Trends: Simulation. Eigenschaften von Polymeren Was kann die Simulation leisten? Molecular Dynamics. Atomistic Force Field.

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Edgar Parsons
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Müller-Plathe www.theo.chemie.tu-darmstadt.

1 Eigenschaften von Polymeren Was kann die Simulation leisten? 100 nm 100 fs 1 µs Trends: Simulation Advances Technology Laser spectroscopy NM, AFM, Synthesis10 µm 10 cm Self organisation 10 ms 10 years Nanotechnology sub nm 1 nm 1 µm 1 mm 1 m Florian Müller-Plathe atoms 10 ps Simulation Hardware Software Methods atoms 10 ns 1 µs Molecular Dynamics Atomistic Force Field Atoms interact Parameters model the chemistry and physics of the system forces act on atoms atoms move f i= mi ai Analysis of the motion 3 6 H H C 6 C 5 5 C3 C 4 4 C 4 H C 1 C 3 C 4 C 4 3 H C 5 C H C 6 6 H V V dihedral nonbond ( r) V V bond angle k k ( r) = bond ( r r ) angle ( φ ) ( φ φ ) = k ( τ ) = dihedral ( 1+ cosn( τ τ )) 1 σ σ qiq j = 4ε + r r 4πε0r

Gas molecules in polymers Diffusion of C in polystyrene Diffusion coefficients (cm /s) Diffusion

cm /s simulation (1998) 1 10-6 cm /s H. Schmitz & F. Müller-Plathe new experiment (1999) 0.

45, 59 (1994) 6 utline Lotus Effect Intro/Molecular dynamics Hydrophobic polymer surfaces Thermal

2 Gas molecules in polymers Diffusion of C in polystyrene Diffusion coefficients (cm /s) Diffusion coefficient of C in atactic polystyrene 80 C, 1 bar calculated ideal old experiment (1997) cm /s simulation (1998) cm /s H. Schmitz & F. Müller-Plathe new experiment (1999) cm /s P. Pekarski &. Kirchheim measured 5 FMP, Acta Polym. 45, 59 (1994) 6 utline Lotus Effect Intro/Molecular dynamics Hydrophobic polymer surfaces Thermal conductivity of polymers Coarse grained polymer models 7 How does the Lotus (and other plants!) do it? Hydrophobic base chemical Surface structure 8

Structure on Various Levels Strategy: : Beat Nature

4 1. 1.0 0.8 0.6 0.4 0. 0.0-0. - -1 0 1 3.

perfluoropolymer y / nm Nature s material:

Qualitative: Water near Hole Water extends into hole

water µ () r = µ () r µ ( bulk) Increased chemical

3 Structure on Various Levels Strategy: : Beat Nature Nature s microstructure Cuticula (15 µm) 1. Microstructure (< 1µm) Si, Al 3, Ti. Nanostructure (< 5 nm) computer simulation z / nm Hydrophobic surface material polyolefine, perfluoropolymer y / nm Nature s material: Epicuticular waxes (100 nm) 9 10 MD simulation Qualitative: Water near Hole Water extends into hole but with a reduced density ρ z n-eicosane crystal water µ () r = µ () r µ ( bulk) Increased chemical potential µ = T ln ρ ρ() r ( bulk ) ( µ(r) < 0 kj/mol: hydrophilic; µ(r) > 0 kj/mol: hydrophobic) y 11 Hole is hydrophobic! 1

) λhole H ( λ) G λ ( flat hole) = dλ λflat λ hole eversibly annihilate/create atoms 13 14 Calculation of interfacial tensions () Conclusion: Nanostructured Surfaces A(flat hole) A(flat protr.

