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fusion coefficient. Typical values of D for molecules in liquids
are on the order of ~1ꢁ10ꢀ5 cm2 sꢀ1 [82–84]
To estimate bounds
Experimental Section
.
The Pd nanoparticle synthesis and characterization details were
provided previously.[7,29] Pd supported on activated carbon (Pd/AC)
was prepared by a wet chemical method with a metal-to-support
loading of 1 wt%. The particles were characterized by TEM and
have a size distribution of 2–8 nm, centered around 4 nm.[29] The
surface Pd comprises 31% of the total Pd atoms (based on
Table 2.1 of Ref. [92]), which is within 10% agreement of approxi-
mating the particles as spheres for most of the particles in the size
distribution used here.
for the value of D, we note that the tabulated value for tolu-
ene in benzene is 1.85ꢁ10ꢀ5 cm2 sꢀ1, that for phenol in water
is 0.89ꢁ10ꢀ5 cm2 sꢀ1, and that for 1-butanol in water is 0.56ꢁ
10ꢀ5 cm2 sꢀ1.[90] We will take bounds of 0.50ꢁ10ꢀ5–2.00ꢁ10ꢀ5
and calculate the estimated steric factor for each of these
bounds. For d, we will use the Stokes diameter of benzyl alco-
hol to give d=0.95 nm.[91] If we use these numbers in Equa-
tion (16), we get bounds of 5.5ꢁ108 <Z<2.2ꢁ109 sꢀ1. Interest-
ingly, this is several orders of magnitude smaller (~103–
106 times smaller) than the frequency of pre-exponentials of
surface reactions.[69–75] If we use these values for the flux in
Equation (15) along with our extracted values for k2, we get an
order of magnitude estimate that 0.04<S0 <0.17, which seems
reasonable (and perhaps fortuitously good). Thus, the kinetic
parameter values obtained from the microkinetic model also
pass this check that they are physically reasonable. As noted in
Ref. [82] (p. 318), the diffusion limit for reactions in solution is
~ ꢄ10ꢀ10 s, and the depletion of molecules here is orders of
magnitude slower than that.
Reactions were performed in a 30 mL glass reactor equipped with
a thermostat and an electronically controlled magnetic stirrer. A
stirring rate of 1250 rpm was used, which was shown previously to
exclude diffusion limitations and to be suitable for chemical kinetic
studies.[7,9,28,35–36,48] The glass reactor was connected by tubing to
a mass-flow controller used to flow gas mixtures, with a second
port connected by tubing to the building exhaust to enable the
continuous flow of gas through the reactor such that the gas-
phase partial pressures remained constant during the experiment.
Thus, the O2 gas-phase pressure could be used as a proxy for the
concentration of O2 in the liquid during kinetic modeling. The gas
flow was 30 mLminꢀ1 and the total pressure was always at 1 bar of
O2 or O2 diluted by N2. We used 60 mg of supported catalyst
(0.6 mg of Pd per sample). Benzyl alcohol was premixed with the
solvent p-xylene, and the total liquid volume was always kept at
10 mL. Reaction time zero was marked by the beginning of stirring,
and the heating to the desired temperature was on the order of
minutes, and reactions were monitored with measurements taken
at intervals until 120 min after reaction time zero (a total of six
measurements per experiment). Each experiment represents 36
data points as there are six product species with concentrations
measured six times per experiment. Based on mass balance, little
to no liquid-phase reactants and products evaporated during the
course of experiment. The TOFs observed in this study are on the
order of 1000 molecules per Pd atom per hour, which is in line
with literature results.[13,24–34,39]
Conclusions
Benzyl alcohol oxidation over Pd nanoparticles supported on
carbon generates six products: benzaldehyde, toluene, benzyl
ether, benzene, benzoic acid, and benzyl benzoate. Microkinet-
ic modeling using the mechanism published by Savara et al.[7]
is able to produce all of the trends observed experimentally
with mostly quantitative agreement. This corresponds to
a total of 18 trends that are reproduced as there are six prod-
ucts and three experimental parameters that varied: alcohol
concentration, oxygen concentration, and temperature. In
most cases, quantitative agreement was achieved for the prod-
uct quantities and selectivities obtained by experiment. Addi-
tional insights on how the rate constants affect the production
of each product (and thus selectivities) were gained from the
analytical equations that were derived from the microkinetic
model. The present study suggests that the most important
activation energies are those of k2, k5, and k6 (Scheme 1), which
we estimate as Ea2 =57.9 kJmolꢀ1, Ea5 =129 kJmolꢀ1, and Ea6 =
175 kJmolꢀ1. Upper limits for the activation energies of the
other rate constants were also identified (Table 4). For a solu-
tion that is 25% benzyl alcohol (2.32 molLꢀ1) under 1 bar O2,
the turnover frequencies (TOFs) for benzaldehyde and toluene
production at 708C can be calculated using the empirical rela-
For microkinetic modeling, it was necessary to translate changes in
the liquid-phase concentrations [molLꢀ1] to units that could be re-
lated to the molecules produced per surface site of Pd per unit
time. Based on the size distribution[29] of the particles and the esti-
mated number of surface Pd atoms per particle,[92] we calculated
an estimated 8.2ꢁ1018 atoms of surface Pd in each experiment,
and we define this as the amount for one monolayer equivalent
(MLE).[69] The density of benzyl alcohol is 1.045 gmLꢀ1 and it has
a molecular weight of 108.138 gmolꢀ1. As the total liquid volume
was kept at 10 mL, the number of molecules to produce a change
of 1 molLꢀ1 is equal to 764 MLE. During microkinetic simulations,
the surface coverages were represented in the usual way with rela-
tive coverage of a given species, qi was bound between 0 and 1,
and the concentration of empty sites was also bound between 0
and 1. The rates of change for the concentrations of the liquid
phase [molLꢀ1] and of the relative coverages (in unitless relative
coverages, qi) were calculated accordingly. The rate equations in
Table 2 rely upon units as follows: surface species concentrations
are in units of theta (unitless relative coverage), gas-phase species
concentrations are in bar, and liquid-phase species are in units of
molLꢀ1. Simulations were performed using Athena Visual Studio,
and fitting was accomplished by sequential parameter optimiza-
tion aided by gradient based parameter optimization with the ob-
jective function defined by the weighted sum of squared residuals.
Although local parametric error estimation is possible with gradi-
ent optimization,[93] global (i.e., true) parameter error estimation is
tionships ln(TOFaldehyde sꢀ1)=(ꢀ57.9 kJmolꢀ1)/RT + 27.6 and
ꢀ1
ln(TOF
s )=(ꢀ129 kJmolꢀ1)/RT + 49.8, respectively, rather
toluene
than performing a full microkinetic simulation. The application
of the concepts of a sticking coefficient and steric factor in so-
lution yielded a steric factor that was physically reasonable,
which is consistent with the kinetic parameters and is physical-
ly realistic. The method used to apply the concept of a sticking
coefficient and steric factor for liquid–solid adsorption was ap-
proximate and is expected to be general.
&
ChemCatChem 2016, 8, 1 – 11
8
ꢀ 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ÝÝ These are not the final page numbers!
Savara, Aditya
