Rebecca CantrellMAE 715 - Professor Zabaras

Atomistic Modeling of MaterialsFinal Project Presentation

May 7, 2007

Background◦ Motivation◦ Goals

Method◦ TINKER software◦ Simulation systems

Results◦ C60-pentacene (3x3x2)◦ Pentacene-pentacene (3x3x2)◦ C60-pentacene (4x4x2)

Conclusion

Pentacene◦ High electron mobility◦ High degree of crystallinity◦ Unit cell: 2 pentacene molecules◦ Electron donor

Buckminsterfullerene (“buckyballs”)◦ High electron mobility◦ Electron acceptor

R. C. Haddon, T. Siegrist, R. M. Fleming, P. M. Bridenbaugh and R. A. Laudise. Band structures of organic thin-film transistor materials. Journal of Materials Chemistry. 1995, Vol 5, p 1719.

S. Yoo, B. Domercq, B. Kippelen. Efficient thin-film organic solar cells based on pentacene/C60heterojunctions. Applied Physics Letters. 2004. Vol 85, p5427.

C60-pentacene organic films have recently studied as flexible organic solar cells

C60-pentacene film in betweenindium tin oxide coated with aconducting polymer as the anodeand CsF/Al as the cathode

Solar power conversion efficiency increases after annealing a C60 organic layer on top of pentacene layers

Molecular ordering increases conversion efficiency!

A. C. Mayer, M. T. Lloyd, D. J. Herman, T. G. Kasen, G. G. Malliaras. Postfabrication annealing of pentacene-based photovoltaic cells. Applied Physics Letters. 2004. Vol 85, No. 25.

Study surface diffusion of C60 on pentacene◦ Optimum temperature for surface diffusion?◦ Is there a site hopping energy barrier?

Molecular dynamics simulation◦ C60-pentacene (3x3x2) system◦ Compare to pentacene-pentacene (3x3x2) system◦ Compare to C60-pentacene (4x4x2) system to

determine effects of periodic boundary size

Molecular dynamics and molecular mechanics software used mainly for organic molecules

Files used to run TINKER: .xyz, .key, .nbs Newton’s equations of motion

◦ velocity Verlet integration method Constant temperature

◦ Nosé-Hoover algorithm Thermalization (canonical ensemble,

constant NVT) Full simulation (micro-canonical ensemble, constant NVE)

2

2

d

d

t

rmF iii

Must specify an interaction potential to solve the equations of motion

Extension of mm2 potential; mm3 better for multi-ringed structures

Incorporates the stretching, bending, and tortional energies as well as the van der Waal interaction energies based on empirical parameters

N. L. Allinger, Y. H. Yuh, J. H. Lii. Molecular Mechanics: The MM3 Force Field for Hydrocarbons. Journal of the American Chemical Society. 1989. Vol 111, No 23.

Three systems considered◦ C60-pentacene (3x3x2)◦ Pentacene-pentacene (3x3x2)◦ C60-pentacene (4x4x2)

Fixed bottom layer, second layer allowed to vibrate

Periodic boundary conditions Pressure: 1 atm; Temperature: 225 K – 400 K

xyz coordinates of the center of mass of the C60 molecule moving on the 3x3 layer of pentacene, collapsed onto one unit cell

T = 225 K T = 250 K T = 275 K T = 300 K

T = 325 K T = 350 K T = 375 K T = 400 K

The coordinate units are in Angstroms. Each dot corresponds to a time step of 1 ps. The red corresponds to the position of the center of mass of the C60 molecule; the green corresponds to the positions of the top hydrogen atoms of one pentacene molecule in the unit cell; and the blue corresponds to the positions of the top hydrogen atoms of the other pentacene molecule in the unit cell.

MSD vs. time vaguely implies an increase in diffusion coefficient with increasing temperature, which is expected

In two dimensions, D is given by:

Local minimum for the D around 275 K?

0 500 1000 15000

500

1000

1500

2000

2500

3000C60 on Pentacene: Mean Squared Displacement vs. Time

Time (ps)

MS

D (

A2 )

225 K

250 K275 K

300 K

325 K

350 K375 K

400 K

0 500 1000 15000

500

1000

1500

2000

2500

3000C60 on Pentacene: Mean Squared Displacement vs. Time

Time (ps)

MS

D (

A2 )

225 K

250 K275 K

300 K

325 K

350 K375 K

400 K

t

rD

4

2

220 240 260 280 300 320 340 360 380 4000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Temperature (K)

Diff

usio

n C

oeff

icie

nt (

A2 /ps)

C60 on Pentacene: Diffusion Coefficient vs. Temperature

220 240 260 280 300 320 340 360 380 4000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Temperature (K)

Diff

usio

n C

oeff

icie

nt (

A2 /ps)

C60 on Pentacene: Diffusion Coefficient vs. Temperature

According to the Arrhenius equation, the diffusion versus temperature graph should follow an exponential curve

The prefactor D0 contains the transition state information according to the following relationship based on transition state theory

Plotting ln(D) vs. 1/T gives:◦ slope = -Ea/kB Ea = 0.076 eV

◦ y-int = ln(D0) D0 = 2.27 Ų/ps

2.5 3 3.5 4 4.5 5

x 10-3

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

1/Temperature (1/K)

ln[D

iffus

ion]

(A2 /p

s)

