聚合物接枝自组装多体势: 机器学习

将纳米颗粒（NPs）掺入聚合物中是一种强有力的策略，可以提高惰性聚合物的热力学性能或引入新的属性（光学、电子、磁性或催化性能）。传统上NPs的表面与聚合物配体接枝，由于聚合物分子在NP中引入排斥力从而能够克服粒子间吸引力。

Fig. 1 Role of three-body interactions in governing the morphology of clusters formed by polymer-grafted NPs.

新的研究发现聚合物接枝也可以用于指导NP组装和获得独特的介观形态，如一维弦和二维薄片。这些低维形态通常表现出与三维对应物（超晶格、球状聚集物）非常不同的功能特性。这种各向异性NP相的形成，来自于NPs之间的高体相互作用，即超过成对距离的粒子高阶排列对自由能的微扰修正。

Fig. 2 Machine learning approach for deriving analytical many-body potentials for modeling the effective interactions between polymer-grafted NPs in a polymer matrix.

然而，在NP组装的模拟中捕获这种相互作用是非常具有挑战性的，这是因为聚合物移植物和熔体链模拟的计算成本非常高。近年来，机器学习（ML）技术已经成为一种有效的工具，以有效地近似多体相互作用的原子系统，并已被用于加速从头计算分子动力学（MD）模拟。

来自杜克大学机械工程与材料科学系的Yilong Zhou等，开发了一种独特的ML方法来发展分析多体势，它可以准确地描述聚合物基体中球形聚合物接枝NPs之间的二体和三体相互作用。

他们的方法包括通过MD模拟计算聚合物基体中NPs的平均力势，并使用置换不变多项式作为粒子间距离库仑变换的函数进行拟合。为了验证所开发的ML势，作者使用它对进行组装的NPs进行MD模拟，并表明所有已知的结构阶段，即一维弦、二维片和三维球状聚集，都被成功复现。

ML势将MD模拟的计算成本降低了至少三个数量级，这使大的长度和时间尺度上的NP组装成为可能，从而发现额外的相。

这一研究成果为材料复合工艺中材料的行为提供了更加准确的研究方案，对材料加工技术有重要意义。相关论文近期发表于npj Computational Materials 9: 224 (2023).

Editorial Summary

The incorporation of nanoparticles (NPs) into polymers is a powerful strategy for improving their thermomechanical propertiesor for introducing new attributes (optical, electronic, magnetic, or catalytic properties) into otherwise inert polymers. The surfaces of the NPs are traditionally grafted with polymer ligands, as the grafts introduce steric (entropic) repulsion between NPs that, if sufficiently large, can overcome the attractive interparticle forces that promote aggregation. However, emerging studies show that polymer grafting can also be used to direct NP assembly and access distinctive mesoscopic morphologies such as 1D strings and 2D sheets. These low-dimensional morphologies often exhibit functional properties very distinct from their 3D counterparts (superlattices, globular aggregates). The formation of such anisotropic NP phases arises from higher-body interactions between NPs, that is, perturbative corrections to the free energy from the higher-order arrangement of particles beyond pairwise distances. However, capturing such interactions in simulations of NP assembly is very challenging because explicit modeling of the polymer grafts and melt chains is highly computationally expensive, even using coarse-grained models. In recent years, machine learning (ML) techniques have been a viable tool to efficiently approximate the many-body interactions in atomistic systems and have been used to speed up ab initio molecular dynamics (MD) simulations. 

Fig. 8 Many-body potential facilitates the exploration of assembly morphologies at different NP core attraction strengths and volume fractions.

Yilong Zhou et al. from the Department of Mechanical Engineering and Materials Science, Duke University, employed ML to develop an analytical potential that can accurately capture many-body interactions between polymer-grafted NPs in a polymer matrix and used the potential to explore NP assembly over large length and time scales. The approach involves the calculation of potentials of mean force for the NPs in the polymer matrix through MD simulations and fitting them using permutationally invariant polynomials cast as functions of Coulomb-transformations of interparticle distances. To validate the developed ML potential, the authors used it to carry out MD simulations of NPs undergoing assembly and showed that all known structural phases, namely the 1D strings, 2D sheets, and 3D globular aggregates, were successfully reproduced. The ML potential reduced the computational cost of MD simulations by at least three orders of magnitude, allowing us to explore NP assembly at large lengths and time scales and thereby discover additional phases. This work provides a more accurate method for the behavior of materials in material composite processes, which is of great significance for material processing technology. This article was recently published in npj Computational Materials 9: 224 (2023).

原文Abstract及其翻译

Many-body potential for simulating the self-assembly of polymer-grafted nanoparticles in a polymer matrix (模拟聚合物接枝纳米粒子在聚合物基体中自组装的多体势)

Yilong Zhou, Sigbjørn Løland Bore, Andrea R. Tao, Francesco Paesani & Gaurav Arya 

Abstract Many-body interactions between polymer-grafted nanoparticles (NPs) play a key role in promoting their assembly into low-dimensional structures within polymer melts, even when the particles are spherical and isotropically grafted. However, capturing such interactions in simulations of NP assembly is very challenging because explicit modeling of the polymer grafts and melt chains is highly computationally expensive, even using coarse-grained models. Here, we develop a many-body potential for describing the effective interactions between spherical polymer-grafted NPs in a polymer matrix through a machine-learning approach. The approach involves using permutationally invariant polynomials to fit two- and three-body interactions derived from the potential of mean force calculations. The potential developed here reduces the computational cost by several orders of magnitude, thereby, allowing us to explore assembly behavior over large length and time scales. We show that the potential not only reproduces previously known assembled phases such as 1D strings and 2D hexagonal sheets, which generally cannot be achieved using isotropic two-body potentials, but can also help discover interesting phases such as networks, clusters, and gels. We demonstrate how each of these assembly morphologies intrinsically arises from a competition between two- and three-body interactions. Our approach for deriving many-body effective potentials can be readily extended to other colloidal systems, enabling researchers to make accurate predictions of their behavior and dissect the role of individual interaction energy terms of the overall potential in the observed behavior.

摘要聚合物接枝纳米颗粒（NPs）之间的多体相互作用在促进它们在聚合物熔体内组装成低维结构方面起着关键作用，即使这些颗粒是球形和各向同性接枝的。然而，在NP组装的模拟中捕获这种相互作用是非常具有挑战性的，因为即使使用粗粒度模型，聚合物移植物和熔体链模拟的计算成本也都非常高。在这里，我们开发了一个多体势，通过机器学习的方法来描述聚合物基体中球形聚合物接枝NPs之间的有效相互作用。该方法涉及使用置换不变多项式来拟合来自平均力计算势的二体和三体相互作用。这里开发的势将计算成本降低了几个数量级，从而使我们能够在很大的长度和时间尺度上探索组装行为。我们发现，该势不仅再现了先前已知的组装相，如一维弦和二维六角形片，这通常不能用各向同性的二体势来实现，而且还可以帮助发现有趣的相，如网络、簇和凝胶。我们展示了这些组装形态本质上是如何从两体和三体相互作用之间的竞争中产生的。我们获得多体有效势的方法可以很容易地扩展到其他胶体系统，使研究人员能够对它们的行为做出准确的预测，并剖析在观察到的行为中整体势能项的个体相互作用。