Kinetics of Enzymatic Synthesis of Cinnamyl Butyrate by Immobilized Lipase

Article abstract of DOI:10.1007/s12010-017-2464-x

This work illustrates the enzymatic synthesis of cinnamyl butyrate by esterification of butyric acid and cinnamyl alcohol. Experiments were performed to study the various operating parameters such as molar ratio, enzyme concentration, temperature, and spe

Full text of DOI:10.1007/s12010-017-2464-x

Appl Biochem Biotechnol
DOI 10.1007/s12010-017-2464-x
Kinetics of Enzymatic Synthesis of Cinnamyl Butyrate
by Immobilized Lipase
Govind V. Waghmare1 & Abhishek Chatterji1
&
Virendra K. Rathod1
Received: 17 December 2016 /Accepted: 20 March 2017
#
Springer Science+Business Media New York 2017
Abstract This work illustrates the enzymatic synthesis of cinnamyl butyrate by esterification
of butyric acid and cinnamyl alcohol. Experiments were performed to study the various
operating parameters such as molar ratio, enzyme concentration, temperature, and speed of
agitation. Also, the suitable kinetic model for esterification reaction was predicted and the
various kinetic parameters were determined. It has been observed that the experimental results
agree well with the simulated results obtained by following the ping-pong bi-bi mechanism
with dead-end inhibition by both the substrate acid and alcohol. The highest 90% conversion
of butyric acid was observed after 12 h at the following reaction conditions: substrate molar
ratio 1:2 (butyric acid/cinnamyl alcohol), temperature 50 °C, enzyme loading 2% (with respect
to the weight of the substrates), and agitation speed 250 rpm. Diffusional mass transfer
limitations between substrate and enzyme surface do not show significant effect on reaction
kinetics. Enzyme reusability study reveals that it retains 85% of its catalytic activity after five
consecutive cycles.
.
.
.
.
Keywords Esterification Flavor synthesis Cinnamyl butyrate Enzymatic catalysis
.
.
Immobilized lipase Kinetic study Ping-pong bi-bi mechanism
Introduction
The short-chain esters having sweet-smelling aroma are commonly used as a flavoring agent in
most of the food products like beverages, candies, jellies, jams, confectionery, dairy products,
and chocolates and ice creams [1]. The long-chain esters derived from fatty acids are mostly
used in cosmetics, pharmaceuticals, and surfactants [2], and also as plasticizers, lubricants,
diesel additives, and water-resistant agents, and in hydraulic fluids and as reaction media [3, 4].
* Virendra K. Rathod
vk.rathod@ictmumbai.edu.in
1
Chemical Engineering Department, Institute of Chemical Technology, Matunga, Mumbai 40019,
India

