Theory, Algorithms and Applications of Dissipative Particle Dynamics. Sept , Shanghai

Transcription

1 Theory, Algorithms and Applications of Dissipative Particle Dynamics Sept , 2015 Shanghai

2 Multiscale simulations Polymer models at coarse-grained (CG) level Combining different scales in one simulation Enhanced sampling Powerful simulation package 2

3 Generic polymer model Dissipative particle dynamics (DPD) : 3

4 With DPD: Generic polymer model Block copolymers with different sequences, flexibilities, topologies, and so on. Polymer grafted nanoparticle with different polymer compositions, nanoparticle shapes, and so on. 4

5 Network morphology Solid-state dye-sensitized solar cell Advantage: A large surface/volume ratio of metal oxide A short diffusion length for exciton to the interface Crossland et al., Nano Lett. 9, 2807,

6 Network morphology Gyroid structure only forms in a very narrow composition window (~3%). Irregular bicontinuous network structure forms in composition window (~10%). Hillmyer et al. Prog. in Polym. Sci., 33, 875, Mahanthappa et al. J. Am. Chem. Soc. 134, 3834,

7 Network morphology Whether asymmetric polydispersity is required -- that is whether the lengths of A blocks must be narrowly distributed? Whether both domains are fully continuous across the entire composition range for which the irregular bicontinuous structure forms? 7

8 Network morphology Schulz-Zimm (SZ) distribution: p( N) N u N n u 1 exp( u ) N ( u) u n, PDI N w N n (1 u) u A x B N-2x A x, N n = 8~18 V box = Simulated systems: System PDI A PDI B Asymmetric PDI (SZ) Symmetric PDI 1.5 (SZ) 1.5 (SZ) 8

9 Network morphology Whether the lengths of A blocks must be narrowly distributed? PDIA=1.00, PDIB=1.50 (SZ) irregular bicontinuous phase (BIC) ~ 10% 9

10 Network morphology Whether the lengths of A blocks must be narrowly distributed? PDI A = 1.50 (SZ), PDI B = 1.50 (SZ) irregular bicontinuous phase (BIC) ~ 20% 10

11 Network morphology Whether both domains are fully continuous across the entire composition range for which the irregular bicontinuous structure forms? The BIC structures have good continuity. 11

12 Network morphology The system of ABA (PDI A =1.00, PDI B =1.50): f B =0.375, cn=62.04 Take a part of the network structure Show polymer beads 12

13 Network morphology Short middle B block Long middle B block Middle-sized B block Selective distribution of blocks with different chain lengths can stabilize the BIC phase. 13

14 Soft Janus particle model Soft Janus particles: Star-like block copolymer with incompatible arms Percec et al. Science, 328, 1009, Soft two-patch (triblock Janus) particles: Small polymer gel with different components and crosslinking densities 14

15 Soft colloidal particle model We need to describe patchy particles with a simple model. We have proposed a potential to represent the interactions between two colloidal particles: as the units. 15

16 Soft colloidal particle model E: elastic modulus d: diameter of colloidal particle Define Substitute r ij by d in U ij, we have d: the range of attraction G: potential well depth 16

17 Soft colloidal particle model If we know the modulus of colloid particle (E), the size of the colloid particle (d), the attraction range ( d), and the attraction strength (G), we can exclusively define the parameters in our model. Suppose: nanoparticle diameter d = 20 nm Elastic modulus E = Pa Attraction range d = 0.4 nm Attraction well depth G = 2 k B T 17

18 Describe the patch size for and The patch parts are hydrophobic. 18

19 Patchy particle self-assembly We then focus on the soft two-patch particle with diameter d ~ 20 nm and modulus E ~ Pa: G=2.0 k B T; =30 o G=9.8 k B T; =30 o 19

20 Patchy particle self-assembly G=2.0 k B T; =60 o G=9.8 k B T; =60 o 20

21 Describe patchy particle The middle part is hydrophobic. 21

22 Patchy particle self-assembly We then focus on the soft two-patch particle with diameter d ~ 20 nm and elastic modulus E ~ Pa, and build up phase diagram by scanning the attraction well depth G and the surface coverage. The volume fraction is. 22

23 Patchy particle self-assembly 23

24 Patchy particle self-assembly Loosely packed hexagonal membrane Tetragonal membrane Kagome membrane densely packed hexagonal membrane 24

25 Multi-patch particle model 25

26 Multi-patch particle model We use quaternion method to integrate equations of motion. 26

27 Multi-patch particle model 27

28 Multi-patch particle model 28

29 (Attraction) Multi-patch particle model (Patch size) 29

30 Combining 2 scales in 1 simulation Reaction models in CG Simulations A and B A-B Reaction coordinate Stochastic-reaction-in-a-cutoff method. Can be used to generate polymerization products. 30

31 Stochastic reaction in a cutoff reaction cutoff Reaction probability P r : predefined, 0 P r 1. Random generator (uniform random number P). reactive end free monomers the chosen one or not If P P r, connect; Else if P > P r, do not connect. Advantages: Simple Ready to be implemented in generic/cg models 31

32 Stochastic reaction in a cutoff 32

33 Epoxy layer structure on carbon fiber Epoxy layer sizing agent carbon fiber Carbon fiber has to be protected by epoxy, otherwise too brittle to use. Sizing agent is important to increase the affinity between epoxy layer and carbon fiber. In experiments, it s difficult to characterize structures and mechanical properties of this complex. 33

