A kinetic analysis methodology to elucidate the roles of metal, support and solvent for the hydrogenation of 4-phenyl-2-butanone over Pt/TiO2

Article abstract of DOI:10.1016/j.jcat.2015.06.007

The rate and, more importantly, selectivity (ketone vs aromatic ring) of the hydrogenation of 4-phenyl-2-butanone over a Pt/TiO₂ catalyst have been shown to vary with solvent. In this study, a fundamental kinetic model for this multi-phase reaction has been developed incorporating statistical analysis methods to strengthen the foundations of mechanistically sound kinetic models. A 2-site model was determined to be most appropriate, describing aromatic hydrogenation (postulated to be over a platinum site) and ketone hydrogenation (postulated to be at the platinum-titania interface). Solvent choice has little impact on the ketone hydrogenation rate constant but strongly impacts aromatic hydrogenation due to solvent-catalyst interaction. Reaction selectivity is also correlated to a fitted product adsorption constant parameter. The kinetic analysis method shown has demonstrated the role of solvents in influencing reactant adsorption and reaction selectivity.

Full text of DOI:10.1016/j.jcat.2015.06.007

Journal of Catalysis 330 (2015) 362–373
Contents lists available at ScienceDirect
Journal of Catalysis
journal homepage: www.elsevier.com/locate/jcat
A kinetic analysis methodology to elucidate the roles of metal, support
and solvent for the hydrogenation of 4-phenyl-2-butanone over Pt/TiO2
a
a
a
c,
b
S.K. Wilkinson a,b, , I. McManus , H. Daly , J.M. Thompson , C. Hardacre , N. Sedaie Bonab ,
⇑
⇑
J. ten Dam c, M.J.H. Simmons a, , C. D’Agostino d, J. McGregor d,1, L.F. Gladden d, , E.H. Stitt c
⇑
⇑
a School of Chemical Engineering, University of Birmingham, Birmingham B15 2TT, UK
b Johnson Matthey Technology Centre, P.O. Box 1, Belasis Avenue, Billingham TS23 1LB, UK
c School of Chemistry and Chemical Engineering, Queen’s University, Belfast BT9 5AG, UK
d Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge CB2 3RA, UK
a r t i c l e i n f o
a b s t r a c t
Article history:
The rate and, more importantly, selectivity (ketone vs aromatic ring) of the hydrogenation of
4-phenyl-2-butanone over a Pt/TiO2 catalyst have been shown to vary with solvent. In this study, a
fundamental kinetic model for this multi-phase reaction has been developed incorporating statistical
analysis methods to strengthen the foundations of mechanistically sound kinetic models.
A 2-site model was determined to be most appropriate, describing aromatic hydrogenation (postulated
to be over a platinum site) and ketone hydrogenation (postulated to be at the platinum–titania interface).
Solvent choice has little impact on the ketone hydrogenation rate constant but strongly impacts aromatic
hydrogenation due to solvent-catalyst interaction. Reaction selectivity is also correlated to a fitted
product adsorption constant parameter. The kinetic analysis method shown has demonstrated the role
of solvents in influencing reactant adsorption and reaction selectivity.
Received 20 April 2015
Revised 2 June 2015
Accepted 3 June 2015
Keywords:
Selective hydrogenation
Solvent effect
Kinetic modelling
Aromatic ketone
Pt
Ó 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://
creativecommons.org/licenses/by/4.0/).
Titania
1. Introduction
may also interact with the metal and/or support of the catalyst. A
classic example of this is shown in the work by Boudart and
Solvents are an indispensable presence in many catalytic
liquid-phase reactions. The choice of solvent should not be arbi-
trary and is one which can be highly beneficial or detrimental to
both activity and selectivity of catalytic reactions. Such a fact is
well known, with observations of solvent effects originating in
works such as those by Menshutkin, who in 1890 stated: ‘By means
of a proper choice of solvent, decisive acceleration or deceleration of a
chemical reaction can be achieved’ [1].
Consequently, solvent effects have become very well docu-
mented in organic synthesis [2] and, over the past 50 years, have
been reported in heterogeneous catalysis [3]. Properties of the
solvent such as dielectric constant and polarity play a role in
determining the solubilities of gases (such as hydrogen), solvation
of reactants and products as well as other mass transfer effects [4].
As well as influencing reactant and product behaviour, the solvent
co-workers [5–7] which explored the liquid phase hydrogenation
of cyclohexene using a variety of silica supported catalysts with a
range of solvents. Therein, the turn-over frequency (TOF) for
Pd/SiO2 was found to be solvent insensitive whilst in contrast,
when using a Ni/SiO2 catalyst, the use of polar or oxygenated sol-
vents resulted in a marked decrease in TOF and a strong adsorption
of the solvent itself on the nickel metal.
Ultimately, numerous effects can arise between solvent, cata-
lyst and substrate which result in catalytic reaction systems whose
behaviour can be very difficult to predict. This presents a particular
challenge to industry where the following problems can be
manifested as a result of these difficulties:
ꢀ High E-factors (kg by-products/kg products), in particular for
the pharmaceutical industry [8,9].
ꢀ ‘Scale-up confidence’
– prediction of plant scale reactor
performance.
⇑
Corresponding authors at: Johnson Matthey Technology Centre, P.O. Box 1,
ꢀ Catalyst, feedstock and solvent choice constraints due to
Belasis Avenue, Billingham TS23 1LB, UK (S.K. Wilkinson).
E-mail addresses: sam.wilkinson@matthey.com (S.K. Wilkinson), c.hardacre@
qub.ac.uk (C. Hardacre), m.j.simmons@bham.ac.uk (M.J.H. Simmons), lfg1@cam.ac.
uk (L.F. Gladden).
economic feasibility and environmental restrictions.
To understand and predict solvent effects, methodologies are
needed that probe reaction behaviour from a fundamental physical
1
Present address: Department of Chemical and Biological Engineering, The
University of Sheffield, Sheffield S1 3JD, UK.
http://dx.doi.org/10.1016/j.jcat.2015.06.007
0021-9517/Ó 2015 The Authors. Published by Elsevier Inc.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
363
Nomenclature
Symbol Description
A
a2
B
hydrogen bond acceptor parameter (–)
pre-exponential factor (minꢁ1 (for 1st order))
sensitivity (–)
B(t)
C(Jk)
Deff
Ea
sensitivity function (–)
D
Hads
heat of adsorption (kJ molꢁ1
dielectric constant (–)
dipole moment (–)
)
cross correlation coefficient (–)
E
M
effective diffusivity (cm2 gꢁ1
)
activation energy (kJ molꢁ1
F-value (–)
)
F
Subscripts
A
I
inhibiting organic species
adsorption step
apparent
aromatic
reaction step
base temperature
desorption step
critical
inhibition step
of reaction i
of parameter j
number of model responses
ketone
number of model parameters
lumped
number of experiments
solvent adsorption step
at particle surface
apparent, volume-based
initial
(mol dmꢁ3
)
App
Arom
B
Base
C
Crit
D
I
k
rate constant (minꢁ1 (for 1st order))
kH
K
Henry’s constant (–)
equilibrium adsorption constant (dm3 molꢁ1 (for 1st or-
der))
L
n
N
P
Par
R
length (m)
reaction order (–)
stirred speed (minꢁ1
)
product organic species (mol dmꢁ3
number of parameters (–)
)
J
K
rate of reaction (mol dmꢁ3 minꢁ1 (for intrinsic rates un-
less noted))
Ket
L
Lump
M
S
s,A
rp
R
Rg
R2
S
particle size radius (cm)
reactant organic species (mol dmꢁ3
)
)
universal gas constant (J Kꢁ1 molꢁ1
sum of square of residuals (–)
solvent species (mol dmꢁ3
)
v
,app
0
Sk
T
parameter sensitivity matrix (–)
reaction time (min)
Acronym Description
T
temperature (K)
CBL
CBN
HPD
LH
PBL
PBN
TOF
4-cyclohexyl-2-butanol
Y
model response (–)
4-cyclohexyl-2-butanone
higher probability density
Langmuir-Hinshelwood
4-phenyl-2-butanol
4-phenyl-2-butanone
turnover frequency
[ ]
⁄
of concentration (mol dmꢁ3
active site (–)
)
Greek letters
hydrogen bond donor parameter (–)
a1
and chemical standpoint but are also pragmatic in nature so that a
broad spectrum of application is possible.
both the F- and T-tests and showed an excellent correlation
between solvent compositions, oxidation rate and the ketone des-
orption parameter.
