18
A Prediction of Nanocomposite Permeability from Monte Carlo Simulations and the Implications of the Constrained Polymer Region Sumit Gogia Patrick Kim Vincent Yu
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
DD
pDnD
'
'
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
td
dp
c
vv
20
1200
dtt
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(vnss
vn
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(vns
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
