Insight into β-carotene thermal degradation in oils with multiresponse modeling

Article abstract of DOI:10.1007/s11746-011-1864-2

The aim of this study was to gain further insight into β-carotene thermal degradation in oils. Multiresponse modeling was applied to experimental highperformance liquid chromatography-diode array detection (HPLC-DAD) data (trans-, 13-cis-, and 9-cis-β-car

Full text of DOI:10.1007/s11746-011-1864-2

J Am Oil Chem Soc (2011) 88:2035–2045
DOI 10.1007/s11746-011-1864-2
ORIGINAL PAPER
Insight into b-Carotene Thermal Degradation in Oils
with Multiresponse Modeling
•
Nawel Achir Caroline Penicaud Sylvie Avallone
•
•
´
Philippe Bohuon
Received: 13 January 2011 / Revised: 22 April 2011 / Accepted: 22 May 2011 / Published online: 12 June 2011
Ó AOCS 2011
Abstract The aim of this study was to gain further
insight into b-carotene thermal degradation in oils. Mul-
tiresponse modeling was applied to experimental high-
performance liquid chromatography–diode array detection
(HPLC–DAD) data (trans-, 13-cis-, and 9-cis-b-carotene
concentrations) during the heat treatments (120–180 °C) of
two b-carotene-enriched oils, i.e., palm olein and copra.
The test of different reaction schemes showed that b-car-
otene isomerization reactions were dominant and revers-
ible. The resulting cis isomers and trans-b-carotene
simultaneously underwent oxidation and cleavage reactions
at the same rate constant. From the kinetic analysis, it
appeared that—contrary to oxidation and cleavage reac-
tions—isomerization rate constants did not follow the
Arrhenius law. However, the isomerization equilibrium
constant increased with temperature, favoring isomer pro-
duction, particularly 9-cis-b-carotene. Its production was
shown to be concomitant with oxidation and cleavage
reactions, indicating that 9-cis-b-carotene could be a good
degradation indicator during oil storage or processing.
Introduction
b-carotene is the most widespread carotenoid and is found
in a high content in orange vegetables, such as pumpkin,
carrot, sweet potatoes, and palm fruit [1, 2]. With its
perfect vitamin A dimer structure, b-carotene is the most
important source of this vitamin. Its conjugated polyenic
system is also responsible for its orange color, but, above
all, for its antioxidant properties. b-carotene is a very
efficient O2 singlet quencher and can protect molecules
against oxidation [3]. However, its unsaturated structure
is very fragile and can degrade via two main reactions:
isomerization and oxidation [4]. b-carotene isomerization
involves a configuration change from its natural trans
form to various cis isomer species. Double bonding is
weakened by resonance, even at ambient temperature,
thus, facilitating this interconversion [5]. However,
isomerization was shown to be favored by temperature
and, to a minor extent, by light [6]. The resulting isomers
can still be converted into vitamin A, but with a lower
yield [7]. Oxidation is the major cause of b-carotene loss
and takes place through a radicalar mechanism. Indeed,
the long double bond chain is an excellent substrate for
free radical attack. These autooxidation reactions have
high activation energies [8] and are irreversible, as the
resulting products are oxicarotenoids and cleavage prod-
ucts such as apocarotenals and apocarotenones [9].
Hundreds of molecules can be produced from b-carotene,
some of which are likely prooxidants [10]. The numerous
reactions involved are strongly influenced by exterior
conditions (i.e., temperature, oxygen pressure) and the
medium composition [11].
Keywords Carotenoid ꢀ Isomerization ꢀ 13-cis-b-
carotene ꢀ 9-cis-b-carotene ꢀ Oxidation ꢀ Reaction scheme ꢀ
Kinetics ꢀ Lipids
´
N. Achir (&) ꢀ C. Penicaud ꢀ P. Bohuon
UMR 95 QualiSud, TA B-95/16, 73 Av. J.F. Breton,
34398 Montpellier Cedex 5, France
e-mail: nawel.achir@cirad.fr
Many studies have aimed at monitoring b-carotene
degradation kinetics in order to control, predict, and opti-
mize its retention during food storage. This dynamic
S. Avallone
UMR 204 NutriPass, 911 Avenue Agropolis,
34394 Montpellier Cedex 5, France
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J Am Oil Chem Soc (2011) 88:2035–2045
approach is interesting for identifying major degradation
pathways and their evolution as a function of exterior
conditions, but most kinetic models described in the
literature only represent b-carotene loss [12, 13]. These
models may help in predicting b-carotene loss in com-
parable conditions but cannot indicate the prevalence of
each degradation pathway, since a single apparent deg-
radation rate constant includes all specific degradation
rates. Some studies have not only monitored b-carotene
loss but also degradation products, such as cis isomers
[14], and, less frequently, oxidized or cleavage products
[15]. However, no kinetic models were developed on
the basis of these experiments. This is probably because
the consideration of different degradation molecules
requires knowledge of the degradation reaction scheme
and the use of multiresponse modeling to identify the
different reaction rate constants. This approach could
still give insight into the reaction, as was the case for
Maillard reactions in the study of van Boekel [16].
