Studies of Nano, Chemical, and Biological Materials by Studies of Nano, Chemical, and Biological Materials by Molecular SimulationsMolecular Simulations
Yanting Wang
Institute of Theoretical Physics, Chinese Academy of Sciences Beijing, China September 25, 2008
Institute of Theoretical Physics, Chinese Academy of Sciences
Atomistic Molecular Dynamics SimulationAtomistic Molecular Dynamics Simulation
i ij ijj
t tF F r
ii
i
tt
m
Fa
1i i it t t t v v a
1 1i i it t t t r r v
Empirical force fields are determined by fitting experimental results or data from first principles calculations
Quality of empirical force fields has big influence on simulation results
Capable of simulating up to millions of atoms (parallel computing)
ijF
Solving Newton’s Equations of Motion.
Quantifying Condensed Matter StructuresQuantifying Condensed Matter Structures
Bond-Orientational Order Parameters
Radial Distribution Function g(r)
• Capture the symmetry of spatial orientation of chemical bonds
• Non-zero values for crystal structures
• 0 for liquid
• Appearance probability of other atoms with respect to a given atom
• Discrete values for solids
• Continuous waves for liquids
• 1 for ideal gas (isotropic structure)
Molecular electronicsIon detection
S. O. Obare et al., Langmuir 18, 10407 (2002)
R. F. Service, Science 294, 2442 (2001)
Electronic lithography
J. Zheng et al., Langmuir 16, 9673 (2000)
Both size and shape are important in experiments!
Chemical etchingGold nanowiresLarger Au particles change color
Some Applications of Gold NanomaterialsSome Applications of Gold Nanomaterials
Thermal Stability of Low Index Gold SurfacesThermal Stability of Low Index Gold Surfaces
Thermal stability of surface: {110} < {100} < {111}
Stable gold interior: FCC structure
Stability of Icosahedral Gold NanoclustersStability of Icosahedral Gold Nanoclusters**
Empirical glue potential model Constant T molecular dynamics (MD) From 1500K to 200K with T=100K, and keep T constant for 21 ns thousands of atoms
Icosahedron at T=200K
Mackay Icosahedron with a missing central atom Asymmetric facet sizes
Simulated annealing from a liquid
* Y. Wang, S. Teitel, C. Dellago Chem. Phys. Lett. 394, 257 (2004)* Y. Wang, S. Teitel, C. Dellago J. Chem. Phys. 122, 214722 (2005)
Strained FCC interior All covered by stable {111} facets
Liquid at T=1500K
Cooling
First-Order Like Melting Transition First-Order Like Melting Transition
Potential energy vs. T
Surface
Interior
Cone algorithm* to group atoms into layers
Sub-layers
Heat to melt
Keep T constant for 43 ns T = 1075K for N = 2624 Magic and non-magic numbers
First-order like melting transition
* Y. Wang, S. Teitel, C. Dellago J. Chem. Phys. 122, 214722 (2005)
SurfaceInterior
Interior keeps ordered up to melting temperature Tm
Surface softens but does not melt below Tm
No Surface Premelt for Gold Icosahedral NanoclustersNo Surface Premelt for Gold Icosahedral Nanoclusters
N = 2624
Mean squared displacements (average diffusion)
All surface atoms diffuse just below melting Surface premelting?
Surface Atoms Diffuse Below MeltingSurface Atoms Diffuse Below Melting
N = 2624
t=1.075ns
4t
Movement
Movement
Average shape
Vertex and edge atoms diffuse increasingly with T Facets shrink but do not vanish below Tm=1075 K Facet atoms also diffuse below Tm because the facets are very small !
““Premelt” of Vertices and Edges but not FacetsPremelt” of Vertices and Edges but not Facets
Mechanism
ConclusionsConclusions
First-order like melting transition for gold nanoclusters with thousands of atoms
Very stable {111} facets result in good thermal stability of icosahedral gold nanoclusters
Vertex and edge “premelt” softens the surface but no overall surface premelting
Very Small Gold Nanoclusters?Very Small Gold Nanoclusters?
Smaller gold nanocluster has more active catalytic ability
Debate if very small gold nanoclusters (< 2 nm ) are solid or liquid
54 gold atoms (only two layers)
Not an icosahedron
All surface atoms are on vertex or edge!
