1

Eigenschaften von Polymeren Eigenschaften von Polymeren Was kann die Simulation leisten?Was kann die Simulation leisten?

Florian Florian MMüüllerller--PlathePlathewww.theo.chemie.tu-darmstadt.de

2

AdvancesLaser spectroscopyNMR, AFM, SynthesisSelf organisationNanotechnology

Trends: SimulationTrends: Simulation

sub nm 1 nm 1 µm 1 mm 1 m

10 µm – 10 cm10 ms – 10 years

2 – 100 nm100 fs – 1 µs

10-1000 atoms10 ps

105 – 108 atoms10 ns – 1 µs

HardwareSoftwareMethods

Simulation

Technology

3

Molecular DynamicsMolecular Dynamics

Atoms interactParameters model the chemistryand physics of the system

forces act on atomsatoms move

Analysis of the motioniii m af =

4

Atomistic Force FieldAtomistic Force Field

( ) ( )20

bondbond 2

rrkrV −=

( ) ( )20

angleangle 2

φφφ −=k

V

( ) ( )( )0dihedral

dihedral cos12

τττ −+= nkV

( )r

qqrr

rV ji

0

612

nonbond 44

πεσσε +

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=

C4

C3 C2

C1

O5C5

O4

C4

C5 O5

C1

C2C3O4 O4

C6

O6H

O3H

HO2

C6

O6H

O2H

O3H

5

Gas molecules in polymersGas molecules in polymers

measured

calc

ulat

ed

ideal

Diffusion coefficients (cm2/s)

FMP, Acta Polym. 45, 259 (1994)6

Diffusion of CODiffusion of CO22 in polystyrenein polystyrene

Diffusion coefficient of CO2 in atactic polystyrene 80°C, 1 bar

• old experiment (1997) 55×10-6 cm2/s

• simulation (1998) 1×10-6 cm2/sH. Schmitz & F. Müller-Plathe

• new experiment (1999) 0.3×10-6 cm2/sP. Pekarski & R. Kirchheim

7

Outline Outline

• Intro/Molecular dynamics

• Hydrophobic polymer surfaces

• Thermal conductivity of polymers

• Coarse grained polymer models

8

Lotus EffectLotus Effect

How does the Lotus (and other plants!) do it?• Hydrophobic base chemical• Surface structure

9

Cuticula (15 µm)

Nature’s material:Epicuticular waxes (100 nm)

StructureStructure on on VariousVarious LevelsLevelsNature’s microstructure

10

StrategyStrategy: Beat Nature: Beat Nature

1. Microstructure (< 1µm)SiO2, Al2O3, TiO2

3. Hydrophobic surface materialpolyolefine, perfluoropolymer

2. Nanostructure (< 5 nm)→ computer simulation

-2 -1 0 1 2-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

y / nm

z /

nm

11

n-eicosane crystal

water

y

z

MD simulationMD simulation

12

Qualitative: Water near HoleQualitative: Water near Hole

• Water extends into hole …

• … but with a reduced density ρ

• Hole is hydrophobic!

( ) ( ) ( ) ( )( )bulk

lnbulkρ

ρµµµ rrr RT−=−=∆

(∆µ(r) < 0 kJ/mol: hydrophilic; ∆µ(r) > 0 kJ/mol: hydrophobic)

• Increased chemical potential µ

13

Water Density at the SurfaceWater Density at the Surface

hole

g/cm3

no holeS. Pal, H. Weiss, H. Keller, FMP, Langmuir 21, 3699 (2005).

14

Calculation of interfacial tensions (1)Calculation of interfacial tensions (1)

• Absolute γ = (∂G/∂σ) cannot be calculated directly

• Calculate differences by thermodynamicintegration

•

• Reversibly annihilate/create atoms

( ) ( )flathole γγ −

∆G(flat→hole)

∆G(flat→protr.)

( ) λλλ

λ

λ

λ

dHG ∫ ∂∂

=→∆hole

flat

)(holeflat

15

Calculation of interfacial tensions (2)Calculation of interfacial tensions (2)

∆A(flat→hole)

∆A(flat→protr.)

