Slow coarsening of ultra-confined phase-separated glass thin films

Diffusion-driven coarsening of droplets is a classical subject in statistical physics, yet coarsening kinetics in confined systems have received little attention. We report here on the coarsening of droplets in thin (50-200 nm) films of phase-separated barium borosilicate glasses. In this ultra-confined geometry where at most one droplet is observed within the film thickness, droplets grow like a power-law of time with an exponent about 0.17 significantly smaller than that of the one of Ostwald ripening ( 1 / 3 ) characteristic of bulk coarsening. We complement these experimental results with two-dimensional Cahn-Hilliard numerical simulations of diffusion, where a wider range of parameters can be varied. In simulations, we recover a slow coarsening behavior in ultra-confined geometry. We explain the anomalous scaling exponent of simulations by ultraconfined geometry, which imposes a different scaling with time of the radius of a droplet and the distance between droplets. In the experimental system, diffusive transport also becomes less efficient with time compared to the bulk case with an additional change of geometry compared to simulations. Flattening of droplets with time is indeed observed, which we attribute to strong variations of the diffusion coefficient with the local matrix composition. We finally propose a simple model assuming a spatial localization of the diffusion paths to account for this effect.