Studies of Nano, Chemical, and Biological Materials by Molecular Simulations Yanting Wang Institute of Theoretical Physics, Chinese Academy of Sciences Institute of Theoretical Physics, Chinese Academy of Sciences Beijing, China September 25, 2008 Atomistic Molecular Dynamics Simulation Solving Newton’s Equations of Motion. Fi t Fij rij t j ai t Fi t mi vi t 1 vi t ai t t ri t 1 ri t vi t 1 t Empirical force fields Fij 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) Quantifying Condensed Matter Structures Bond-Orientational Order Parameters • Capture the symmetry of spatial orientation of chemical bonds • Non-zero values for crystal structures • 0 for liquid Radial Distribution Function g(r) • 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) Some Applications of Gold Nanomaterials Ion detection Larger Au particles change color S. O. Obare et al., Langmuir 18, 10407 (2002) Molecular electronics Electronic lithography Gold nanowires R. F. Service, Science 294, 2442 (2001) Chemical etching J. Zheng et al., Langmuir 16, 9673 (2000) Both size and shape are important in experiments! Thermal Stability of Low Index Gold Surfaces Stable gold interior: FCC structure Thermal stability of surface: {110} < {100} < {111} Stability of Icosahedral Gold Nanoclusters* Simulated annealing from a liquid 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 Cooling Liquid at T=1500K Strained FCC interior All covered by stable {111} facets Icosahedron at T=200K Mackay Icosahedron with a missing central atom Asymmetric facet sizes * Y. Wang, S. Teitel, C. Dellago Chem. Phys. Lett. 394, 257 (2004) * Y. Wang, S. Teitel, C. Dellago J. Chem. Phys. 122, 214722 (2005) First-Order Like Melting Transition Heat to melt Keep T constant for 43 ns T = 1075K for N = 2624 Magic and non-magic numbers Cone algorithm* to group atoms into layers Potential energy vs. T Surface Interior First-order like melting transition * Y. Wang, S. Teitel, C. Dellago J. Chem. Phys. 122, 214722 (2005) Sub-layers No Surface Premelt for Gold Icosahedral Nanoclusters Interior Surface N = 2624 Interior keeps ordered up to melting temperature Tm Surface softens but does not melt below Tm Surface Atoms Diffuse Below Melting Mean squared displacements (average diffusion) N = 2624 All surface atoms diffuse just below melting Surface premelting? “Premelt” of Vertices and Edges but not Facets Movement t=1.075ns Movement 4t Average shape Mechanism 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 ! 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 108 steps at each T Easy to disorder due to less binding energy Melting transition from Ts ≈ 300 K to Te ≈ 1200 K Te Ts Average potential energy per atom * Y. Wang, S. Rashkeev J. Phys. Chem. C 113, 10517 (2009). Heat capacity Snapshots at Different Temperatures Both layers premelt below 560 K No inter-layer diffusion below 560 K Inter- and Intra- Layer Diffusion r 2 t 2 1 M N r t t r t i j i j MN j 1 i 1 r 2 t 6 Dt Moved atoms: moving to the other layer at least once at each temperature Ti Ti Td Atomic self diffusion starts at Td ≈ 340 K Inter-layer diffusion starts at Ti ≈ 560 K Liquid crystal-like structure between 340 K and 560 K More Layers in Between: Approaching First-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). 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 Thermal Stability of Gold Nanorods* Increasing total E continuously to mimic laser heating Experimental model T=5K T=1064K T=515K T=1468K Pure FCC interior Z. L. Wang et al., Surf. Sci. 440, L809 (1999) Two steps * Y. Wang, C. Dellago J. Phys. Chem. B 107, 9214 (2003). Surface-Driven Bulk Reorganization of Gold Nanorods* Surface Second sub layer Cross sections 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 Yellow: {111} Green: {100} Red: {110} Gray: other Yellow: fcc Green: hcp Gray: other * 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 Benifit: maller numbers of degrees of freedom and faster dynamics Assuming central pairwise effective forces Minimizing force residual N IN C G v v 2 11 I , A A I , C G Y = F F å å a a 3 N N C G II a 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). Multiscale Coarse-Graining by Force Minimization CG Effective force: F (r ) = fd dD (r - d ) Each CG site: Central pairwise, linear approximation v C G C G ˆ F r r ) åF a = a b( a b a b b Residual: C G v v 2 1 1 NI N IA ,A IC ,G Y = F -F åå a a 3 N N I a C G I ö 1æ ÷ ç ÷ = G ff 2 b f + c ç å å ¢ ¢ d d d ÷ d , d d ç ÷ 3 Nç è¢ ø ,d C G d d Multidimensional parabola 1 Iˆ I I I ˆ ¢ G = R g R d R d d R d ( ) ( ) ( ) å å å ¢ a b a g D a b D a g d , d N Ia b , g I v 1 Î I , A A I b = R g F d R d ( ) ( å å å d a b a) D a b N I I ab v v 1 I , A A I , A A c = å F F å a g a N I I a Obtained from all-atom configurations Force Minimization by Conjugate Gradient Method Residual: æ ö 1 ÷ ç ÷ Solving matrix directly Y = ç