发表机构
Universität Leipzig; Instituto IMDEA Nanociencia（莱比锡大学; IMDEA纳米科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构建理论将机理特征（最近邻数k）与共聚物序列空间关联，证明机理可映射到de Bruijn图，揭示周期性序列数量爆炸性增长，并制定简单组装规则（SAR）以描述和设计文献系统。
AI 中文摘要
聚合物化学中的结构观察通常通过潜在的机理见解来合理化。对机理家族——以及可能伴随它们的现象学和规律性行为——的研究较少见。在这里，我们构建了一个理论，将机理特征——影响单体掺入的最近邻数$k$——与可访问的共聚物序列空间联系起来。我们发现反应机理可以一一映射到度为$k$的正则de Bruijn图。我们计算了作为邻位数$k$和单体数$s$函数的周期性共聚物序列。我们表明，周期性序列的数量随$s,k$爆炸性增长，下界为$s!^{s^{k-1}}/s^k$。我们发现周期性k-聚合受几个简单定律支配，这些定律描述了允许的序列、特定反应的数量、重复单元长度以及嵌段共聚物中允许和不允许的序列共存。我们制定了简单组装规则（SAR），以捕捉常见观察到的行为和文献系统的设计，并表征它们根据对称性允许访问的可能k-聚合（$k\leq2$），并用配位化学和超分子化学文献中的报道实例说明我们的发现。我们讨论了形成非平凡（$k>1$）序列的化学-结构贡献，强调了空间位阻、长程相互作用和自由度的重要性。
英文摘要
Structural observations in polymer chemistry are often rationalized through underlying mechanistic insights. The study of families of mechanisms - and the phenomenology and lawlike behavior that can accompany them - is less common. Here we construct a theory that links a mechanistic feature - the number of nearest neighbors $k$ that influence monomer incorporation - with the accessible copolymer sequence space. We find that the reaction mechanisms can be mapped 1-to-1 to a regular de Bruijn graph of degree $k$. We calculate the periodic copolymer sequences as function of neighbor index $k$, and number of monomers $s$. We show that the number of periodic sequences grows explosively with $s,k$, bounded from below by $s!^{s^{k-1}}/s^k$. We find that periodic k-polymerization is governed by several simple laws describing allowed sequences, number of specific reactions, repeating unit length and the allowed and disallowed sequence coexistence in block copolymers. We formulate Simple Assembly Rules (SAR) that capture commonly observed behavior and design of literature systems, and characterize the possible k-polymerizations they are allowed to access ($k\leq2$) as function of symmetries and illustrate our findings with reported examples from the coordination chemistry and supramolecular chemistry literature. We discuss chemical-structural contributions by which nontrivial ($k>1$) sequences are formed, highlighting the importance steric hindrance, long-range interactions and degrees of freedom.
Comments14 pages, 10 figures
