MD simulation of the effect of side-chain MD simulation of the effect of side-chain

length on dynamics in the PEO systemlength on dynamics in the PEO system

Andi HektorAndi Hektor11, Alvo Aabloo, Alvo Aabloo22, Mattias Klintenberg, Mattias Klintenberg33 & &

Josh ThomasJosh Thomas44

1. Institute of Materials Science, Tartu University, Tähe 4, 51010 TARTU, Estonia.2. Institute of Physics, University of Tartu, Tähe 4, 51010 TARTU, Estonia.3. Condensed Matter Theory Group, Department of Physics, Uppsala University, Box 530, SE-751 21 Uppsala, Sweden.4. Materials Chemistry, Ångström Laboratory, Uppsala University, Box 538, SE-751 21 Uppsala, Sweden.

E-mail: andi@ut.ee

IntroductionIntroduction

Poly(ethylene oxide) (PEO): -(CHPoly(ethylene oxide) (PEO): -(CH22-CH-CH22-O)-O)nn--

Fig. 1. PEO unit – ethylene oxide (EO). Fig. 2. PEO chain (80 EO units).

IntroductionIntroduction

Electrolyte, side-chainElectrolyte, side-chain

Fig. 3. Electrolyte (PEO+LiCl) including a single side-chain.

IntroductionIntroduction

PEO topologyPEO topology

A long PEO backbonewith shorter side-chains

A long PEO connected by short cross-links

A 3-D polymer network

Fig. 4. Different PEO topologies.

IntroductionIntroduction

Fig. 5. PEO backbone with a side-chain (1) and the zoomed-in linkage region (2).

12

PEO chain with a side-chain and linkage-pointPEO chain with a side-chain and linkage-point

IntroductionIntroduction

Effects of side-chainEffects of side-chain

• Side-chains affect the dynamics of PEO

• From experiment: the biggest effect is around the 6-8 EO monomers

• Can we use MD to understand these effects?

IntroductionIntroduction

Molecular Dynamical (MD) simulationsMolecular Dynamical (MD) simulations

• Classical Newtonian mechanics

• Potentials

2

1 2U( ,..., )

i

iN im t

r

rr r

1 internal external

internal bond angle torsion

external electrostatic long-range

U( ,..., ) ,

,N U U

U U U U

U U U

r r

IntroductionIntroduction

MD simulation analyseMD simulation analyse

• Radial distribution function (RDF):

1 1,

1RDF( ) ( )

N N

iji j

j i

r r rN

• Mean Squared Displacement (MSD) and 3D diffusion coefficient (D):

• Average Velocity (AV):

2MSD( ) ( ) (0) ,r t r r

1D lim MSD( )

6tt

t

0

1AV

T

nnT

v

MethodMethod

PotentialsPotentials

• The majority of the potentials we use for PEO originate from earlier work

• The torsional potential for the C-C-C-O dihedral angle in the side-chain linkage region is calculated by Quantum Mechanics (QM)

Fig. 6. The region of the calculated torsional potential.

C

C

C

O

• QM method and basis-sets: HF/6-31G**, HF/6-31++G**

• Technical information: A total of 784 CPU hours was used on our in-house Linux PC-cluster using NWChem software

• Analytical torsion potential function:

MethodMethod

Calculation of torsion potential C-C-C-OCalculation of torsion potential C-C-C-O

3

0 2 1 21

[ cos( ) sin( )],k kk

u u k u k

ui are constants and is the torsion angle.

-3

-2

-1

0

1

2

3

0 100 200 300

Angle

Energ

y /

kcal/

mol/

Fig. 7. Fitting of the calculated data (the red squares) to a 7th order trigonometric polynom.

MethodMethod

Fig. 8. The “unpacked” configuration with a single side-chain for MD simulation.

• 9 side-chain systems (marked as s5-s9, s11, s15, s19 and s23): a cubic periodic box (24.5 x 24.5 x 24.5 Å) containing a 186 EO-monomer PEO chain with a 5-9, 11, 15, 19, and 23 EO-monomer PEO side-chains.

• Reference system (marked as r): a cubic periodic box (24.5 x 24.5 x 24.5 Å) containing a single PEO chain involving 193 EO-monomers with no side-chain.

Simulation boxes generated by controlled pivotal Monte Carlo growth. The density maintained around 1.0 g/cm3.

MD configurationsMD configurations

MD simulationsMD simulations

• Intramolecular force fields: rigid bonds; angle and torsional potentials

• Long-range force fields: electrostatic and Buckingham’s potentials

• Calculation: Ewald summation of long-range forces used

• Configuration: a cubic MD box (24.5 x 24.5 x 24.5 Å) with periodic boundary conditions; density maintained at ~1 g/cm3

• Simulation process: time-step 0.5 fs, temperature 290 K, starting with NVT and followed by NpT for the 1000 ps

• Technical information: a total of 3900 CPU hours used on our in-house Linux PC cluster using DLPOLY software

ResultsResults

Animation 1. ”Unpacked” chain

Animation 2. Zoomed-in version

Animations of the MD simulationsAnimations of the MD simulations

ResultsResults

Radial distribution function (RDF)Radial distribution function (RDF)

0.0

0.4

0.8

1.2

1.6

2.0

2 3 4 5 6 7 8 9 10

r (Å)

RD

F in

arb

itra

ry u

nit

s

Fig. 9. RDF (C-C and C-O) identical for all the systems.

