This study introduces a computational framework for simulating the self-assembly of diblock copolymers using a novel peridynamic (PD)-enhanced Fourier spectral method (FSM). Diblock copolymers, composed of two distinct polymer blocks, are capable of forming nanostructured domains with applications in nanoelectronics, photonics, and advanced membranes. Current simulation techniques face challenges in capturing the multiscale dynamics of polymer systems and are often limited by computational inefficiencies. Our approach combines a phase-field model with FSM for spatial discretization and leverages a PD-based diffusion operator to overcome the stability restrictions of explicit time-stepping schemes. This integration allows for larger time steps, ensuring both stability and computational efficiency. The method’s scalability is enhanced through parallel implementation using C++ and OpenMP, optimized for multi-core CPUs. Validation through phase diagrams of copolymer melts and simulations of evaporation-induced self-assembly (EISA) processes demonstrates the capability of the proposed method to accurately capture large-scale, dynamic morphologies. Our approach provides a versatile framework and was found in certain examples to improve computational efficiency by more than a factor of 6 compared to forward-Euler FSM approach.

中文翻译：

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使用近场动力学增强傅里叶光谱法对自组装二嵌段共聚物进行高效模拟


本研究介绍了一种计算框架，用于使用新型近动力 （PD） 增强傅里叶光谱法 （FSM） 模拟二嵌段共聚物的自组装。二嵌段共聚物由两个不同的聚合物嵌段组成，能够形成纳米结构域，应用于纳米电子学、光子学和高级膜。当前的仿真技术在捕获聚合物系统的多尺度动力学方面面临挑战，并且通常受到计算效率低下的限制。我们的方法将相场模型与 FSM 相结合进行空间离散化，并利用基于 PD 的扩散算子来克服显式时间步长方案的稳定性限制。这种集成允许更大的时间步长，从而确保稳定性和计算效率。通过使用 C++ 和 OpenMP 的并行实现，该方法的可扩展性得到了增强，并针对多核 CPU 进行了优化。通过共聚物熔体的相图和蒸发诱导自组装 （EISA） 过程的模拟进行验证，证明了所提出的方法能够准确捕获大规模、动态形态。我们的方法提供了一个通用的框架，并且在某些示例中发现，与前向 Euler FSM 方法相比，计算效率提高了 6 倍以上。