Correlation between the temperature evolution of the interfacial region and the growing dynamic cooperativity length scale

We study experimentally the temperature evolution of the thickness of the interfacial layer, L_int(T), between bulk matrices and the surface of nanoparticles in nanocomposites through broadband dielectric spectroscopy. Analyses revealed a power-law dependence between the logarithm of structural relaxation time in the interfacial layer, τ_int(T), and the L_int(T): ln(τint(T)/τ0)∞L_int^β(T)/T, with τ₀ ∼10^-12 s, and β index ∼0.67 at high temperatures and ∼1.7 at temperatures close to the glass transition temperature. In addition, our analysis revealed that the L_int(T) is comparable to the length scale of dynamic heterogeneity estimated from previous nonlinear dielectric measurements and the four-point NMR [ζ_NMR(T)], with L_int(T) ∼ζ_NMR(T). These observations may suggest a direct correlation between the L_int(T) and the size of the cooperatively rearranging regions and have strong implications for understanding the dynamic heterogeneity and cooperativity in supercool liquids and their role in interfacial dynamics.