Smeared Melting Transition for Smeared Melting Transition for NN = 54 = 54**
Heat up sequentially
timestep 2.86 fs
108 steps at each T
Average potential energy per atom Heat capacity
Easy to disorder due to less binding energy
Melting transition from Ts ≈ 300 K to Te ≈ 1200 K
Ts
Te
* Y. Wang, S. Rashkeev J. Phys. Chem. C 113, 10517 (2009).
Snapshots at Different TemperaturesSnapshots at Different Temperatures
Both layers premelt below 560 K
No inter-layer diffusion below 560 K
Inter- and Intra- Layer DiffusionInter- and Intra- Layer Diffusion
Inter-layer diffusion starts at Ti ≈ 560 KAtomic self diffusion starts at Td ≈ 340 K
Td
Ti
22
1 1
1 M N
i j i jj i
r t t t tMN
r r
2 6r t Dt
Moved atoms: moving to the other layer at least once at each temperature
Ti
Liquid crystal-like structure between 340 K and 560 K
More Layers in Between: Approaching More Layers in Between: Approaching First-Order Melting TransitionFirst-Order Melting Transition**
Onset Temperature Ts and Complete Temperature Te of Melting Transition, Self
Diffusion Temperature Td, and Interlayer Diffusion Temperature Ti
atoms layers Ts Te Ti Td
54 2 300 1200 560 340
146 3 350 1000 300 450
308 4 400 900 400 500
560 5 550 850 500 600
Melting temperature region narrows down for more layers
Only two-layer cluster has intra-layer diffusion first
* Y. Wang, S. Rashkeev J. Phys. Chem. C 113, 10517 (2009).
ConclusionsConclusions
Smeared melting transition for two-layer gold nanocluster
Mechanism consistent with icosahedral gold nanoclusters
Liquid-crystal like partially melted state for two-layer gold nanocluster: intra-layer diffusion without inter-layer diffusion
Approaching well-defined first-order melting transition for gold nanoclusters with more layers
Very small gold nanoclusters have abundant phase behavior that can not be predicted by simply extrapolating the behavior of larger gold nanoclusters
Increasing total E continuously to mimic laser heating
T=5K T=515K
T=1064K T=1468K
Experimental model
Z. L. Wang et al., Surf. Sci. 440, L809 (1999)
Pure FCC interior
Thermal Stability of Gold NanorodsThermal Stability of Gold Nanorods**
Two steps
* Y. Wang, C. Dellago J. Phys. Chem. B 107, 9214 (2003).
Surface-Driven Bulk Reorganization of Gold NanorodsSurface-Driven Bulk Reorganization of Gold Nanorods**Surface Second sub layer
Yellow: {111} Green: {100}Red: {110} Gray: other
Cross sections
Yellow: fcc Green: hcp Gray: other
Temperature by temperature step heating
Minimizing total surface area
Surface changes to all {111} facets
Interior changes fcc→hcp→fcc by sliding planes, induced by surface change
Interior fcc reorients
* Y. Wang, S. Teitel, C. Dellago Nano Lett. 5, 2174 (2005).
ConclusionsConclusions
Thermal stability of gold nanoclusters and gold nanorods is closely related to specific surface structures (not only surface stress matters)
Shape change of gold nanorods comes from the balance between surface and internal free energetics
Multiscale Coarse-Graining (MS-CG) MethodMultiscale Coarse-Graining (MS-CG) Method** to Rigorously to Rigorously Build CG Force Fields from All-Atom Force FieldsBuild CG Force Fields from All-Atom Force Fields
• Pioneer work by Dr. Sergey Izvekov with block-averaging
• Theory by Prof. Will Noid (Penn State U), Prof. Jhih-Wei Chu (UC-Berkeley), Dr. Vinod Krishna, and Prof. Gary Ayton
• Help from Prof. Hans C. Andersen (Stanford)
• I implemented the force-minimization approach
Assuming central pairwise effective forces Minimizing force residual
2, ,1 13
I CGN NI AA I CG
ICG I
F FN N a a
a
Y = -å åv v
Well rebuild structural properties Can eliminate some atoms at CG level Does NOT consider transferability!
