Computational Polymer Field Theory: Revisiting the Sign Problem

该项目将建立在pi及其同事的场论模拟方法的最新发展基础上，使聚合物和软材料的场论模型无需近似即可直接进行数值研究。该框架允许对各种复杂流体、聚合物和软材料进行有效的计算机模拟，对致密、高分子量、自组装的聚合物系统特别有效。拟议的研究旨在在进行模拟的方法上取得根本性的突破，这应该能够在微电子图案，水净化，能源和医疗设备等新兴应用的软材料的计算设计中加速两个数量级。拟议研究的更广泛影响包括继续pi在理论和计算聚合物科学的研究生和博士后培训方面的良好记录。通过与加州大学圣迭戈分校化学工程、材料和化学实验组的密切合作，将重点放在让接受过经典物理训练的学生和博士后接触更广泛的软材料/聚合物科学学科。UCSB的复杂流体设计联盟是一个工业-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，该联盟将进一步利用在拟议项目中获得的基本知识。该项目将建立在pi及其同事的场论模拟方法的最新发展基础上，使聚合物和软材料的场论模型无需诉诸平均场近似即可直接进行数值研究。提出的研究旨在通过挑战当前与复值模型相关的“符号问题”的方法，在理解和方法上取得根本性的、变革性的突破。pi的方法将使研究全新种类的聚合物和软材料以及新兴聚合物技术的应用成为可能。项目的具体组成部分包括：1。复到实的映射方法。将开发（d+1）维复值微观聚合物场理论模型到d维实值密度显式模型的系统映射方法。这种方法将能够在前所未有的长度尺度上高效地模拟不同家族的纳米结构聚合物。混合蒙特卡罗-复朗之万方法。pi将利用一种新的“无基函数”方法，这种方法的灵感来自于硬凝聚物质的混合量子经典处理。该技术将提供改进的稳定性，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. 具有挑战性的聚合物形态问题的应用。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，例如最近发现的mikto-arm聚合物合金中的“砖块和砂浆”波动稳定相。计算效率的提高将用于指导先进光刻技术的定向自组装方法的研究。拟议研究的更广泛影响包括继续pi在理论和计算聚合物科学的研究生和博士后培训方面的良好记录。通过与加州大学圣迭戈分校化学工程、材料和化学实验组的密切合作，将重点放在让接受过经典物理训练的学生和博士后接触更广泛的软材料/聚合物科学学科。UCSB的复杂流体设计联盟是一个工业-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，该联盟将进一步利用在拟议项目中获得的基本知识。

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.