RESULTSRESULTS

The self-assembly of polymer blends directed by a patterned substrate is a promising methodfor rapid nano-manufacturing.

The numerical simulation of this process can be used to investigate the mechanism of the evolution and to estimate the material properties & optimal process parameters.

• The 3D numerical model for ternary system is established

• The evolution mechanism is investigated, and verifies that R(t)∝t1/3 rule as expected.

• The simulation is validated by the experiments

• A method to benchmark the immeasurable parameters by comparison of the simulation and the experimental results are developed.

• The patterned substrate is implemented into the ternary system with solvent evaporation

• The effects of different parameters, such as the spin coating rotation speed, polymer weight ratios, and the PAA molecular weight are investigated.

• The numerical results are compatible with the experimental results and can be used to assist the experimental and theoretical work.

The Cahn-Hilliard equation for a ternary system is established as:

F: total free energy

f: local free energy

: the composition gradient energy coefficient

Ci: the composition of component i

The system then can be described as a function of the compositions. Considering C

1+C

2+C

3=1, yhe

evolution equation can then be written as a function of only C

1 and C

2,

i,j: represent components 1 and component 2.

Mij: mobility of component i through j

The mobility M should is a function of the compositions of polymer 1 and polymer 2. The free energy of ternary system can be plotted in a 3D view. The spinodal line can also be calculated.

CONCLUSIONSCONCLUSIONS

Numerical Simulation of the Phase Separation of a Ternary Systems on a Heterogeneously Functionalized Substrate

Yingrui Shang, Liang Fang, David Kazmer, Ming Wei, Joey Mead, and Carol BarryUniversity of Massachusetts Lowell

BACKGROUNDBACKGROUND

APPROACHAPPROACH• A numerical model for a polymer-polymer-

solvent ternary system has been established.

• The free energy profile of the domain is described by the Cahn-Hilliard equation.

• The discrete cosine transform method is used to to solve the evolution equation with numerical stability and efficiency.

• The functionalization of the template is implemented numerically, and the relation of the domain size and the time are investigated.

SIGNIFICANCESIGNIFICANCE

• The numerical model can be used to investigate the evolution mechanism of the phase separation.

• The optimized parameters can be virtually established from numerical & sensitivity studies.

• Materials parameters which are difficult to measure can also be estimated via the simulation.

• A user friendly software can be designed to assist the experiments and practical production.

Nanoscale Science and Engineering Center for High-rate NanomanufacturingEEC-0425826

Spinodal line

Starting point of phase separation

Ternary phase diagram

Free energy of ternary mixture

The morphology evolution of a polymer-polymer-solvent ternary phase separation with a initial random distribution, where Cpolymer 1=Cpolymer 2.

The influence of the concentration of the solvent on the interface of the two polymer domains is significant.

The evolution of the domainsize, R(t)~t, which fits therule that R(t)∝t1/3

And it can be see that the less the solvent, the faster the agglomeration of the domains.

Experimental results Simulation results

Polymer 1 Polymer 2 Solvent Polymer 1 Polymer 2 Solvent

t*=1024

t*=4096

t*=2048

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

1

10

100 1000 10000

t*

R(t)

C3=0.20C3=0.35Series3Power (Series3)

Elements

64

16128

MATERIALS/PROCESSESMATERIALS/PROCESSES

Experimental system: PS/PAA/DMF ternary solution spin coated in 3000rpm in 30 s. Patterned substrate: ODT/NH2. The characteristic length, R, and the compatibility parameter, Cs, are measured from the SEM images.

The solvent evaporation is considered and the simulation is compared with the experimental results.To determine the mobility, M, and the gradient energy coefficient, the simulation is benchmarked with the experimental results.

Effect of different parameters

The faster rotation speed results in a smaller R value, due to the effects of the faster solvent evaporation

The pattern size has to match the intrinsic R value The simulation results generally matches the experimental value

The volume ratio of PS/PAA has to match the functionalized pattern area ratio

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