Driving Force of Colloidal Nanoparticle Self-Assembly

By defining the driving force for colloidal nanoparticle self-assembly as the negative gradient of the Helmholtz free energy difference with respect to generalized coordinates, $F=-\partial \left(\Delta A\right)/\partial \xi$, this work establishes a universal thermodynamic framework for diverse assembly pathways. Using advanced multiscale molecular simulations, we elucidate the enthalpic and entropic origins and regulatory mechanisms of driving forces in three canonical processes: solvent evaporation, solvent destabilization, and particle growth. For solvent evaporation, the driving force originates from a tunable interplay between enthalpy and entropy, rather than being purely entropy-driven, with ligand shell rigidity and particle size serving as key control parameters. In contrast, solvent destabilization is predominantly enthalpy-driven, where the width of the interparticle potential well plays a critical role in governing phase behavior. For particle-growth-mediated assembly, we demonstrate that van der Waals interactions alone cannot account for the assembly of small nonmetallic nanoparticles; instead, core-core van der Waals forces become the dominant driving force only when the nanoparticle size is sufficiently large (interparticle potential well depth exceeding ∼3 k_BT). The study thus presents a unified, predictive theory that bridges molecular interactions to macroscopic order, offering a robust foundation for the rational design of functional nanomaterials.