G f f 2 b f + c å å ¢ ¢ d d d ÷ d , d d ç ÷ ç 3 N è ø ¢ d , d d C G Variational principle: gd = ¶Y =0 ¶fd åG f d¢ =b d dd , ¢d¢ Or finding the minimal solution by conjugate gradient minimization with Ψ and gd Subtract the Ewald Sum (long-range electrostatic) of point net charges Match bonded and non-bonded interactions separately Only one minimal solution! Ψ can be used to determine the best CG scheme Effective Force Coarse-Graining (EF-CG) Method* Problems with MS-CG • Very limited transferability: temperature, surface, sequence of amino acids Wrong pressure (density) without further constraint EF-CG non-bonded effective forces • Explicitly calculating pairwise atomic interactions between two groups All-atom MD to get the ensemble of relative orientations r i j i j r M N i 1 j1 ˆ R RR r ij D MN RR R D F R RR D i 1j 1 RR D ˆ ˆ F rRR rR MN i 1j 1 ij ij ij D RR D * Y. Wang, W. Noid, P. Liu, G. A. Voth to be submitted. 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. Some Applications of Ionic Liquids Ionic liquid = Room temperature molten salt Non-volatile High viscosity Environment-friendly solvent for chemical reactions Lubricant Propellant Multiscale Coarse-Graining of Ionic Liquids* EMIM+/NO3- ionic liquid 64 ion pairs, T = 400 K Electrostatic and VDW interactions * Y. Wang, S. Izvekov, T. Yan, and G. Voth, J. Phys. Chem. B 110, 3564 (2006). Satisfactory CG Structures of Ionic Liquids Site-site RDFs (T = 400K) Good structures No temperature transferability Spatial Heterogeneity in Ionic Liquids* 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 C1 C2 C4 C6 C8 * Y. Wang, G. A. Voth, J. Am. Chem. Soc. 127, 12192 (2005). Heterogeneity Order Parameter* Define Heterogeneity order parameter (HOP) • For each site hi exp(r / 2 ) 2 ij j 2 L N 1/3 • Average over all sites to get <h> • Invariant with box size L Larger HOP represents more heterogeneous configuration. 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). Thermal Stability of Tail Domain in Ionic Liquids* 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? * Y. Wang, G. A. Voth, J. Phys. Chem. B 110, 18601 (2006). 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 1 ci M M h ij j 1 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 Liquids* CG force library Extendibility, transferability, and manipulability 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). Disordering and Reordering of Ionic Liquids under an External Electric Field* From heterogeneous to homogeneous to nematic-like due to the effective screening of the external electric field to the internal electrostatic interactions. * Y. Wang J. Phys. Chem. B 113, 11058 (2009). 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 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 Membranes UBE.com CO2 Capturer Air Dryer Environmental applications Energy applications Industrial applications Military applications … Air Mask Determining Crystalline Structure of Polymers Polybenzimidazole (PBI) H H H H H N H H N N N H H H H H n 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 Infinitely-Long Crystalline Polymers at T = 300 K X-Z Plane Polybenzimidazole (PBI) H H H H H N H H N H N N H H H n H Poly[bis(isobutoxycarbonyl)benzimidazole] (PBI-Butyl) O O N N N N O O n Kapton O O N N O O O n Y-Z Plane CO2 and N2 inside PBI PBI + CO2 Very stiff H H H H H N H H N N N H H H H n H PBI + N2 Sizes along Y are expanded. Gas molecules can hardly get in between the layers. 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 CO2 and N2 inside PBI-Butyl PBI-Butyl + CO2 Open up spaces O O N N N N O O PBI-Butyl + N2 n No dimension sizes are changed. Gas molecules are free to diffuse between layers. 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 CO2 and N2 inside Kapton Kapton + CO2 Flexible O O N N O O O Kapton + N2 n Sizes along Z are expanded. Gas molecules change the crystal structure of Kapton. 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 Conclusions 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. Cracking of Crystalline PBI by Water (I) 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 (II) Initial 16 water molecules Middle Water molecules stick together by hydrogen bonds PBI crystal structure change slightly Final Cracking of Crystalline PBI by Water (III) Initial 160 water molecules Final Water molecules form hydrogen bonding network PBI crystal structure change drastically Conclusions 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. Fluctuation Theorems Jarzynski’s equality: ensemble average over all nonequilibrium trajectories C. Jarzynski Phys. Rev. Lett. 78, 2690 (1997) æ DF ÷ ö ç ÷= exp çç÷ çè kBT ÷ ø æ W ö ÷ ÷ exp ççç÷ ÷ çè kBT ø Crook’s theorem: involving nonequilibrium trajectories for both ways G. E. Crooks Phys. Rev. E 60, 2721 (1999) PF W W F exp PR W k T B 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