Other approaches include the use of Michaelis–Menten-type
expressions [13]. This method was shown to be pragmatic in
describing solvent effects in ethyl pyruvate hydrogenation by
discriminating a lumped reaction term from one relating to
adsorption. The limited number of parameters in this model
compromises quality of fit and, therefore, may be difficult to
implement in multi-response systems.
1.1. Kinetic modelling of solvent effects in the literature
When modelling kinetics to describe solvent effects in catalytic
liquid multi-phase reactions it is essential that proposed models
have a fundamental mechanistic basis, together with estimated
parameters that are physically meaningful in value and are statis-
tically significant to justify their presence.
A number of studies have attempted to include a competitive
solvent adsorption term, KS, in their models. Kishida and
Teranishi [14] developed a model for the hydrogenation of acetone
using n-hexane as the solvent and, subsequently, fixed the rate
constants in order to measure KS for other solvents. The assump-
tion that the solvent does not influence rate constants was not jus-
tified in the work and the study also did not consider the effect of
hydrogen solubility as a function of solvent. In contrast, Lemcoff
[15] developed models with thermodynamically sound adsorption
parameters for a mixture of polar and apolar solvents, again for
acetone hydrogenation and found the Ks term was only significant
in the kinetic expressions for polar solvents such as water and
2-propanol. Recently, Mukherjee and Vannice [16] demonstrated
a similar approach for citral hydrogenation. Their model was
developed around citral conversion and validated against predic-
tion of product formation. In this work, the assumption that the
solvent competes for an active site is based around the fact that
Table 1 provides a summary of rate models that have previously
been used for this area of study. Bertero et al. [10] considered a
wide range of Langmuir–Hinshelwood (LH) expressions to describe
the hydrogenation of acetophenone. Quality of fit (R2) for all mod-
els used in this work was very high (0.999) possibly because at
least some were parametrically over-determined. Optimal model
choice was, therefore, based on the physical meaning of measured
parameters (such as discounting models with negative adsorption
constants) and using model selection criteria based upon compar-
ison of residuals and degrees of freedom in each final model.
Mathew et al. [11] utilised a similar approach and also checked
adsorption parameters for thermodynamic consistency.
Mounzer et al. [12] modelled the kinetics of 2-octanol oxidation
performed using a variety of n-heptane/dioxane mixtures as sol-
vents. A LH approach including a product ketone desorption
parameter, which was experimentally measured, provided the best
description. This model was found to be statistically significant via

364
S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
Table 1
Rate model approaches previously employed to model kinetics of solvent effects within liquid phase hydrogenations in the literature.
Ref.
Rate model
Mechanistic basis
kb ꢂKaꢂ½Rꢃ
ꢀ Bertero et al. [10]
ꢀ LH approach with competitive adsorption of organics
ꢀ Surface reaction rate determining step (r.d.s.)
ꢀ LH approach with product desorption term
ꢀ Surface reaction r.d.s.
P
r ¼
r ¼
n
1þKa ꢂ½Rꢃþ
Kd ½Iꢃ
ð
ð
Þ
ꢀ Mathew et al. [11]
ꢀ Mounzer et al. [12]
kb ꢂKa ꢂ½Rꢃ
n
½Pꢃ
1þKa ꢂ½Rꢃþ
Ka;b;c ꢂ½Rꢃ
Þ
K
c
ꢀ Gamez et al. [13]
ꢀ Michaelis–Menten approach
r ¼
r ¼
ð1þKa;c ½RꢃÞ
kb ꢂKaꢂ½Rꢃ
ꢀ Kishida and Teranishi [14]
ꢀ Lemcoff [15]
ꢀ LH approach with a competitive solvent adsorption term
ꢀ Assumes solvent interacts with catalyst surface
ꢀ Surface reaction r.d.s.
n
ð1þKaꢂ½RꢃþKs½SꢃÞ
ꢀ Mukherjee and Vannice [16]
Symbols denote the following:
ꢀ
ꢀ
ꢀ
r: rate of reaction (mol dmꢁ3 minꢁ1), k: rate constant (minꢁ1 (for 1st order)), K: equilibrium constant (L molꢁ1 (for 1st order)).
[ ]: concentration (mol dmꢁ3), R, P, I and S: reactant, product, inhibiting species and solvent respectively.
Subscripts a, b, c, d and s: reactant adsorption, surface reaction, product desorption, inhibition and solvent adsorption steps respectively.
other possible solvent effects namely, mass transport limitations,
liquid phase H2 solubility and liquid-phase non-ideality were
found to be insignificant in terms of influencing the large changes
in rate behaviour observed between different solvents. In all cases,
experimental validation for KS was not undertaken which limits
the physical meaning of this estimated parameter. The competitive
adsorption of the solvent onto an active site, whilst possible with
some solvent choices, is not necessarily a universal effect.
A key element which is missing from the aforementioned stud-
ies is a detailed statistical analysis which can ascertain the signif-
icance of each of the parameters in the models developed. Such
an approach could take model critique beyond R2 and the removal
of parameters due to lower or upper bound constraints. A possible
approach is afforded by Quiney and Schuurman [17] who described
the modelling of the water gas shift reaction kinetics under contin-
uous flow and used a methodology which examined parameter
sensitivities, parameter cross correlation and influence of parame-
ter removal on R2 values via use of the F-test.
[18]. Therein, a variety of solvents were tested which were found
to impact on the reaction pathway selectivity and rate of reaction.
In general, protic, polar solvents (primary and secondary alcohols)
favoured selectivity towards ketone hydrogenation whilst apolar,
aprotic solvents (alkanes) favoured the aromatic ring hydrogena-
tion route. In terms of the rates, those observed for alkanes and
secondary alcohols were much greater than those for aromatic or
primary alcohol solvents. A two-site active site model was postu-
lated, whereby the aromatic ring hydrogenation was proposed to
be occurring over the Pt, with ketone hydrogenation occurring at
the interface between the Pt and the TiO2 support with activation
of the C@O group through adsorption in the titania oxygen
vacancies.
In this paper, a kinetic model is presented utilising these data.
In this work, an aim is to stress the importance of using established
statistical analysis methods in the development of mechanistically
based kinetic models, with application in this case to liquid phase
hydrogenations and solvent effects. The approach, inspired by the
work of Quiney and Schuurman [17], is used to strengthen the
foundations of these kinetic models. A fundamental kinetic model
for ketone and aromatic hydrogenation catalysis in this system is
determined using an expansive dataset which employs n-hexane
as the solvent. From this model, the effects of a wide range of
solvents have been determined. This information provides a clear
demonstration of not only the role of solvents in influencing reac-
tion selectivity and reactant adsorption but also their interaction
with the metal and support of the catalyst during reaction.
1.2. Study of 4-phenyl-2-butanone hydrogenation over a Pt/TiO2
catalyst
In this paper
a detailed study of the hydrogenation of
4-phenyl-2-butanone (PBN) has been undertaken. This reaction
has two distinctive routes to produce the fully hydrogenated
product, 4-cyclohexyl-2-butanol (CBL). Intermediate compounds
are 4-phenyl-2-butanol (PBL), produced by hydrogenation of the
carbonyl group and 4-cyclohexyl-2-butanone (CBN), by hydro-
genation of the aromatic ring. The reaction scheme is shown in
Fig. 1 and features two reaction types, namely ketone (dashed
arrows) or aromatic ring (solid arrows) hydrogenation.
