Transcript Thrust 4 Modeling

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 Barry
University of Massachusetts Lowell
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Objective
Phase separation of polymer blends on a patterned substrate
Polymer A
Polymer B
Unguided
Template directed assembly
Highly ordered
structures
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 (CahnHilliard 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
cij : 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
– l 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*=2048
(a)
t*=4096
(a) Csolvent=60%
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(b)
(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)∝t1/3
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Effects of the Patterned Substrate
(a)
(b)
(c)
(d)
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(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.
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Phase Separation with Solvent Evaporation
t*=1024, Csolvent=0.088
Lz=L0+exp(-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
Polymer 2
Solvent
t*=4096, Csolvent=0
Thickness
Polymer 1
t*=2048, Csolvent=0.018
Time
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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)∝t1/3 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
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