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Numerical Simulation of the Phase Separation of a Ternary System on a

Heterogeneously Functionalized Substrate

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

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ObjectivePhase separation of polymer blends on a patterned substrate

Unguided

Template directed assembly

Highly ordered structures

Polymer A Polymer B

PAA/PS (30/70) polymer blends in a solvent

Ming, Wei et.al., ACS meeting, Spring 2008, New Orleans US

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• Numerical simulation– The morphology in the bulk of the material– The morphology near patterned surfaces– Dynamics of the morphology development– Influence of the process parameters and material

properties on morphology

Experimental results Simulation results

Yingrui Shang & David Kazmer, J. Chem. Phys, 2008, accepted

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Introduction

Template Resulting concentration:

• Modeling assumptions– Random distribution initial situation– Incompressible fluid– Isothermal– Bulk-diffusion-controlled coarsening

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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

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Fundamentals

Cahn-Hilliard Equation

C1+C2+C3=1

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

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Flory-Huggins Free Energy

• The bulk free energy

– R : gas constant– T : absolute temperature

– mi : degree of polymerization of i

– ij : interaction parameter of i and j

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Phase Diagram

Free energy of ternary blends

Phase diagram of ternary blends

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Numerical Method

• Discrete cosine transform method for PDEs

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

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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%

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Evolution Mechanisms

• Measurement of the characteristic length, R

– The evolution of the domain size, R(t)~t, fits the rule that R(t) t∝ 1/3

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Effects of the Patterned Substrate

(a).Csolvent=60%;

(b).Csolvent=50%;

(c). Csolvent=40%;

(d). Csolvent=30%,

where Cpolymer 1=Cpolymer 2, t*=4096

The more condensed the blends, the higher surface attraction needed for a refined pattern. This may be due to the stronger intermolecular force of the polymers.

(a)

(b)

(c)

(d)

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Phase Separation with Solvent Evaporation

Lz=L0+exp(-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

t*=1024, Csolvent=0.088

t*=2048, Csolvent=0.018

t*=4096, Csolvent=0

Polymer 1 Polymer 2 Solvent

Time

Thickn

ess

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Compatibility of the Substrate Pattern to the Blend Surface

• Compatibility between template and ternary system is measured by Cs defined as:

• Examples:

– Cs=0.606

– Cs=0.581

– Cs=0.413

– Cs=0.376

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Compatibility of the Substrate Pattern to the Blend Surface

• There is a critical time and solvent for the evolution of Cs

• Cs will decrease for lower solvent concentrations• The evaporation will stabilize the decrease of Cs

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Conclusion

– The 3D numerical model for ternary system is established

– The evolution mechanism is investigated. The R(t) t∝ 1/3 rule is fitted.

– The condensed system has a faster agglomeration pace.

– In the situation with patterned substrate the condensed solution patterns evolute faster in the early stage but in the late stage the surface pattern tends to phase separate randomly.

– The evaporation of the solvent can stabilize the replication of the patterns according to the patterned substrate.

– The modelling will be verified by the experiment data in the spin coating of polymer solvent

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Acknowledgement

• National Science Foundation funds (#NSF-0425826)

• All the people contributed to this work

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Questions