Simulation of Polymer Morphology in Nano-feature Replication Yingrui Shang & David Kazmer Department of Plastics Engineering UML Nanomanufacturing Center
Application Fast fabrication of polymer products with nano-scale features Template guided self-assembly in a polymer blends/block copolymers. Objective
Objective • Usea numerical simulation method to investigate: • The morphology in the bulk of the material • The morphology near patterned surfaces • Dynamics of the morphology development • Influence of the process parameters andmaterial properties on morphology Patterned substrate Surface induced self-assemble Polymer B Matrix Polymer A Minor polymer droplets Center of the model
Outline • In the bulk material - coarsening of polymer particles • Generally two groups of theories • Ostwald Ripening • Brownian Coalescence • Numerical simulation – volume-of-fluid method • In the surface domain – preference to the component with lower free energy • Free energy profile of the surface domain • Numerical simulation – Cahn-Hilliard simulation • Future work
Coalescence of Polymer Droplets in the Bulk Material • Two theories-Ostwald Ripening and Brownian Coalescence • Thedescriptions of droplet radius-time dependenceare generally the same: • The derivations of kare different according to the mechanisms and observed results. Average radii of droplets at time t and t0, respectively Constant to be determined.
Ostwald Ripening More concentrated More dilute Small droplet R Big droplet Polymer B Matrix of polymer A with dissolved polymer B of concentration Cm • Small droplets dissolve and large ones grow • R increases until Rc • Rc is dependent on the concentration Cm • Cm reaches a critical value Ccm
Brownian Coalescence • Approach of the droplets • Removal of the continuous phase • Rupture of the laminar between droplets • Formation of the dumbbell shape • Resulting droplet I II III IV V • Coalescence of the particles is the dominate effect; • Five steps in the process of coalescence.
Simulation of Coalescence in the Bulk Polymers Draw a control volume • Governing Eq.s • Incompressible fluids • Mass conservation Velocity vector Vector normal to the interface Interfacevelocity Characterization function 1 in phase 1, 0 in phase 2
Simulation of Coalescence in the Bulk Polymers Draw a figure ofcapillary force • Governing Eq.s • Navier Stokes Equation (Momentum Conservation) Denotes the influence of the capillary force. Interfacial tension Curvature of interface Characterization function
Simulation of Coalescence in the Bulk Polymers Finite element method • In each element: • Continuity equation • Momentum conservation • Mass conservation Polymer B Polymer A Interface position determined by the volume fraction in each element Volume fraction in elements
Self-assembly of Microstructures Near Patterned Surfaces Draw a figure ofG vs phi • Governing Eq. Free energy per lattice site Chain length of polymer A Chain length of polymer B Volume fraction of A Florry-Huggins parameter
Self-assembly of Microstructures Near Patterned Surfaces What’s this? Cahn-Hilliard Simulation PatternedSurface Free energy profile for each element Polymer B Polymer A Surface domain is concentrated by the component with the lower free energy.
Self-assembly of Microstructures Near Patterned Surfaces Schematic presentation of free energy profile in the surface and the resulting patterns in a 3-D simulation work
1-D and 2-D numerical simulation in the bulk and surface domains during nano-feature replication 3-D simulation Verification of the simulated data with experimental results PMMA-PS Materials Annealing of spin coated specimens 50 nm by 100 nm domain size with 1 nm element length References I Fortelny, A. Zivny and J. Juza, 1999 L. Kielhorn and M. Muthukumar, 1999 John W. Cahn, 1976 J. H. Jeong and D. Y. Yang, 1998 Ruben Scardovelli and Stephane Zaleski, 1999 Mark Geoghegan and Georg Krausch, 2002 Future Work