* W. Noid, P. Liu, Y. Wang et al. J. Chem. Phys. 128, 244115 (2008).
Benifit: maller numbers of degrees of freedom and faster dynamics
( )̂CG CGF F r ra ab ab abb
=åv
Residual:
Each CG site:
Effective force: ( ) ( )dCG
DF fr r dd= -
2, ,
,,
1 13
12
3
I CGN NI AA I CG
ICG I
ddddd dCG
d dd
F FN N
G b cff fN
a aa
¢¢
¢
Y = -
æ ö÷ç ÷= - +ç ÷ç ÷çè ø
å å
å å
v v
( ) ( ) ( ),,
1 ˆ ˆI I I ID Ddd
II
G R R R d R dN ab ag ab ag
a b g
d d¢ ¢= - -å å å g
( ) ( ),1 ˆI I AA Id D
II
b R F R dN ab a ab
a b
d= -å å åvg
, ,1 I AA I AA
II
c F FN a a
a
= å åv v
g
Central pairwise, linear approximation
Multidimensional parabola
Obtained fromall-atom configurations
Multiscale Coarse-Graining by Force MinimizationMultiscale Coarse-Graining by Force Minimization
Residual: ,,
12
3 d dd ddddd dCG
ff fb cN ¢ ¢
¢
æ ö÷ç ÷Y = - +ç ÷ç ÷çè øå åG
Variational principle: 0dd
gf
¶Y= =¶ , d ddd
d
f b¢¢
¢=å G
Or finding the minimal solution by conjugate gradient minimization with Ψ and g
d
Only one minimal solution!
Ψ can be used to determine the best CG scheme
Subtract the Ewald Sum (long-range electrostatic) of point net charges
Match bonded and non-bonded interactions separately
Force Minimization by Conjugate Gradient MethodForce Minimization by Conjugate Gradient Method
Solving matrix directly
• Explicitly calculating pairwise atomic interactions between two groups All-atom MD to get the ensemble of relative orientations
• Very limited transferability: temperature, surface, sequence of amino acids Wrong pressure (density) without further constraint
* Y. Wang, W. Noid, P. Liu, G. A. Voth to be submitted.
Effective Force Coarse-Graining (EF-CG) MethodEffective Force Coarse-Graining (EF-CG) Method**
EF-CG non-bonded effective forces
Problems with MS-CG
1 1
1 1
ˆ
ˆˆ
M N
ij Di jD
D D
M N
ij ij ij Di j
D
r R RR R
F RR R R R
F r R R
R R
R
R
r R
1 1
M N
ij iji j
r r
ConclusionsConclusions
CG methods enable faster simulations and longer effective simulation time
MS-CG method rebuilds structures accurately but has very limited transferability
MS-CG method can eliminate some atoms (e.g., implicit solvent)
EF-CG method has much better transferability by compromising a little accuracy of structures
MS-CG MD Study of Aggregation of PolyglutaminesMS-CG MD Study of Aggregation of Polyglutamines**
Polyglutamine aggregation is the clinic cause of 14 neural diseases, including Huntington’s, Alzheimer's, and Parkinson's diseases
All-atom simulations have a very slow dynamics that can not be adequately sampled
Water-free MS-CG model
CG MD simulations extend from nanoseconds to milliseconds
CG MD results consistent with experiments:
Longer chain system exhibits stronger aggregation
Degrees of aggregation depend on concentration
Mechanism based on weak VDW interactions and fluctuation nature
* Y. Wang, G. A. Voth to be submitted.
Ionic liquid = Room temperature molten salt Non-volatile High viscosity
Some Applications of Ionic LiquidsSome Applications of Ionic Liquids
Environment-friendly solvent for chemical
reactions Lubricant Propellant
* Y. Wang, S. Izvekov, T. Yan, and G. Voth, J. Phys. Chem. B 110, 3564 (2006).
