1. UNIVERSITY OF MASSACHUSETTS LOWELL
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 1

2. Outline Introduction Mechanisms of Phase Separation
Thermodynamics
Numerical assumptions
Theoretical fundamentals
Numerical methods
Mechanisms of Phase Separation
Validation of Modeling
Conclusions and Future Work
Acknowledgement

3. Nanomanufacturing Through High-rate/High-volume Templates for Guided Assembly of Nanoelements
Surface functionalization
Templates directed phase separation

4. Introduction Spinodal decomposition
Phase separation can be induced by small composition fluctuations
The spinodal decomposition can be directed by substrate functionalization

5. Local Free Energy in Ternary Blend
Spinodal line
Starting point
of phase separation
Free energy of ternary mixture
Ternary phase diagram

6. 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) 6

7. Fundamentals
The total free energy of the ternary (Cahn- Hilliard equation),
F : total free energy
f : local free energy
: the composition gradient energy coefficient
Ci : the composition of component i 7

8. Mass Flux Ji, net : the net mass flux Mi : mobility of component i
mi: chemical potential of component i
Ci : composition of component i 8

9. Flory-Huggins Free Energy
The bulk free energy
R : gas constant
T : absolute temperature
mi : degree of polymerization of i
Greater D. P., higher energy barrier for mixing
ij : immiscibility parameter of i and j
vsite: Molar volume of reference site 9

10. Fundamentals Cahn-Hilliard Equation C1+C2+C3=1 Mass flux: ,
i,j : represent component 1 and component 2.
Mij : mobility 10

11. Determination of Controlling Factors
Flory-Huggins interaction parameter, c
c12,c : critical interaction parameter. c>c12,c for spinodal decomposition to occur.
Determines the miscibility of the polymer pair
di: solubility parameter of component i
The difficulties to obtain accurate solubility parameters.
c =0.221, when m1=174,m2=22
c12,c =0.0417 11

12. Determination of Controlling Factors
Gradient energy coefficient, k
a : Monomer size, the affecting radius of van de Waals force
Determines the domain size and interface thickness
D: Diffusivity
Determines the kinetics of the phase transaction.
The values of k and D are estimated by benchmarking with the experimental results, as shown later. 12

13. Numerical Method Discrete cosine transform method for PDEs
and are the DCT of and
is the transformed discrete Laplacian, 13

14. Outline Mechanisms of Phase Separation Validation of Modeling
‏Introduction
Mechanisms of Phase Separation
Linear relation of log(R)~log(t)
Pattern size should match the value of R
Effects of solvent and evaporation
Validation of Modeling
Conclusions and Future Work
Acknowledgement 14

15. Constant Solvent Concentration
Polymer 1 Polymer Solvent
Polymer Polymer Solvent
t*=1024
t*=4096
t*=2048
(a)‏
(b)‏
(a) Csolvent=60%
(b) Csolvent=30% 15

16. Constant Solvent Concentration
Measurement of the characteristic length, R
Index numbers are shown on the figure
The evolution of the domain size, R(t)~t, fits the rule that R(t)∝t1/3
0.369
0.341 16

17. Results in a Binary (Annealing) System: With Patterns
Characteristic length 64 17

18. Phase Separation with Solvent Evaporation
Lz=L0exp(-a*t), where t is the time, a is a constant, and Lz is the thickness of the film at time t, and L0 is the thickness at t=0
Time
Polymer 1
Polymer 2
Solvent 18 18

19. Effects of Solvent and Evaporation
The compatibility, Cs, on the solution-substrate interface evolution with time.

20. Outline Mechanisms of Phase Separation Validation of Modeling
‏Introduction
Mechanisms of Phase Separation
Validation of Modeling
Summary
Determination of parameters
Effects of processing conditions
Conclusions and Future Work
Acknowledgement 20

21. Validation Experiments
Chemically heterogeneous substrate on Au surface
Ebeam lithography followed by self-assembly of alkanethiol monolayer
Hydrophylic strips covered by 11-Amino-1-undecanthiol (NH2)
Hydrophobic strips covered by 1-octadecanethiol (ODT)
Ternary system of polymers used
Polyacrylic acid (PAA): Negative static electrical force
Polystyrene (PS): Hydrophobic
Dimethylformamide (DMF): Solvent, on the order of 98% weight
Experimental procedure
Polymer solution placed on substrate by pipette
6 minutes quiescence at room temperature and low humidity
Polymer solution spin coated at varying RPM for in 30 seconds

22. Validation Experiments
Investigated factors
Spin coating speed: 1000rpm, 3000rpm, 7000rpm
Pattern substrate strip width: 667nm, 1000nm, 133nm
Polymer composition ratio PS/PAA: 30/70, 50/50, 70/30
Molecular weight of PAA: 2k, 50k, 450k
Image acquisition
Field emission scanning electron microscopy (JEOL 7401)
Atomic force microscopy (non-contact mode, Veeco NanoScopella)
Fourier transform analysis (PSIA, v. 1.5)
Model parameters then tuned by inspection of experimental and simulation results

23. Determination of M and k
Experimental condition:
Spin coating speed: rpm
Time: 30 seconds
Solvent w%: 99%
PS/PAA (weight) : 7:3
Characteristic length, R=0.829mm
Experiment
Experiment
After comparison of the simulation and the experimental results
M=3.63·10-21 m5/(J*s)
k=1.82·10-7J/m

24. The Effects of the Rotation Speed
The initial and final thickness of the film is measured experimentally. The evaporation constant a, in h=hexp(at) can then be determined.
The faster the rotation speed, the faster the evaporation, the smaller the a (a<0)
The faster rotation speed results in a smaller R value, due to the effects of the faster solvent evaporation
Increase in the mobility, M, or in the value of k result in larger domain size.
Higher mobility will amplify the effects of the rotation speed.

25. Validation with the Experiments -- with the Patterned Substrate
Measure of the compatibility parameter, Cs
Experiment: SEM images are compared with the template patterns
Simulation: Comparison of result pattern and substrate template are compared element by element
s1(k) - the parameter in the surface energy expression for polymer one
Sk - the quantitative representation of the substrate attraction.
, and the greater the better match of the morphology to the pattern substrate.

26. Different Pattern Strip Widths
The pattern size has to match the intrinsic R value
The simulation results generally matches the experimental value

27. Different PS:PAA Weight Ratios
The volume ratio of PS/PAA has to match the functionalized pattern area ratio

28. 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

29. Self-assembly in Thick Film
128 64 64
4mm
8mm
2mm
Initial thickness: 1mm, final thickness 8 mm
Thickness dimension scaled by 2:1
The phase separation in the bulk domain will affect the morphology in the surface in a thick film

30. More Complicated Substrate Pattern
12mm
12mm
The substrate pattern
Substrate pattern directed phase separation with different attraction forces

31. Graphic User Interface Program in MATLAB and C

32. 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), k=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. 32

33. 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 )‏
All the people helped in this work
Professor Jan Huang
Ms. Lois Heath, and Ms. Adrianna Morris
Ms. Ying Zeng 33

34. 34