Numerical Simulation of the Phase Separation of a Ternary Systems on a Heterogeneously Functionalized Substrate Yingrui Shang, Liang Fang, David Kazmer, Ming Wei, Joey Mead, and Carol Barry University of Massachusetts Lowell Center for High-rate Nanomanufacturing . ABSTRACT.
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Numerical Simulation of the Phase Separation of a Ternary Systems on a Heterogeneously Functionalized Substrate Yingrui Shang, Liang Fang, David Kazmer, Ming Wei, Joey Mead, and Carol Barry University of Massachusetts Lowell Center for High-rate Nanomanufacturing ABSTRACT MATERIALS AND METHODS RESULTS • A numerical model for a polymer-polymer-solvent ternary system has been established. • The free energy profile of the domain is described by the Cahn-Hilliard equation. • The discrete cosine transform method is used to to solve the evolution equation with numerical stability and efficiency. • The functionalization of the template is implemented numerically, and the relation of the domain size and the time are investigated. Polymer 1 Polymer 2 Solvent Polymer 1 Polymer 2 Solvent The Cahn-Hilliard equation for a ternary system is established as: F: total free energy f: local free energy : the composition gradient energy coefficient Ci: the composition of component i The system then can be described as a function of the compositions. Considering C1+C2+C3=1, the evolution equation can then be written as a function of only C1 and C2, i,j: represent components 1 and component 2. Mij: mobility of component i through j The mobility M should is a function of the compositions of polymer 1 and polymer 2. The free energy of ternary system can be plotted in a 3D view. The spinodal line is also calculated. 128 64 Elements 16 t*=1024 • Pattern Size: Should match the intrinsic polymer domain size value t*=2048 t*=4096 (a) Csolvent=60% (b) Csolvent=30% The evolution of the domain size, R(t)~t, fits therule that R(t)∝t1/3. The influence of the solvent concentration on the rate of morphology evolutionis significant. The less the solvent, the faster the agglomeration of the domains. • Volume Ratio: Should match the functionalized pattern area ratio SIGNIFICANCE • The numerical model can be used to investigate the evolution mechanism of the phase separation. • The optimized parameters can be virtually established from numerical & sensitivity studies. • Materials parameters which are difficult to measure can also be estimated via the simulation. • A user friendly software can be designed to assist the experiments and practical production. Experimental system:PS/PAA/DMF ternary solution spin coated at 3000rpm in 30 s. Patterned substrate: ODT/NH2. The characteristic length, R, and the compatibility parameter, Cs, are measured from the SEM images. To determine the mobility, M, and the gradient energy coefficient, k, the simulation is benchmarked with the experimental results. • Molecular Weight: Affects the shape of the Flory-Huggins local free energy, with lower molecular weight resulting in a more compatible pattern CONCLUSIONS • The 3D numerical model for ternary system is established. • The evolution mechanism is investigated, and verifies that R(t)∝t1/3 rule as expected. • The simulation is validated by experiments. • A method to benchmark the immeasurable parameters by comparison of simulation and the experimental results are developed. • The patterned substrate is implemented into the ternary system with solvent evaporation. • The effects of different parameters, such as the spin coating rotation speed, polymer weight ratios, and the PAA molecular weight are investigated. • The numerical results are compatible with the experimental results and can be used to assist the experimental and theoretical work. APPLICATIONS • The self-assembly of polymer blends directed by a patterned substrate is a promising method for rapid nano-manufacturing. • The numerical simulation of this process can be used to investigate the mechanism of the evolution and to estimate the material properties & optimal process parameters. MAIN EFFECTS Free energy of ternary mixture Starting point of phase separation Spinodal line • Rotation Speed: The faster rotation speed results in a smaller domain size due to the effects of the faster solvent evaporation. Experimental results Simulation results Ternary phase diagram Nanoscale Science and Engineering Center for High-rate Nanomanufacturing EEC-0425826