Multiscale Coarse-Graining of Ionic LiquidsMultiscale Coarse-Graining of Ionic Liquids**
EMIM+/NO3- ionic liquid
64 ion pairs, T = 400 K Electrostatic and VDW interactions
Site-site RDFs (T = 400K)
Good structures No temperature transferability
Satisfactory CG Structures of Ionic LiquidsSatisfactory CG Structures of Ionic Liquids
Spatial Heterogeneity in Ionic LiquidsSpatial Heterogeneity in Ionic Liquids**
C1
C2
C4
C6
C8
With longer cationic side chains:
Polar head groups and anions retain local structure due to electrostatic interactions
Nonpolar tail groups aggregate to form separate domains due to VDW interactions
* Y. Wang, G. A. Voth, J. Am. Chem. Soc. 127, 12192 (2005).
Quantifying degrees of heterogeneous distribution by a single value Detecting aggregation Monitoring self-assembly process
* Y. Wang, G. A. Voth J. Phys. Chem. B 110, 18601 (2006).
Define Heterogeneity order parameter (HOP)
hi exp( rij2 / 2 2)
j
L
N 1/3
• Invariant with box size L
• Average over all sites to get <h>
• For each site
Larger HOP represents more heterogeneous configuration.
Heterogeneity Order ParameterHeterogeneity Order Parameter**
Thermal Stability of Tail Domain in Ionic LiquidsThermal Stability of Tail Domain in Ionic Liquids**
* Y. Wang, G. A. Voth, J. Phys. Chem. B 110, 18601 (2006).
Heat capacity plot shows a second order transition at T = 1200 K Contradictory: HOP of instantaneous configurations do not show a transition at T = 1200 K?
Tail Domain Diffusion in Ionic LiquidsTail Domain Diffusion in Ionic Liquids Instantaneous LHOPs at T = 1230 KDefine Lattice HOP
Divide simulation box into cells
In each cell the ensemble average of HOP is
taken for all configurations
ci 1
Mhij
j1
M
Mechanism
Heterogeneous tail domains have fixed positions at low T
(solid-like structure)
Tail domains are more smeared with increasing T
Above Tc, instantaneous tail domains still form (liquid-like
structure), but have a uniform ensemble average
Extendable EF-CG Models of Ionic LiquidsExtendable EF-CG Models of Ionic Liquids**
Extendable CG models correctly rebuild spatial heterogeneity features
CG RDFs do not change much for C12 from 512 (27,136) to 4096 ion pairs (217,088 atoms)
Proving spatial heterogeneity is truly nano-scale, not artificial effect of finite-size effect
* Y. Wang, S. Feng, G. A. Voth J. Chem. Theor. Comp. 5, 1091 (2009).
CG force library Extendibility,
transferability, and manipulability
Disordering and Reordering of Ionic Liquids under Disordering and Reordering of Ionic Liquids under an External Electric Fieldan External Electric Field**
* Y. Wang J. Phys. Chem. B 113, 11058 (2009).
From heterogeneous to homogeneous to nematic-like due to the effective screening of the external electric field to the internal electrostatic interactions.
ConclusionsConclusions
Spatial heterogeneity phenomenon was found in ionic liquids, attributed to the competition of electrostatic and VDW interactions
Solid-like tail domains in ionic liquids go through a second order melting-like transition and become liquid-like above Tc
EF-CG method was applied to build extendable and transferable CG models for ionic liquids, which is important for the systematic design of ionic liquids
Ionic liquid structure changes from spatial heterogeneous to homogeneous to nematic-like under an external electric field
Polymers for Gas-Separation MembranesPolymers for Gas-Separation Membranes
CO2 Capturer Air Dryer Air Mask
Environmental applications
Energy applications
Industrial applications
Military applications
…
UBE.com
AMBER force field
Put one-unit molecules on lattice positions
Relax at P = 1 atm and T = 10 K
Measure lattice constants in relaxed configuration
Polybenzimidazole (PBI)
N
N N
NH
H
nH
HH
H
H H
HH
H H
Determining Crystalline Structure of PolymersDetermining Crystalline Structure of Polymers
Polybenzimidazole (PBI)
N
N N
NH
H
nH
HH
H
H H
HH
H H
Poly[bis(isobutoxycarbonyl)benzimidazole] (PBI-Butyl)
N
N N
N
n
O
O
OO
Kapton
N N O
O
O O
O
n
X-Z Plane Y-Z Plane
Infinitely-Long Crystalline Polymers at T = 300 KInfinitely-Long Crystalline Polymers at T = 300 K
N
N N
NH
H
nH
HH
H
H H
HH
H H
System X (Å) Y (Å) Z (Å) Volume (nm3)
PBI 75.09 ± 0.11 28.38 ± 0.09 25.83 ± 0.12 55.05 ± 0.19
PBI + CO2 75.08 ± 0.05 29.97 ± 0.11 25.82 ± 0.08 58.10 ± 0.17
PBI + N2 75.09 ± 0.06 29.57 ± 0.18 26.03 ± 0.10 57.68 ± 0.17
PBI + CO2
PBI + N2
Sizes along Y are expanded.Gas molecules can hardly get in between the layers.