Surprisingly, very little work has been done on b-car-
otene with multiresponse modeling, whereas b-carotene
degradation forms a very dense reaction scheme, the
mechanisms of which are still very unclear [11]. Zepka
et al. [17] proposed a simplified multiresponse model to
represent carotenoid degradation in a model cashew
apple juice. The reaction scheme involved parallel
reactions of both trans-b-cryptoxanthin and trans-b-
carotene to yield degradation compounds and mono-cis
isomers. Therefore, through the global monitoring of the
two types of product (volatile and non-volatile, respec-
tively), they could identify the different rate constants,
differentiate the two pathways, and even evaluate the
temperature effect. However, specific studies on b-car-
otene degradation mechanisms could not be found. For
instance, the very early stages of b-carotene autooxi-
dation are not yet clear. Mordi [18] supposed that
isomerization could be the first step of oxidation,
whereas Mohamed et al. [19] suggested that oxidation
could more easily occur directly on trans-b-carotene at
its b-ring. Concerning the kinetic aspect, the main
b-carotene isomerization rate constants are only avail-
able at low temperature when oxidative reactions are
negligible [20]. Therefore, the influence of temperature,
which can affect the reaction dynamics and, thus,
change the main reaction pathways, has not yet been
studied. cis isomer concentrations can be easily deter-
mined using reliable high-performance liquid chroma-
tography (HPLC) devices developed for this purpose
[21]. However, oxidized and cleavage molecules are
much harder to monitor because of their high number
due to random oxygen attack and their variable prop-
erties (different functions, volatility, etc.).
The aim of this study was to apply multiresponse
modeling to the experimental data of b-carotene thermal
degradation, along with high-performance liquid chro-
matography–diode array detection (HPLC–DAD) analysis
in two frying oils at temperatures ranging from 120 to
180 °C. Firstly, simplified reaction schemes are proposed
on the basis of the analysis of trans-b-carotene and its cis
isomer concentrations during heat treatments. The focus
was placed on the reversibility or not of the isomerization
reactions and on their relationship with the formation of
oxidized products. For each system, the rate constants
were estimated by non-linear regression, via multire-
sponse modeling. After the election of the best scheme,
the effect of temperature and oil type on the distinct
reaction constants of isomerization and oxidation are
discussed.
Materials and Methods
Thermal Treatment of b-Carotene-Enriched Oils
The experimental procedure used to collect experimental
data was presented in a previous paper [22]. Briefly, ther-
mal treatments were carried out on two commercial oils,
i.e., palm olein and copra fat, previously enriched in
b-carotene at an average concentration of 220 mg kg-1
,
which is close to that found in red palm oil [23]. The
isothermal treatment was achieved by using a small
quantity of oil (1 mL) in vials placed in an instrumented
reaction block providing high thermal homogeneity. The
whole experimental device was covered with aluminum
foil to prevent b-carotene degradation by light. The thermal
degradation kinetics experiments were performed in
duplicate with six points at four temperatures: 120 °C,
140 °C, 160 °C, and 180 °C. The 160 °C experiment was
carried out in triplicate and the variation coefficients were
extrapolated to other temperatures.
Determination of Isomers and Oxidized
and Cleavage Concentrations
Trans- and cis-b-carotene analysis was done with an
HPLC–DAD method adapted from Kimura and Rodriguez-
´
Amaya [24] and de Sa and Rodriguez-Amaya [25] with a
polymeric YMC-30 column (YMC Inc., Wilmington, NC,
USA) in isocratic conditions [26].
All isomers were analyzed. Oxidized and cleavage
products were evaluated by the following mass balance:
Oxidation and cleavage products OCPðtÞ
X
¼ Trans-b-carotenet¼0
ꢁ
cis isomerðtÞ
ð1Þ
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J Am Oil Chem Soc (2011) 88:2035–2045
Kinetic Modeling
2037
MATLABÒ software (The MathWorks, Inc., Natick, MA,
USA).
