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),

– F : total free energy– f : local free energy

– : the composition gradient energy coefficient

– Ci : the composition of component i

Mass Flux

• Ji, net

: the net mass flux

• Mi : mobility of component i

• i: chemical potential of component i

• Ci : composition of component i

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

Fundamentals

Cahn-Hilliard Equation

C1+C2+C3=1

Mass flux: ,

– i,j : represent component 1 and component 2.– Mij : mobility

Determination of Controlling Factors• Flory-Huggins interaction parameter,

– 12,c

: critical interaction parameter. >12,c

for spinodal

decomposition to occur.

– Determines the miscibility of the polymer pair

–

–

– i: solubility parameter of component i

– The difficulties to obtain accurate solubility parameters.

– =0.221, when m1=174,m2=22

– 12,c

=0.0417

Determination of Controlling Factors

• Gradient energy coefficient,

– 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 and D are estimated by benchmarking with the experimental results, as shown later.

Numerical Method

• Discrete cosine transform method for PDEs

– and are the DCT of and – is the transformed discrete Laplacian,

Outline

• 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

Constant Solvent Concentration

Polymer 1 Polymer 2 Solvent Polymer 1 Polymer 2 Solvent

t*=1024

t*=4096

t*=2048

(a) (b)

(a) Csolvent=60% (b) Csolvent=30%

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

0.3690.341

Results in a Binary (Annealing) System:With Patterns

64Characteristic length

Phase Separation with Solvent Evaporation

Lz=L0exp(-a*t), where t is the time, a is a constant, and Lz is the thicknessof the film at time t, and L0 is the thickness at t=0

Polymer 1 Polymer 2 Solvent

Time

Effects of Solvent and Evaporation

The compatibility, Cs, on the solution-substrate interface evolution with time.

Outline

• Introduction

• Mechanisms of Phase Separation

• Validation of Modeling− Summary

− Determination of parameters

− Effects of processing conditions

• Conclusions and Future Work

• Acknowledgement

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

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

Determination of M and

After comparison of the simulation and the experimental results

M=3.63·10-21 m5/(J*s)=1.82·10-7J/m

Experimental condition:• Spin coating speed: 3000 rpm• Time: 30 seconds• Solvent w%: 99%• PS/PAA (weight) : 7:3

Characteristic length, R=0.829m

Experiment

Experiment

The Effects of the Rotation Speed

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)

• All the people helped in this work

• Professor Jan Huang

• Ms. Lois Heath, and Ms. Adrianna Morris

• Ms. Ying Zeng