A novel experimental approach involving fluorescence nonradiative
energy transfer (NRET)
is employed to study the Fickian diffusion of small molecules in
rubbery polymer films near the glass
transition. A theoretical formalism has been developed which
directly relates the small molecule
translational diffusion coefficient, 𝒟, to changes in the energy
transfer efficiency, E. Values of 𝒟 as
low
as 5 × 10-16 cm/s have been
measured. In this approach, two thin polymer films are sandwiched
together,
one labeled with either NRET donor or acceptor chromophores and the
second doped with the
complementary chromophore. Upon annealing for a time t,
dopant chromophore diffusion occurs in which
E is proportional to
(𝒟t)1/2/w, where
w is the donor film thickness. Values of 𝒟 for
pyrene, N-(2-hydroxyethyl)-N-ethyl-4-(tricyanovinyl)aniline (TC1),
bis(phenylethynylanthracene) (BPEA), and decacyclene in poly(isobutyl methacrylate) (PiBMA) and for BPEA in
poly(ethyl methacrylate) (PEMA) have
been measured over temperatures ranging from ca.
T
g to T
g + 20 °C.
Among these chromophores,
significant differences in both the magnitude and temperature
dependence of 𝒟 were observed and are
attributed to differences in molecule size, shape, and flexibility.
Two anomalous effects are observed
from a comparison of translational diffusion and rotational
reorientation dynamics of TC1 in PiBMA
near T
g. The first is an apparent
enhancement in translational diffusion relative to rotational
reorientation
dynamics, with the average translational displacement of a chromophore
during an average rotational
relaxation time, 〈τrot〉, being a couple orders of
magnitude larger than the length of the molecule.
This
behavior may be explained by significant local-scale heterogeneity in
the polymer, i.e., the broad
distribution of polymer α-relaxation times. The second regards
the different temperature dependencies
of 〈τrot〉 and 𝒟 near
T
g. This may be explained qualitatively by
a strong temperature dependence of the
breadth of the distribution of α-relaxation times, an effect known to
be present in the TC1−PiBMA system
employed in this comparison as well as a variety of other polymer
systems near T
g.