For a given operating condition, m = 1,000 datasets
were randomly drawn using adequate equation(s) and the m
values of parameters to be determined were identified as
described above on m separate datasets. The standard
deviation was estimated for each rate constant from the m
values.
Carotene change was described by a first-order kinetics
equation:
d½Xꢂ
¼ ꢁk½Xꢂ
ð2Þ
dt
where X represents trans-b-carotene or a cis isomer, [X] the
concentration in mol l-1, t the time (min), and k the
reaction rate constant (min-1).
Model Discrimination
Observable reaction schemes were drawn up according
to the experimental findings. Once a reaction scheme was
determined, it was translated into a system of four differ-
ential equations (one per compound, i.e., trans-b-carotene,
9-cis isomer, 13-cis isomer, and oxidation and cleavage
products).
To discriminate the proposed models, the residual sum of
squares (RSS) and the Akaike information criterion (AIC)
were compared. The RSS is expressed as follows:
n
X
2
RSS ¼
ð½Xoptipredꢂ ꢁ ½XexpꢂÞ
ð5Þ
The reaction rate constants of this system of four dif-
ferential equations were iteratively adjusted to the good-
ness of fit merit function with the Levenberg–Marquardt
minimization procedure [27] using MATLABÒ software
(The MathWorks, Inc., Natick, MA, USA). This merit
function was the root mean square error (RMSE)
between experimental ([Xexp]) and calculated ([Xpred])
i¼1
where n is the number of data points, [Xexp] the experi-
mental result, and [Xoptipred] the optimized simulated result.
The RSS is a measure of the discrepancy between the
experimental and simulated data. A small RSS indicates a
good fit of the model to the data.
The AIC is a complementary measure of goodness of fit
used by van Boekel [16]. It describes the trade-off between
the accuracy (RSS) and complexity of the model (number
of parameters). It is expressed as follows:
concentrations:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
n
X
where n is the number of data.
1
2
RMSE ¼
ð½Xpredꢂ ꢁ ½XexpꢂÞ
ð3Þ
n ꢁ 1
i¼1
ꢀ
ꢁ
RSS
AIC ¼ n ln
2þ2ðp þ 1Þ
ð6Þ
n
Reaction rate constants were identified independently
for each temperature studied.
where n is the number of data points and p the number of
estimated parameters.
A stochastic method was used to evaluate the uncer-
tainty of the identified parameters. The standard devia-
tions of identified rate constants were determined via
Monte Carlo simulations [28]. In order to simulate virtual
data, a random scatter was added to each data point
[Xexp]:
A small AIC indicates that the model has a good fit to
the experimental data with a limited number of parameters.
Influence of Temperature
The rate constants k were assumed to vary with the abso-
lute temperature T (K) according to the Arrhenius law:
~
½Xꢂ ¼ ½Xexpꢂ þ Uxd
ð4Þ
~
ꢀ
ꢁ
with ½Xꢂ being the virtual data generated (carotene con-
centrations), ½Xexpꢂ the real measured value, Ux the esti-
mated error on the measured value, and d a random number
whose elements are normally distributed with mean 0 and
variance 1. The estimated error considered for each caro-
tene was calculated from the variation coefficients obtained
from the experiment at 160 °C, which was carried out in
triplicate.
ꢁEa
k ¼ k0 exp
ð7Þ
RT
where k0, Ea, T, and R are the pre-exponential factor (min-1),
the activation energy (J mol-1), the oil temperature (K), and
the gas constant (8.314 J mol-1 K-1), respectively. Because
of the close correlation between k0 and Ea, a simple
reparametering was achieved by introducing a reference
temperature as follows:
These normally distributed random errors were consid-
ered to be independent (thus, their covariance was zero).
