Kinetic study of homogeneous alkene hydrogenation by model discrimination

Article abstract of DOI:10.1002/adsc.200303220

Model discrimination is one of the methods of choice to obtain a valid kinetic description of a catalytic reaction with minimal experimental effort. It allows fast judgement of catalyst behavior and its suitability for process development. Using dynamic experiments and modeling, the kinetics of a homogeneous hydrogenation with cationic rhodium-PyrPhos {[Rh(PyrPhos)(COD)] BF₄} were investigated. A set of three batch experiments allowed the discrimination between 6 models. Qualitative and quantitative descriptions of the kinetic behavior could be derived. Most importantly, evidence for catalyst deactivation was gained.

Full text of DOI:10.1002/adsc.200303220

FULL PAPERS
Kinetic Study of Homogeneous Alkene Hydrogenation by Model
Discrimination
Lasse Greiner,a,* Michel Brik Ternbachb
a
Institut für Technische und Makromolekulare Chemie, RWTH Aachen, Worringerweg 1, 52072 Aachen, Germany
Fax: (þ49)-241-802-2177, e-mail: l.greiner@itmc.rwth-aachen.de
b
Institut für Biotechnologie, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
Received: December 2, 2003; Revised: June 25, 2004; Accepted: July 2, 2004
SupportingInformation for this article is available on the WWW under http://asc.wiley-vch.de/.
Abstract: Model discrimination is one of the methods between 6 models. Qualitative and quantitative de-
of choice to obtain a valid kinetic description of a cat- scriptions of the kinetic behavior could be derived.
alytic reaction with minimal experimental effort. It al- Most importantly, evidence for catalyst deactivation
lows fast judgement of catalyst behavior and its suita- was gained.
bility for process development. Usingdynamic experi-
ments and modeling, the kinetics of a homogeneous
hydrogenation with cationic rhodium-PyrPhos Keywords: deactivation; dihydrogen; homogeneous
{[Rh(PyrPhos)(COD)]BF4} were investigated. A set catalysis; hydrogenation; model discrimination; simu-
of three batch experiments allowed the discrimination lation
Introduction
ly low concentrations are necessary to obtain complex-
bindingconstants from initial rates.
Hydrogenationwithtransitionmetalcomplexes is among
Furthermore, conversion data from small numbers of
the best studied and developed fields of homogeneous samplesof dynamicexperiments are often insufficient to
catalysis.[1] In spite of this, only a small number of these support even a simplified model and alternative models
processes has evolved so far for the enantioselective pro- may seem equally valid. It is advantageous to use on-line
duction of fine chemicals on larger scale.[1,2] Amongother
techniques with higher sampling rates to obtain a good
factors, a lack of quantitative kinetic descriptions under basis for dynamic modeling.[7]
catalytic conditions is named as a reason.[3]
In this paper, we report the simulation of dynamic ki-
A thorough kinetic description of catalytic systems al- netic models to batch reactor data. The homogeneous
lows optimization of reaction conditions in order to im- hydrogenation of N-acetylaminocinnamic acid (2) by a
prove the stability and activity of the catalyst as ex- PyrPhos-based rhodium complex[8] {[Rh(PyrPhos)-
pressed by total turnover number and turnover frequen- (COD)]BF4; 1-COD} was used as a model system. The
cies, respectively.[3] Whereas a number of studies on the reaction was monitored in a constant pressure reaction
effect of hydrogen pressure and mass-transfer on the se- autoclave by measuringhydrogen uptake rate on-line.
lectivity of homogeneous catalytic hydrogenations have Various models were fitted to experimental hydrogena-
been reported,[4] kinetic studies are rare.[3,5]
tion rates to obtain the best kinetic description via mod-
Description of the kinetics of homogeneous catalysis el discrimination.[9]
faces several difficulties. The use of initial rate measure-
ments is often problematic as the true catalyst is first
formed from a precatalyst species. Therefore, the con- Results and Discussion
centration of active catalyst is a function of time and
true initial rates may not be accessible. This activation The investigated catalyst is the rhodium(I) complex of
may be a complex phenomenon, heavily dependingon
the pyrrolidine-based diphosphine ligand PyrPhos and
experimental conditions, e.g., mass transfer and sub- cyclooctadiene with tetrafluoroborate as counterion
strate to catalyst ratio.[6] To be undisturbed by such acti- {[Rh(PyrPhos)(COD)]BF4, 1-COD}.[8] The catalyst 1 is
vation phenomena, commonly a large excess of starting liberated from the precatalyst complex and catalyzes
material has to be employed in order to reach the max- the hydrogen-consuming main hydrogenation reaction
imum reaction rate after activation. In contrast, relative- of 2 to the phenylalanine derivative 3 (Figure 1).
