Controlling the Discrete Aggregation of Single-Polymer-Grafted Nanoparticles via Size-Dependent Steric Effects

The precise design of “colloidal molecules” with specific arrangements is essential for the bottom-up assembly of hierarchical superstructures. However, achieving discrete, “quantized” control over the aggregation number remains a critical challenge. The physical mechanism by which the size-dependent steric hindrance of the nanoparticle core regulates this precise assembly remains unexplored and unclear. To address this issue, we investigate the aggregation of single-polymer-grafted nanoparticles (SPGNPs) as a minimal model system through molecular dynamics simulations and a mean-field theoretical framework. The potential of mean force between two SPGNPs reveals that the assembly is governed by the competition between polymer-mediated attraction and shape-dependent steric hindrance. The nanoparticle shape influences the overall potential profile and furthers the effective range of attraction. We then introduce a chain length sensitivity coefficient ( S c = d n */d N ) to quantify the responsiveness of the cluster size n * to the polymer length N . Scaling analysis demonstrates that S c scales as 1/ R 4, where R is the characteristic nanoparticle dimension. It indicates that increasing the nanoparticle size relative to the polymer core significantly strengthens the many-body steric penalty. This pronounced repulsion forms a “steric bottleneck” that suppresses the system’s responsiveness to attractive forces, thereby expanding the thermodynamic stability intervals for specific cluster sizes. Targeted simulations further confirm that by systematically tuning the nanoparticle volume to offset the polymer attraction, discrete oligomeric states, including dimers, trimers, and tetramers, can be accurately stabilized. This work proposes a rational, purely physical design pathway for the precise “digital” regulation of colloidal molecules with programmable coordination numbers, relying exclusively on fundamental geometric and thermodynamic mechanisms.