Effect of film thickness on the glass transition temperature and fragility. (a) The temperature dependence of relaxation time τ(h, T) from the intermediate scattering function F(q 0, t). In this T range, τ decreases as we decrease the thickness of the film. The inset shows a magnification of the behavior of τ at low T. (b) Glass transition temperature T g and (c) fragility m relative to the pure melt as a function of the thickness h g ≡ h(T g ); the determination of h g is explained when we present the film density profile. We find a depression of T g and fragility up to a critical thickness, where the behavior is reversed. The inset of (c) shows a magnification of the data at large h g .
Spatial dependence of the density and relaxation of films. (a) Representative monomer density profile of ρ(z) for a supported film on an attractive surface for a range of T for film thickness h g = 15.03, corresponding to about 30 nm in physical polymer units. It is apparent from ρ(z, T) that the thickness of the film decreases on cooling. The inset shows the density profile of monomers for various thicknesses scaled by the bulk value. We see that the peaks are independent of film thickness and that there is a bulk-like region far from the interfaces. (b) Relaxation time τ s as function of distance z from the wall for various T for h g = 15.03. τ s (z) is altered from the bulk, even near the center of the film where the density is the same as the bulk. The deviation of τ s from the bulk becomes more significant at low temperature.
Temperature dependence of film thickness. Thickness h is plotted relative to its low temperature limit h 0, which demonstrates an approximate Arrhenius behavior. We use this Arrhenius behavior to estimate h(T g ). Note that the color representation corresponds to that used for film thicknesses in Fig. 1(a).
Scale of the surface layers from relaxation and density. (a) Dynamical length scale ξτ of substrate and free surfaces function of T with two thicknesses. The dynamical length scales at both interfaces grow upon cooling, but ξτ of substrate is constrained when its value ≈h g /2. (b) Length scale from density of substrate and free surface as function of T. We see that the length scale of the substrate grows, while the length scale of the free surface shrinks upon cooling.
Spatial dependence of the density ρ(z) of the film averaged over intervals δz equal to the monomer size to eliminate the oscillatory behavior shown in Fig. 2(a). Data are shown for a representative film thickness h g = 15.03.
The effect of film thickness on the local variation of T g and fragility. (a) T dependence of the relaxation time τ s for representative distances from the surface for h g = 7.76. We observe that there is a rapid increase of τ s near the attractive surface, consistent with an increase of fragility at the attractive surface. (b) T g and (c) fragility as a function of distance z from the wall. The region closest to the attractive wall has a locally increased T g , resulting from an increasing fragility near the wall. Hence, the high fragility near the supporting surface has a large effect on the overall film dynamics.
Chain conformation and anisotropy of relaxation. (a) Radius of gyration R g of the polymer chains relative to the bulk as a function of position z of the center mass of the chain at T = 0.4 and thickness h g = 15.03. We also resolve the perpendicular and parallel components to the surface, which we label by R g⊥ and R g∥. (b) Relaxation times in the perpendicular τ⊥ and parallel τ∥ directions at T = 0.6 and thickness h g = 15.03. Near the substrate, we find that τ⊥ is much larger than τ∥.
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