Signature of collective elastic glass physics in surface-induced long-range tails in dynamical gradients

Glass formation and dynamics of model polymer films with one versus two active interfaces

“…We arrive at a dynamically neutral substrate by tuning the polymer-substrate interaction energy parameter e ps until dynamics are essential unperturbed near the substrate. As shown in our recent paper, 32 a value of e ps = 0.515 yields a negligible dynamical gradient at the substrate, and we confirm in the results section that this yields a negligible T g gradient near the substrate.…”

“…25,[29][30][31] Beyond about 10 segmental diameters, a likely inverse power law gradient tail extends much further into the film. 32 A recent experimental study probing surface diffusion as a function of the penetration depth of surface molecules across a range of liquids supports the nearsurface double-exponential decay. 27 The temperature dependence of this gradient is now fairly well understood as well: at low enough temperatures, the fractional reduction in activation barrier relative to bulk is nearly temperature invariant at any given distance from the surface, leading to a fractional power law relation between local, film, and bulk relaxation times.…”

“…We compute the value of this function at a wavenumber q = 7.07 (comparable to the first peak of the structure factor) by averaging in a radially symmetric manner over multiple wavevectors with magnitudes in a narrow band around this wavenumber, as is standard for many studies probing dynamics near various interfaces including free surfaces and rigid substrates and particles. 20,21,29,32,45,46 A relaxation time and stretching exponent are extracted by fitting F s (q, t) to the Kohlraush-Williams-Watt (KWW) stretched exponential function, 47,48…”

“…As discussed in our prior work, there are appreciable downward deviations (for intermediate thickness films) and upward deviations (for ultrathin films) from the two-exponential-gradient superposition model in the case of freestanding films. This is a consequence of the overlap of long-range elastic power-law tails in the intermediate film, 32 and of a saturation of elastic effects from two interfaces in ultra-thin films. 36 Evidently, these two-interface effects are relatively weak when one of the two interfaces is dynamically neutral.…”

“…Some second order corrections to this additivity were observed for intermediate films and attributed there to potential elasticity-related finite size effects; more recent work suggests that a more precise description may be that these deviations result from additivity of a low-magnitude elasticity-driven power law gradient tail found beyond the first B10 nm from the surface. 32 Stronger deviations from gradient additivity were found in ultrathin films, where the overall suppression of elastic contributions to the activation barrier saturates such that little to no more reduction of this barrier contribution is possible as thickness is further reduced. 36 Earlier simulation evidence from Hsu et al suggested that this leading-order gradient additivity scenario may extend to a broader array of systems involving distinct types of interfaces.…”