4 no hole Water Density at the Surface S. Pal, H. Weiss, H. Keller, FMP, Langmuir 1, 3699 (005). Calculation of interfacial tensions (1) Absolute γ = ( G/ σ) cannot be calculated directly Calculate differences γ hole integration ( ) γ ( flat) by thermodynamic g/cm 3 G(flat hole) G(flat protr.) λhole H ( λ) G λ ( flat hole) = dλ λflat λ hole eversibly annihilate/create atoms Calculation of interfacial tensions () Conclusion: Nanostructured Surfaces A(flat hole) A(flat protr.) Both structures enhance hydrophobicity Effects are of same order Good correlation with contact counting: 0.45 γ = A/σ = 7.1±1 mj/m γ = A/σ = 6.3±1 mj/m 0.7 S. Pal, D. occatano, H. Weiss, H. Keller, FMP, ChemPhysChem 1, 1641 (005) Does nanostructuring improve hydrophobicity? Yes Which surface structures are most effective? round holes > stripes best diameter ~-3 nm holes ~ protrusions Which chemistry is most effective? CF x > CH x effects of topography are generic What about salt solutions? No problem for halides Can surface tensions be calculated? Absolute γ: no γ differences: yes 16

5 Intro/Molecular dynamics Hydrophobic polymer surfaces utline Thermal conductivity of polymers Coarse grained polymer models Fourier s law: Thermal conductivity λ J q heat flux response Problems with MD simulation: J q cannot be defined unambiguously J q converges slowly Thermal Conductivities = λ FMP, J. Chem. Phys. 106, 608 (1997). dt dz temperature gradient perturbation 17 everse Non-equilibrium Molecular Dynamics everse Non-equilibrium MD Traditional NEMD calculate impose everse NEMD dt dt J q = λ J q = λ dz dz impose calculate J q dt = λ dz Heat flow temperature energy transport (unphysical) slab number

Velocity exchange (unphysical) Thermal Conductivity of Molecular Liquids What we want Hot Find the hottest particle in the cold region and the coldest particle in the hot region 1 Swap their v 1

6 Velocity exchange (unphysical) Thermal Conductivity of Molecular Liquids What we want Hot Find the hottest particle in the cold region and the coldest particle in the hot region 1 Swap their v 1 Simulation Experiment W/K m W/K m Lennard-Jones (red. units) (Ar) FMP, J. Chem. Phys. 106, 608 (1997). z Cold If m 1 =m : no change in total linear momentum no change in total kinetic energy no change in total energy water 0.81± n-hexane (semirigid) 0.107± n-hexane (flexible) 0.134± benzene cyclohexane M. Zhang, E. Lussetti, L.E.S. de Souza, FMP, J. Phys. Chem. B 109, (005). Thermal Conductivity of Polyamide-6,6 Simulation Experiment W/K m W/K m amorphous (1.07 g/cm 3 ) Thermal Conductivity of Polymers, Conclusions Method works for liquids and polymer materials (biomembranes) Accuracy: Deviation from experiment < 50% Problem: assical treatment of quantum vibrations stretched amorphous (0.95 g/cm 3 ) parallel to stretching 0.43 perpendicular 0.0 Solution: constraints, united-atom models cf. heat capacity E. Lussetti, FMP, unpublished. 3 4

Intro/Molecular dynamics Hydrophobic polymer surfaces utline Thermal conductivity of polymers Coarse grained polymer models time Polymers: Scales & Methods Polymerisation Solvation, permeation

Crystallisation, rheology Morphology Processing Soft fluid Coarse-grained model Atomistic simulation Finite element 5 length 6 Polymers: Structure Multiscale Simulation of Polymers Chemistry