C60 on Pentacene: ln[Diffusion] vs. 1/T

2.5 3 3.5 4 4.5 5

x 10-3

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

1/Temperature (1/K)

ln[D

iffus

ion]

(A2 /p

s)

C60 on Pentacene: ln[Diffusion] vs. 1/T

)/exp(0 TkEDD Ba

vib

vibB

q

qr

h

TkD

2

2

0

K. D. Dobbs, D. J. Doren. Dynamics of molecular surface diffusion: Origins and consequences of long jumps. J. Chem. Phys. 1992. Vol 97, No 5.

xyz coordinates of the center of mass of the C60 molecule moving on the 3x3 layer of pentacene, collapsed onto one unit cell

T = 250 KT = 225 K T = 275 K T = 300 K

T = 325 K T = 350 K T = 375 K T = 400 K

The coordinate units are in Angstroms. Each dot corresponds to a time step of 1 ps. The red corresponds to the position of the center of mass of the C60 molecule; the green corresponds to the positions of the top hydrogen atoms of one pentacene molecule in the unit cell; and the blue corresponds to the positions of the top hydrogen atoms of the other pentacene molecule in the unit cell.

MSD vs. time clearly implies an increase in diffusion coefficient with increasing temperature, which is expected

Again, D is given by:

Overall greater diffusion coefficients than C60-pentacene (3x3x2) due to less sharing of electrons with the surface

0 200 400 600 800 1000 1200 1400 1600 1800 20000

2000

4000

6000

8000

10000

12000

14000

16000Pentacene on Pentacene: Mean Squared Displacement vs. Time

Time (ps)

MS

D (

A2 )

225 K

250 K275 K

300 K

325 K

350 K375 K

400 K

0 200 400 600 800 1000 1200 1400 1600 1800 20000

2000

4000

6000

8000

10000

12000

14000

16000Pentacene on Pentacene: Mean Squared Displacement vs. Time

Time (ps)

MS

D (

A2 )

225 K

250 K275 K

300 K

325 K

350 K375 K

400 K

220 240 260 280 300 320 340 360 380 4000.8

1

1.2

1.4

1.6

1.8

2

Temperature (K)

Diff

usio

n C

oeff

icie

nt (

A2 /ps)

Pentacene on Pentacene: Diffusion Coefficient vs. Temperature

220 240 260 280 300 320 340 360 380 4000.8

1

1.2

1.4

1.6

1.8

2

Temperature (K)

Diff

usio

n C

oeff

icie

nt (

A2 /ps)

Pentacene on Pentacene: Diffusion Coefficient vs. Temperature

t

rD

4

2

Again, according to the Arrhenius equation, the diffusion versus temperature graph should follow an exponential curve

The prefactor D0 contains the transition state information according to the following relationship based on transition state theory

Plotting ln(D) vs. 1/T gives:◦ slope = -Ea/kB Ea = 0.039 eV

◦ y-int = ln(D0) D0 = 5.81 Ų/ps

2.5 3 3.5 4 4.5 5

x 10-3

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1/Temperature (1/K)

ln[D

iffus

ion]

(A2 /p

s)

Pentacene on Pentacene: ln[Diffusion] vs. 1/T

2.5 3 3.5 4 4.5 5

x 10-3

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1/Temperature (1/K)

ln[D

iffus

ion]

(A2 /p

s)

Pentacene on Pentacene: ln[Diffusion] vs. 1/T

)/exp(0 TkEDD Ba

vib

vibB

q

qr

h

TkD

2

2

0

4x4x2 simulation cells significantly increased computation cost

Different results than 3x3x2 simulation cell◦ Strange oscillation occurring◦ No clear trend for D vs. T

Possible reasons: simulation time too short or cell size still not big enough to determine accuracy of results

0 100 200 300 400 500 600 700 800 900 10000

1000

2000

3000

4000

5000

6000C60 on Pentacene(4x4x2): Mean Squared Displacement vs. Time

Time (ps)

MS

D (

A2 )

225 K

250 K275 K

300 K

325 K

350 K375 K

400 K

0 100 200 300 400 500 600 700 800 900 10000

1000

2000

3000

4000

5000

6000C60 on Pentacene(4x4x2): Mean Squared Displacement vs. Time

Time (ps)

MS

D (

A2 )

225 K

250 K275 K

300 K

325 K

350 K375 K

400 K

220 240 260 280 300 320 340 360 380 400

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Temperature (K)

Diff

usio

n C

oeff

icie

nt (

A2 /ps)

C60 on Pentacene(4x4x2): Diffusion Coefficient vs. Temperature

220 240 260 280 300 320 340 360 380 400

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Temperature (K)

Diff

usio

n C

oeff

icie

nt (

A2 /ps)

C60 on Pentacene(4x4x2): Diffusion Coefficient vs. Temperature

Useful information about the previously unknown surface diffusion of a C60 molecule on crystalline pentacene.

D vs. T trends not as smooth as hoped, but comparing data to pentacene-pentacene data still insightful ◦ D for the C60-pentacene (3x3x2) system was overall lower than for

pentacene-pentacene (3x3x2) system◦ Ea of site hopping was higher for the C60-pentacene (3x3x2) system

(~0.076 eV) than for the pentacene-pentacene (3x3x2) system (~0.039 eV)

Periodic boundary size analasis revealed unexpected deviatations; further investigation necessary

Future work would include also investigating the diffusion properties of multiple C60 molecules on the surface of crystalline pentacene to determine whether they tend to attract or repel