Studies of Nano, Chemical, and Biological Materials by Molecular Simulations Yanting Wang Institute of Theoretical Physics, Chinese Academy of SciencesBeijing, ChinaSeptember 25, 2008 Institute of Theoretical Physics, Chinese Academy of Sciences

Atomistic Molecular Dynamics Simulation  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)  Solving Newton’s Equations of Motion.

Quantifying 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 electronics Ion detection S. O. Obare et al., Langmuir 18, (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 etching Gold nanowires Larger Au particles change color Some Applications of Gold Nanomaterials

Thermal Stability of Low Index Gold Surfaces  Thermal stability of surface: {110} < {100} < {111}  Stable gold interior: FCC structure

Stability 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, (2005)  Strained FCC interior  All covered by stable {111} facets Liquid at T=1500K Cooling

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, (2005)

SurfaceInterior  Interior keeps ordered up to melting temperature T m  Surface softens but does not melt below T m No 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 Melting N = 2624

t=1.075ns 4t4t Movement Average shape  Vertex and edge atoms diffuse increasingly with T  Facets shrink but do not vanish below T m =1075 K  Facet atoms also diffuse below T m because the facets are very small ! “Premelt” of Vertices and Edges but not Facets Mechanism

Conclusions  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?  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 N = 54*  Heat up sequentially  timestep 2.86 fs  10 8 steps at each T Average potential energy per atom Heat capacity  Easy to disorder due to less binding energy  Melting transition from T s ≈ 300 K to T e ≈ 1200 K TsTs TeTe * Y. Wang, S. Rashkeev J. Phys. Chem. C 113, (2009).

Snapshots at Different Temperatures  Both layers premelt below 560 K  No inter-layer diffusion below 560 K

Inter- and Intra- Layer Diffusion Inter-layer diffusion starts at T i ≈ 560 KAtomic self diffusion starts at T d ≈ 340 K TdTd TiTi Moved atoms: moving to the other layer at least once at each temperature TiTi Liquid crystal-like structure between 340 K and 560 K

More Layers in Between: Approaching First-Order Melting Transition* Onset Temperature T s and Complete Temperature T e of Melting Transition, Self Diffusion Temperature T d, and Interlayer Diffusion Temperature T i atomslayersTsTs TeTe TiTi TdTd  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, (2009).

Conclusions  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 Nanorods* Two steps * Y. Wang, C. Dellago J. Phys. Chem. B 107, 9214 (2003).

Surface-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).

Conclusions  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) Method* to Rigorously Build 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  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, (2008). Benifit: maller numbers of degrees of freedom and faster dynamics

Residual: Each CG site: Effective force: Central pairwise, linear approximation Multidimensional parabola Obtained from all-atom configurations Multiscale Coarse-Graining by Force Minimization

Residual: Variational principle:  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 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) Method*  EF-CG non-bonded effective forces  Problems with MS-CG

Conclusions  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 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 Liquids Environment-friendly solvent for chemical reactions LubricantPropellant

* Y. Wang, S. Izvekov, T. Yan, and G. Voth, J. Phys. Chem. B 110, 3564 (2006). Multiscale Coarse-Graining of Ionic Liquids*  EMIM + /NO 3 - 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 Liquids

Spatial 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, (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, (2006). Define Heterogeneity order parameter (HOP) Invariant with box size L Average over all sites to get For each site  Larger HOP represents more heterogeneous configuration. Heterogeneity Order Parameter*

Thermal Stability of Tail Domain in Ionic Liquids* * Y. Wang, G. A. Voth, J. Phys. Chem. B 110, (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 Liquids  Instantaneous LHOPs at T = 1230 K Define Lattice HOP  Divide simulation box into cells  In each cell the ensemble average of HOP is taken for all configurations Mechanism  Heterogeneous tail domains have fixed positions at low T (solid-like structure)  Tail domains are more smeared with increasing T  Above T c, instantaneous tail domains still form (liquid-like structure), but have a uniform ensemble average

Extendable 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 an External Electric Field* * Y. Wang J. Phys. Chem. B 113, (2009). From heterogeneous to homogeneous to nematic-like due to the effective screening of the external electric field to the internal electrostatic interactions.

Conclusions  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 T c  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 Membranes CO 2 CapturerAir DryerAir 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) Determining Crystalline Structure of Polymers

Polybenzimidazole (PBI) Poly[bis(isobutoxycarbonyl)benzimidazole] (PBI-Butyl) Kapton X-Z PlaneY-Z Plane Infinitely-Long Crystalline Polymers at T = 300 K

SystemX (Å)Y (Å)Z (Å)Volume (nm 3 ) PBI75.09 ± ± ± ± 0.19 PBI + CO ± ± ± ± 0.17 PBI + N ± ± ± ± 0.17 PBI + CO 2 PBI + N 2 Sizes along Y are expanded. Gas molecules can hardly get in between the layers. Very stiff CO2 and N2 inside PBI

PBI-Butyl + CO 2 PBI-Butyl + N 2 SystemX (Å)Y (Å)Z (Å)Volume (nm 3 ) PBI-Butyl75.55 ± ± ± ± 0.31 PBI-Butyl + CO ± ± ± ± 0.39 PBI-Butyl + N ± ± ± ± 0.37 No dimension sizes are changed. Gas molecules are free to diffuse between layers. Open up spaces CO2 and N2 inside PBI-Butyl

Kapton + CO 2 Kapton + N 2 Sizes along Z are expanded. Gas molecules change the crystal structure of Kapton. Flexible SystemX (Å)Y (Å)Z (Å)Volume (nm 3 ) Kapton84.77 ± ± ± ± 0.15 Kapton + CO ± ± ± ± 0.16 Kapton + N ± ± ± ± 0.18 CO2 and N2 inside Kapton

 PBI forms a very strong and closely packed crystalline structure.  CO 2 and N 2 can hardly diffuse in PBI crystal.  Crystal structure of PBI-Butyl is rigid, but the butyl side chains make the interlayer distances larger.  CO 2 and N 2 can freely diffuse between the layers.  Kapton crystal structure is also closely packed, but the interlayer coupling is weaker than in PBI.  CO 2 and N 2 can be accommodated between the layers which increases the interlayer distances.  CO 2 and N 2 behave similar in these three crystalline polymers. Conclusions

Water PBI InitialFinal  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)

InitialMiddleFinal  Water molecules stick together by hydrogen bonds  PBI crystal structure change slightly 16 water molecules Cracking of Crystalline PBI by Water (II)

InitialFinal  Water molecules form hydrogen bonding network  PBI crystal structure change drastically Cracking of Crystalline PBI by Water (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. Conclusions

Fluctuation Theorems  Jarzynski’s equality: ensemble average over all nonequilibrium trajectories C. Jarzynski Phys. Rev. Lett. 78, 2690 (1997)  Crook’s theorem: involving nonequilibrium trajectories for both ways G. E. Crooks Phys. Rev. E 60, 2721 (1999)  Calculate free energy difference from fast nonequilibrium simulations.  Transiently absorb heat from environment.

高级研究生课程 分子建模与模拟导论： 2009 年秋季 星期三下午 15:20 – 17:00 S102 教室