2
6.6
6.0
5.4
4.8
4.2
3.6
3.0
2.4
1.8
1.2
0.6
0
Rectangle
Rectangle
Square Plate
Conclusions
Solvent Ordering Around Nanocrystal Surfaces
Promotes Growth of 1D Nanostructures
Leads to Mesocrystal States
Faster Aggregation on Smaller Facets
Collaborators
Mozhgan Alimohammadi
Haijun Feng
Azar Shahraz
Jin Pyo Hong
Dr. Ya Zhou
Dr. Yangzheng Lin
Alums
Dr. Yong Qin
Dr. Rajesh Sathiyanarayanan
Dr. Leonidas Gergidis
Fritz Haber Institute
Alexander Tkatchenko
Victor Gonzalo Ruiz Lopez
Matthias Scheffler
Univ. of Pittsburgh
Dr. Wissam Al-Saidi
Funding
NSF DMR-1006452, NIRT CCR-0303976, CBET-0730987
DOE DE-FG0207ER46414
ACS, EPA, NCSA