Symmetry and Asymmetry in Mutations and Memory Retention during the Evolutionary Growth of Carbon Nanotubes

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