Projecting dynamic heterogeneity into nanoconfinement: the enduring legacy of the Long-Lequeux model

In the early 2000s, Long and Lequeux established the first quantitative link between dynamic heterogeneity in the bulk and shifts in the glass transition temperature $T_g$ of thin films. Their minimal mean-field model demonstrated that equilibrium density fluctuations give rise to nanometric slow domains, the percolation of which governs vitrification. By showing how geometrical confinement alters this percolation pathway, they predicted $T_g$ shifts using only bulk properties, without fitting interfacial parameters. This conceptual breakthrough, in which finite-size effects emerge from projecting bulk dynamic heterogeneity onto a restricted geometry, constitutes the enduring legacy of their work. Subsequent experiments have confirmed this picture, showing that $T_g$ depression in free-standing films scales with the thickness of a liquid-like surface layer, while in supported systems mobility gradients reflect the reorganization of slow domains anchored at the interface. Looking forward, I outline at the end of this perspective several possible directions for refining this framework so as to capture a broader spectrum of relaxation channels, thereby enriching our understanding of dynamics in both bulk and confined polymer melts.