However, each set of generated data included joint effects
of errors on all carotenes, since the identifications were
done considering all of the experimental results for each
temperature. These virtual data were generated with
ꢀ
ꢀ
ꢁꢁ
ꢁEa
1
1
k ¼ kref exp
ꢁ
ð8Þ
R
T
Tref
In this reparametering, the pre-exponential factor kref
becomes the rate constant at the reference temperature
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chosen in the middle of the studied temperature range, i.e.,
The experimental results presented in Fig. 1 were pre-
sented in a previous paper [22]. In both oils, the decrease in
trans-b-carotene (Fig. 1a, e) was concomitant to the for-
mation of isomers (Fig. 1b, c and f, g) and oxidized and
cleavage products (Fig. 1d, h). Therefore, isomerization,
oxidation, and cleavage were simultaneous reactions that
may be interlinked, as suggested by Mordi [18]. The main
isomers identified were 13-cis- and 9-cis-b-carotene. This
result is consistent with the b-carotene isomers most often
identified after heat treatment [14, 29, 30]. Mohamed et al.
[19] also showed via molecular modeling that, among cis
isomers, the lowest energy configurations were 9-cis- and
13-cis-b-carotene. Their initial production rate was very
high, suggesting that they could be primary degradation
products of trans-b-carotene. There was a relatively high
amount of cis isomers in both oils: the average maximum
sum of isomers was 30–40%. This amount was even higher
at lower temperatures in copra fat. In comparison, during
the heat treatment of carrot juice, Marx et al. [30] found
only 13 and 3% of 13-cis- and 9-cis-b-carotene, respec-
tively, after 60 min at 100 °C. Dhuique-Mayer et al. [31]
did not identify any b-carotene isomers, whereas they
noted a similar trans-b-carotene degradation rate during
the heat treatment of citrus juice. Chen and Huang [6]
stated that the b-carotene isomerization level was depen-
dent on the solvent and that higher levels were reached in
non-polar solvents. The high cis isomer concentration may
have been due to the hydrophobic properties of the oils.
150 °C.
Statistical Analysis
A principal component analysis was done with XLSTATÒ
(Addinsoft, Paris, France).
Results and Discussion
Description of Experimental Results
Figure 1 shows the experimental data for trans-b-carotene
(all-E) thermal degradation in palm olein (a–d) and in
copra (e–h) at four oil temperatures, 120, 140, 160, and
½Xꢂ
180 °C. The reduced concentrations
are presented
½all - Eꢂ0
at different heating time intervals t, where [X] is the
carotene form (trans or cis) concentration and [all-E]0 is
the initial concentration of trans-b-carotene in the vials.
Figure 1a and e present variations in the reduced con-
centration of trans-b-carotene, while Fig. 1b, c and f, g
show the reduced concentrations of the major cis isomers
identified during the heat treatment, i.e., 13-cis (13-Z)
and 9-cis-b-carotene (9-Z), respectively. Finally, Fig. 1d
and h present the oxidized or cleaved products of
b-carotene calculated by the mass balance according to
Eq. 1.
Fig. 1 Experimental reduced
concentration of trans-b-
carotene (all-E), 13-cis- (13-Z),
and 9-cis-b-carotene (9-Z)
during heat treatments at four
oil temperatures (filed circles
120, filled triangles 140,
asterisks 160, and filled
diamonds 180 °C) in palm olein
(a–c) and copra (e–g). The error
bars represent the standard
deviation (n = 3). The
concentration of oxidized and
cleavage products (OCP) was
calculated by the mass balance
(Eq. 1) in palm olein (d) and
copra (h)
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J Am Oil Chem Soc (2011) 88:2035–2045
2039
Maximum 9-cis-b-carotene concentrations were reached
after those of 13-cis-b-carotene, suggesting that 9-cis-b-
carotene was produced after 13-cis-b-carotene. This
phenomenon has been observed in many other studies,
suggesting that 9-cis-b-carotene is produced under more
severe treatment [14, 30]. Like trans-b-carotene, 13-cis-
and 9-cis-b-carotene also underwent oxidation and cleav-
age degradation as their concentrations decreased as a
function of the heating time. Besides, their concentrations
dropped to zero at the end of some experiments. They
could, therefore, be considered as intermediary com-
pounds. The oxidized and cleavage product concentrations
were nil at t = 0, but they kept increasing as a function of
the heating time, so they could be considered as secondary
products. This indicated that the dynamics of isomerization
and oxidation/cleavage reactions differed markedly. Note
that, at 120 °C in copra (Fig. 1e–h), only the isomerization
of trans-b-carotene took place at the chosen time scale.
This indicated that isomerization required less energy in
comparison to oxidation and cleavage reactions. Oxidation
and cleavage reactions occurred at 120 °C in palm olein.
This could have been due to the more unsaturated nature of
this oil in comparison to hydrogenated copra fat and to the
possible oxidation of fatty acids.