Very stiff
CO2 and N2 inside PBICO2 and N2 inside PBI
PBI-Butyl + CO2
PBI-Butyl + N2
N
N N
N
n
O
O
OO
System X (Å) Y (Å) Z (Å) Volume (nm3)
PBI-Butyl 75.55 ± 0.05 52.35 ± 0.18 30.25 ± 0.07 119.51 ± 0.31
PBI-Butyl + CO2 75.52 ± 0.05 52.05 ± 0.20 30.30 ± 0.08 119.08 ± 0.39
PBI-Butyl + N2 75.52 ± 0.05 52.41 ± 0.20 30.22 ± 0.08 119.61 ± 0.37
No dimension sizes are changed. Gas molecules are free to diffuse between layers.
Open up spaces
CO2 and N2 inside PBI-ButylCO2 and N2 inside PBI-Butyl
Kapton + CO2
Kapton + N2
Sizes along Z are expanded. Gas molecules change the crystal structure of Kapton.
Flexible
N N O
O
O O
O
n
System X (Å) Y (Å) Z (Å) Volume (nm3)
Kapton 84.77 ± 0.10 27.50 ± 0.04 27.02 ± 0.07 62.97 ± 0.15
Kapton + CO2 84.91 ± 0.06 27.80 ± 0.09 28.36 ± 0.10 66.94 ± 0.16
Kapton + N2 84.65 ± 0.08 26.63 ± 0.11 30.43 ± 0.14 68.58 ± 0.18
CO2 and N2 inside KaptonCO2 and N2 inside Kapton
PBI forms a very strong and closely packed crystalline structure.
CO2 and N2 can hardly diffuse in PBI crystal.
Crystal structure of PBI-Butyl is rigid, but the butyl side chains make the interlayer distances larger.
CO2 and N2 can freely diffuse between the layers.
Kapton crystal structure is also closely packed, but the interlayer coupling is weaker than in PBI.
CO2 and N2 can be accommodated between the layers which increases the interlayer distances.
CO2 and N2 behave similar in these three crystalline polymers.
ConclusionsConclusions
Water
PBI
Initial Final
Water molecules are attracted to PBI surface
Water molecules do not penetrate inside PBI
Water cluster suppresses the collective thermal vibration of PBI crystal
Cracking of Crystalline PBI by Water (I)Cracking of Crystalline PBI by Water (I)
Initial Middle Final
Water molecules stick together by hydrogen bonds
PBI crystal structure change slightly
16 water molecules
Cracking of Crystalline PBI by Water (II)Cracking of Crystalline PBI by Water (II)
Initial Final
Water molecules form hydrogen bonding network
PBI crystal structure change drastically
Cracking of Crystalline PBI by Water Cracking of Crystalline PBI by Water (III)(III)
160 water molecules
To crack the crystal structure, PBI must have defects.
Strong binding of water molecules by hydrogen bonding network is possible to destroy local PBI crystal structures, thus to crack the crystal.
ConclusionsConclusions
Fluctuation TheoremsFluctuation Theorems Jarzynski’s equality: ensemble average over all nonequilibrium trajectories
exp expB B
F Wk T k T
æ ö æ öD ÷ ÷ç ç÷ ÷- = -ç ç÷ ÷ç ç÷ ÷÷ ÷ç çè ø è ø
C. Jarzynski Phys. Rev. Lett. 78, 2690 (1997)
Crook’s theorem: involving nonequilibrium trajectories for both ways
expF
R B
P W W F
P W k T
G. E. Crooks Phys. Rev. E 60, 2721 (1999)
Calculate free energy difference from fast nonequilibrium simulations. Transiently absorb heat from environment.