Toward a Deterministic Nucleation Theory for Chirality-Controlled Nanotube Synthesis

TL;DR

This paper introduces a rigorous topological framework for understanding the nucleation process in carbon nanotube synthesis, revealing that chirality is deterministically encoded during nucleation rather than during growth, enabling predictable synthesis.

Contribution

It develops a topological model linking cap structure to chirality and demonstrates that chirality is set during nucleation through specific cap formation on catalysts.

Findings

Cap topology is quantitatively related to chirality via the vector sum rule.

Chirality enrichment is due to deterministic cap formation during nucleation.

The framework explains patterning in chirality space and shifts the paradigm to nucleation programming.

Abstract

The electronic properties of carbon nanotubes are governed by their chirality, specified by the integer indices (n,m). While chirality-controlled synthesis has achieved notable successes, theoretical understanding remains predominantly focused on post-nucleation growth. Two fundamental obstacles impede deeper insight: the absence of a clear description of nucleation cap topology and its connection to tube chirality, and an incomplete understanding of atomic-level mechanisms governing templated cap formation. Here we address these challenges directly. First, we develop a mathematically rigorous topological framework for carbon networks that provides both a concise definition of cap structures and a quantitative relationship between cap architecture and chirality-the vector sum rule. Second, contrary to conventional perspectives attributing chirality enrichment to edge matching during growth, we demonstrate that chirality is deterministically encoded during nucleation through selective formation of specific cap structures on catalyst surfaces. For the specific case of (12,6) nanotubes, we show that their enrichment arises from a six-fold symmetric cap with epitaxial matching to catalyst facets. Our deterministic nucleation theory not only provides a coherent explanation for chirality enrichment but also elucidates its pattern in chirality space. This work establishes a theoretical framework that redefines the field, shifting the paradigm from stochastic growth kinetics to deterministic nucleation programming and paving the way toward predictable synthesis.