Symmetry and Asymmetry\nin Mutations and Memory Retention\nduring the Evolutionary Growth of Carbon Nanotubes

Symmetry is a motif featured in almost all areas of science,\nand\nunderstanding the mechanism of symmetry breaking is challenging. Similar\nto mutations that disrupt symmetry in evolution, defects in materials\noffer insight into symmetry breaking. Here, we investigate symmetry\nin intragenerational mutations and symmetry breaking in transgenerational\nmutations in the evolutionary growth system of carbon nanotubes (CNTs).\nMutations caused by pentagon–heptagon (5–7) pairs in\ndifferent conformations shorten the lifespans of single-walled carbon\nnanotubes (SWNTs) by acting as time markers during growth. Symmetric\ndistributions are observed for intragenerational mutations from (<i>n</i>, <i>m</i>) to (<i>n</i> + <i>i</i>, <i>m</i>–<i>i</i>) (where <i>i</i> ∈ caslon Z) with different appearance orders of\npentagon and heptagon. Such symmetry breaks occur in transgenerational\nmutations. Intragenerational mutations occur multiple times on a SWNT,\noscillating regularly between <i>i</i> and – <i>i</i> until termination occurs. These types and effects are\nretained in the form of memory to encode SWNTs during subsequent growth,\nresulting in a length reduction after each mutation. Our results provide\na profound understanding of symmetry breaking and memory retention\nand offer guidance for the controlled synthesis of materials.