Self-assembly is a fundamental concept in biology and of significant interest to nanotechnology. Significant progress has been made in characterizing and controlling the properties of the resulting structures, both experimentally and theoretically. However, much less is known about kinetic constraints and determinants of dynamical properties like time efficiency, although these constraints can become severe limiting factors of self-assembly processes. Here, we investigate how the time efficiency and other dynamical properties of reversible self-assembly depend on the morphology (shape) of the building blocks for systems in which the binding energy between the constituents is large. As paradigmatic examples, we stochastically simulate the self-assembly of constituents with triangular, square, and hexagonal morphology into two-dimensional structures of a specified size. We find that the constituents’ morphology critically determines the assembly time and how it scales with the size of the target structure. Our analysis reveals three key structural parameters defined by the morphology: the nucleation size and attachment order, which describe the effective order of the chemical reactions by which clusters nucleate and grow, respectively, and the growth exponent, which determines how the growth rate of an emerging structure scales with its size. Using this characterization, we formulate an effective theory of the self-assembly kinetics, which we show exhibits an inherent scale invariance. This allows us to identify general scaling laws that describe the minimal assembly time as a function of the size of the target structure. We show how these insights on the kinetics of self-assembly processes can be used to design assembly schemes that could significantly increase the time efficiency and robustness of artificial self-assembly processes.

中文翻译：

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快速高效的自组装过程的设计原则

自组装是生物学的一个基本概念，对纳米技术具有重要意义。在实验和理论上表征和控制所得结构的性能方面已经取得了重大进展。然而，人们对动力学约束和动力学特性（如时间效率）的决定因素知之甚少，尽管这些约束可能成为自组装过程的严重限制因素。在这里，我们研究了可逆自组装的时间效率和其他动力学特性如何取决于成分之间的结合能较大的系统的构建块的形态（形状）。作为范例，我们随机模拟具有三角形、正方形和六边形形态的成分自组装成指定尺寸的二维结构。我们发现成分的形态关键决定了组装时间以及它如何随目标结构的尺寸缩放。我们的分析揭示了由形态定义的三个关键结构参数：成核尺寸和附着顺序，它们分别描述了簇成核和生长的化学反应的有效顺序，以及生长指数，它决定了簇的生长速率新兴结构与其规模成比例。利用这种表征，我们制定了有效的自组装动力学理论，我们证明该理论表现出固有的尺度不变性。这使我们能够确定一般的缩放定律，将最小组装时间描述为目标结构尺寸的函数。我们展示了如何利用这些关于自组装过程动力学的见解来设计组装方案，从而显着提高人工自组装过程的时间效率和鲁棒性。