Multiscale Simulation of Polymers

near (Metal) SurfacesK. Kremer

Max Planck Institute for Polymer Research, Mainz

09/2005

Max-Planck Institute for Polymer Research Mainz

Time

Quantum

Atomistic

Soft fluid

Local Chemical Properties Scaling Behavior of Nanostructures Energy Dominance Entropy Dominance of Properties

Finiteelements

Characteristic Time and Length Scales

Length

bilayerbucklesMolecular

Open Source Software: ESPResSo

Extensible Simulation Package for Research on Soft matter

Modular Simulation Package by C. Holm et alMethod development will continue!!

Central Topics of the Theory Group

Method Development, Scientific Open Source Software (ESPResSo)Charged Systems (SFB, Transregio, Gels)Long Range Interactions, HydrodynamicsMembranes,….Biophysics

Multiscale ModelingAnalytic Theory of disordered SystemsComplex FluidsComputational Chemistry of Solvent-Solute SystemsMelts, Networks – Relaxation, NEMD …

COWORKERS:L. Delle SiteN. Van der Vegt

D. Andrienko, M. Praprotnik, X. Zhou (Los Alamaos Nat. Lab.)N. Ardikari, W. Schravendijk, M.E. Lee

F. Müller-Plathe ( TU Darmstadt)O. Hahn (Würzburger Druckmaschinen)D. Mooney (Univ. College Dublin)H. Schmitz (Bayer AG)W. Tschöp (DG Bank)S. Leon (UPM Madrid)C. F. Abrams (Drexel)H. J. Limbach (Nestle)

BMBF Center for Materials SimulationBayer, BASF, DSM, Rhodia, Freudenberg

Modern application of PolycarbonateNew football stadium, Cologne, World Championship 2006

Why Polycarbonate?

Grooves and address pits of a die cast sample of polycarbonate for a high storage density optical disc

Bayer Materials

Why study Polycarbonate and the PC/Ni interface?

Why study Polycarbonate and the PC/Ni interface?

“only” high tech commodity polymer

d=λ/4(100nm)

Specific Adsorption

Two extreme casesend adsorption only “inert” surfaceenergy dominated entropy dominated

• Structure Property Relations for Polymers - Linking Scales – Interplay universal - system specific

aspects

Soft Matter??Thermal energy of particles/ per degree of freedom

E=kT Room temperature 300K:

kTJ

KKJE

21

23

101.4

300/1038.1

Chemical Bond

Hydrogen Bond kTkTE

kTJE

106

80103 19

Soft Matter: Thermal Energy dominates properties

molkJkT

molkcalkT

cmkT

pNnmkT

EkT

eVkT

JkT

KKJE

H

/5.2

/6.0

200

1.4

105.9

105.2

101.4

300/1038.1

1

4

2

21

23

Energy Scale kT for T=300K

Quantum Chemistry

Electronic structure, CPMD

Biophysics Membranes, AFM

Spectroscopy

Time and length scales

(Sub)atomicelectronic structurechemical reactionsexcited states

MicroscopicL 1Å - 3ÅT 10-13 secEnergy dominates

MesoscopicL 10Å - 50ÅT 10-8 - 10-4 secEntropy dominates

MesoscopicL 10Å - 50ÅT 10-8 - 10-4 secEntropy dominates

Semi macroscopicL 100Å - 1000ÅT 0 (1 sec)

Macroscopicdomains etc.

generic/universal *** chemistry specific

Properties

Mixtures Polymer A, B#AA, #BB, #AB contacts =O(N)

1 Nconstceff

Phase separation, critical interaction

Intra-chain entropy invariant => small energy differences => phase separation

“chemistry” “generic”

ABeff

BBAA

ABAB

NUU

NUNNR )(2

Microscopic materials/ chemistry specific Prefactor

L 1Å – 3Å (e.g. function of glass transition)

T 10-13 sec A MX

“Energy dominated“

,TG

Example Viscosity of a polymer melt (extrusion processes ....)

A MX

varies for many decades

varies for many decades

e.g.: M 2M T =500 K 470K(T =470 K ) T

(typical values for BPA-PC)

Mesoscopic generic/universal Properties

L 10Å – 50Å A MX X = 3.4

T 10-8 – 10-4 sec M molecular weight“Entropy dominated“

Micro-Meso-Macro

Simulation

(SEMI-)MACROSCOPIC“Coarse Graining“ Inverse Mapping

MESOSCOPICSimpler Models

“Coarse Graining“ Inverse Mapping

ATOMISTIC/MOLECULAR

TODAY

Interplay Energy Entropy

Free Energy Scale: kBT

Polycarbonate on Metal Surface

• Linking Scales for Bisphenol-A-Polycarbonate (BPA-PC)– Molecular Coarse-Graining– Inverse Mapping, (Phenol Diffusion)

• BPA-PC Melts near Nickel Surfaces– Ab initio calculations: Surface/molecule energetics– Multiscale simulation: Molecular orientation at liquid/metal interface– Adsorption at a step– Shearing a melt