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DOI: 10.1002/adsc.200303220
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Kinetic Study of Homogeneous Alkene Hydrogenation
FULL PAPERS
All models are hyperbolic in the concentration of 2
and share the same nominator as the drivingforce of
the reaction.
ð2Þ
Denominator D reflects adsorption equilibria of the cat-
alyst with the reaction partners. The different denomi-
nators for each model are given in Table 2.
To account for the deactivation of active catalyst, a
first order irreversible decay to an inactive form was as-
sumed and combined with simple Michaelis–Menten ki-
netics (model 1) togivemodel 5. Analogously, combina-
tion of model 4 takinginto account inhibition of both
substrate and product gave model 6. The respective
equations formed the system of ordinary differential
equations for each model.
Figure 1. Simplified reaction scheme for the hydrogenation
of 2-N-acetylaminocinnamic acid (2) to N-acetylphenylala-
nine (3) by catalyst 1, which is liberated from its COD com-
plex 1-COD.
Table 1. Symbols and abbreviations.
ð3Þ
Symbol Usage
Unit
[A]
D
kact
kdeact
K2
concentration of substance A
denominator of Equation (2)
mmol LÀ1
mmol LÀ1
hÀ1
Initial concentrations of substrate 2 were estimated
within 95–105% of the amount which was weighed in
for each experiment, because of the strongsensitivity
of the results of the simulation with respect to this con-
centration in the final phase of the experiments. Conver-
sion of the substrate was found to be quantitative in each
experiment as determined independently by capillary
electrophoresis. This complete conversion at the end
of the experiment is met by the simulations with the es-
rate constant for catalyst activation
rate constant for catalyst deactivation hÀ1
À1
complex bindingconstant for 2
inihibition constant for A
limitingreaction frequency
mmol L
Ki,A
vmax
mol LÀ1
mmol L
À1
Six different dynamical models were fitted to the timated adjusted initial concentrations.
measured hydrogen uptake rates of the system per
The parameters of the respective system of ordinary
used volume (symbols and abbreviations in Table 1). differential equations of all models fitted to the three ex-
The measured values were weighed by the estimated periments simultaneously are shown in Table 3 together
standard deviations which were 7.0·10À4, 5.0·10À4 and with the 95% accuracy limits.
11·10À4 for experiments 1, 2 and 3, respectively.
Even though the mechanism of the hydrogenation is
All models presume irreversible first order kinetics most likely to be more complex, the kinetics can be de-
for the activation of the catalyst:
scribed rather well by the simplified rate equations,[5] un-
der the boundary conditions of our experiments (con-
stant hydrogen pressure/concentration and tempera-
ture). This also holds for the simple first-order deactiva-
ð1Þ
A fraction of the catalyst was assumed to be already in tion of the catalyst where a much more complex deacti-
the active form 1 at the beginning of the experiment. vation route is likely as shown for the DIOP ligand.[10]
This fraction was estimated as an extra parameter for
each experiment.
The difference between model predictions and meas-
urements was weighed by the standard deviation and vi-
Table 2. Denominators D in Equation (2) and whether equation (3) for deactivation was included in the model.
Model
D in Equation (2)
Eq. (3)
Description
1
2
3
4
5
6
K2 þ[2]
–
–
–
–
Michaelis–Menten kinetics
substrate surplus inhibition
competitive product inhibition
both inhibition types
as model 1 but with deactivation
as model 4 but with deactivation
K2 þ[2](1þ[2]/Ki,2)
K2 (1þ[3]/Ki,3)þ[2]
K2 (1þ[3]/Ki,3)þ[2](1þ[2]/Ki,2)
K2 þ[2]
þ
K2 (1þ[3]/Ki,3)þ[2](1þ[2]/Ki,2)
þ
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Table 3. Parameter estimates with the estimated 95% accuracy bounds and reduced c2 values. (‡ these values are at the upper
boundary).
