Theoretical Studies of Inhomogeneous Polymers

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A comprehensive theoretical and computational investigation of the equilibrium properties on inhomogeneous polymers will be carried out. The research will build on the recent developments by the PI and co-workers on the field-theoretic computer simulation (FTS) method, enabling numerical investigations of field theory models of polymers and complex fluids without any simplifying assumptions such as the mean-field approximation. The research will have the following components: (1) Foundations of the FTS method: This will include development of improved algorithms for solving the complex diffusion equation central to the method and development of efficient numerical schemes for time integration of the complex Langevin equations used to implement chemical potential field updates. Real-space renormalization group theory will also be applied to isolate lattice cutoff effects and to enable systematic coarse-graining of polymer solution models. (2) Micelle phases in copolymer alloys: The FTS method will be applied to investigate micelle formation in block copolymers-homopolymer blends near mesophase unbinding transitions, where mean-field theory is expected to fail. (3) Block and graft copolymer systems with chemical disorder: Simplified models of poydisperse star-block and graft-block copolymers will be constructed in which both annealed and quenched disorder averages can be exactly carried out. The models will be numerically and analytically investigated to study the differences in self-assembly behavior between systems with the two types of disorder, the role of fluctuation effects, and the existence of compositional glass transitions. The overall objective is to gain a fundamental understanding of how chemical disorder, unavoidable in commercial copolymer materials, influences structure and thermodynamics. (4) Defect control in thin copolymer films: Translational and bond-orientational order will be examined in FTS simulations of block copolymer films with special perimeter boundary conditions. The results will be used to assess the efficacy of graphoepitaxy for creating defect-free copolymer films that can be used in ultra-high density patterning of advanced electronic, optical, and magnetic devices. The research will be closely coupled with experiments in the laboratory of E.J. Kramer at UCSB. The research will involve training of graduate students and post-doctoral researchers. The fundamental understanding gained through this project will be leveraged through a new Complex Fluids Design Consortium at UCSB, an industry-national lab-academic partnership that will address computational design of industrial polymer and complex fluid formulations.%%%A comprehensive theoretical and computational investigation of the equilibrium properties on inhomogeneous polymers will be carried out. The research will involve training of graduate students and post-doctoral researchers. The fundamental understanding gained through this project will be leveraged through a new Complex Fluids Design Consortium at UCSB, an industry-national lab-academic partnership that will address computational design of industrial polymer and complex fluid formulations.***