A Prediction of Nanocomposite Permeability from Monte Carlo Simulations and the Implications of the Constrained Polymer Region Sumit Gogia Patrick Kim.

A Prediction of Nanocomposite Permeability from Monte Carlo Simulations and the

Implications of the Constrained Polymer Region

Sumit GogiaPatrick KimVincent Yu

Sumit GogiaPatrick Kim

Vincent Yu

Introduction

• Nanoparticles– Generally between 1-100 nm in length– High surface area to volume ratio

• Nanocomposites– Polymers with dispersed nanoparticles– Polymer-clay nanocomposites• Increased tensile strength• Increased elastic modulus• Decreased gas permeability

Sumit GogiaPatrick Kim

Vincent Yu

Applications

• Food packaging– Prolong shelf life

• Tennis balls– Prevent depressurization

• Protective equipment– Reduce thickness

Sumit GogiaPatrick Kim

Vincent Yu

Tortuous path model

• Impermeable clay plates create tortuous paths for permeating molecules

• Nanocomposite is less permeable as a result (Nielsen, 1967)

Sumit GogiaPatrick Kim

Vincent Yu

Tortuous path model

• Two main factors determine the magnitude of the tortuous path– Aspect ratio (α)

– Volume fraction (ϕ)

Sumit GogiaPatrick Kim

Vincent Yu

Constrained polymer model

• Polymer-clay interactions– May cause phase changes in the pristine polymer– Significant effect observed in amorphous polymers

(Adame and Beall, 2009)

Sumit GogiaPatrick Kim

Vincent Yu

Computer simulation

• Allows complete control over variables• Easily reproducible and verifiable• Quicker than gas permeation measurements

Sumit GogiaPatrick Kim

Vincent Yu

Quantifying tortuosity

• Tortuosity

• is the diffusion coefficient of pristine polymer• is the diffusion coefficient of resulting

nanocomposite

• is the distance that a molecule has to travel to diffuse through the nanocomposite• is the distance that a molecule has to travel to

diffuse through the pristine polymer

n

p

D

D

pD

nD

'

'

Sumit GogiaPatrick Kim

Vincent Yu

Monte Carlo simulation

Sumit GogiaPatrick Kim

Vincent Yu

Monte Carlo simulation

Sumit GogiaPatrick Kim

Vincent Yu

Simulation parameters• Run on a supercomputing grid over a period of

one month• Data obtained for and

• Other parameters (t is time)

10

t

d d

p

c

v

v

20

1200

dt

t

ad

d

z

yx

1

8

8

1.00

Sumit GogiaPatrick Kim

Vincent Yu

Data

Sumit GogiaPatrick Kim

Vincent Yu

Results and discussion

• We suggest considering τ as a function of χ, where

– μ is a geometric factor depending on clay shape– s is the cross-sectional area of a clay plate– is the number of clay plates per volume

1(v

nss

v

n

Sumit GogiaPatrick Kim

Vincent Yu

Data

Sumit GogiaPatrick Kim

Vincent Yu

Results and discussion

• χ is composed of two main components:

–

• Cross-sectional area of clay plates per volume of polymer

–

• Average distance travelled by a molecule to get around a clay plate

1(v

ns

s

Sumit GogiaPatrick Kim

Vincent Yu

Conclusion

• Established τ as a function of χ• χ is more accurate than αϕ• Monte Carlo simulations– Improved efficiency– Feasible

Sumit GogiaPatrick Kim

Vincent Yu

Further research

• Account for more variables in simulations– Clay plate size– Orientation– Incomplete exfoliation

• Calculate effect of constrained polymer region

Sumit GogiaPatrick Kim

Vincent Yu

Acknowledgements

• Gary Beall, Texas State University• Max Warshauer, Texas State University• Siemens Foundation• University of Texas at Austin• Our families

Further information

Website: code.google.com/p/rwalksim