Enhanced Structure-Dynamics Correlation via Local-Average Free Volume in the 3D Kob-Andersen Glass Former

The structural origin of dynamical slowdown in glass-forming liquids remains a central challenge in physical chemistry. Using molecular dynamics simulations of the 3D Kob-Andersen binary Lennard-Jones model, we show that the locally averaged free volume, V₂, exhibits stronger correlations with dynamical heterogeneity and structural relaxation than single-particle free volume, V₀, as quantified by spatial enrichment, probability density shifts, and scaling with local relaxation times. The structural relaxation time τ_α is closely matched by τ_long, the lifetime of particles with the largest, most anisotropic free volumes, indicating that anisotropy seeds relaxation events. Large V₂ values correlate with enhanced local configurational freedom, as evidenced by increased particle mobility and anisotropic displacement distributions. Upon cooling, an exponential loss of such "active regions" suppresses cooperative motion and drives the super-Arrhenius growth of τ_α. These results support a unified free volume framework where local spatial correlations and anisotropy are key to understanding the glass transition.