Numerical simulation for the self-assembly of polymer blends with nano-scaled features

The phase separation of polymer blends is numerically modeled. The free energy profile of the blends in the diffusion controlled process is described by the Cahn-Hilliard equation, which is composed with the local free energy and the gradient energy coefficient. The Flory-Huggins equation is used for the local free energy of the blends. The gradient energy coefficient, kappa, determines the contribution of the gradient to the total free energy.;The phase separation of binary and ternary blends is studied numerically. The mechanisms of the evolution of the phase separation are investigated. It is observed that the characteristic length, R, is proportional to t⅓, where t is the time. In the situation when a strip patterned substrate is present, the characteristic length of the interface of the polymer and substrate is confined by the characteristic length on the pattern in the direction perpendicular to the strip. The composition profile of the phase separation in the lateral direction of the film is also investigated.;The self-assembly of a polymer-polymer-solvent ternary system on a heterogeneously functionalized substrate was investigated in a 3-dimensional numerical model. The numerical results are verified with the experiment result. The experiments are conducted in a system of PS/PAA in DMF solution. The ternary blends were spin coated on a substrate functionalized by MUAM/ODT on Au surface. The experiment parameters are implemented into the simulation. The results are verified with the experiments. The similarity of the simulation and experimental results are measured by a factor, Se. The characteristic length of the simulation and experimental results are also compared. The effects of the parameters such as the composition of polymers, the pattern size, and the attracting force on the substrate are also compared in the simulation and experiment.