Computational Polymer Field Theory: Revisiting the Sign Problem

非技术概述本项目将建立在场理论模拟方法的PI和同事的最新发展的基础上，使聚合物和软材料的场理论模型能够在不进行近似的情况下直接进行数值研究。该框架允许对各种复杂流体、聚合物和软材料进行高效的计算机模拟，尤其适用于高密度、高相对分子质量、自组装的聚合物系统。这项拟议的研究旨在实现模拟方法的根本性突破，这将使用于微电子构图、水净化以及能源和医疗设备等新兴应用的软材料的计算设计加速两个数量级。拟议研究的更广泛影响包括继续保持私人投资机构在理论和计算聚合物科学方面的研究生和博士后培训的良好记录。一个特别的重点将是通过与加州大学伯克利分校化学工程、材料和化学的实验小组的密切结合，让接受经典物理培训的学生和博士后接触更广泛的软材料/聚合物科学学科。通过UCSB的复杂流体设计联盟，将进一步利用在提议的项目中获得的基本理解，UCSB是一个行业-国家实验室-学术合作伙伴关系，致力于商业聚合物和复杂流体配方的计算设计。技术概述该项目将建立在场论模拟方法的PI和同事的最新发展的基础上，使聚合物和软材料的场理论模型能够直接进行数值研究，而无需求助于平均场近似。这项拟议的研究旨在通过挑战与复值模型相关的“符号问题”的现有方法，在理解和方法论方面取得根本性的、变革性的突破。PIS的方法将使研究全新类别的聚合物和软材料以及应用于新兴聚合物技术成为可能。该项目的具体组成部分包括：1。复杂到真实的映射方法。将开发将(d+1)维复数值微观聚合物场理论模型系统地映射到d维实数值、密度显式模型的方法。这种方法将能够在前所未有的长度范围内高效地模拟不同的纳米结构聚合物家族。蒙特卡罗复合朗之万法。PI将利用一种新的“无基函数”方法，灵感来自于硬凝聚态物质的量子-经典混合处理。这项技术将提供更好的稳定性，并支持多种采样选项，例如力偏置蒙特卡罗方法和平面直方图方法。3.应用于具有挑战性的聚合物形态问题。在这个项目中开发的新的场论模拟方法将用于解决困难的材料问题，例如最近在微臂聚合物合金中发现的“砖块和砂浆”波动稳定相。计算效率的提高将在指导定向自组装方法实现先进光刻的研究中得到利用。拟议研究的广泛影响包括持续保持PI在理论和计算聚合物科学方面的研究生和博士后培训记录。一个特别的重点将是通过与加州大学伯克利分校化学工程、材料和化学的实验小组的密切结合，让接受经典物理培训的学生和博士后接触更广泛的软材料/聚合物科学学科。通过UCSB的复杂流体设计联盟将进一步利用拟议项目中获得的基本理解，该联盟是一个行业-国家实验室-学术合作伙伴关系，致力于商业聚合物和复杂流体配方的计算设计。

Nontechnical SummaryThis 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 SummaryThis 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.