Simulation of Polymer Morphology in Nano-feature Replication Yingrui Shang & David Kazmer Department of Plastics Engineering UML Nanomanufacturing Center

Objective Application Fast fabrication of polymer products with nano-scale features  Template guided self- assembly in a polymer blends/block copolymers.

Objective Use a 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 and material properties on morphology Center of the model Patterned substrate Surface induced self-assemble Minor polymer droplets Matrix Polymer B Polymer A

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 The descriptions of droplet radius-time dependence are generally the same: The derivations of k are different according to the mechanisms and observed results. Average radii of droplets at time t and t 0, respectively Constant to be determined.

Ostwald Ripening Small droplet Matrix of polymer A with dissolved polymer B of concentration C m More dilute More concentrated Small droplets dissolve and large ones grow R increases until R c R c is dependent on the concentration C m C m reaches a critical value C c m R Big droplet Polymer B

Brownian Coalescence I IIIIIIV I. Approach of the droplets II. Removal of the continuous phase III. Rupture of the laminar between droplets IV. Formation of the dumbbell shape V. Resulting droplet Coalescence of the particles is the dominate effect; Five steps in the process of coalescence. V

Simulation of Coalescence in the Bulk Polymers Governing Eq.s  Incompressible fluids  Mass conservation Velocity vector Interface velocity Vector normal to the interface Characterization function 1 in phase 1, 0 in phase 2 Draw a control volume

Simulation of Coalescence in the Bulk Polymers Governing Eq.s  Navier Stokes Equation (Momentum Conservation) Denotes the influence of the capillary force. Characterizatio n function Curvature of interface Interfacial tension Draw a figure of capillary force

Simulation of Coalescence in the Bulk Polymers Finite element method Polymer B Polymer A Interface position determined by the volume fraction in each element Volume fraction in elements In each element: Continuity equation Momentum conservation Mass conservation

Self-assembly of Microstructures Near Patterned Surfaces Governing Eq. Free energy per lattice site Chain length of polymer A Chain length of polymer B Volume fraction of A Florry-Huggins parameter Draw a figure of G vs phi

Self-assembly of Microstructures Near Patterned Surfaces Patterned Surface Surface domain is concentrated by the component with the lower free energy. Free energy profile for each element Polymer B Polymer A Cahn-Hilliard Simulation What’s this?

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

Future 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