The most comprehensive study to date of the effects of size,
shape, and flexibility on the
translational diffusion of small probe molecules in polymer solutions
has been completed by Taylor
dispersion, which directly yields D
probe, and
phosphorescence quenching, which yields k
q, the
concentration
dependence of which is identical to that of
D
probe for appropriate conditions.
Diffusion of 16 probes ranging
by a factor of 6 in molar volume was investigated using both Taylor
dispersion in solutions of up to 400
g/L polystyrene in tetrahydrofuran and phosphorescence quenching in
solutions of up to 700 g/L
polystyrene in tetrahydrofuran, cyclohexane, and carbon tetrachloride.
Results were compared quantitatively to modified Vrentas−Duda free volume theory for ternary
solutions to obtain probe jumping
unit sizes relative to the solvent, ξprobe,s, which
correlate with probe volume. With the exception of
3,4-hexanedione (a highly flexible and small probe), the PS concentration
dependencies of D
probe and
k
q were
approximately equal to or greater than that of solvent (0.9 ≤
ξprobe,s ≤ 1.75). The data fell into two
types
of behavior: when ξprobe,s was plotted against the
ratio of probe to solvent molar volume,
Ṽ(0)probe/Ṽ(0)s,
the vast majority of data fell around a line of slope 0.13, while for
two of the probes ξprobe,s fell near a line
of slope unity. Literature data for five probes in several
polymer−solvent systems could also be described
by these two types of behavior. The former behavior indicates that
for most probes the concentration
dependence can be described by modified free volume theory, with the
understanding that the critical
hole free volume for a jump unit for these probes is but a fraction of
the probe molar volume. The apparent
dichotomy in the probe volume dependence of ξprobe,s
raises the question of whether only two dependencies
are possible or whether, by virtue of the probes selected, only these
two distinct behaviors are observable.
Small effects of flexibility and shape on
D
probe for probes with large aspect ratios were
also observed and
discussed in terms of anisotropic diffusion. A comparison of
concentration dependence data with limited
temperature dependence data from the literature shows a consistency
based on the modified free volume
picture. This, along with an understanding of the “bimodal”
ξprobe,s data, indicates that the modified
free
volume theory for ternary systems forms a reasonably robust picture by
which to interpret probe diffusion
in polymer solutions.