Molecular Dynamics Simulations of Diffusion in Polymers

Zach Eldridge

Department of Mechanical EngineeringUniversity of Arkansas

Fayetteville, AR 72701 USA

REU Advisor: Dr. Douglas SpearotGrad Student Advisor: Mr. Alex Sudibjo

Research Symposium – July 20, 2009

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

Background

• What is Molecular Dynamics?• Molecular dynamics is a form of computer simulation used to

observe the behavior of atoms and molecules, which cannot be easily observed during experiments.

• Through the use of computer algorithms and known laws of physics, mathematics, and chemistry we are able conduct an experiment and model it through a simulation.

• Through analysis of the simulation we are able to study the behavior of the material.

Nano Indention

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

My Project

• Objectives• The main objective of this research is to study diffusion of methane

gas penetrates through PDMS (Polydimethylsiloxane)• PDMS – the most widely used silicon based organic polymer. It is composed of Oxygen,

Siliocon and a methyl, CH3. Common uses include contact lenses and shampoo.

• Penetrate – Methane, CH4

PDMS 1 PDMS 2

• Molecular dynamics simulation will allow us to calculate the diffusion coefficients of the penetrate through the PDMS and evaluate the role of concentration and distribution of penetrates

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

My Project

• Simulations Conditions• Concentrations – percent of the total weight of the system

• .264% = 15 atoms, .529% = 30 atoms, .793% = 45 atoms, 1.06% = 60 atoms

• Volumes – Initial volume of methane molecules

• 1000 Å3, 8000 Å3, 27000 Å3, 64000 Å3, 125000 Å3

• Temperatures – Temperature the simulation runs at

• 200 K, 250 K, 300 K, 350 K, 400 K

1000 Å3 initial volume 125000 Å3 initial volume

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

Research Methods

• Create simulation in Linux using Lammps code

• Run simulation through a super computer, Trillion

• Output visual data to Ensight

• Output mean squared displacement data to Excel

• Normalize data and create graphs

• Use slope of trendline to calculate the diffusion coefficient D

• Solve for Q, activation energy Kcal/mol, using the value of D

• Average all Q and calculate D0, diffusion constant (cm2/s)

• Equations

• D = (1/6)slope

• Q = (Rln(D1 / D2))/( 1/T2 – 1/T1)

• D0 = D1/exp(-Q/RT1)

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

Results

-20

0

20

40

60

80

100

120

140

10 20 30 40 50 60

Tota

l MSD

(Å

2 )

Time (ps)

Conc. = 1.06% Vol = 125000 Å3

200k

250k

300k

350k

400k

•Equilibrium Reached at 10 ps•Low fluctuation in MSD

-10

0

10

20

30

40

50

60

25 30 35 40 45 50 55

Tota

l MSD

(Å

2 )

Time (ps)

Conc. = .793% Vol = 125000 Å3

200k

250k

300k

350k

400k

•Equilibrium reached at 25 ps•Low fluctuation in MSD

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

Results Cont.

•Equilibrium reached at 30 ps•High fluctuation in MSD

-10

0

10

20

30

40

50

60

30 35 40 45 50 55

Tota

l MSD

(Å2 )

Time (ps)

Conc. = 1.06 Vol = 1000 Å3

200k

250k

300k

350k

400k

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

Results Cont.

Concentration Volume (Å3)

Temperature (K)

Average Q (Kcal/mol)

D0 x 10-3

(cm2/s)

1.06% 1000

125000

200250300350400

200250300350400

2.789

2.642

2.4 1.23 1.61 1.351.50

3.431.251.311.291.25

.793% 125000 200250300350400

2.704 4.51.01.1

5.971.0

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

Conclusion

• Smaller the initial volume – longer it takes to reach equilibrium

• Larger concentration – less fluctuation in MSD values

• Smaller the initial concentration – longer it takes reach equilibrium

• D0 is concentration dependent• The values of D0 for concentration of .793% were between 19% -

37% below the values for 1.06%.

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

Works cited

• (2009, May 11). Polydimethylsiloxane. Retrieved May 26, 2009, from Wikipedia Web site: http://en.wikipedia.org/wiki/Polydimethylsiloxane

• (2009, April 14). Arkansas High Performance Computing Center. Retrieved May 26, 2009, Web site: http://hpc.uark.edu/about.html

• Kam Liu, Wing Ensight.com. Retrieved May 26, 2009, Web site: http://www.ensight.com/component/option,com_zoom/Itemid,41/PageNo,2/catid,4/hit,1/key,15/page,view/

• Wag.caltech.edu. Retrieved May 26, 2009, from Gallery of Polymers and Polymer Simulation Web site: http://www.wag.caltech.edu/gallery/pvcdco2.gif

• Dr. Douglas Spearot – Faculty Advisor, Alex Sudibjo – Graduate Student Advisor

Multiscale Mechanics of Materials Laboratory, Department of Mechanical Engineering

Conclusion

Questions?