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Yingrui Shang, David Kazmer, Ming Wei, Joey Mead, and Carol Barry

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. Objective. Polymer A. Polymer B. Unguided. Template directed assembly.

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Yingrui Shang, David Kazmer, Ming Wei, Joey Mead, and Carol Barry

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  1. 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

  2. Objective Polymer A Polymer B Unguided Template directed assembly Highly ordered structures Phase separation of polymer blends on a patterned substrate PAA/PS (30/70) polymer blends in a solvent Ming, Wei et.al., ACS meeting, Spring 2008, New Orleans US

  3. Experimental results Simulation results • 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 Yingrui Shang & David Kazmer, J. Chem. Phys, 2008, accepted

  4. Introduction Modeling assumptions Random distribution initial situation Incompressible fluid Isothermal Bulk-diffusion-controlled coarsening Template Resulting concentration:

  5. 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

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

  7. 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

  8. Phase Diagram Free energy of ternary blends Phase diagram of ternary blends

  9. Numerical Method • Discrete cosine transform method for PDEs • and are the DCT of and • lis the transformed discrete laplacian,

  10. Constant Solvent Concentration Polymer 1 Polymer 2 Solvent Polymer 1 Polymer 2 Solvent t*=1024 t*=2048 t*=4096 (b) (a) (b) Csolvent=30% (a) Csolvent=60%

  11. 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

  12. Effects of the Patterned Substrate (a)‏ (b)‏ (c)‏ (d)‏ (a).Csolvent=60%; (b).Csolvent=50%; (c). Csolvent=40%; (d). Csolvent=30%, where Cpolymer1=Cpolymer2, 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.

  13. Phase Separation with Solvent Evaporation Polymer 1 Polymer 2 Solvent Thickness Time t*=1024, Csolvent=0.088 t*=2048, Csolvent=0.018 t*=4096, Csolvent=0 Lz=L0+exp(-a*t), where t is the time, a is a constant, andLz is the thicknessof the film at time t, and L0 is the thickness at t=0

  14. 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

  15. 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

  16. 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

  17. Acknowledgement • National Science Foundation funds (#NSF-0425826) • All the people contributed to this work

  18. Questions

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