Quantifying the Fragility–Elasticity Relationship in Uncharged Ultrasmall Polymeric Colloids

Soft colloids play a vital role in modern life and provide insights into the physics of vitrification. Soft colloidal glasses exhibit significant variations in dynamic fragility─the sensitivity of relaxation dynamics to concentrations. While particle softness, including cross-linking density and charge, influences fragility, their complex interplay obscures the fundamental physics. This study conducts a systematic investigation of 16 uncharged polystyrene soft nanoparticles (SNPs) with independently controlled diameter and elasticity. The research quantifies relaxation time as a function of particle concentration, diameter, and cross-linking density using two fitting parameters. Through this analysis, fragility is determined and correlated to the elastic energy per particle (particle elasticity multiplied by volume). Particles below a threshold elastic energy (smaller or softer) would deform readily under thermal energy, exhibiting strong glass behavior. In contrast, larger or stiffer particles undergo fragile glass transitions through a cooperative relaxation. This investigation establishes a dynamic phase diagram that predicts fragility transitions, addresses existing contradictions, and presents design principles for colloidal suspensions.