C-C

C-O

ResultsResults

Mean Square Displacement (MSD) (e.g., for r and Mean Square Displacement (MSD) (e.g., for r and s7)s7)

0

2

4

6

8

10

0 50 100 150 200 250 300 350 400 450 500

Time (ps)

MS

D (

Å2 )

Fig. 10. MSD for the carbon atoms: Cr – the reference system, Cs7 – the side-chain system s7.

Cr

Cs7

ResultsResults

3D diffusion coefficients3D diffusion coefficients

Fig. 11. 3D diffusion coefficents for the C and O atoms. Note: the strong “immobilising” effect around 6-8 EO monomers.

0.005

0.007

0.009

0.011

0.013

0.015

0.017

0.019

0 2 4 6 8 10 12 14 16 18 20 22 24

Number of EO monomers in a side-chain

Dif

fusio

n c

oeff

icen

t (1

0-9 m

2 /s)

C

O

ResultsResults

Diffusion coefficents for the side-chain C-atomDiffusion coefficents for the side-chain C-atom

Fig. 13. Diffusion coefficents for the side-chain C-atoms.

C

O

5

6

7

8

9

1115

19

23

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

4 6 8 10 12 14 16 18 20 22 24

Number of EO monomers in a side-chain

Diff

. coeffic

ent (1

0-9

m2/s

)

0.7

0.8

0.9

1.0

1.1

0 1 2 3 4 5 6 7 8

Side-chain atom

Avera

ge v

elo

cit

y (

Å/p

s)

ResultsResults

Average velocity (AV) for O-atoms along the side-Average velocity (AV) for O-atoms along the side-chain (e.g., s7)chain (e.g., s7)

Fig. 14. AV for O-atoms along the side-chain (e.g. s7); “1” means the first from the linkage-point; “7” means the free end.

ResultsResults

AV for O-atoms along the side-chain for different side-chains AV for O-atoms along the side-chain for different side-chains lengthslengths

Fig. 15. AV for O-atoms along the side-chain for different lengths.“1”: 1st atom“max”: end of side-chain

1.2

1.4

1.6

1.8

2.0

2.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Side-chain atom

Aver

age v

elocit

y (Å/

ps)

s23

s11

s8

s6

s5

s7

ResultsResults

Averaged AV for O-atoms at different side-chain Averaged AV for O-atoms at different side-chain lengthslengths

5 6

7

8

9

11

15

1923

1.30

1.35

1.40

1.45

1.50

1.55

1.60

1.65

0 2 4 6 8 10 12 14 16 18 20 22 24 26

Number of EO monomers in the side-chain

Av

era

ge

ve

loc

ity

(Å

/ps

)

Fig. 16. Averaged AV for O-atoms at different side-chain lengths (s5-s9, s11, s15, s19 and s23).

SummarySummary

• RDF for the reference system (r) and all the side-chain systems (s5-s9, s11, s15, s19, s23) are identical

• The addition of side-chains decreases chain mobility

• A minimum occurs in the diffusion coefficents between 6 and 9 EO side-chain units – in excellent agreement with experiment!

• A maximum occurs in the side-chain diffusion coefficents between 5 and 11 EO side-chain units

• A maximum occurs in the side-chain atoms AVs between 6 and 8 EO side-chain units

• The average AV depends the side-chain length: two maxima a appear - at 8 and 15 EO side-chain units

ReferencesReferences

1. F. M. Gray, “Polymer Electrolytes”, Royal Society of Chemistry, Cambridge, 1997.

2. A. Nishimoto, K. Agehara, N. Furuya, T. Watanabe and M. Watanabe, Macromolecules, 1999, 32, 1541.

3. W. Krawiec, L. G. Scanlon, Jr., J. P. Fellner, R. A. Vaia, S. Vasudevan and E. P. Giannelis, J. Power Sources,

1995, 54, 310.

4. S. Neyertz, D. Brown and J. O. Thomas, J. Chem. Phys., 1994, 101, 10064.

5. S. Neyertz, D. Brown and J. O. Thomas, Comp. Poly. Sci., 1995, 5, 107.

6. A. Aabloo and J. O. Thomas, Comp. and Theor. Poly. Sci., 1997, 7, 47.

7. A. Aabloo and J. O. Thomas, Electrochimica Acta, 1998, 43, 1361.

8. A. Aabloo, M. Klintenberg and J. O. Thomas, Electrochimica Acta, 2000, 45, 1425.

9. R. J. Harrison et al, ”NWChem, A Computational Chemistry Package for Parallel Computers Version 4.0.1"

(2001), Pacific Northwest National Laboratory, Richland, Washington 99352-0999, USA

10. The DL_POLY Project, W. Smith and T. Forester, TCS Division, Daresbury Laboratory, Daresbury, Warrington

WA4 4AD, England.

AcknowledgementsAcknowledgements

• The Nordic Energy Research Programme (NERP)

• The Swedish Natural Science Research Council (NFR, now VR)

• The Estonian Science Foundation (ETF), grant no 4513