2. Materials and methods
2.1. Experimental reaction studies
The reaction system was chosen as the selectivity of the two
pathways from the original 4-phenyl-2-butanone reactant can be
influenced by the choice of solvent as shown by McManus et al.
The experimental materials and methods are described in detail
in the study by McManus et al. [18]; therefore, only a brief
recapitulation is given, herein.
The 4% Pt/TiO2 catalyst was supplied by Johnson Matthey and
was prepared by incipient wetness from Pt(NO3)4 (Johnson
Matthey) as the precursor with titania as the support (P25,
Degussa). The catalyst was dried for 12 h at 120 °C and then
calcined at 500 °C for 6 h. The catalyst was ground using a mortar
and pestle and sieved to 645 lm for all reactions. The BET surface
area of the catalyst Pt/TiO2 (P25) was 56 m2 gꢁ1 with a pore size of
2.2 nm. The titania had an anatase to rutile ratio of 3:1 as deter-
mined by XRD and TEM analysis showed a metal particle size of
2.2 nm with a dispersion of 33%.
Reaction studies were carried out using a 100 ml Hazard
Evaluation Laboratory (HEL) autoclave pressure reactor. In all
cases, 0.1 g catalyst and 30 ml solvent were added to the autoclave
and pre-reduced in situ under 1 bar H2 pressure, 60 °C, stirrer speed
Fig. 1. Hydrogenation pathway of 4-phenyl-2-butanone (PBN) to 4-phenyl-2-
butanol (PBL), 4-cyclohexyl-2-butanone (CBN) and 4-cyclohexyl-2-butanol (CBL).
Solid arrows indicate aromatic ring hydrogenation and dashed arrows indicate C@O
group hydrogenation.

S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
365
Table 2
shown in Fig. 1, so the models must be solved implicitly using a
set of differential equations:
Experimental data modelled in this study.
Series Variables
Constants
dy
dt
¼ fðy; bÞ
ð1Þ
A
B
Effect of PBN concentration
– 0.13–0.39 mol d mꢁ3 (5 points)
Effect of temperature
– n-Hexane solvent
– 70 °C operation
– n-Hexane solvent
– 0.26 mol dmꢁ3 starting
PBN concentration
In Eq. (1), y denotes model responses, t denotes time and b denotes
the model parameters. A direct decoupled method is used to esti-
mate parametric sensitivities [21,25]:
30–80 °C (6 points)
C
Effect of solvent
– Alkanes
– 0.26 mol dmꢁ3 starting
PBN concentration
@yðtÞ
– Aromatics
– 70 °C operation
BðtÞ ¼
ð2aÞ
@b
– Primary alcohols
– Secondary alcohols
– Halogenates
– Ethers
ꢀ
ꢁ
d
dy
d
dt
df
dy
df
db
¼
BðtÞ ¼
ꢂ BðtÞ þ
ð2bÞ
db dt
In Eq. (2a), B(t) defines the sensitivity function for each model
response with respect to the model parameters. In Eq. (2b) it can
be seen that defining sensitivities as a function of time allows them
to be solved alongside the main system differential equations,
improving solver efficiency and performance.
800 rpm for 1 h. Following reduction,
a
solution of
4-phenyl-2-butanone in a further 20 ml solvent was added to the
reactor; reactions were carried out at 70 °C, 5 bar H2 and
1400 rpm stirrer speed. The reaction kinetics are intrinsic and
not from transport limitations [18].
To minimise cross-correlation between the energy (activation
energy, Ea or equilibrium adsorption energy,
DHads) and
pre-exponential factor (Ai) parameters,
a
re-parameterised
Table 2 summarises the three strategies of the experimental
programme which have been taken in this work to build a
mechanistically sound kinetic model that will link selectivity and
adsorption constants to the choice of solvent. Series A utilises
isothermal data with different starting concentrations of
4-phenyl-2-butanone. This dataset will allow the impact of
concentration driving force on the kinetics to be explored. A
number of Langmuir–Hinshelwood type models (varying in rate
determining step and types of site) will be discriminated on the
basis of parameter estimate quality and model response residuals.
The best candidate models will be taken forward to Series B,
which incorporates multi-temperature data. Here, the activation
energies will be estimated and the models further refined. Model
fitting parameters will be strongly criticised from a statistical
and physico-chemical perspective. This will further discriminate
remaining models and potentially lead to additional fundamental
understanding of the prevailing reaction mechanism.
Arrhenius or van’t Hoff equation was used:
ꢀꢀ
ꢁ ꢀ
ꢁꢁ
Ea
Tbase ꢂ R
Tbase
T
ki ¼ Ai;343 ꢂ exp
ꢂ
1 ꢁ
ð3aÞ
ð3bÞ
ꢀꢀ
ꢁ ꢀ
ꢁꢁ
D
Hads
Tbase
T
Ki ¼ Ai;343 ꢂ exp
ꢂ
1 ꢁ
Tbase ꢂ R
where the base temperature, Tbase = 343 K and Ai,343 is the value of
the rate constant ki or Ki at 343 K. 343 K is chosen as this tempera-
ture was used for the isothermal stage (Series A) of the parameter
estimation process. Hence, this provides an accurate initial predic-
tion for the Ai parameters during the multi-temperature data fitting
stage, thus facilitating a more accurate estimation of Ea or
parameters.
The fitting process can be further improved by solving Ai,343 as
an exponential term and lumping fitted value, Ea or Hads with
constants Tbase and ideal gas constant, R (J Kꢁ1 molꢁ1) to give fitting
DHads
D
The most suitable model will finally be tested against experi-
ments using a range of solvents (Series C) with the purpose of
demonstrating the link between solvent, selectivity and the
dominant adsorption constant.
parameter Ea,lump or
Ai,343 and Ea,lump or
D
Hads,lump. This typically brings the values of
D
Hads,lump into the same order of magnitude
(typically 1–10) further reducing cross-correlation in this
expression:
ꢀ
ꢀ
ꢀ
ꢀ
ꢁꢁꢁ
ꢂ
ꢂ
ꢃ
ꢃ
2.2. Kinetic modelling procedure
Tbase
T
ki ¼ exp Ln Ai;343
þ
þ
Ea;lump
ꢂ
1 ꢁ
ð4aÞ
ð4bÞ
Parameter estimation within the kinetic models was carried out
using Athena Visual Studio v14.2Ó software [19]. The kinetic
models tested within this work contain non-linear parameters
(e.g. activation energies in the Arrhenius equation) and also
include multiple concentration responses. To handle these chal-
lenges, two estimation methods were used in succession, namely,
non-linear least squares and Bayesian estimation.
ꢀ
ꢀ
ꢁꢁꢁ
Tbase
T
Ki ¼ exp Ln Ai;343
D
Hads;lump
ꢂ
1 ꢁ
3. Results and discussion
In general, the non-linear least squares method was used for
initial discrimination of each of the kinetic models. The objective
function of this method is the total residual sum of squares for
the entire model. Subsequently the Bayesian estimation method
was used to fine tune the parameter estimation outputs. This
method considers the error covariance matrix between responses
and aligns the objective function accordingly. By this method,
any prejudice towards the smaller magnitude responses in the
3.1. Kinetic modelling of the effect of initial 4-phenyl-2-butanone
concentration in a n-hexane solvent
In the study by McManus et al. the reaction profiles as a func-
tion of time were shown to be very similar up to 60 min for all
starting concentrations [18]. Initial rates which are independent
of initial organic reactant concentrations have also been previously
seen for acetophenone hydrogenation [22]. This has been described
as an apparent zero order observation as it is relevant to the initial
stage of the reaction. Mechanistically, this observation suggests
that adsorption of 4-phenyl-2-butanone is strong on the catalyst
surface and may dominate in terms of surface coverage.
Therefore, it is important to incorporate 4-phenyl-2-butanone
dataset is largely eliminated enabling
a sounder basis for
multi-response estimation and a stronger critique of model perfor-
mance [20,21].