∆γ = ∆A/σ = 7.1±1 mJ/m2

∆γ = ∆A/σ = 6.3±1 mJ/m2

• Both structures enhance hydrophobicity• Effects are of same order • Good correlation with contact counting:

0.450.25

0.27 S. Pal, D. Roccatano, H. Weiss, H. Keller, FMP, ChemPhysChem 12, 1641

(2005).

16

• Does nanostructuring improve hydrophobicity? Yes• Which surface structures are most effective?

round holes > stripesbest diameter ~2-3 nmholes ~ protrusions

• Which chemistry is most effective?CFx > CHxeffects of topography are generic

• What about salt solutions? No problem for halides• Can surface tensions be calculated?

Absolute γ: noγ differences: yes

Conclusion: Conclusion: NanostructuredNanostructured SurfacesSurfaces

17

Outline Outline

• Intro/Molecular dynamics

• Hydrophobic polymer surfaces

• Thermal conductivity of polymers

• Coarse grained polymer models

• Fourier’s law: Thermal conductivity λ

heat flux temperature gradientresponse perturbation

• Problems with MD simulation: Jq cannot be defined unambiguouslyJq converges slowly

Thermal ConductivitiesThermal ConductivitiesFMP, J. Chem. Phys. 106, 6082 (1997).

⎟⎠⎞

⎜⎝⎛−=

dzdTJ q λ

Traditional NEMD

Reverse Non-equilibrium Molecular Dynamics

Reverse NEMD

calculate impose calculateimpose

⎟⎠⎞

⎜⎝⎛−=

dzdTJ q λ ⎟

⎠⎞

⎜⎝⎛−=

dzdTJ q λ

Reverse NonReverse Non--equilibrium MDequilibrium MD

energy transport (unphysical)

Heat flow

0 2 4 6 8 100.60

0.65

0.70

0.75

0.80

slab number

tem

pera

ture

⎟⎠⎞

⎜⎝⎛−=

dzdTJq λ

Find the hottest particle in the cold region and the coldest particle in the hotregion

Velocity exchange (unphysical)Velocity exchange (unphysical)

Swap their v

If m1=m2: no change in total linear momentumno change in total kinetic energyno change in total energy

z

What we want

Hot

Cold

1

2

1

2

22

Simulation ExperimentW/K m W/K m

Lennard-Jones (red. units) 6.8 7.02 (Ar)FMP, J. Chem. Phys. 106, 6082 (1997).

water 0.81±0.01 0.607n-hexane (semirigid) 0.107±0.002 0.12n-hexane (flexible) 0.134±0.002 0.12benzene 0.199 0.141cyclohexane 0.24 0.123

M. Zhang, E. Lussetti, L.E.S. de Souza, FMP, J. Phys. Chem. B 109, 15060 (2005).

Thermal Conductivity of Molecular LiquidsThermal Conductivity of Molecular Liquids

23

Thermal Conductivity of PolyamideThermal Conductivity of Polyamide--6,66,6

Simulation ExperimentW/K m W/K m

amorphous (1.07 g/cm3) 0.33 0.25

stretched amorphous (0.95 g/cm3) parallel to stretching 0.43perpendicular 0.20

E. Lussetti, FMP, unpublished. 24

• Method worksfor liquids and polymer materials(biomembranes)

• Accuracy: Deviation from experiment < 50%

• Problem: Classical treatment of quantum vibrations

• Solution:constraints, united-atom modelscf. heat capacity

Thermal Conductivity of Polymers, ConclusionsThermal Conductivity of Polymers, Conclusions

25

Outline Outline

• Intro/Molecular dynamics

• Hydrophobic polymer surfaces

• Thermal conductivity of polymers

• Coarse grained polymer models

26

Polymers: Scales & MethodsPolymers: Scales & MethodsReview: FMP, Review: FMP, Soft Materials Soft Materials 11, 1, 1--31 (2003).31 (2003).

length

time

Quantum chemistry

Atomisticsimulation

Coarse-grained model

Soft fluid

Finiteelement

Polymer-isation

Solvation,permeation

Crystallisation,rheology

MorphologyProcessing

27

Polymers: StructurePolymers: Structure

• Chemistry

rubber brittle

• Tacticity

insoluble water-soluble

• Sequence HIPS synthetic rubber

• Topology

shopping bag bullet-proof vest

CH3H3C CH3H3C CH3H3CClCl ClCl Cl

Cl

O

CH2OH

O

HO

HO

O

O

CH2OHHO

HO

OO

CH2OH

O

HO

HO

O

O

CH2OH

HO

OH

O

S-S-S-S-B-B-B-B S-B-S-S-B-S-B-B

28

MultiscaleMultiscale Simulation of PolymersSimulation of Polymers

Why?