7 Intro/Molecular dynamics Hydrophobic polymer surfaces utline Thermal conductivity of polymers Coarse grained polymer models time Polymers: Scales & Methods Polymerisation Solvation, permeation Quantum chemistry eview: FMP, Soft Materials 1,, (003). Crystallisation, rheology Morphology Processing Soft fluid Coarse-grained model Atomistic simulation Finite element 5 length 6 Polymers: Structure Multiscale Simulation of Polymers Chemistry Tacticity Sequence H3 C CH 3 CH H 3 3 C H 3 C CH H H H rubber insoluble S-S-S-S-B-B-B-B HIPS H CH H H CH 3 CH H H H brittle water-soluble S-B-S-S-B-S-B-B synthetic rubber CH H H H Why? Large systems, long time scales with near-atomistic accuracy Better atomistic structures and properties map morphology, rheology, NM, n-scattering remap Topology shopping bag bullet-proof vest 7 equilibrate 8

Coarse Graining Coarse-Grain Grained Model eproduces Structure F. Müller-Plathe, ChemPhysChem 3,, 754 (00).

Structure Coarse-grained model Distribution (arb. units) 0.035 0.030 0.05 0.00 0.015 0.010 0.005 Angles 0.000 60 90 10 150 180 H φ Angle (degrees) H H DF 1.4 1. 1.0 0.8 0.6 0.4 0.

8 Coarse Graining Coarse-Grain Grained Model eproduces Structure F. Müller-Plathe, ChemPhysChem 3,, 754 (00). bjectives for coarse-grained model: Simpler than atomistic model: ~10 real atoms 1 superatom eproduce structure of atomistic model Atomistic simulation Structure Coarse-grained model Distribution (arb. units) Angles H φ Angle (degrees) H H DF Example: poly(vinyl alcohol) Distances between different chains Target Best fit LJ 6-9 Best fit DF Target Best fit LJ 6-9 Best fit H Distance (nm) Iterative Boltzmann Inversion Tabulated numerical potential V(r) Starting guess V 0 (r) DF 0 (r) DF target (r) Potential correction DF0 V1 () r = V0 () r + kt ln DFtarget Iterate DF Vn+ 1() r = Vn () r + kt ln DF () r () r () r () r until V n (r) DF n (r) = DF target (r) Converges in few iterations Density/pressure correction can be added D. eith, H. Meyer, FMP, Comput. Phys. Commun. 148, 99 (00). 31 n target Coarse-Grained Poly(vinyl alcohol): Crystallisation H. Meyer, FMP, J. Chem. Phys. 115, 7807 (001) 3

9 Na + C - C - Na + Na + C - Na + C - Poly(acrylic acid) D. eith, B. Müller, FMP, S. Wiegand, J.Chem. Phys. 116, 9100 (00) Accounting for Tacticity Na + Atomistic: 10 atoms 10 3 H Mesoscopic: 3 particles no H DF, 1st & nd excluded Hydrodynamic radius (nm) Simulation Dynamic Light Scatt. 1 = H Molecular weight (monomers) 1 1 N i, j ij m-diads and r-diads treated as different monomers different interaction potentials G. Milano, FMP, J. Phys. Chem. B 109, (005) m r r m r 34 Accounting for Tacticity () Accounting for Tacticity,, esults Atactic polystyrene melt Atactic polystyrene melt 35 G. Milano, FMP, J. Phys. Chem. B 109, (005) 36

10 Coarse Graining, Conclusions Many polymers: Melt, solution Automation is crucial Meso/macroscopic properties with experimental accuracy Latest: tacticity n-going: dynamics, viscoelasticity Hydrophobic polymer surfaces Sandeep Pal : BASF, BMBF Danke Thermal conductivity of polymers Enrico Lussetti, Meimei Zhang, Luis de Souza, Takamichi Terao : DFG, Schwerpunkt Coarse grained polymer models Dirk eith, Hendrik Meyer, oland Faller, Kurt Kremer Sylvain Goudeau, Giuseppe Milano : BMBF, hodia, Humboldt-Stiftung 38

Systematic Coarse-Graining and Concurrent Multiresolution Simulation of Molecular Liquids

Systematic Coarse-Graining and Concurrent Multiresolution Simulation of Molecular Liquids Cameron F. Abrams Department of Chemical and Biological Engineering Drexel University Philadelphia, PA USA 9 June