activation energy Ea 337 T 20 kJ mol–1, in
agreement with existing literature (18, 20, 23).
In conclusion, by employing the stepped-film
geometry and analyzing the resulting flow, we
report quantitative evidence for the existence of a
thin layer of liquid-like material at the free sur-
face of glassy, low-molecular-weight polystyrene
films. The sample thicknesses and preparation are
such that annealing effects, chain confinement,
and substrate effects can be neglected. The tran-
sition from whole-film flow to flow localized in
a thin surface layer has been measured and ob-
served to occur sharply at the bulk Tg value. For
temperatures inside the transition region, we were
able to measure time-dependent evolutions from
glassy to liquid behavior. This technique provides
an opportunity to accurately follow the transition
from surface flow to bulk flow within a single
sample. Below Tg, a fit to the measured profile
gives a surface mobility parameter h3 m=ð3hm Þ that
can be used to estimate a surface viscosity. In
particular, we obtain hm 108 Pa · s at 20 K
below Tg. Independent determination of either
the size hm(T) of the surface region or its vis-
cosity hm(T) would allow a complete determi-
nation of the temperature-dependent properties
of the near-surface region.
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Fig. 4. Temperature dependence of the correlation function and thermal expansivity. The
correlation function c(T) defined in Eq. 3 is given by the green square and black diamond symbols (left
axis) for samples with h1 = h2 = 90 nm. The thermal expansivity for an independent flat 87-nm sample is
given by the purple triangles (right axis). The black diamond symbols are c(T) for a single sample that was
held first for 90 hours at T < Tg, then measured and heated to T > Tg until the self-similar profile was
reached. The inset shows the temporal evolution of c for T = 343 K and 348 K data that lie in the
transition region (blue circles are for T = 343 K; orange diamonds are for T = 348 K). Error bars are
indicated once for each subplot.
Fig. 5. Temperature dependence of the mobility. This figure is made of two subplots representing
h1 = h2 = 90-nm samples. The mobility H3/(3h) is determined by a fit to either the analytical GTFE solution
(blue circles) or the numerical TFE solution (red squares), with h and H as defined in the legend.