Model
1
2
3
4
5
6
Unit
hÀ1
kact
kdeact
K2
vmax
Ki,2
Ki,3
c2
1.541Æ0.012
1.566Æ0.012
1.403Æ0.010
–
5.96Æ0.17
1.404Æ0.010
–
7.61Æ0.21
1.045Æ0.007
1.103Æ0.008
–
–
0.012Æ9·10À5
0.012Æ13·10À5 hÀ1
25.3Æ0.11
27.4Æ0.18
17.6Æ0.09
20.5Æ0.23
12.0Æ0.019
14.8Æ0.45
11.8Æ2.6
3.0
mmol LÀ1
minÀ1
10.8Æ0.006
11.0Æ0.013
10.7Æ0.005
10.9Æ0.012
11.6 Æ0.009
–
–
7.0
40‡
–
–
40‡
–
–
3.4
mol LÀ1
mol LÀ1
0.177Æ0.007
0.221Æ0.008
4.2
6.8
4.3
Figure 2. Experimental data (dots) and simulation according
to model 5 (straight line).
Figure 3. Weighed residuals of models 1, 3, and 5 for all meas-
ured values of the three experiments
sualized in a residual plot (Figure 3). Due to weighing,
more than 95% of the residuals from well-fittingmodels
should lie in the interval [À2;2]. Proper models should Model 6, with inhibitions, fits slightly better than mod-
furthermore not show trends in their residual plots. el 5. Model 6, however, uses 2 parameters more than
Clearly, the deviation between model prediction and model 5, and the values of these inhibition constants
measured values is systematic for models which do not are too high to be physically meaningful.
take into account deactivation [Equation (3)] (models
Better discrimination between the models 5 and 6
1–4) (Figure 3). Especially, simulated rates towards should be possible at higher substrate concentrations.
the end of the experiments deviate significantly from Simulation of the models with initial substrate concen-
measured values.
trations of more than 2 mol LÀ1 show significant differ-
The substrate inhibition constants Ki,2 for models 2 ence in the predicted reaction rates (data not shown).
and 4 are at the upper boundary of the allowed parame- However, the solubility limit of 2 is approximately
ter space and do not have a significant influence on the 1.2 mol LÀ1 (methanol, 208C), so that experimental ver-
course of the simulation. All inhibition constants for ification is not possible in this way. At and below the sol-
both substrate surplus and product inhibition are gener- ubility limit models 5 and 6 predict practically identical
ally too large to be physically meaningful, especially rates.
when compared to substrate complex bindingconstants
K2 which are at least 29 times smaller and were fitted
within the same boundaries. Furthermore, parameters Conclusion
Ki,3 and K2 are strongly correlated in models 3 and 4 (cor-
relation coefficients>0.98, data not shown).
Model discrimination usingsimulation of dynamic mod-
The model which describes the course of the reaction els, together with on-line measurement of reaction rates,
without systematic deviations with the minimum num- provides a powerful tool for the investigation of the ki-
ber of parameters is model 5 (Figure 2): a Michaelis– netics of homogeneous catalytic reactions. By this
Menten type model with deactivation of the catalyst means a system in which initial rates are not accessible
and without inhibition.
was investigated.
Model discrimination reveals that the investigated
The reduced c2 values confirm that the models with
deactivation (i.e., model 5 and 6) perform best (Table 2). catalyst is unstable under the reaction conditions. The
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Kinetic Study of Homogeneous Alkene Hydrogenation
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personal computer with software written in LabView (Nation-
al Instruments, Austin, USA).
fit of models takinginto account first-order deactivation
shows best results in describingthe course of the reac-
tion. For continuous processes, the stability of the cata-
lyst must be higher than that resulting from deactivation
of kdes ¼0.012 hÀ1. The correspondinghalf life time of
t1/2 ꢀ 58 h[11] did not favor further efforts aimingfor con-
tinuous catalysis.
As all experiments reach quantitative conversion
within a reasonable time, a less detailed kinetic investi-
gation would have missed deactivation of catalyst. Thus,
combination of on-line monitoringand kinetic modeling
points out catalyst robustness under truly catalytic con-
ditions. This result emphasizes that development of new
homogeneous catalysts should be accompanied by thor-
ough kinetic investigations at an early stage.
Modeling
Modelingwas performed in Matlab/Simulink (The Math-
works) on a personal computer. The models were limited to de-
scribe the system at constant pressure (10 bar) in methanol at
258C. Models were fitted to experimental data of three experi-
ments simultaneously. Experiments differed in the starting
concentration of substrate (0.46 M, 0.46 M, and 1.00 M in ex-
periments 1, 2 and 3, respectively) and catalyst (0.10 mM,
0.05 mM, and 0.10 mM in experiments 1, 2 and 3 respectively).