Coarse-graining:map bead-spring chain over molecular structure.=> Many fewer degrees of freedom

Inverse mapping: grow atomic structure on top of coarse-grained backbone=>Large length-scale equilibrationin an atomically resolved polymer

Molecular Coarse-Graining of Bisphenol-A-Polycarbonate

Mapping Scheme

Quantum Chemistry

Monte Carlo, isolated

all atom chain

sample CG distributions on basis of all atom chain

Intra-chain potentials

for CG melts at given temperature

Original Ansatz 1:2 Mapping

O C O

O

C O C O

O

C

))P()P(P(),,P( ll

))P()P(P(),,P( ll

DistributionFunctions

Thermodynamic Potential V

Distributions include temperature! MD simulation at one temperature, but with variable distributions.

Algorithmic speed up : !410

)(ln)(ln)(ln

),,(ln),,(

PPlP

lPlV

Interaction Energies in the Coarse-Grained Model

• Excluded volume• Bonds• Angles• Torsions

U

P

Angle potentials are T-dependent Boltzmann inversions; e.g., at carbonate:

T = 570 K

Fast motion (e.g. bond vibration) is properly averaged over;CG chain represents a multitude of underlying atomic structures

Molecular Coarse-Graining of Bisphenol-A-Polycarbonate Melts

A particular conformation ofa 10-repeat-unit moleculeof BPA-PC at atomic resolution;356 atoms

Its coarsened representation in the4:1 mapping scheme; 43 “beads”;

‹Rg2›1/2 = 20.5 Å; lp ~ 2

r.u.

9.3-11.5 Å

C. F. Abrams, KK, Macromol. 36, 260(2003)

Results for Melts, N=20….120

– Molecular Coarse-Grained Melt– Inverse Mapping

End to end distance of coarse grained simulationsagree to n-scattering experiments!

22

A37)( o

G

NNR

Viscosity => Time Mapping

• Melt simulation• Viscosity from

chain diffusioncoefficient

• Property of entire chains

(new data 2005)

[W. Tschöp, K. Kremer, J. Batoulis, T. Bürger, O. Hahn, Acta Polym. 49, 61 (1998); ibid. 49, 75].

DNsTkR BN 36)1( 232

sec102.2 11

How good are generated conformation?Inverse Mapping:

Reintroduce Chemical Details

Coarse grained BPA-PC chain

All atom model

Structure factors of (deuterated) BPA-PC

Right: standard BPA-PCBottom: fully deuterated BPA-PC

[J. Eilhard, A. Zirkel, W. Tschöp, O. Hahn, K. K., O. Schärpf, D. Richter,U. Buchenau,J. Chem. Phys. 110, 1819 (1999)]

Comparison: Simulation n-Scattering

Polycarbonate on Metal Surface

• Linking Scales for Bisphenol-A-Polycarbonate (BPA-PC)– Molecular Coarse-Graining– Phenol Diffusion (need atomistic resolution!)– Inverse Mapping, (atomistic trajectories for entangled melts for

up to 10-4sec!!)

• BPA-PC Melts near Nickel Surfaces– Ab initio calculations: Surface/molecule energetics– Multiscale simulation: Molecular orientation at liquid/metal

interface– Adsorption on a step– Shearing a melt

Simulating BPA-PC/Metal Interfaces

Simulation of coarse-grainedBPA-PC liquids (T = 570K)next to metal surface

Specific surface interactionsinvestigated via ab initio calculations

Molecular structure coarse-grainedonto bead-spring chain

Ab initio Investigations of Comonomeric Analogues on Nickel

(CPMD Program: M. Parrinello)

CPMD: Propane and Carbonic Acid on Nickel

Adsorption energy: +0.01 eV (0.2 kT @ 570K) for d 3.2 Å Strongly repulsed, regardless of orientation

propane

carbonic acid

CPMD: Benzene and Phenol on Nickel

• Benzene: Eads = -1.05 eV (21 kT @ 570K) at d = 2 Å.

• Phenol: Eads = -0.92 eV at d = 2 Å.

• Both: Horizontal orientation strongly preferred, short-ranged: |Eads| < 0.03 eV for d > 3 Å

CPMD: Dependence of Phenol-Ni Interaction on Ring Orientation

Interaction verysensitive to orientation!

CPMD: Conclusions

• Strong repulsion of propane and carbonic acid + the strong orientational dependence + short interaction range of phenol with Ni {111} Internal phenylene comonomers in BPA-PC are sterically hindered from adsorbing on Ni {111}. Torsional freedom in carbonate group allows for terminal phenoxy groups to adsorb

Coarse-Grained BPA-PC with End-Group Resolution (Dual Scale MD)

•Phenol-Ni interactionstrongly dependent onC1-C4 phenol orientation

•In standard 4:1 model,phenoxy end orientationnot strictly accounted for

•Resolving only the terminal carbonatesspecifies 1-4 orientationand is inexpensive

Abrams CF, Delle Site L, KK, PRE 67, 021807 (2003)

Results: Chain-end adsorption

N = 10 monomersM = 240 chainsRg

21/2 = 20.5 Å

3 clear regimes:• z < Rgbulk :

both ends adsorbed• Rgbulk < z < 2Rgbulk :

single ends adsorbed

• z > 2Rgbulk:no ends adsorbed

Chain center-of-massdensity profiles

Schematic structure of “End-Sticky” Melts

Chains “compressed”

Chains “elongated”

Normal Bulk conformations

Coupling Surface Bulk?