In addition, concentrations of oxidized and cleavage
products were overevaluated. The negative constant of
trans-b-carotene obtained in this first scheme could
indicate that this compound may be ‘‘formed’’ during
its degradation. This phenomenon could be possible,
providing that there is a back-isomerization reaction. This
is a realistic assumption since, experimentally, 13-cis- and
9-cis-b-carotene maximums seemed to be constrained. For
both isomers, no more than 30% were produced and, as
stated earlier, the sum of isomers did not exceed 40%. This
fact suggests a possible equilibrium in the isomerization
reactions. In addition, the repeatability of the trans-b-
carotene analysis was better than that of cis isomers
(variation coefficient of 5% as compared to 10–15%). This
highlights the instability of isomers that could be involved
´
in both cleavage and back-isomerization. Molnar [20]
showed, in experiments involving isomers of zeaxanthin in
benzene, that isomerization is a reversible reaction.
Moreover, other studies have showed that, generally,
9-cis- and 13-cis-b-carotene could not convert to each
other [32].
In the second reaction scheme, the back-isomerization
of both 13-cis- and 9-cis-b-carotene to trans-b-carotene is
considered with the new rate constants k3 and k4. To
simplify the model, only one oxidation and cleavage
constant, k5, was employed for trans-, 13-cis-, and 9-cis-
b-carotene (Fig. 2, scheme 2). Indeed, the same model
with different oxidation and cleavage constants exhibited
results that were not any better (not shown here). The
corresponding system of differential equations is pre-
sented below:
Proposal of Simplified and Observable
Reaction Schemes
From the previous experimental observations, a first sim-
plified and observable scheme is proposed in Fig. 2
(scheme 1). The main assumptions for building this model
were the conversion of trans-b-carotene (all-E) into its
major cis isomers (13-cis- and 9-cis-b-carotene) and oxi-
dation and cleavage products (OCP) at rate constants k1, k2,
and k3, respectively. 13-cis- and 9-cis-b-carotene were also
assumed to give rise to OCP with rate constants k4 and k5,
respectively.
d½allEꢂ
¼ ꢁðk1 þ k2 þ k5Þ½allEꢂ þ k3½13Zꢂ þ k4½9Zꢂ ð13Þ
dt
d½13Zꢂ
¼ k1½allEꢂ ꢁ ðk3 þ k5Þ½13Zꢂ
¼ k2½allEꢂ ꢁ ðk4 þ k5Þ½9Zꢂ
ð14Þ
ð15Þ
ð16Þ
dt
d½9Zꢂ
dt
The corresponding set of ordinary differential equations
for the first reaction scheme is:
d½OCPꢂ
dt
¼ k5ð½allEꢂ þ ½13Zꢂ þ ½9ZꢂÞ
d½allEꢂ
¼ ꢁðk1 þ k2 þ k3Þ½allEꢂ
¼ k1½allEꢂ ꢁ k4½13Zꢂ
ð9Þ
ð10Þ
ð11Þ
ð12Þ
dt
Model 2, with the same number of constants as model 1,
was found to be much more adapted. The experimental
data fit was very good, as shown in Fig. 3. With respective
values of 0.033 and -459, the RSS (Eq. 5) and the AIC
(Eq. 6) were better (i.e., lower) than those found for model
1 (0.365 and -296, respectively). Back-isomerization,
thus, seemed to be a reliable assumption. This model also
showed that a single oxidation and cleavage constant for
trans and cis isomers was suitable. Therefore, trans and cis
isomers were equally sensitive to oxidation and cleavage.
This is out of line with some assumptions of higher
degradation of cis isomers [18].
d½13Zꢂ
dt
d½9Zꢂ
¼ k2½allEꢂ ꢁ k5½9Zꢂ
dt
d½OCPꢂ
dt
¼ k3½allEꢂ þ k4½13Zꢂ þ k5½9Zꢂ
The results of the experimental data fit are presented in
Fig. 3, scheme 1. A poor experimental data fit was
obtained, especially for trans-b-carotene and 13-cis-b-
carotene, whose concentrations were underestimated.