All response variables in the 4-phenyl-2-butanone hydrogena-
tion reaction network are dependent upon the multiple reactions

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S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
adsorption within mechanistic descriptions of the kinetics. In all
individual experiments however, 4-phenyl-2-butanone shows an
apparent order dependence of greater than one with reaction time,
irrespective of starting 4-phenyl-2-butanone concentration. These
observations are, therefore, consistent with a reaction mechanism
that may feature the following:
Eley–Rideal-type mechanism the denominator will remain
first-order.
ꢀ The first order in H2 behaviour in the paper of McManus et al.
would suggest that H2 behaves in an associative rather than
dissociative manner in the reaction mechanisms. In the latter,
an apparent order closer to 0.5 would be expected.
ꢀ H2 solubility into the liquid phase does change with either
solvent choice or temperature. This was incorporated into the
kinetic expressions [23].
ꢀ An adsorption term for the reactant 4-phenyl-2-butanone, as
apparent zero order observations in the work of McManus
et al. suggest a strong interaction of this species on the catalyst
surface.
Based on the elementary steps described in Eqs. (5a-5d), eight
candidate models were derived which may be suitable for the
4-phenyl-2-butanone hydrogenation system (see Table 3). These
models will systematically explore three key features of the
reaction mechanism:
ꢀ An influence of product adsorption effects, slowing the overall
progress of 4-phenyl-2-butanone conversion over time.
In order to explore these effects the following generalised
sequence of elementary steps was used as a basis for the kinetic
models in this study to describe the dataset in Series A:
ꢀ Rate determining step of mechanism: organic adsorption
(Eq. (5a)) or surface reaction/hydrogen adsorption (Eq. (5b));
the latter two steps cannot be decoupled in the dataset utilised.
ꢀ Apparent competition between organics and hydrogen for a
specific active site, or an Eley–Rideal type mechanism with H2
playing a gas-phase role only.
kA
⎯⎯→
R +*
R*i
ð5aÞ
ð5bÞ
ð5cÞ
ð5dÞ
i ←⎯⎯
kA'
kB
⎯⎯→
R*i
P*i
P*i
ꢀ The presence of different active sites for the ketone and
←⎯⎯
kB'
aromatic ring hydrogenation reaction routes.
kC
⎯⎯→
P +*i
The Series A dataset was fitted to all eight of the models described
in Table 3. The dataset comprised 25 independent experimental
observations (5 start concentrations ꢄ 5 batch-time sampling
points), each containing concentration responses for 4-phenyl-2-
butanone, 4-phenyl-2-butanol, 4-cyclohexyl-2-butanone and
4-cyclohexyl-2-butanol. Fig. 2 shows the residuals for all concentra-
tion responses in the eight models when a first estimation pass was
carried out using non-linear least squares.
←⎯⎯
kC'
kD
⎯⎯→
I +*
I *i
i ←⎯⎯
kD'
where *i denotes a particular active site on the catalyst surface
(where i = 1, 2, . . ., n). In conjunction with this the following are
noted:
Inspection of Fig. 2 affords some initial discrimination; models
6b, 6d and 6f systematically contain the lowest residuals for all
responses, models 6a and 6e exhibit poorer residuals for the
4-phenyl-2-butanone and 4-cyclohexyl-2-butanone responses
and models 6c, 6g and 6h are, in general, poorer in the prediction
for all responses. Further inspection of the batch-time predictions
of the latter three models showed the experimental results were
poorly captured. This was further confirmed by running the
parameter estimation routine using the Bayesian approach.
Before selecting a smaller group of strong candidate models,
the quality of the parameter estimates was also investigated
for the eight candidate models. As models 6a and 6e show a
clear compromise in residuals for 4-phenyl-2-butanone and
ꢀ The rate of hydrogenation of 4-phenyl-2-butanone was found to
be apparent first order in H2 in the study of McManus et al. In
the proposed models (Table 3), the hydrogen driving force is
always taken as first order. The H2 pressure varied data in
McManus et al. were explored at one starting
4-phenyl-2-butanone concentration (0.26 mol dmꢁ3). The need
for an additional H2 adsorption (and/or dissociation) equilib-
rium constant term was found to be negligible across these
data. This suggests either H2 does not adsorb onto the surface
(i.e. plays an Eley–Rideal type role) or its adsorption is signifi-
cantly weaker than the organics in competing for the same site.
ꢀ In order to explore the above possibilities, an ‘apparent’ site
competition effect will be explored by placing a square term
on the denominator of the kinetic expressions, and for the
4-cyclohexyl-2-butanone concentration responses,
a
further
Table 3
Candidate rate models for describing reactions in the 4-phenyl-2-butanone hydrogenation network.
Equation no.
(6a and 6b)
Generalised rate model
Basis
kb ꢂKaꢂ½Rꢃꢂ½H2
ꢃ
ꢀ Surface reaction or H2 ads. (Eq. (5b)) is the r.d.s.
P
r ¼
n
1þKa ꢂ½RꢃþKc ½Pꢃþ
Kd½Iꢃ
ð
Þ
ꢀ Same site for ketone and aromatic ring hydrogenation
ꢀ n = 1 (6a)a; n = 2 (6b)b
kb;ket ꢂKa;ket ꢂ½Rꢃꢂ½H2
1þKa;ket ꢂ½RꢃþKc;ket ½Pꢃþ
kb;arom ꢂKa;arom ꢂ½Rꢃꢂ½H2 ꢃ
1þKa;arom ꢂ½RꢃþKc;arom ½Pꢃþ
ꢃ
(6c and 6d)
ꢀ Surface reaction or H2 ads. (Eq. (5b)) is the r.d.s.
ꢀ Different site for ketone and aromatic ring hydrogenation
ꢀ n = 1 (6c)a; n = 2 (6d)b
P
rket
¼
n
Kd;ket ½Iꢃ
ð
Þ
P
rarom
¼
n
Kd;arom ½Iꢃ
ð
Þ
ka½Rꢃꢂ½H2
ꢃ
(6e and 6f)
(6g and 6h)
ꢀ Organic adsorption (Eq. (5a)) is the r.d.s.
ꢀ Same site for ketone and aromatic ring hydrogenation.
ꢀ n = 1 (6e)a; n = 2 (6f)b
P
r ¼
n
1þK ½Pꢃþ
Kd½Iꢃ
ð
Þ
b;c
ka;ket ½Rꢃꢂ½H2
ꢃ
ꢀ Organic adsorption (Eq. (5a)) is the r.d.s.
ꢀ Different site for ketone and aromatic ring hydrogenation
ꢀ n = 1 (6g)a; n = 2 (6h)b
P
rket
¼
n
1þK
½Pꢃþ
Kd;ket ½Iꢃ
ð
¼
Þ
b;c;ket
ka;arom ½Rꢃꢂ½H2ꢃ
P
rarom
n
1þK
½Pꢃþ
Kd;arom ½Iꢃ
ð
Þ
b;c;arom
a
n = 1 implies different adsorption site for organics and H2.
n = 2 implies same adsorption site for organics and H2.
b

S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
367
5
4.5
4
as they provide the best fitted description of the data matched by
the best parameter confidence intervals. All three models have
apparent site competition between organics and hydrogen in com-
mon, which is in line with observations discussed at the start of
this section.
Models 6b, 6d and 6f were subsequently tested using the
Bayesian estimation method for additional model refinement and
to identify parameters of importance in each model. The results
are presented in Table 4.
Each model is similar in overall performance, irrespective of the
objective function approach (e.g. Bayesian objective function and
residual sum of squares). For the rate constant (ln(k)) parameters,
a key difference is seen with model 6d which suggests that the
onward 4-cyclohexyl-2-butanone to 4-cylohexyl-2-butanol
(CBN ? CBL) reaction does not occur. For the adsorption (ln(K))
parameters there is a clear difference in the dominant product
inhibition, in both magnitude and confidence interval. The intro-
duction of temperature varied data is a necessary next step to
understand the difference between these models and discriminate
further.