• Large systems, long time scales with near-atomistic accuracy

• Better atomistic structures and properties

morphology,rheology, …

NMR,n-scattering

map remap

equilibrate

29

Coarse GrainingCoarse Graining

Atomistic simulation Coarse-grained model

Structure

0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

RD

F

Target Best fit LJ 6-9 Best fit 6-8-10-12

Objectives for coarse-grained model:• Simpler than atomistic model: ~10 real atoms → 1 “superatom”• Reproduce structure of atomistic model

30

CoarseCoarse--GrainGrained Model Reproduces Structureed Model Reproduces StructureF. F. MMüüllerller--PlathePlathe, , ChemPhysChemChemPhysChem 33, 754 (2002)., 754 (2002).

60 90 120 150 1800.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

Dis

tribu

tion

(arb

. uni

ts)

Angle (degrees)

Angles

0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

RD

F

Distance (nm)

Target Best fit LJ 6-9 Best fit 6-8-10-12

Distances betweendifferent chains

OH

HO

OH

OH

φ

Example: poly(vinyl alcohol)

31

Iterative Iterative BoltzmannBoltzmann InversionInversion

• Tabulated numerical potential V(r)• Starting guess V0(r) → RDF0(r) ≠ RDFtarget(r) • Potential correction

• Iterate

until Vn(r) → RDFn(r) = RDFtarget(r) • Converges in few iterations• Density/pressure correction can be added

D. Reith, H. Meyer, FMP, Comput. Phys. Commun. 148, 299 (2002).

( ) ( ) ( )( )rrkTrVrV

target

001 RDF

RDFln+=

( ) ( ) ( )( )rrkTrVrV n

nntarget

1 RDFRDFln+=+

32

CoarseCoarse--Grained Grained Poly(vinylPoly(vinyl alcohol): alcohol): CrystallisationCrystallisation

H. Meyer, FMP, J. Chem. Phys. 115, 7807 (2001)

33

Mesoscopic:23 particlesno H2O

Poly(acrylicPoly(acrylic acid)acid)

Atomistic:102 atoms103 H2O

CO2-

CO2-

CO2- CO2

-

Na+

Na+

Na+

Na+

Na+

0.0 0.5 1.0 1.5 2.00

2

4

6

8

10

12

RD

F, 1

st &

2nd

exc

lude

d

100 1000 10000

1

10

100

Hyd

rody

nam

ic ra

dius

(nm

)

Molecular weight (monomers)

Simulation Dynamic Light Scatt.

∑=ji ijH RNR ,

2111

D. Reith, B. Müller,FMP, S. Wiegand,

J.Chem. Phys. 116,9100 (2002)

34

Accounting for Accounting for TacticityTacticity

RR R

R

RR R

R

m r r m r

RR R

R

RR R

R

• m-diads and r-diads treatedas different monomers

• different interaction potentials

G. Milano, FMP, J. Phys. Chem. B 109, 18609 (2005)

35

Accounting for Accounting for TacticityTacticity (2)(2)

Atactic polystyrene melt

36

Accounting for Accounting for TacticityTacticity, Results, Results

Atactic polystyrene melt

G. Milano, FMP, J. Phys. Chem. B 109, 18609 (2005)

37

Coarse Graining, ConclusionsCoarse Graining, Conclusions

• Many polymers: Melt, solution• Automation is crucial• Meso/macroscopic properties with experimental accuracy• Latest: tacticity• On-going: dynamics, viscoelasticity

38

DankeDanke

• Hydrophobic polymer surfacesSandeep Pal€: BASF, BMBF

• Thermal conductivity of polymersEnrico Lussetti, Meimei Zhang, Luis de Souza, Takamichi Terao€: DFG, Schwerpunkt 1155

• Coarse grained polymer modelsDirk Reith, Hendrik Meyer, Roland Faller, Kurt KremerSylvain Goudeau, Giuseppe Milano€: BMBF, Rhodia, Humboldt-Stiftung