Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellization, emulsion formation, and polymer mixing are well understood. However, the principles behind emergence of structures with competing length scales in soft matter systems remain unknown. Examples include droplet-inside-droplet assembly in many biomacromolecular systems undergoing liquid-liquid phase separation, analogous multiple emulsion formation in oil-surfactant-water formulations, and polymer core-shell particles with internal structure. We develop here a microscopic theoretical model based on effective interactions between the constituents of a soft matter system to explain self-organization both at single and multiple length scales. The model identifies how spatial ordering at multiple length scales emerges due to competing interactions between the system components, e.g., molecules of different sizes and different chemical properties. As an example of single and multiple length scale assembly, we map out a generic phase diagram for a solution with two solute species differing in their mutual and solvent interactions. We further connect the phase diagram to a molecular system via molecular simulations of a block-copolymer system that has a transition from regular single-core polymer particles to multicore aggregates that exhibit multiple structural length scales. The findings provide guidelines to understanding the length scales rising spontaneously in biological self-assembly but also open venues to the development and engineering of biomolecular and polymeric functional materials and pharmaceutical formulations.

中文翻译：

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具有多种长度尺度的软物质中的自组装

分子系统中的自发自组装是获得生物和工程软物质的基本途径。简单的胶束化，乳液形成和聚合物混合是众所周知的。但是，在软物质系统中出现具有竞争性长度尺度的结构背后的原理仍然未知。例子包括在许多经历液相-液相分离的生物大分子系统中的液滴-内部-液滴组装，在油表面活性剂-水制剂中类似的多重乳液形成以及具有内部结构的聚合物核-壳颗粒。我们在此建立一个基于软物质系统各组成部分之间有效相互作用的微观理论模型，以解释单个和多个长度尺度上的自组织。该模型确定了由于系统组件（例如，不同大小和不同化学性质的分子）之间的竞争性相互作用，如何在多个长度尺度上出现空间排序。作为单长度和多长度刻度装配的示例，我们绘制了一种具有两种溶质物种在相互和溶剂相互作用方面不同的溶液的通用相图。我们进一步通过嵌段共聚物系统的分子模拟将相图连接到分子系统，该嵌段共聚物系统具有从规则的单核聚合物颗粒过渡到显示多种结构长度尺度的多核聚集体的功能。