PBN
PBL
CBN
CBL
Overall
3.5
3
2.5
2
1.5
1
0.5
0
6a
6b
6c
6d
6e
6f
6g
6h
Model Name
Fig. 2. Residual sum of squares for individual and overall concentration responses
for the Series A dataset when fitted to the eight candidate models in Table 3.
assessment can be made by looking at the quality of the parameter
estimate for the rate constant of the 4-phenyl-2-butanone to
4-cyclohexyl-2-butanone aromatic ring hydrogenation reaction
(PBN ? CBN), as shown in Fig. 3.
3.2. Kinetic modelling of the effect of temperature in a n-hexane
solvent
Critically, Fig. 3 shows that the confidence intervals for this
reaction are much larger for 6a and 6e than for the 6b, 6d and 6f
models. Similar trends were seen for the parameters describing
adsorption of 4-phenyl-2-butanone onto the surface. In line with
this, models 6b, 6d and 6f were taken forward for further analysis
Fig. 4 shows that in n-hexane, the selectivity is highest to the
product 4-cyclohexyl-2-butanone at all temperatures, formed via
hydrogenation of the aromatic ring in 4-phenyl-2-butanone. This
selectivity significantly increases with temperature. Selectivity
towards 4-phenyl-2-butanol (via ketone group hydrogenation) is
0
90
80
70
60
50
40
30
20
10
0
ln(k) (PBN-->CBN)
-1
-2
-3
-4
-5
-6
-7
-8
300
310
320
330
340
350
360
6a
6b
6c
6d
6e
6f
6g
6h
Temperature (K)
Model Name
Fig. 4. % Selectivity of products at different temperatures after 10 min (closed
symbols) and 120 min (open symbols) reaction. Symbols denote: ( ) 4-phenyl-
2-butanone, ( ) 4-cyclohexyl-2-butanone, ( ) 4-cyclohexyl-2-butanol.
Fig. 3. Estimated parameter values and 95% asymptotic confidence intervals for the
ln(k) parameter for the 4-phenyl-2-butanone to 4-cyclohexyl-2-butanone
(PBN ? CBN) reaction using the non-linear least squares method.
,
,
,
Table 4
Final Bayesian estimation results for models 6b, 6d and 6f using the Series A dataset.
Model 6b
Model 6d
Model 6f
Number of parameters
Bayesian objective function
Residual sum of squares
6
7
7
ꢁ94.0
ꢁ94.9
ꢁ97.4
9.35 ⁄ 10ꢁ4
7.63 ⁄ 10ꢁ4
6.86 ⁄ 10ꢁ4
a
Ln(k) rate constants (minꢁ1
PBN ? PBL
)
ꢁ4.08 0.17
ꢁ2.69 0.13
ꢁ6.59 0.20
ꢁ5.30 0.27
ꢁ5.75 0.34
ꢁ4.45 0.29
ꢁ5.70 0.32
Negligible
ꢁ5.87 0.21
ꢁ4.44 0.20
ꢁ5.56 0.23
ꢁ6.76 0.32
PBN ? CBN
PBL ? CBL
CBN ? CBL
Ln(K) equilibrium constants (dm3 molꢁ1
a
)
PBN
ꢁ0.16 0.69
2.69 0.35 (ketone site)
2.04 0.20 (aromatic site)
4.38 0.71
2.03 0.16
PBL
CBN
4.39 0.16
Negligible
3.76 0.56
0.46
2.86 0.23
a
Values are 95% higher probability density (HPD) intervals as determined by the Bayesian estimation method.

368
S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
considerably lower and decreases with temperature. These temper-
ature dependent observations suggest that the activation energy for
aromatic ring hydrogenation is higher than that for ketone group
hydrogenation, which agrees with the literature [22]. Selectivity
to the fully hydrogenated product 4-cyclohexyl-2-butanol,
increases with both time and temperature. In Fig. 4, after
120 min, the selectivity to 4-cyclohexyl-2-butanol appears to
increase with temperature at the expense of 4-phenyl-2-butanol
30
25
20
15
10
5
Model 6b (Rxn rds, 1 site, competitive)
Model 6d (Rxn rds, 2 site, competitive)
Model 6f (Ads rds, 1 site, competitive)
F-crit
selectivity.
4-Phenyl-2-butanol
to
4-cyclohexyl-2-butanol
(PBL ? CBL) is an aromatic ring hydrogenation route, again
demonstrating the prevalence of this reaction in n-hexane.
0
The Series B dataset was fitted to the three models taken
forward from Section 3.1. The dataset comprised 30 independent
experimental observations (6 reaction temperatures ꢄ 5
batch-time sampling points), each containing concentration
-5
0
1
2
3
4
5
6
Number of parameters removed from the fitting
procedure
responses
for
4-phenyl-2-butanone,
4-phenyl-2-butanol,
4-cyclohexyl-2-butanone and 4-cyclohexyl-2-butanol. Here the
rate and equilibrium constants fitted in Section 3.1 were expanded
into full Arrhenius and van’t Hoff equation form, as described in
Section 2.2.
Fig. 5. Calculated F-statistic for successive parameter removals across the entire
system response for different models. N.B.: Lines are to guide the eye.
Table 5
Models 6b, 6d and 6f comprised 12, 14 and 14 fitting parame-
ters respectively. The parameter values for the three isothermal
models displayed in Table 4 were used as the initial predictions
for the pre-exponential factors in the fitting in this section.
The first parameter estimation pass using Bayesian estimation
revealed similar residuals for all three models and a number of
parameters with large 95% HPD intervals. This suggested that all
three models were over-parameterised to describe the
multi-temperature dataset. Statistical analysis was carried out on
Parameter estimates and 95% HPD intervals for Model 6d using the Bayesian
estimation method.
Parameter
Estimate
95% HPD interval
Ln (A1,ket,343) (minꢁ1) (PBN ? PBL)
Ln (A1,arom,343) (minꢁ1) (PBN ? CBN)
Ln (A2,arom,343) (minꢁ1) (PBL ? CBL)
ꢁ5.80
ꢁ4.47
ꢁ5.68
27.9
50.9
2.74
0.12
0.05
0.10
3.47
2.00
0.24
0.18
0.09
Ea,ket (kJ molꢁ1
Ea,arom (kJ molꢁ1
Ln (Kket,PBN) (dm3 molꢁ1
Ln (Karom,PBN) (dm3 molꢁ1
Ln (Karom,CBN) (dm3 molꢁ1
)
)
)
)
1.98
2.81
each model using
a methodology based on Quiney and
)
Schuurman, [17] in order to remove non-influential parameters
from the fitting procedure. An example of this process, for a model
based on Eq. (6d) is shown in the Supplementary Information.
Each time a parameter is removed from an overall set of rate
expressions, an F-test is then invoked which addresses whether
the change in residuals of model responses in the ‘n ꢁ 1’ parameter
model in comparison with the ‘n’ parameter one is statistically
significant. This is often defined as a ‘nested model’ problem and
the F-statistic can be calculated as follows:
were equated with one another. In each case, this involved ‘pairing’
of reaction pathways which have the same mechanism: ketone
hydrogenation and aromatic ring hydrogenation.
For the most successful model, 6d, the adsorption parameter
Kket,PBL, featuring in the ketone hydrogenation routes, was found
to be insignificant. Meanwhile Karom,CBN was found to be a highly
significant parameter for the aromatic ring hydrogenation route.
The removal of the Karom,CBN parameter was found to have a signif-
icant effect on the residuals.
