66
SUN, FARNETH, AND HARMER
This expression suggests two limiting kinetic regimes. When materials since the proton donor in all cases is a perfluoro-
k2[AMS] ꢆ kꢄ1, then the rate expression reduces to
R = k1[AMS][AH].
sulfonic acid residue. The relative rates then might be re-
lated to different numbers of accessible acid sites within the
different microstructures. Under nonswelling conditions,
we estimate the accessible acid site density from the num-
ber of sulfonic acid residues on the exterior surface of the
[2]
The rate should appear first order in AMS concentration,
and the observed rate constant is the product of the ele-
mentary rate constant for formation of the carbenium ion,
k1, and the effective acid catalyst concentration. On the
other hand, when kꢄ1 ꢆ k2[AMS] then the rate expression
reduces to
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Nafion resin particulates. The ratio of the BET surface
areas in 1.0/50/17500. Of course for the composite, most of
the BET surface area is the noncatalytic, silica surface. Mi-
croscopy data suggests that in the Nafion/silica composite,
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the Nafion resin is uniformly dispersed as 20–60 nm par-
ticulates within the silica matrix. Therefore if we presume
that the Nafion resin surface area in the composite is given
R = Kk2[AMS]2[AH],
[3]
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where K is the equilibrium constant for proton transfer be-
tween AMS and whatever the effective acid AH is. The
first-order behavior of all of the acid catalysts (vide infra)
suggests that we can rationalize their relative catalytic ac-
tivities within the framework of Eq. [2].
by the weight fraction times the BET surface area, then the
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Nafion resin surface area ratios would be 1.0/50/2280. For
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the supported catalyst this presumes that the Nafion resin
is well dispersed over the support. This ratio is very close
to the relative rate ratio in cumene, although both the sup-
ported and composite materials appear to be a factor of 2
or so less active than this rough model suggests. It is quite
In the case of the homogeneous acids it seems likely that
the reaction is specific acid-catalyzed and that the proton
donor is a solvated proton. This appears to be implicitly
assumed by Beltrame et al. (14). It is suggested by the clear
trend in rates with pKa that we observe and is also consistent
with the modest activity of oxalic acid ( pKa ꢃ 1) reported
by Chaudhuri et al. in phenol (8). Since the effective pro-
ton donor is the protonated solvent, SH+, for all homoge-
neous acids, k1, kꢄ1, and k2 in Eq. [1] will be independent of
the nature of the added acid. Relative rates are then deter-
mined bythe effective concentrationsofSH+, fixed bya pre-
equilibrium between the added Bronsted acid and p-cresol,
i.e., CF3COOH + S ↔ CF3COOꢄ + ꢄSH+, where S repre-
sents a solvent molecule. Assuming complete dissociation
for the strongest acid, triflic acid, this interpretation implies
that the equilibrium constant for the dissociation of p-TSA
is about 0.2, and for TFA is about 4 ꢇ 10ꢄ3 in this medium.
Furthermore, the entry in Table 1 for triflic acid represents
the turnover frequency for the solvated proton within this
set of assumptions, since [AH] = [SH+] = [TFA]0. This can
be a benchmark for other proton sources.
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likely that the Nafion resin is not uniformly dispersed on
the supported catalyst and that the weight fraction overes-
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timates the Nafion resin surface area fraction in the com-
posite (15).
We can pursue this picture a little further by estimat-
ing the absolute number of acid residues on the external
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surface of Nafion NR-50 resin. Assuming a bulk den-
sity of 2 g/cc, and a BET surface area of 0.02 m2/g we
calculate that the fraction of sulfonic acid residues within
the average acid–acid site separation distance of the sur-
face is 4.0 ꢇ 10ꢄ5, the so-called noninteraction accessibil-
ity suggested by Buttersack [16]. This implies that the ac-
tivity/accessible acid site, or turnover frequency, for aꢄs5ul-
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fonic acid residue in Nafion NR-50 resin is 0.1/4.0 ꢇ 10
=
2500 hꢄ1. This is about a factor of 6 lower than we esti-
mated above for the solvated proton in homogeneous me-
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dia and suggests that the sulfonic acid residues in Nafion
resin have a high inherent activity even in nonsolvating me-
dia. This is consistent with previous work comparing struc-
turally identical sulfonic acid sites in heterogeneous and
homogeneous acids which shows similar but slightly lower
enthalpies for proton transfer from the solid acid systems
to a variety of bases (17).
It is clear from Table 1 that the same interpretation can-
not be applied to the resin acids. The reaction cannot be spe-
cific acid catalyzed. The absence of a solvent effect for the
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supported catalyst, the Nafion resin/silica composite and
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Amberlyst-15 , suggests that these processes must be gen-
From this point of view, we may look at the composite as a
way of increasing the accessible fraction of acid residues by
eral acid catalyzed, with proton transfer occurring directly
from the resin acid to AMS. Relative rates for different
catalysts can then be described within the context of Eq. [2],
where both k1, and the nature and concentration of the ef-
fective proton donor, AH will differ for each solid acid.
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stabilizing Nafion resin spheres of approximately 30-nm
radius. Since the specific surface area of a collection of uni-
form spheres is given by S = 3/rp, where r is the radius and
p is the bulk density, then we would expect that decreasing
a sphere radius from 75 ꢁm in NR-50 resin to 30 nm in the
composite, the number of surface accessible sites would in-
crease by about 2.5 ꢇ 103. We observe a rate increase of
about 1100 in cumene. Again, the estimated increase in
accessible sites is likely to be high, since the spheres are
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Let us consider first, the three Nafion resin-based cata-
lysts. The ratio of the observed first-order rate constants
per acid equivalent in the nonpolar solvent, cumene, is
1.0/39/1100 for NR-50/supported/composite. We might be-
gin by assuming that k1 will be the same for these three