Computational Polymer Field Theory: Revisiting the Sign Problem

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

Nontechnical Summary This project will build on recent developments by the PIs and co-workers of the field-theoretic simulation method, enabling direct numerical investigations of field theory models of polymers and soft materials without approximation. This framework permits efficient computer simulations to be conducted for a wide variety of complex fluids, polymers and soft materials and is particularly effective for dense, high molecular weight, self-assembling polymer systems. The proposed research aims to make fundamental breakthroughs in the methodology for conducting simulations, which should enable up to two orders of magnitude acceleration in computational design of soft materials for emerging applications in microelectronics patterning, water purification, and energy and medical devices. Broader impacts of the proposed research include a continuance of the PIs' strong record in graduate and post-doctoral training in theoretical and computational polymer science. A particular focus will be to expose students and post-docs with classical physics training to broader soft materials/polymer science disciplines through a close coupling with experimental groups at UCSB in chemical engineering, materials, and chemistry. The fundamental understanding gained under the proposed project will be further leveraged through the Complex Fluids Design Consortium at UCSB, an industry-national lab-academic partnership that is addressing the computational design of commercial polymer and complex fluid formulations. Technical Summary This project will build on recent developments by the PIs and co-workers of the field-theoretic simulation method, enabling direct numerical investigations of field theory models of polymers and soft materials without resorting to the mean-field approximation. The proposed research aims to make fundamental, transformative breakthroughs in understanding and methodology by challenging current approaches to the "sign problem" associated with complex-valued models. The PIs' approach will enable studies of entirely new classes of polymers and soft materials and applications to emerging polymer technologies. Specific components of the project include: 1. Complex to real mapping methods. Methods will be developed for systematic mapping of (d+1)-dimensional complex-valued microscopic polymer field theory models to d-dimensional real-valued, density explicit models. Such a methodology will enable highly efficient simulations of diverse families of nano-structured polymers on unprecedented length scales. 2. Hybrid Monte Carlo -Complex Langevin methods. The PIs will utilize a new "basis function free" approach inspired by hybrid quantum-classical treatments of hard condensed matter. This technique will offer improved stability and enable a diverse set of sampling options, e.g. force-bias Monte Carlo method and flat histogram methods. 3. Applications to challenging polymer morphology problems. The new field-theoretic simulation methods developed in this program will be used to address difficult materials problems such as recently discovered "bricks-and-mortar" fluctuation-stabilized phases in mikto-arm polymer alloys. The computational efficiency gains will be exploited in studies guiding directed self-assembly approaches to advanced lithography. Broader impacts of the proposed research include a continuance of the PIs strong record in graduate and post-doctoral training in theoretical and computational polymer science. A particular focus will be to expose students and post-docs with classical physics training to broader soft materials/polymer science disciplines through a close coupling with experimental groups at UCSB in chemical engineering, materials, and chemistry. The fundamental understanding gained under the proposed project will be further leveraged through the Complex Fluids Design Consortium at UCSB, an industry-national lab-academic partnership that is addressing the computational design of commercial polymer and complex fluid formulations.