The final parameter estimates for model 6d, the most appropri-
ate model to describe the reaction kinetics of the system, are
detailed in Table 5. Full details of the final statistical plots (parity,
residual) for this model can be found in Supplementary
Information. The final rate equations for the model are as follows:
ꢄ
ꢅ
RSS1ꢁRSS2
par2ꢁpar1
RSS2
ꢄ
ꢅ
F ¼
ð7Þ
obsꢁpar2
where F is the F-statistic, RSS1 and RSS2 are the residual sum of
squares in the nested and original model respectively, par1 and
par2 are number of parameters and obs is the total number of obser-
vations. The F statistic generated is compared with Fcrit (p = 0.05)
under these constraints. If the F statistic is smaller than Fcrit, the
removal, equating or fixing of a parameter is deemed acceptable
as a statistically significant increase in residuals has not been
induced.
Fig. 5 shows the successive F-statistic values obtained when
parameters are removed from each of the model descriptions.
Model 6b showed statistically significant changes to the residuals
when more than 2 parameters are removed. Up to that point, the
model also contained indeterminate parameters when solved. A
similar outcome was seen for model 6f, albeit after the removal
of a large number of parameters. These models were discarded
due to both of these issues. Model 6d was the most successful
and did not exceed Fcrit during the removal of 6 parameters. At this
point, the model contained no indeterminate parameters or esti-
mates with 95% HPD intervals greater than 100% of the estimated
value.
k1;ket ꢂ Kket;PBN ꢂ ½PBNꢃ ꢂ ½H2ꢃ
rketðPBN ! PBLÞ ¼
ð8aÞ
ꢂ
ꢃ
2
1 þ Kket;PBN ꢂ ½PBNꢃ
k1;arom ꢂ Karom;PBN ꢂ ½PBNꢃ ꢂ ½H2ꢃ
raromðPBN ! CBNÞ ¼
raromðPBL ! CBLÞ ¼
ð8bÞ
ð8cÞ
2
ð1 þ Karom;PBN ꢂ ½PBNꢃ þ Karom;CBN½CBNꢃÞ
k2;arom ꢂ ½PBLꢃ ꢂ ½H2ꢃ
ð1 þ Karom;PBN ꢂ ½PBNꢃ þ Karom;CBN½CBNꢃÞ
2
Examining the results summarised in Table 5, the Ea for the aro-
matic ring hydrogenation steps is higher than that for ketone
hydrogenation, which was discussed following experimental
observation in Section 3.2. The Ea values estimated are in line with
a surface reaction limited mechanism rather than an organic
adsorption limited step. Previous work on a similar system, p-isobutyl
acetophenone hydrogenation [11] estimated Ea,ket and Ea,arom to be
42 and 47 kJ molꢁ1, respectively, whilst the heat of adsorption of
the reactant was ꢁ5 kJ molꢁ. 1 Similarly, in a kinetic study of ketone
A finding for all three candidate models was that the parameter
reduction procedure contained steps where two activation energies

S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
369
hydrogenation [23], heat of adsorption parameters was found to be
in the range ꢁ5 to ꢁ15 kJ molꢁ1. In the current study, the fitted heats
of adsorption parameters were found to be indiscriminate from zero,
which is feasible in line with the low value estimates from previous
studies. The removal of these heats of adsorption parameters for
model 6d is demonstrated in Table S3 of Supplementary Information.
The presence of the parameter Karom,CBN in the final model has
significant similarities with the study by Mounzer et al. [12]. This
suggests that desorption of this intermediate, the selective product
using n-hexane as the solvent, is a critical component of reaction
progress and selectivity. In parallel to this, the final model found
the subsequent ketone hydrogenation of 4-cyclohexyl-2-butanone
final stage of the aromatic hydrogenation reaction mechanism.
This suggests that in developing kinetics of solvent effects through
Langmuir–Hinshelwood descriptions, solvation and adsorption of
reactants and products may be coupled in many systems and care
must be taken in the interpretation.
3.3. Kinetic modelling of 4-phenyl-2-butanone hydrogenation in a
range of solvents
The kinetic model elucidated in Sections 3.1 and 3.2 can now be
applied to a range of solvent types (Series C in Section 2.1). In all
cases, individual solvent reaction data were fitted to a two site
model with competition between hydrogen and the organics. The
parameter reduction method of Quiney and Schuurman [17] used
above was again applied to reduce the expression if necessary.
As Fig. 6 shows, the generalised model for 4-phenyl-2-butanone
hydrogenation shows a good correlation when applied to a range of
different solvents and gives good predictions. The next step is to
assess the key parameters (karom, kket and Karom,CBN) across the
entire range of solvents.
Fig. 7 shows a log-linear plot of fitted adsorption constant,
Karom,CBN against 4-cyclohexyl-2-butanone selectivity after
120 min. A good correlation is seen for the majority of the solvents,
with acceptable 95% HPD intervals for the individual solvents in
most cases. This correlation was also observed at all reaction times
(see Supplementary Information, Fig. S4 for an example after
10 min). This relationship suggests that desorption of the
4-cyclohexyl-2-butanone product is a key factor in determining
the reaction selectivity in each of the solvents studied. For the
alkanes examined, the adsorption constant is low and the
4-cyclohexyl-2-butanone product is easily desorbed into the liquid
phase, giving rise to a high 4-cyclohexyl-2-butanone selectivity. In
primary and secondary alcohol solvents, the adsorption constant is
much higher and desorption of the 4-cyclohexyl-2-butanone
product back into the solvent is much more difficult. This may
be understood by the weaker solvation of the 4-cyclohexyl-
2-butanone in the hydrophilic alcohol solvents due to its greater
hydrophobicity. The result, when using these solvents, is a less
favourable desorption process for the 4-cyclohexyl-2-butanone
to be
a
negligible parameter, owing to the fact that
4-cyclohexyl-2-butanone shows a preference to adsorb on the
aromatic hydrogenation site rather than the ketone hydrogenation
site.
The final model confirms that the organic reactants, for both
reactions, compete with adsorbed hydrogen. In the study by
McManus et al. it was postulated that two active sites were pre-
sent, namely a Pt site which is largely selective to aromatic hydro-
genation and a site at the interface between the platinum and
titania support for ketone hydrogenation; C@O adsorption in an
oxygen vacancy weakening the C@O bond for hydrogenation. In
this study it was discussed that the former site could be sup-
pressed by the use of certain solvents such as aromatics, which
could strongly adsorb on the Pt. The success of the two site model
gives credence to this postulation and will be further tested for a
range of solvents in Section 3.3.
Qualitative discussion may be afforded around partition coeffi-
cients of the different reactants and products in this system (based
on their relative distribution in octanol vs. water at equilibrium)
which could explain the importance of Karom,CBN but not Kket,PBL
.
An examination of log P values reveals only a small transition
when 4-phenyl-2-butanone is converted to 4-phenyl-2-butanol
(2.46 ? 2.47) but it is significant when 4-phenyl-2-butanone is
converted to 4-cyclohexyl-2-butanone (2.46 ? 2.77). The strength
of 4-cyclohexyl-2-butanone adsorption appears to be a critical sol-
vent parameter in this case and more hydrophobic solvents, such
as the n-hexane examined, herein, may be critical to assisting this
0.25
0.25
A
B
0.2
0.2
0.15
0.1
0.15
0.1
0.05
0
0.05
0
0
20
40
60
80
100
120
0
20
40
60
80
100
120
Reaction Time (min)
Reaction Time (min)
0.25
0.2
0.15
0.1
0.05
0
0.25
0.2
0.15
0.1
0.05
0
C
D
0
20
40
60
80
100
120
0
20
40
60
80
100
120
Reaction Time (min)
Reaction Time (min)
Fig. 6. Batch concentration-reaction time plots for 4-phenyl-2-butanol hydrogenation in (A) n-hexane, (B) toluene, (C) 1-propanol, (D) 2-propanol at 70 °C, 5 bar H2 pressure
and 0.26 mol dmꢁ3 [PBN]. Symbols denote experimental readings, lines denote model predictions: ( ) 4-phenyl-2-butanone, ( ) 4-phenyl-2-butanol, ( ) 4-cyclohexyl-2-
butanone, ( ) 4-cyclohexyl-2-butanol.

