Diverse Self-assembly Pathways in Nematic Compartment Network: Topological Percolation and Pathfinding

The self-assembly of nematic molecules in microcompartments with unambiguously defined surface anchoring is well predictable and is likely to have a single stable topological structure. Here, in contrast, a confined nematic system comprising an array of microcompartments interconnected by channels is demonstrated, exhibiting diverse molecular assembly pathways leading to the formation of four types of topological structures and twelve different patterns randomly distributed. Intercompartment communication via channels plays a crucial role in the diversity of patterns and distributions. It determines the sizes and structures of domains separated by channel defects. The domain structure, which features a pathfinding algorithm and reverse tree structure, can be modelled by an isotropically directed bond percolation with additional restrictions. This system serves as a model for controlled randomness and restricted growth of networks, with potential applications in anticounterfeit protection as a physically unclonable function (PUF) with multiple-level communication protocols.