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J Am Oil Chem Soc (2011) 88:2035–2045
Fig. 2 Observable reaction
schemes for the thermal
degradation of trans-b-carotene
in oils
The aim of the following section was to test the
robustness of model 2 for different oil temperatures and
types, and to consider their effects on the kinetic constants
of isomerization and oxidation/cleavage reactions.
oils. Besides, the RSS values obtained for each oil and
each temperature were lower than the 0.365 value
obtained with model 1 (Fig. 3). This indicated that the
model was robust and could successfully predict the
contents of carotenes and oxidation products in the tem-
perature range studied and for both oils. This was
confirmed by the low AIC values, ranging from -192 to
-491. The AIC is sensitive to the number of experimental
data, n (Eq. 6). For the same RSS value, the AIC value
decreases as the number of data points increases, and the
better the model fits. Indeed, the higher number of points
represented well by a model, the better is the model. As
shown in Table 1, the number of data points n was lower
for experiments conducted in copra fat. Therefore, the
resulting AIC values were higher than those obtained in
palm olein. The highest AIC value of -192 was obtained
at 160 °C, which also corresponded to the highest RSS
value of 0.121.
Effect of Experimental Conditions of Kinetic
Parameters on Identified Rate Constants from Model 2
On the basis of model 2, reaction constants were identi-
fied from the experimental data of Fig. 1, obtained in the
two oils, i.e., palm olein and copra, at four temperatures,
ranging from 120 to 180 °C. The corresponding rate
constants are presented in Table 1. Moreover, the RSS
(Eq. 5) and the AIC (Eq. 6) are presented in order to
evaluate the goodness of fit. The resulting simulated data
are illustrated in Fig. 4 for the extreme temperatures of
the studied domain, i.e., 120 and 180 °C. This figure
shows that the experimental data fit was good for both
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2041
Fig. 3 Model fit (lines) to experimental data (dots) of the thermal degradation of trans-b-carotene for schemes 1 and 2 presented in Fig. 2.
Experimental data were obtained in palm olein at 160 °C
Table 1 Identified kinetic constants obtained from the model fit
Oil
Temperature Reaction rate constants (min-1
)
Model goodness evaluation
( °C)
k1
k2
k3
k4
k5
RSS
n
AIC
Palm olein 120
0.063 0.010 0.021 0.002 0.185 0.031 0.077 0.012 0.011 0.001 0.008
0.568 0.163 0.033 0.003 0.939 0.315 0.038 0.005 0.025 0.002 0.074
0.824 0.190 0.178 0.022 1.259 0.325 0.152 0.036 0.047 0.060 0.033
0.779 0.156 0.396 0.049 1.095 0.260 0.296 0.060 0.089 0.011 0.082
0.141 0.015 0.042 0.002 0.269 0.032 0.128 0.008 0.000 0.000 0.055
0.106 0.012 0.037 0.007 0.239 0.026 0.082 0.019 0.004 0.001 0.008
0.045 0.014 0.039 0.007 0.078 0.036 0.069 0.020 0.020 0.002 0.121
0.556 0.127 0.394 0.117 1.366 0.463 1.141 0.424 0.168 0.112 0.079
24
32
36
32
24
20
20
24
-371
-376
-491
-370
-280
-300
-192
-263
140
160
180
Copra
120
140
160
180
The standard deviations were obtained by Monte Carlo simulations
Globally, in both oils, the rate constants increased as a
function of temperature. The only exception was in copra
fat at 160 °C, where the rate constants were significantly
lower than those obtained at 140 °C. However, as stated
earlier, the worst model fit was obtained for this tempera-
ture. This was possibly due to experimental bias in this set
of experiments.
isomerization were never nil and, sometimes, were over
1 min-1 (Table 1). This indicates that isomerization and
back-isomerization are very highly dynamic reactions in
oils. For both oils, the highest rate constant values were
obtained for k1 and k3, which were related to 13-cis-b-
carotene. Indeed, k1 and k3 reached maximums of 0.824
and 1.259 min-1 at 160 °C in palm olein and 0.556 and
1.366 min-1 at 180 °C in copra fat. Those results explain
the overall higher amount of 13-cis-b-carotene (Figs. 1 and
4). This configuration, thus, seemed to be favored.
