near (Metal) Surfaces
K. Kremer
Max Planck Institute for Polymer Research, Mainz
09/2005

Max-Planck Institute for Polymer Research
Mainz

Characteristic Time and Length Scales
Soft fluid
Time
Atomistic
Quantum Length
Local Chemical Properties  Scaling Behavior of Nanostructures
Energy Dominance  Entropy Dominance of Properties

Modular Simulation Package by C. Holm et al
Method development will continue!!
E xtensible S imulation P ackage for Res earch on So ft matter


Method Development,
Scientific Open Source Software (ESPResSo)

Charged Systems (SFB, Transregio, Gels)

Long Range Interactions, Hydrodynamics
 Membranes,….Biophysics


Analytic Theory of disordered Systems

Complex Fluids

Computational Chemistry of Solvent-Solute Systems

Melts, Networks – Relaxation, NEMD …

COWORKERS:
L. Delle Site
N. 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 Simulation
Bayer, BASF, DSM, Rhodia, Freudenberg

Why Polycarbonate?
Modern application of Polycarbonate
New football stadium, Cologne, World Championship 2006

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

d=λ/4
(

100nm)
“only” high tech commodity polymer

Two extreme cases end adsorption only
“inert” surface energy dominated entropy dominated

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

Thermal energy of particles/ per degree of freedom
E=kT

Room temperature 300K:
E

1 .
38

10

23
J / K

300 K

4 .
1

10

21
J
 kT
Chemical Bond
Hydrogen Bond
E
E


3
6

10 kT

19
J

80 kT

10 kT
Soft Matter: Thermal Energy dominates properties

E

1 .
38

10

23
J / K

300 K kT kT kT

4 .
1

10

21
J

2 .
5

10

2 eV

9 .
5

10

4
E
H

4 .
1 pNnm
Electronic structure, CPMD
Quantum Chemistry kT
Biophysics Membranes, AFM kT kT kT



200
0 .
6 kcal / mol
2 .
5 cm kJ /

1 mol
Spectroscopy



Properties
Macroscopic domains etc.
Semi macroscopic
L
 100Å - 1000Å
T

0 (1 sec)
Mesoscopic
L
 10Å - 50Å
T  10 -8 - 10 -4 sec
Entropy dominates
 
Mesoscopic
L
 10Å - 50Å
T

10 -8 - 10 -4 sec
Entropy dominates
Microscopic
L
 1Å - 3Å
T

10 -13 sec
Energy dominates
(Sub)atomic electronic structure chemical reactions excited states generic/universal *** chemistry specific

A
B
# AA , # BB , # A B contacts =O(N)
R
2
( N )

N
U
AB

N

AB
U
 eff
AA



U
AB
BB



N

Phase separation, critical interaction
 c eff



1
“chemistry ” “generic”
Intra-chain entropy invariant => small energy differences => phase separation

Example Viscosity h of a polymer melt
(extrusion processes ....)
Microscopic
L

1 Å – 3 Å
T

10 -13 sec materials/ chemistry specific Prefactor
T , h  A M X
“Energy dominated“ h A M X
Mesoscopic generic/universal Properties
L

10 Å – 50 Å
T

10 -8 – 10 -4 sec h  A M X X = 3.4
M molecular weight
“Entropy dominated“ varies for many decades varies for many decades e.g.: M 2M h (2M)  10h(M)
T =500 K 470K h ( T =470 K )  10 h(
T
 500 K)
(typical values for BPA-PC)

Micro-Meso-Macro
Simulation
Interplay Energy

Entropy
Free Energy Scale: k
B
T
(SEMI-)MACROSCOPIC
“Coarse Graining“
Inverse Mapping
MESOSCOPIC
Simpler Models
“Coarse Graining“
Inverse Mapping
ATOMISTIC
/
MOLECULAR
TODAY

•
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

Molecular Coarse-Graining of
Bisphenol-A-Polycarbonate
Coarse-graining : map bead-spring chain over molecular structure.
=> Many fewer degrees of freedom
Inverse mapping: grow atomic structure on top of coarsegrained backbone
=>Large length-scale equilibration in an atomically resolved polymer

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
O C O
O
C
1:2 Mapping
O C O
O
C
P(
P( l v
, l v
, a b v
,
, j
) j
)


P(
P( l v l v
)P(
)P( a b
)P(
)P( j
) j
)
}
Distribution
Functions
Thermodynamic Potential V
V ( l , b
, j
)
 
 ln
  ln
P ( l )
 ln
P ( l , b
, j
)
P ( b
)
 ln
Algorithmic speed

10 !
P ( j
)
}
Distributions include temperature!
MD simulation at one temperature, but with variable distributions .

