Center for High-rate Nanomanufacturing 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

Center for High-rate Nanomanufacturing Objective Phase 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

Center for High-rate Nanomanufacturing 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

Center for High-rate Nanomanufacturing Introduction TemplateResulting concentration: Modeling assumptions –Random distribution initial situation –Incompressible fluid –Isothermal –Bulk-diffusion-controlled coarsening

Center for High-rate Nanomanufacturing Fundamentals The total free energy of the ternary (Cahn- Hilliard equation), –F : total free energy –f : local free energy –  : the composition gradient energy coefficient –C i : the composition of component i

Center for High-rate Nanomanufacturing Fundamentals Cahn-Hilliard Equation C 1 +C 2 +C 3 =1 –i,j : represent component 1 and component 2. –M ij : mobility

Center for High-rate Nanomanufacturing Flory-Huggins Free Energy The bulk free energy –R : gas constant –T : absolute temperature –m i : degree of polymerization of i –  ij : interaction parameter of i and j

Center for High-rate Nanomanufacturing Phase Diagram Free energy of ternary blends Phase diagram of ternary blends

Center for High-rate Nanomanufacturing Numerical Method Discrete cosine transform method for PDEs – and are the DCT of and – is the transformed discrete laplacian,

Center for High-rate Nanomanufacturing Constant Solvent Concentration Polymer 1 Polymer 2 Solvent t * =1024 t * =4096 t * =2048 (a) (b) (a) C solvent =60% (b) C solvent =30%

Center for High-rate Nanomanufacturing 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

Center for High-rate Nanomanufacturing Effects of the Patterned Substrate (a).C solvent =60%; (b).C solvent =50%; (c). C solvent =40%; (d). C solvent =30%, where C polymer 1 =C polymer 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)‏

Center for High-rate Nanomanufacturing Phase Separation with Solvent Evaporation L z =L 0 +exp(-a*t), where t is the time, a is a constant, and L z is the thickness of the film at time t, and L 0 is the thickness at t=0 t * =1024, C solvent =0.088 t * =2048, C solvent =0.018 t * =4096, C solvent =0 Polymer 1Polymer 2Solvent Time Thickness

Center for High-rate Nanomanufacturing Compatibility of the Substrate Pattern to the Blend Surface Compatibility between template and ternary system is measured by C s defined as: Examples: –C s =0.606 –C s =0.581 –C s =0.413 –C s =0.376

Center for High-rate Nanomanufacturing Compatibility of the Substrate Pattern to the Blend Surface There is a critical time and solvent for the evolution of C s C s will decrease for lower solvent concentrations The evaporation will stabilize the decrease of C s

Center for High-rate Nanomanufacturing 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

Center for High-rate Nanomanufacturing Acknowledgement National Science Foundation funds (#NSF ) All the people contributed to this work

Center for High-rate Nanomanufacturing Questions