Influence of Temperature on Isomerization
and Back-Isomerization Rate Constants
Globally, when the oil temperature increased, the rate
constant of production of a cis isomer increased at the same
order of magnitude as its rate of back-isomerization to
trans-b-carotene (Table 1). Therefore, k1 and k3 and k2 and
k4 (cf. Scheme 2) varied in the same manner. This reflected
the equilibrium of the isomerization reactions. Regarding
their values, k1 and k3 and k2 and k4 obviously did not
Generally, the rate constants obtained for the isomerization
reactions were much higher than those obtained for the
reaction and cleavage reactions. Indeed, with values rang-
ing from 0 to 0.168 min-1, the rate constant k5 always
exhibited the lowest value for each experiment. Con-
versely, the rate constants of isomerization and back-
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J Am Oil Chem Soc (2011) 88:2035–2045
Fig. 4 Model fit (lines) to experimental data (dots) of the thermal degradation of trans-b-carotene (all-E). Experimental data were obtained in
palm olein at (a) 120 and (b) 180 °C or in copra at (c) 120 and (d) 180 °C
follow the Arrhenius law. For instance, in palm olein, k1
and k3 exhibited a maximum at 160 °C and their value
decreased at 180 °C. In copra fat, k2 and k4 stagnated from
120 to 160 °C and then sharply increased at 180 °C.
However, a general pattern could be observed in their
values. For both cis isomers, at low temperature, their
production rate constant was lower than their rate of back-
isomerization to the trans form. For instance, the produc-
tion rate constants of 13-cis- and 9-cis-b-carotene in palm
olein at 120 °C were 0.063 and 0.021 min-1, respectively,
as compared to the highest values of back-isomerization
constants of 0.185 and 0.077 min-1, respectively. The
same pattern was observed in copra oil. At 120 °C,
k1 = 0.141 \ k3 = 0.269 and k2 = 0.042 \k4 = 0.128.
However, in palm olein, when the temperature increased, the
production rate increased markedly and sometimes surpassed
the back-isomerization rate. For instance, at 180 °C, in the
case of 9-cis-b-carotene, its production rate constant of
0.329 min-1 was higher than its back-isomerization value of
0.296 min-1. This reflects a modification of the equilibrium
constants of reactions Kk =k and Kk =k as a function of the
increased. Therefore, the reaction was equilibrated but the
temperature favored the isomerization reaction. Indeed, from
120 to 180 °C, K
increased from 0.34 to 0.71 and K
k2=k4
k1=k3
from 0.27 to 1.34 (Fig. 5a, b). For both isomers, the corre-
sponding curves reached a horizontal asymptote, which was
\1 for Kk =k and[1 for Kk =k : Thus, from 160 °C, the trans-
1
3
2
4
to 9-cis-b-carotene reaction was dominant. This could explain
why 9-cis-b-carotene was more dominant under more severe
heat treatments. In the case of copra oil, no significant varia-
tions in Kk =k and Kk =k as a function of temperature were
1
3
2
4
observed. In addition, the simulated data at 160 °C were
hampered by uncertainty. The influence of temperature on the
isomerization equilibria was, therefore, not as clear as it was
for palm olein. Nevertheless, in that oil, irrespective of the
temperature, Kk =k and Kk =k values of less than 1 implied a
1
3
2
4
dominant reaction from cis isomers to the trans form.
Influence of Temperature on the Oxidation
and Cleavage Constant
Contrary to isomerization, the oxidation and cleavage
reactions are not equilibrated, but they are irreversible
reactions. In both oils, the influence of temperature on the
1
3
2
4
temperature. TheirpatternsarepresentedinFig. 5a, b.Inpalm
olein, when the temperature increased, Kk =k and Kk =k also
1
3
2
4
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J Am Oil Chem Soc (2011) 88:2035–2045
2043
Fig. 5 Variations in
equilibrium constants (log
scale) of (a) trans-b-carotene
isomerization in 13-cis-b-
carotene (k1/k3), (b) in 9-cis-b-
carotene (k2/k4), and
(c) oxidation/cleavage constant
(k5) as a function of temperature
in palm olein (filled circles) and
copra (filled triangles)
oxidation and cleavage rate constant k5 was marked. k5
values followed the Arrhenius law (Eq. 7) as they
increased exponentially as a function of the oil temperature
(Fig. 5c). Experimentally, the increase in k5 was closely
linked to the decoloration of the oils. For instance, in copra
fat, at 120 °C, while k5 was nil, the absorbance at 450 nm
of the oil barely decreased during the 120-min experiment.