Angle potentials are
T-dependent Boltzmann inversions; e.g., at carbonate:
U
P
• Excluded volume
• Bonds
• Angles
• Torsions
T = 570 K

Molecular Coarse-Graining of
Bisphenol-A-Polycarbonate Melts
9.3-11.5 Å
A particular conformation of a 10-repeat-unit molecule of BPA-PC at atomic resolution;
356 atoms
Its coarsened representation in the
4:1 mapping scheme;
43 “beads”;
‹
R g
2 › 1/2 = 20.5 Å; l p
~ 2 r.u.
Fast motion (e.g. bond vibration) is properly averaged over;
CG chain represents a multitude of underlying atomic structures
C. F. Abrams, KK, Macromol.
36 , 260(2003)

– Molecular Coarse-Grained Melt
–
Inverse Mapping
End to end distance of coarse grained simulations agree to n-scattering experiments!
R
G
2
( N )
N
 o
37 A
2

h  
R
N
2 k
B
T s
3
( N

1 )
2
36 D
• Melt simulation
• Viscosity from chain diffusion coefficient
•
Property of entire chains
 
2 .
2

10

11
(new data 2005) sec
[W. Tschöp, K. Kremer, J. Batoulis, T. Bürger, O. Hahn, Acta Polym.
49 , 61
(1998); ibid. 49 , 75].

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-PC
Bottom: 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)]

• 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 -4 sec!!
)
•
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

Molecular structure coarse-grained onto bead-spring chain
Simulation of coarse-grained
BPA-PC liquids (T = 570K) next to metal surface
Specific surface interactions investigated via ab initio calculations

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: E ads
• Phenol: E ads
= -1.05 eV (21 kT @ 570K) at
= -0.92 eV at d
= 2 Å.
d = 2 Å.
• Both: Horizontal orientation strongly preferred, short-ranged: |E ads
| < 0.03 eV for d
> 3 Å

CPMD: Dependence of Phenol-Ni
Interaction on Ring Orientation
Interaction very sensitive to orientation!

• 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 interaction strongly dependent on
C
1
-C
4 phenol orientation
•In standard 4:1 model, phenoxy end orientation not strictly accounted for
Abrams CF, Delle Site L, KK, PRE 67, 021807 (2003)
•Resolving only the terminal carbonates specifies 1-4 orientation and is inexpensive

Chain center-of-mass density profiles N = 10 monomers
M = 240 chains
 R g
2  1/2 = 20.5 Å
3 clear regimes:
• z <  R g
 bulk
: both ends adsorbed
•  R g
 bulk
2  R g
 bulk
< z <
: single ends adsorbed
• z > 2  R g
 bulk
: no ends adsorbed

Chains “compressed”
Chains “elongated”
Normal Bulk conformations
 Coupling Surface  Bulk?

Energy - Entropy Competition
Delle Site, Leon, KK, JACS, 126 , 2944(2004)

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

end adsorption energy dominated case: phenolic chain ends
Surface Potential for Ends




0


  
1
Rouse



10
 
1
Rouse
Sheared melts
Both ends at surface
One end at surface
No end at surface



100
 
1
Rouse
EPL 70, 264-270 APR 2005

BPA-PC plus 5% additives

BPA-PC plus 5% additives

BPA-PC plus 5% (weight) additives under shear:
BPA-PC + 5-mers BPA-PC + DPC
Blue: major component Yellow: minor component

BPA-PC plus 5% additives under shear:
JCP 123 Art. No. 104904 SEP 8 2005

Specific Surface Morphologies – Multiscale
Approach
Coarse-graining onto beadspring chain
PC near Ni
Competition Energy- Entropy
Simulation of coarse-grained polymer next to metal surface (BPA-
PC)
Specific surface interactions ab initio calculations
(CPMD)
“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

•
Dual-Triple… Scale Simulations/Theory
–
Adaptive quantum
 force field
 coarse grained
…
• Nonbonded Interactions: NEMD, Morphology…
– Accuracy k
B
T O(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

Adaptive Multiscale methods – Static and Dynamic
Simple test case
Polymers at surfaces,
VW Foundation Project
M. Praprotnik, L. DelleSite, KK, JCP, Nov. 2005

Tetrahedron, repulsive LJ Particles,

Hybrids
 “Softer” Sphere
FENE bonds
Explicit Atom

Transition

Coarse Grained regime regime regime

 Same center-center g(r)
 Same mass density
 Same Pressure (=>Eq. of state)
 Same temperature
 Free exchange between regimes
 Simple two body potential

Can be viewed as 1 st order phase transition

Phase equilibrium

Thermostat has to provide/take out latent heat due to change in degrees of freedom

Coarse Grained Model
Study explicite atom and CG system seperately
=> fit CG Interaction Potential:
U cm
( r )
 
{ 1
 exp[
 
( r
 r
0
)]}
2
 ex
=
 cg
, p ex
=p cg
, T ex
=T cg

explicit hybrid coarse grained
F ab
 w ( X a
) w ( X b
) F atom ab

[ 1
 w ( X a
) W ( X b
)] F cm ab
Interactions explicit-explicit
CG-CG hybrid-hybrid
CGhybrid: CG-CG explicithybrid: explicit-explicit

Particle Exchange Radial Distributions,
Number of neighbours

 Practical proof of principle
Many open questions:

Higher densities
 “real” systems

Inhomogeneous systems

Dynamics
 Other geometries

Multi level systems

•
Dual-Triple… Scale Simulations/Theory
–
Adaptive quantum
 force field
 coarse grained
…
• Nonbonded Interactions: NEMD, Morphology…
– Accuracy k
B
T O(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

van der Vegt, DelleSite
Combined CPMD and atomistic simulations for benzene adsorption out of water
=> Extension to more complicated systems

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

•
Dual-Triple… Scale Simulations/Theory
–
Adaptive quantum
 force field
 coarse grained
…
• Nonbonded Interactions: NEMD, Morphology…
– Accuracy k
B
T O(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