The experiments were carefully chosen to be free from mass
transfer limitations.
The measured data were used as obtained without smooth-
ing. Measured data from the initial period of each experiment
duringwhich the flow control settled, typically about 30 mi-
nutes, were discarded before fittingthe models to the data.
The model parameters were estimated by minimizingthe
sum of squares of the deviations between the measured and si-
mulated hydrogen consumption rates, weighed by the standard
deviations of the measured values. For each experiment, a con-
stant absolute value for the standard deviation was estimated
from the measured values in a period with an essentially con-
stant hydrogen consumption rate. Constant values were taken
as it was assumed that the deviations were mainly caused by
fluctuations which are independent of the measured uptake
rates. The normal distribution assumption was checked by a
normal probability plot (data not shown).
Experimental Section
Methanol, N-acetylaminocinnamic acid (2), and both enan-
tiomers of N-acetylphenylalanine (3) were obtained in analyt-
ical grade from Sigma (Taufkirchen, Germany). Gases were of
99.9990% purity and obtained from Messer (Krefeld, Germa-
ny). PyrPhos-based rhodium cyclooctadiene (COD) {[Rh(Pyr-
Phos)(COD)]BF4 complex; 1-COD} as tetrafluoroborate salt
was a kind gift of Degussa AG, Hanau, Germany.[8] Conversion
and enantiomeric excess were determined by capillary electro-
phoresis[12] {Beckman Pace/MDQ equipped with an uncoated
fused silica capillary (Supelco CElectFS25, Sigma-Aldrich,
Taufkirchen, Germany) (length to detection window 50 cm, to-
As quality indicator for the fit of models, ꢁreduced c2ꢂ values
were calculated (Table 3).[13] Moreover, modelingresults were
evaluated by judging the obtained residual plots. Residuals in
the plots were weighed by the estimated standard deviations
of the measurements. Accuracy bounds on the model param-
eters were calculated from the diagonal of the estimated cova-
riance-matrix for each parameter.[14]
tal length 57 cm) in a 125 mmol LÀ1 potassium phosphate buf-
fer at pH 10.2 containing25 mmol L
trin, 168C, 30 kV, migration times: 2 13.4 min, 3: S 14.1 min,
R 14.3 min}. Solvents were degassed prior to use by purging
with helium and argon. Sensitive compounds were handled us-
ingstandard Schlenk-type techniques.
À1
dimethyl-b-cyclodex-
Conversion of the substrate was found to be quantitative in
each case as determined by capillary electrophoresis. The
enantioselectivity of the reaction was confirmed to be pres-
sure-independent (enantiomeric ratio 32, enantiomeric ex-
cess 94%).[8] The hydrogenation was investigated in a constant
pressure autoclave (Mechanical Workshop of the Institute of
Biotechnology, Forschungszentrum Jülich, Germany). The
stainless steel autoclave (100 mL total volume) was equipped
with a glass insert and magnetic stirring bar. The reaction vessel
was charged with substrate 2 evacuated (<0.1 mbar) and
purged with argon three times, before the precatalyst 1-COD
in 50 mL of methanol was transferred into the reactor under
positive argon pressure. The reaction mixture was stirred to
bring 2 into solution (2–3 min as determined by independent
experiments). The reactor was then pressurized with hydrogen
and tested for leakage. The reaction was started by stirring with
an external magnetic stirrer. The autoclave was equipped with
electronically controlled pressure and mass flow controllers
(Bronkhorst, Rurloo, Netherlands). By this means a constant
pressure was maintained (deviation less than 1% duringreac-
tions) and the hydrogen uptake of the system was monitored.
Once the reaction mixture is saturated with hydrogen the up-
take rate equals the reaction rate due to reaction stoichiometry.
Data storage and control of the system were performed on a
Acknowledgements
We wish to thank Jens Wöltinger and Dietmar Reichert (Degus-
sa AG, Hanau, Germany) for the kind gift of catalyst and discus-
sion; Andreas Franz, Daniela H. Müller, and Christian R. Reim-
ers (all of Forschungszentrum Jülich) for skilful technical sup-
port. We both thank Christian Wandrey (Forschungszentrum
Jülich) for his continuous support. Our research was facilitated
by financial support from the German Federal Ministry of Edu-
cation and Research (BMBF) and Degussa AG.
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