370
S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
catalyst. In Fig. 9, the rate constants for ketone and aromatic
hydrogenation for the solvents are examined. Whilst the rate of
phenyl group hydrogenation (karom) is strongly dependent on
choice of solvent, the ketone group hydrogenation rate (kket) is
found to largely independent of the solvent used. The exception
to this is the secondary alcohol solvents and these will be discussed
later. The change in selectivity as a function of solvent is thus lar-
gely driven by its effect on the rate of phenyl group hydrogenation.
This is consistent with the proposed dual site nature of the catalyst
[18]. Again, the correlations shown in Fig. 9 were observed at all
different reaction times (see Supplementary Information, Fig. S5
for an example after 10 min).
An important note is that the normalised cross correlation
values between estimates of karom and Karom,CBN never reached
significant values (>0.95) [24]. This statistical observation further
shows that the key kinetic parameters used in fitting solvent data
describe different effects, in this case availability of sites and/or
rate (kket and karom-) as well as the ease of desorption of CBN over
Pt (Karom,CBN). Full details of condition numbers for all solvents
are given in Supplementary Information.
Fig. 7. Fitted adsorption constant, Karom,CBN plotted against 4-cyclohexyl-2-bu-
tanone %selectivity after 120 min for a range of solvents tested. ( ) denotes alkane
solvents, ( ) aromatics, ( ) primary alcohols, ( ) secondary alcohols, (⁄) ethers.
N.B.: No significant adsorption constant was found for halogenates.
The aromatic hydrogenation route has been discussed to occur
on the Pt sites of the catalyst surface [18]. Based upon this, karom
could be described as kPt(1 ꢁ hsolv) which relates the number of
vacant sites available as a function of solvent adsorption strength.
The flatness of the k1,ket parameter across most solvents suggests
that solvent inhibition is not a factor over this site. This site is
postulated to be the interfacial site which hydrogenates the C@O
bond, a functional group not present in any of the solvents used.
Product inhibition over the ketone hydrogenation site was
ultimately found to be a low sensitivity parameter in Section 3.2.
The clear exception in Fig. 9 is the secondary alcohols which
show karom sites in comparable levels to an alkane solvent and a
higher level of kket sites. In Fig. 6B, the selectivity to
4-cyclohexyl-2-butanone is found to be low in secondary alcohols,
which would suggest that these solvents do not strongly adsorb on
the Pt sites, but still inhibit reactant adsorption mode via a differ-
ent mechanism. An examination of dipolarity (px1) in [26] shows
that 1-propanol and 2-propanol have values of 0.52 and 0.48
respectively, whilst n-hexane has a value of ꢁ0.08. Hence, the large
difference in karom observed between primary and secondary
alcohols suggests that electronic effects are an unlikely cause of
this disparity. This indicates that the effect observed is likely to
be steric in nature, owing to the difference in adsorption conforma-
tion of primary and secondary alcohols.
product. A weaker trend is found for the aromatic solvents with
toluene and p-xylene showing low 4-cyclohexyl-2-butanone selec-
tivity and high Karom,CBN in contrast to tert-butyl-toluene which fea-
tures an alkyl group in its structure so may display aromatic-alkane
hybrid behaviour.
Fig. 8 shows the ratio of the rate constants for the two pathways
(karom/kket) with solvent. There is a clear connection between the
ratios of the rate constants (reflecting selectivity to
4-cyclohexyl-2-butanone) with solvent type: with high values
found for solvents with little interaction with the catalyst and
low values (61) for solvents which strongly interact with the
6
5
4
3
2
1
0
4-Cyclohexyl-2-butanone selectivity is also low in secondary
alcohols as this product does not desorb easily into the liquid
phase due to hydrophobicity factors discussed earlier. The higher
kket parameter for secondary alcohols may suggest this parameter
may be coupled in this instance, i.e. ketone hydrogenation is
Fig. 8. Calculated karom/kket ratios for the hydrogenation of 4-phenyl-2-butanone in
all solvents. The dotted line indicates a karom/kket ratio of 1 where there is no
preference for either pathway.
0.4
0.4
A
B
0.35
0.35
0.3
0.25
0.2
0.3
0.25
0.2
0.15
0.1
0.15
0.1
0.05
0
0.05
0
0
20
40
60
80
100
0
20
40
60
80
100
CBN Selectivity after 120 min (%)
CBN Selectivity after 120 min (%)
Fig. 9. Fitted rate constant, (A) kket and (B) karom plotted against 4-cyclohexyl-2-butanone % selectivity after 120 min for a range of solvents tested. ( ) denotes alkane
solvents, ( ) aromatics, ( ) primary alcohols, ( ) secondary alcohols, (⁄) ethers, (+) halogenates.

S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
371
occurring both at the interface sites (C@O activated by adsorption
in the vacancies on TiO2) and on Pt. In the study by McManus et al.
ketone hydrogenation in 2-propanol was possible over a Pt/SiO2
catalyst which lacks the vacancy sites found on a TiO2 support
showing the reaction can be facilitated by Pt.
Examining the use of doped solvents in Table 6 depicts the sep-
arate parameters which impact selectivity and active site availabil-
ity. kket is again largely unchanged across the results, whilst karom
drops by ꢅ60% when a small amount of toluene is added to the
n-hexane and by ꢅ85% when the solvent is completely switched
to toluene. Overall, 4-phenyl-2-butanone conversion over
120 min follows a similar trend. Selectivity is tuned much more
aggressively by the addition of toluene with a small amount influ-
encing the Karom,CBN parameter.
any kinetic study is the number of proposed models to which data
are subsequently fitted. Use of a range of models that include dif-
ferent rate determining steps in their mechanism [10,12,24],
assumptions of non-competitive and competitive reactant adsorp-
tion [16,22], dissociative or associative molecular adsorption
[11,22] and inhibition effects [12,16] all defines this scope. At a
maximum of these possibilities, model comparison without a sys-
tematic statistical analysis is likely to provide limited conclusions
which have a physical meaning. In the current work, such a range
of steps were condensed down into eight, ‘over-parameterised’,
starting models with different rate determining steps and active
site basis. From there, parameter reduction via sensitivity, condi-
tion number and F-test analysis takes each model to a defined stop
point. In this case, the bi-directional problem of over-simplifica
tion/complication of kinetic models can be avoided.
In the work of Bergault et al. [22], the batch-time acetophenone
hydrogenation behaviour draws comparison with the current
study, particularly with initial rate behaviour at different ace-
tophenone start concentrations. All possible adsorption effects
(including inhibition) were considered and led to indeterminacy
in their estimation when the data were fitted, as is seen in the cur-
rent study. This was circumvented by normalising the adsorption
constant values; however, therein the statistical significance of
the newly estimated parameters is not discussed. Similarly, their
proposed model does not link parameters in identical reaction
pathways, of which the estimated parameters in the work would
suggest to be a viable move. A similar process is found in the study
by Mathew et al. [11]. In this work, two Ea values for aromatic ring
hydrogenation are estimated at 47 and 44 kJ molꢁ1 but are left
unpaired. A parameter pairing approach in the current work was
found to have little impact on residuals and freed up extra degrees
of freedom to aid in the parameter estimation process, building on
these studies.
In Table 6, a comparison is made with parameter estimation
results estimated using the competitive solvent adsorption
approach described in Table 1, with the aim of comparing the cur-
rent method with a previous literature approach using concentra-
tion varied data. In this model, 5 adsorption parameters are fitted,
namely, Karom,CBN, Karom,hexane, Karom,toluene, Kket,hexane, and Kket,toluene
.
The hexane solvent adsorption terms were found to be insignifi-
cant on both sites, as was the adsorption of toluene on the ketone
hydrogenation site. A strong adsorption of toluene was estimated,
as postulated, and smaller but still significant adsorption strength
of 4-cyclohexyl-2-butanone was seen. The Karom,CBN parameter
returned a large 95% HPD interval but the removal of this parame-
ter showed a significant drop in model quality as ascertained by the
F-test. To further examine this result this parameter was reinstated
and the predictions using this model were examined (Fig. 10).