Extension I: Other Chain EndsEnergy - Entropy Competition

Delle Site, Leon, KK, JACS, 126, 2944(2004)

Extension II: Stepped Surface

Line Defect Induced Ordering

L. DelleSite, S. Leon, KK, J. Phys. Cond. Matt.17, L53, 2005

Extension III: Shearing a Melt

end adsorption energy dominated case:phenolic chain ends

Surface Potential for Ends

Sheared melts

0

1

Rouse 1

10

Rouse

1100

Rouse

Both ends at surfaceOne end at surfaceNo end at surface

EPL 70, 264-270 APR 2005

Extension IV: Jamming Lubricants

BPA-PC plus 5% additives

Extension IV: Jamming Lubricants

BPA-PC plus 5% additives

Jamming Lubricants

BPA-PC plus 5% (weight) additives under shear:

BPA-PC + 5-mers BPA-PC + DPC

Blue: major component Yellow: minor component

Jamming Lubricants

BPA-PC plus 5% additives under shear:

JCP 123 Art. No. 104904 SEP 8 2005

Specific Surface Morphologies – Multiscale Approach

PC near Ni Competition Energy- Entropy

“sticky” chain ends “neutral”Coating/contamination with oligomers

C.F. Abrams, et al. PRE 021807 (2003)L. DelleSite, et al. PRL 156103 (2002)BMBF Zentrum MatSim

Coarse-grainingonto bead-spring chain

Simulation of coarse-grainedpolymer next to metal surface (BPA-PC)

Specific surface interactions ab initio calculations (CPMD)

A few Challenges • Dual-Triple… Scale Simulations/Theory

– Adaptive quantumforce fieldcoarse grained …

• Nonbonded Interactions: NEMD, Morphology…– Accuracy kBTO(1/N) needed!

• Conformations Electronic Properties– E.g. coupling of aromatic groups to backbone conformation, or to other chains

• Online Experiments: – Nanoscale Experiments, long Times

Simple test case

Polymers at surfaces,VW Foundation ProjectM. Praprotnik, L. DelleSite, KK, JCP, Nov. 2005

Adaptive Methods:Changing degrees of freedom on the fly

Adaptive Multiscale methods – Static and Dynamic

Adaptive Methods:Changing degrees of freedom on the fly

Tetrahedron, repulsive LJ Particles, Hybrids “Softer” SphereFENE bonds

Explicit Atom Transition Coarse Grainedregime regime regime

Same center-center g(r)Same mass densitySame Pressure (=>Eq. of state)Same temperatureFree exchange between regimes

Simple two body potential

Can be viewed as 1st order phase transition Phase equilibrium Thermostat has to provide/take out latent heat due to change in degrees of freedom

Requirements

ex = cg, pex=pcg, Tex=Tcg

Study explicite atom and CG systemseperately => fit CG Interaction Potential:

20)]}(exp[1{)( rrrU cm

Coarse Grained Model

Transition Regime

cm

atom

FXWXw

FXwXw

F

)]()(1[

)()(

explicit hybrid coarse grained

Interactions

explicit-explicitCG-CGhybrid-hybrid

CG- hybrid: CG-CGexplicit-hybrid: explicit-explicit

Particle Numbers, Density

Particle Exchange Radial Distributions, Number of neighbours

Adaptive Methods:Changing degrees of freedom on the fly

Practical proof of principle

Many open questions:

Higher densities“real” systemsInhomogeneous systemsDynamicsOther geometriesMulti level systems

A few Challenges • Dual-Triple… Scale Simulations/Theory

– Adaptive quantumforce fieldcoarse grained …

• Nonbonded Interactions: NEMD, Morphology…– Accuracy kBTO(1/N) needed!

• Conformations Electronic Properties– E.g. coupling of aromatic groups to backbone conformation, or to other chains

• Online Experiments: – Nanoscale Experiments, long Times

Solute Solvent Systems van der Vegt, DelleSite

Combined CPMD and atomistic simulationsfor benzene adsorption out of water=> Extension to more complicated systems

Ad-/Desorption Process

P. Schravendijk, N. van der Vegt, L. Delle Site, KK, ChemPhysChem 6, 1866 (2005)

A few Challenges • Dual-Triple… Scale Simulations/Theory

– Adaptive quantumforce fieldcoarse grained …

• Nonbonded Interactions: NEMD, Morphology…– Accuracy kBTO(1/N) needed!

• Conformations Electronic Properties– E.g. coupling of aromatic groups to backbone conformation, or to other chains

• Online Experiments: – Nanoscale Experiments, long Times