Computational Polymer Field Theory: Revisiting the Sign Problem

非技术摘要本项目将建立在最近的发展由PI和同事的场论模拟方法，使直接的数值研究的场论模型的聚合物和软材料没有近似。该框架允许对各种复杂的流体、聚合物和软材料进行有效的计算机模拟，并且对于致密的、高分子量的、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突破，这应该能够使软材料的计算设计加速两个数量级，用于微电子图案化，水净化，能源和医疗设备等新兴应用。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研究生和博士后培训方面的良好记录。一个特别的重点将是通过与UCSB化学工程，材料和化学实验组的紧密结合，使学生和博士后接受经典物理学培训，从而获得更广泛的软材料/聚合物科学学科。在拟议的项目下获得的基本理解将通过UCSB的复杂流体设计联盟进一步发挥作用，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。技术摘要该项目将建立在PI和现场理论模拟方法的同事的最新发展基础上，使得能够直接数值研究聚合物和软材料的场论模型，而无需诉诸平均场近似。拟议的研究旨在通过挑战与复值模型相关的“符号问题”的当前方法，在理解和方法上取得根本性的变革性突破。 PI的方法将使全新类别的聚合物和软材料的研究以及新兴聚合物技术的应用成为可能。该项目的具体内容包括：1。复杂到真实的映射方法。方法将开发系统的映射（d+1）维复值微观聚合物场理论模型的d维实值，密度显式模型。这样的方法将能够在前所未有的长度尺度上高效地模拟不同的纳米结构聚合物家族。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，该方法受到硬凝聚态混合量子经典处理的启发。这种技术将提供更好的稳定性，并使一组不同的采样选项，例如力偏置蒙特卡罗方法和平坦直方图方法。3.应用于具有挑战性的聚合物形态问题。在该计划中开发的新的场论模拟方法将用于解决困难的材料问题，如最近发现的“砖和砂浆”波动稳定相在mikto臂聚合物合金。计算效率的提高将在指导定向自组装方法的研究中得到利用，以先进lithographic.Broader的影响，拟议的研究包括继续PI在理论和计算聚合物科学的研究生和博士后培训的良好记录。一个特别的重点将是通过与UCSB化学工程，材料和化学实验组的紧密结合，使学生和博士后接受经典物理学培训，从而获得更广泛的软材料/聚合物科学学科。在拟议项目下获得的基本理解将通过UCSB的复杂流体设计联盟进一步利用，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.