Narrow acoustic impedance matching layer accelerates long-range coupling of local modulus between glassy and rubbery polymer domains

We test and demonstrate that the fundamental origin for long-range ∼200 nm local property gradients between glassy and rubbery polymer domains is an acoustic impedance matching framework of boson peak wavelengths. Recent research has suggested that the transmission of λ ∼ 5 nm acoustic waves across glassy-rubbery interfaces is the cause of dynamical gradients leading to the broad ≈250 nm glass transition Tg(z) and modulus G̃(z) profiles observed between polymer domains. These acoustic waves with wavelength λ ∼ 5 nm are of comparable energy to the boson peak and the collective vibrations associated with precursors of structural rearrangements. In this work, we directly test this proposed conceptual framework by inserting a 5 nm impedance-matching random copolymer layer at the interface between glassy polystyrene (PS) and rubbery polybutadiene (PB) domains. The resulting viscoelastic changes of PS/PB bilayer films are studied using a quartz crystal microbalance, where an acoustic transfer-matrix continuum mechanics model is used to determine the change in depth-dependent modulus G̃(z) imparted by the added 5 nm styrene-butadiene copolymer P(S-r-B). We find the emergence of the broad modulus gradient to be accelerated by the added 5 nm copolymer layer. These results demonstrate a direct correlation between compositional interfacial widths wI ≈ 5-10 nm and the broad ≈100-300 nm G̃(z) modulus gradient that emerges between glassy and rubbery domains, supporting the idea that it is the transmission of λ ∼ 5 nm acoustic waves across dynamically distinct domains that is key to the mechanism behind the coupling of local properties between them. More broadly, these findings provide new insight into the fundamental nature and mechanisms behind the length scales impacting local dynamical heterogeneity of glasses.