Adaptive ligand-mediated frustrated assembly of gold tetrahedral nanoparticles

Polyhedral packing provides a fundamental framework for understanding how anisotropic nanoscale building blocks organize into ordered superstructures. However, controlling the assembly pathways of tetrahedral nanoparticles remains challenging due to their intrinsic geometric frustration and complex free-energy landscapes. Herein, we develop an adaptive solution-phase assembly strategy for gold tetrahedral nanoparticles by regulating their frustrated packing pathways. Thiol-terminated polyethylene glycol (PEG) ligands grafted onto tetrahedra provide dynamic interparticle interactions through Hofmeister-effect-mediated conformational adaptation. Concurrently, strongly hydrated carbonate ions (CO₃^2-) regulate the hydration environment of PEG chains, inducing controllable hydrophilic-hydrophobic transitions and tuning effective interactions between tetrahedral nanoparticles. This ion-mediated solvation switching enables adaptive regulation of the frustrated packing landscape and promotes ordered assembly of tetrahedral building blocks in solution. The interplay between geometric frustration of tetrahedra and adaptive flexibility of PEG ligands generates diverse hierarchical packing states, including textile-like ordered assemblies, pentagonal bipyramidal motifs, and trigonal crystalline arrays.