Indeed, cis isomers also absorbed light at 450 nm. On the
contrary, at 180 °C, while k5 = 0.168 min-1, almost total
decoloration was observed within the first 10 min. This
color change was due to the cleavage of b-carotene, giving
rise to smaller compounds whose absorbance maxima were
much less than 450 nm. As no oxidation products were
found in the oils, these products likely have a very small
life expectancy and, once produced, cleavage products
would be immediately formed. Therefore, the choice of one
apparent oxidation/cleavage constant was warranted.
this fat in comparison to the values of 0.01 to 0.04 min-1 in
palm olein from 120 to 160 °C. However, k5 became
twofold superior in copra at 180 °C (0.168 min-1 com-
pared to 0.089 min-1). Therefore, oxidation and cleavage
reaction rate constants were globally higher in palm olein
but less sensitive to temperature than in copra. These dif-
ferences could be attributed to differences in oil composi-
tion in terms of their fatty acid contents. Indeed, palm olein
contains unsaturated fatty acids, which are more prone to
oxidation than those of copra, which may explain the
oxidation and cleavage reactions which occurred at 120 °C.
On the other hand, there could be competition between
unsaturated lipids and b-carotene as oxidation substrates,
which would limit the decrease in b-carotene. This phe-
nomenon was observed by Rossi et al. [33] in the case of
vitamin E degradation in oils.
By using the k5 values (Table 1) in Eq. 8, the activation
energy of oxidation/cleavage reactions were calculated and
were equal to 51 kJ mol-1 (R2 = 0.99), with a k5ref of
3.4 9 10-2 min-1 for palm olein and 171 kJ mol-1
(R2 = 0.99) and k5ref = 6.8 9 10-3 min-1 for copra fat.
Therefore, the influence of temperature on the k5 values
differed markedly as a function of the oil type. Indeed, in
copra, temperature had a more substantial influence. For
instance, with values of 0 to 0.02 min-1, k5 was inferior in
Relationship Between Isomerization
and Cleavage Reactions
To analyze the correlation between kinetic constants, a
principal component analysis (PCA) was carried out using
the kinetic constant values of Table 1, i.e., from palm olein
and copra fat. The results are shown in Fig. 6. Only two
principal components (factors 1 and 2) were necessary to
account for 96% of the total variance. Temperature was the
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J Am Oil Chem Soc (2011) 88:2035–2045
carotene underwent oxidation and cleavage reactions at the
same rate. Isomerization reactions of b-carotene in oils,
therefore, involved a ceaseless backwards and forwards
change in configuration, while the oxidation/cleavage
reactions were irreversible. These reactions were all con-
comitant but very different in their nature and kinetics.
Isomerization and back-isomerization reaction constants
generally exhibited high values in oils. All constants
increased with temperature. However, the temperature-
dependency differed markedly for isomerization and for
oxidation/cleavage reactions. For the latter reactions, the
rate constants followed the Arrhenius law. The activation
energy calculations revealed that these reactions could be
activated very differently as a function of the oil compo-
sition. In the case of isomerization rate constants, the
Arrhenius law was not suitable. However, when repre-
senting the equilibrium constant of these reactions, an
increase in temperature clearly displaced the equilibrium of
the reaction to the benefit of isomerization. The study of
the relationship between all rate constants showed that
isomerization and back-isomerization reactions were clo-
sely linked. In addition, the oxidation and cleavage con-
stant was correlated with 9-cis isomer production. This was
very interesting, since this latter isomer is easier to monitor
than cleavage products and could be an indicator of oxi-
dation/cleavage reactions during a process. This strategy,
which will have to be confirmed in other oils, could be
interesting to increase b-carotene retention during the
storage of b-carotene-rich oils or during processing
involving the heating of oils during oil refining or deep-fat
frying.
Fig. 6 Projection circle of kinetic constant variables obtained by
principal component analysis (PCA) and from the numerical data of
Table 1
dominant feature in the first principal component,
accounting for 79.37% of the total variability. The main
conclusions are that all constants were correlated with
temperature but the isomerization reaction constant k2
(trans- to 9-cis-b-carotene) and the oxidation/cleavage
constant were the most sensitive to a temperature change.
Constants k1 and k3 were closely correlated, i.e., when
isomerization to 13-cis-b-carotene increased, the back-
isomerization of 13-cis-b-carotene into the trans form
concomitantly increased. The other reaction constants rel-
ative to 9-cis-b-carotene, k2 and k4, were also correlated
with each other. Temperature, therefore, increased the
dynamics of change from trans to cis and cis to trans
configurations. Interestingly, k5, the oxidative and cleavage
constant, was closely correlated with the k2 constant.
Several authors have noticed that the 9-cis isomer appears
under severe treatment conditions [14]. This was confirmed
by our findings and, in addition, the 9-cis-b-carotene iso-
mer appeared concomitantly to cleavage and to the inten-
sification of oxidative reactions.
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