The solvent adsorption parameter model provides a reasonable
prediction of 4-phenyl-2-butanone consumption across the three
datasets but there are discrepancies in the selectivity prediction
of PBL and CBN, chiefly at high toluene concentrations. This is
matched by the high uncertainty but remaining importance of
the Karom,CBN parameter which suggests that this is changing as a
function of solvent concentration. This suggests the observations
cannot be related to adsorption strength of the catalyst surface
alone and factors such as solubility of the reactants and products
in the solvent, as discussed, must play a role in the overall observed
kinetics in this system.
A parallel can be drawn between the current study and the
mixed ketone hydrogenation study of Chang et al. [24]. The latter
eliminated parameters based on insignificant t-values and wide
95% confidence intervals. A product desorption term was found
to be a significant parameter for the dominant ketone hydrogena-
tion pathway but not the other reaction pathways. Instead, this
desorption term appears as an inhibition factor for the other path-
ways, again as reported in this study. The study also demonstrated
that all ketone hydrogenation routes could be adequately lumped
together into one expression, which is similar to the linking of
the reaction pathways demonstrated in this work.
3.4. Findings in context to previous solvent effects work
In Section 1.1, it was stressed that the pursuit of elucidating sol-
vent effects in liquid-phase reactions via kinetic modelling should
The importance of a product desorption term is also in line with
the work of Mounzer et al. [12], whereby desorption of product P
from active sites was driven by solvent composition. In the current
work, the ring hydrogenated product, 4-cyclohexyl-2-butanone,
incorporate
a strong statistical and mechanistic basis. The
approach demonstrated in this work is discussed in reference to
these critical requirements. The critical pre-determining step in
Table 6
Parameter estimates and 95% HPD intervals for fits of experimental data using mixtures of n-hexane and toluene as solvent. Comparison with results when fitting all experiments
at once using solvent adsorption approach.
Parameter
n-Hexane solvent
n-Hexane solvent doped with 5.7 wt%
toluene
Toluene solvent
Estimate
Estimate
95% HPD interval
Estimate
95% HPD interval
95% HPD interval
kket
karom
Karom,CBN
0.08
0.22
0.95
0.01
0.02
0.55
0.06
0.08
19.68
0.01
0.02
7.47
0.07
0.03
16.94
0.01
0.01
5.44
Estimate
95% HPD Interval
All three experiments fitted at once
kket
karom
Karom,CBN
Karom,Toluene
0.002
0.008
0.55
0.0002
0.0001
2.02
2.92
1.11

372
S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
3.00E-01
2.50E-01
2.00E-01
1.50E-01
1.00E-01
5.00E-02
0.00E+00
A further comparison can be made with previous works which
have used KS to describe the inhibition role of the solvent
[14,15,27]. In the current work, the essence of this parameter is
seen in the analysis of the full solvent range; values of karom are sig-
nificantly reduced in primary alcohols and aromatic solvents hence
providing a measure of inhibition to catalytically active sites com-
pared to solvents which adsorb weakly (e.g. alkanes). As described
earlier, solvent to substrate ratios are often high in batch-time
kinetic studies and so the magnitude of the [S] variable can induce
a bias towards KS in the fitting procedure, swamping the impor-
tance of other variables in the regression.
In the current work, the use of the Ks fitting approach was
explored over three datasets where hexane and toluene solvent
concentrations were varied. Whilst this approach clearly high-
lighted the strong adsorption of toluene over the sites for aromatic
ring hydrogenation, it was unable to achieve an encompassing
description across the dataset. This was attributed to the changing
Karom,CBN-parameter as a function of solvent choice which the
authors believe to be linked to ease of product desorption back into
the solvent. It is therefore recommended that care is taken when
considering the Ks parameter in the analysis and a prudent first
step is to analyse individual experimental runs without it.
A
0% Toluene
5.7% Toluene
100% Toluene
0
20
40
60
80
100
120
Time on stream (min)
6.00E-02
5.00E-02
4.00E-02
3.00E-02
2.00E-02
1.00E-02
0.00E+00
0% Toluene
B
5.7% Toluene
100% Toluene
4. Conclusions
The role of the solvent can be critical in many catalytic liquid
phase reactions, in particular influencing adsorption/desorption
of reactants and products as well as influencing overall catalytic
turnover rates and gas phase solubility. Development of a physi-
cally sound model of this role, as well as catalyst metal/support
and reactants/products is very complex due to the influence and
interdependencies between each of the model parameters. Data
from an experimental study of 4-phenyl-2-butanone hydrogena-
tion over a 4% Pt/TiO2 catalyst have been used to develop a kinetic
analysis methodology to elucidate solvent effects and unify solva-
tion, dominant adsorption constant and product selectivity.
The methodology has successfully drawn upon previous mech-
anistic descriptions proposed in the literature [11,12,22]. The fit-
ting of data to these models has been combined with a rigorous
statistical analysis procedure to eliminate non-influential parame-
ters in their descriptions [17]. During this procedure, the physical
and chemical meaning of estimated parameters was considered
and this led to pairing of similar reaction pathways (e.g. initial
reactant and intermediate ketone hydrogenation). The final model
assumed the surface reaction of the organic species with hydrogen
to be the rate determining step and included a selective product,
4-cyclohexyl-2-butanone, desorption term. Desorption of this pro-
duct was found to vary with solvent and was directly linked to the
observed product selectivity.
0
20
40
60
80
100
120
Time on stream (min)
1.60E-01
1.40E-01
1.20E-01
1.00E-01
8.00E-02
6.00E-02
4.00E-02
2.00E-02
0.00E+00
C
0% Toluene
5.7% Toluene
100% Toluene
0
20
40
60
80
100
120
The kinetic analysis methodology proposed can quickly eluci-
date a fundamentally and statistically sound kinetic model for a
chosen system even with limited experimental data. This can sub-
sequently be used to understand the link between solvent, domi-
nant mode of adsorption and selectivity as well as predict
catalytic turnover rates based on availabilities of different catalyti-
cally active sites in the presence of a range of solvents. In terms of
4-phenyl-2-butanone hydrogenation over 4% Pt/TiO2, kinetic mod-
elling has confirmed the presence of two active sites, the impact of
solvent on availability of Pt active sites and the role of the solvent in
assisting desorption of intermediate 4-cyclohexyl-2-butanone [18].
Time on stream (min)
Fig. 10. Experimental (squares) against model predictions (lines) for (A) 4-phenyl-
2-butanone (PBN), (B) 4-phenyl-2-butanol (PBL) and (C) 4-cyclohexyl-2-butanone
(CBN) for the approach incorporating a solvent adsorption parameter for three
experiments varying hexane to toluene solvent concentration.
exhibits greater hydrophobicity than that of the ketone hydro-
genated product 4-phenyl-2-butanol. The former has a greater like-
lihood of removal from the catalyst surface by apolar aprotic
solvents such as n-hexane compared with the alcohols. The correla-
tion between solvent selectivity towards 4-cyclohexyl-2-butanone
and Karom,CBN may be a reflection of this. It is suggested that for
future study, this selective adsorption effect could be explored
computationally via the use of density functional theory (DFT), such
as the approach used in the work explored in [4].
Acknowledgments
We acknowledge EPSRC for funding as part of the CASTech
grant (EP/G011397/1) and the Department of Employment and

S.K. Wilkinson et al. / Journal of Catalysis 330 (2015) 362–373
[8] R.A. Sheldon, Green Chem. 9 (2007) 1273.
373
Learning for a studentship (IM). NSB was funded by a PhD scholar-
ship from the University of Birmingham. SKW was supported by an
Engineering Doctorate Studentship in Formulation Engineering at
the University of Birmingham sponsored by the EPSRC
(EP/G036713/1) and Johnson Matthey. The authors would also like
to acknowledge Dr Mike J. Watson (of Johnson Matthey) for valu-
able discussions on this topic.
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Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.jcat.2015.06.007.
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