34 Chemicals in epoxy and sizing agent DDS: DGEBA (RA): Sizing agent (SA): M A =248.30g/mol M B =312.40g/mol M C =289.97g/mol M v A ( M ) g/mol i A~ C i i 3 Length scale: L=1.07nm 34

35 Carbon fiber-epoxy complex The coarse grained model represents a system with more than 10,000,000 atoms We use DPD to study the influence of reaction on the distribution of different chemicals. The interaction parameters between them are obtained from their c parameters. 35

36 Reaction kinetics Reaction kinetics: R NH 2 + H 2 C CH R 1 O K1 RNH CH 2 CH R 1 OH OH RNH CH 2 CH R 1 OH K2 + H 2 C CH R 1 R N O CH 2 CH 2 CH R 1 CH R 1 OH CH OH + H 2 C CH O CH O H 2 C CH OH Typical network structure formed in curing process 36

37 Reaction+diffusion Composition of different chemicals in these layers 37

38 Time evolution of epoxy groups Curing process slows down with time, because the number of functional groups deceases largely with time and big molecules are difficult to move. 38

39 Chemical distribution Chemical distribution along the normal direction of carbon fiber surface. 39

40 Mechanical properties Generate all-atom model based on the chemical distribution in different layers; Run MD simulations and calculate mechanical properties. sample Up slice Middle slice Down slice Shear Modulus (GPa) 1.217± ± ±

41 Timescales (Sampling) It is still difficult to approach equilibrium even with CG representation. A7B3 block copolymer model. SDK CG model for PEG surfactants f A =0.30, cn=26 Klein et al., JCTC, 7, 4135, x x x x x10 7 time steps 41

42 energy distribution Integrated tempering sampling (ITS) T1 T2 T3 T4 T5 ITS Generalized distribution: Temperature 42

43 Implementation of ITS For : 43

44 How to obtain n k? Define the energy U kp, at which the values of two adjacent terms in W(r) are equal: Therefore For energy The value of W(r) is dominated by its k-th term. 44

45 Potential energy distribution How to obtain n k? Define the energy U kq, at which the potential energy distribution of the canonical ensemble at temperature T k is equal to that of the canonical ensemble at temperature T k+1. P k-1 (U) P k (U) Since P k+1 (U) So For energy there is a maximum for function P k (U). U k-1 q U k q Potential energy 45

46 How to obtain n k? To optimize the energy distribution generated in ITS simulation, when W(r) is dominated by the k-th term in the range of U k-1 p < U < U kp, the maximum of the potential energy distribution should be in the same range: Thus The slope of a secant line is approximated by average of the slopes of tangent lines at two line terminals. 46

47 The temperature distribution Define overlap factor t, which gives the ratio between energy distributions at two adjacent temperatures. Thus: Finally we have: 47

48 The temperature distribution Compare to replica exchange method: In ITS: If a set of temperatures could give a reasonable acceptance ratio in REM simulations, there should be enough overlap between adjacent temperatures in ITS. 48

49 Simulation procedure 49

50 Coil-to-globule transition T N=100 In ITS: t=exp(0.5) T= Simulate 1.0X10 9 steps In conventional MD: 31 temperatures 50

51 GPU simulation package GALAMOST: GPU-accelerated large-scale molecular simulation toolkit Free to download! Functions: CGMD; Brownian Dynamics; Dissipative Particle Dynamics; Particle-field coupling (MDSCF); Numerical potential (e.g. from iterative Boltzmann inversion & inverse Monte Carlo); NVE; NVT; NPT (Nose-Hoover; Andersen); Anisotropic soft particle model; Stochastic polymerization model; Integrated tempering sampling. 51

52 GALAMOST: Structures User interfaces Call modules Build up modules Users Script UGI Python Python Tkinter C++ CUDA C More characteristics of this package: Specifically designed for running on GPUs only Standard format of input and output file: xml, mol2, dcd... 52

53 time (s) GALAMOST: Performances Performances: the average costing time per time step of GALAMOST and HOOMD. System size: up to 2.2 M LJ liquid particles or 3.0 M DPD liquid particles on GTX 580 with 1.5 GB device memory LJ Liquid GALAMOST LJ Liquid HOOMD DPD Liquid GALAMOST DPD Liquid HOOMD DPD: ~1.5 days for 3.0M particles 1.0M steps N/

54 Summary Approaching larger spatiotemporal scales in polymer simulations: Generic polymer model Stochastic polymerization model Soft patchyparticle model Enhanced sampling (ITS) DPD Kinetic network analysis DPD with SCF treatment Numerical potential with DPD thermstating DPD with electrostatics 54

55 Acknowledgement Financial supports from National Natural Science Foundation of China. Financial supports from Ministry of Science and Technology of China. All my group members! Collaborators: Prof. Zhao-Yan Sun and Prof. Lijia Changchun Inst. Appl. Chem. Prof. De-Yue Yan and Prof. Yongfeng Shanghai Jiaotong U. Prof. Aatto Stockholm U. Prof. Florian TUDarmstadt Prof. Giuseppe Salerno U. Prof. Yi-Qin Peking U. Prof. An-Chang McMaster U. Prof. Zhihong Maryland U. Prof. Xuhui HKUST 55

56 Thank you for your attention! Changbai mountain in Jilin province 56