Numerical Simulation for the Self-assembly of Polymer Blends with Nano- scaled Features BY YINGRUI SHANG PhD Dissertation UNIVERSITY OF MASSACHUSETTS LOWELL 2008 Dissertation Supervisors: David O. Kazmer, Ph.D., Carol F. Barry, D. Eng., and Joey Mead, Ph.D. November 25, 2008
34
Embed
Numerical Simulation for the Self- assembly of Polymer Blends with Nano-scaled Features BY YINGRUI SHANG PhD Dissertation UNIVERSITY OF MASSACHUSETTS LOWELL.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Numerical Simulation for the Self-assembly of Polymer Blends with
Nano-scaled Features
BYYINGRUI SHANG
PhD DissertationUNIVERSITY OF MASSACHUSETTS LOWELL
2008
Dissertation Supervisors: David O. Kazmer, Ph.D., Carol F. Barry, D. Eng., and Joey Mead, Ph.D.
November 25, 2008
Outline
• Introduction– Thermodynamics
– Numerical assumptions
– Theoretical fundamentals
– Numerical methods
• Mechanisms of Phase Separation
• Validation of Modeling
• Conclusions and Future Work
• Acknowledgement
Nanomanufacturing Through High-rate/High-volume Templates for Guided Assembly of Nanoelements
Surface functionalization
Templates directed phase separation
Introduction
• Spinodal decomposition– Phase separation can
be induced by small composition fluctuations
– The spinodal decomposition can be directed by substrate functionalization
Local Free Energy in Ternary Blend
Ternary phase diagram
Spinodal line
Starting point of phase separation
Free energy of ternary mixture
Introduction to Numerical Simulation
Template Resulting concentration:
• Modelling assumptions– Random distribution initial situation– Incompressible fluid– Isothermal– Bulk-diffusion-controlled coarsening– Evaporation rate: h=h0exp(t)
Fundamentals
• The total free energy of the ternary (Cahn-Hilliard equation),
The initial and final thickness of the film is measured experimentally. The evaporation constant , in h=hexp(t) can then be determined. The faster the rotation speed, the faster the evaporation, the smaller the The faster rotation speed results in a smaller R value, due to the effects of the faster solvent evaporationIncrease in the mobility, M, or in the value of result in larger domain size. Higher mobility will amplify the effects of the rotation speed.
Validation with the Experiments-- with the Patterned Substrate
Measure of the compatibility parameter, Cs
Experiment: SEM images are compared with the template patterns
, and the greater the better match of the morphologyto the pattern substrate.
Simulation: Comparison of result pattern and substrate template are compared element by element
s1(k) - the parameter in the surface energy expression for polymer oneSk - the quantitative representation of the substrate attraction.
Different Pattern Strip Widths
The pattern size has to match the intrinsic R value The simulation results generally matches the experimental value
Different PS:PAA Weight Ratios
The volume ratio of PS/PAA has to match the functionalized pattern area ratio
Effects of PAA Mw
The molecular weight of PAA will affect the shape of the Flory-Huggins local free energy Smaller molecular weight results in a more compatible pattern
Self-assembly in Thick Film
Initial thickness: 1mm, final thickness 8 m
Thickness dimension scaled by 2:1
The phase separation in the bulk domain will affect the morphology in the surface in a thick film
4m
8m
2m
128
64
64
More Complicated Substrate Pattern
Substrate pattern directed phase separation with different attraction forces
The substrate pattern
12m
12m
Graphic User Interface Program in MATLAB and C
Conclusion
The 3D numerical model for ternary system is established
The evolution mechanism is investigated. The R(t)∝t1/3 rule is fitted.
The model is fully tested and the numerical results are validated with the experimental results
The parameters are benchmarked, such as the mobility the gradient energy coefficient, and the surface energy M=3.63E-22m5/(J*s), =1.82E-7J/m, |fs|=4.82E3J/m2
Effects of different parameters are investigated. Recommendations for processing parameters
A GUI program is developed and tested, which can be used to assist the experiment and theoretical work.
Acknowledgement• Advisor, Professor David O. Kazmer
• Professor Joey Mead and Professor Carol Barry
• Liang Fang and Dr. Ming Wei assisted in the experimental results
• Center of High rate Nano-manufacture at UMass Lowell
• National Science Foundation funds (#NSF-0425826)