Appl Biochem Biotechnol
Many short-chain fatty acid esters exhibit characteristic fruity smell such as ethyl butyrate [5]
(pineapple or strawberry flavor), methyl butyrate [6] (pineapple or apple flavor), butyl butyrate
[7] and butyl isobutyrate [8] (pineapple flavor), isoamyl isovalerate [9] (apple flavor), and
isoamyl acetate [10] and isoamyl butyrate [11, 12] (banana flavor). Also, some cinnamyl esters
possess characteristic aroma and are used in various cosmetic products. One of the cinnamyl
esters, i.e., cinnamyl acetate, is synthesized by transesterification of cinnamyl alcohol and
vinyl acetate using chemical and enzyme as a catalyst [13–15]. Cinnamyl butyrate has also
wide applications in pharmaceutical, flavor, and cosmetic industry. Belsito et al. presented the
detailed toxicological and dermatological studies of cinnamyl butyrate along with other
cinnamyl esters [16], which show that cinnamyl butyrate possesses the nearly similar test
results as compared to cinnamyl acetate and could be considered as a potential candidate
instead of cinnamyl acetate. However, the synthesis part of the cinnamyl butyrate is not well
explored in the literature. As per authors’ knowledge, there are no articles reported on the
detailed synthesis of cinnamyl butyrate. Hence, this work reports an insight to the synthesis of
cinnamyl butyrate.
Ester synthesis using enzymes as a catalyst proved to be much better than traditional
methods due to their mild reaction conditions, high efficiency and high regio- and stereo-
selectivity, minimizes the use of hazardous chemicals [17]. Various groups of lipase
enzyme have been identified and used to catalyze esterification and transesterification
reactions due their robust and high catalytic activity. It can be used in both free and
immobilized forms [18–23], but the latter is mostly utilized due to its high operational
stability, easy recovery, and high reusability [24, 25]. Thus, biocatalysis is a promising
alternative for the production of esters from considerably cheaper and abundant raw
materials. Esterification reaction in the presence of organic solvents is widely reported in
the literature along with its influence on the course of the reaction [26–34]. The reaction
temperature along with the other parameters has a significant effect on the reaction rate
due to their thermal sensitivity [35]. In the production of esters using biocatalyst, it is
important to determine the optimal conditions of reactions for the maximum efficiency of
the process along with its reaction kinetics. Many hypothetical models have been
proposed to elucidate the kinetics of the esterification reaction catalyzed by an
immobilized enzyme in the organic media [36]. The enzyme-catalyzed reactions con-
taining a single substrate generally follow the simple Michaelis–Menten mechanism, and
the bisubstrate reaction mainly follows two types of mechanisms: the ping-pong mech-
anism (non-sequential) and the ternary complex mechanism (sequential) [26, 37]. It is
necessary to study the inhibition effect by substrates in the enzyme-catalyzed reaction.
The inhibition caused by one or both the substrates was due to the formation of inactive
ternary complex with the enzyme. Considering enzyme-catalyzed esterification, some
literature reports the inhibition by only one substrate, by acid [26, 29, 32, 38], or by
alcohol [14, 27, 31, 34, 39–41] and others do not find any inhibitory effect by both the
substrates [1, 42–44]. Some literature also reports inhibition by both the substrates
[2, 11, 30, 44, 45].
In this work, the aim was to synthesize cinnamyl butyrate by an immobilized
enzyme as a catalyst in the presence of hexane as organic media. The detailed
experimental investigation was performed to study the effect of various parameters
such as a substrate molar ratio, enzyme loading, temperature, and speed of agitation.
Also, the kinetic model was fitted and kinetic constants are calculated by solving the
ping-pong bi-bi rate equation.

Appl Biochem Biotechnol
Material and Methods
Enzyme and Chemicals
Immobilized enzyme Candida antarctica lipase B (CAL-B) was provided by Fermenta
Biotech, Ltd., Thane, Mumbai, as Fermase CALB 10000, having the particle size
300–500 μm, and immobilized on polyacrylate resin beads using covalent bonding.
All other chemicals such as cinnamyl alcohol, butyric acid, ethanol, hexane, p-
nitrophenyl acetate, chloroform, isoamyl alcohol, sodium phosphate, acetone, gum
arabic, 2-propanol, and sodium chloride were procured from reputed firms and used
directly without further purifications.
Experimental
All reactions were carried out in a 50-cm3 baffled glass reactor equipped with an overhead
stirrer having the provision to control speed. The desired quantity of the reactants was
measured and transferred to the reactor. The rector was further sealed using vacuum grease.
A known amount of solvent (hexane) is also added to the reaction to improve the enzyme
activity as well as to act as the reaction medium. The whole reactor assembly was immersed in
a water bath equipped with a temperature controller to maintain the desired temperature in the
order of 2 °C. The reaction is initiated by the addition of a measured amount of enzyme as a
catalyst, and the addition of enzyme is considered to be the start of the reaction. As water is the
byproduct of esterification reactions, molecular sieves were added to act as a scavenger for
water. Samples were withdrawn periodically from reaction mass, centrifuged using a centri-
fuge machine at the speed of 8000 rpm for 5 min. The supernatant liquid was then transferred
to the fresh vial and analyzed using gas chromatography and standard titrimetric analysis
method.
Statistical Analysis
Statistical analysis is a very useful technique to analyze, interpret, and summarize the
experimental data. Data obtained from the results were analyzed using single-factor
ANOVA with the help of Microsoft Office Excel. All the experiments were carried out
in triplicate, and the data is reported as mean
considered to be significant.
SD. p values less than 0.05 are
Gas Chromatography Analysis
Gas chromatography (Chemito GC 8610) equipped with a flame ionization detector
(FID), packed column 5% OV 101 (1/8 in. diameter, 3 m length). Nitrogen was used as
a carrier gas at the flow rate of 30 cm3 min−1, and air and hydrogen are used at the
flow rate of 300 and 20 mL min−1, respectively. Both the injector and detector were
held at a constant temperature of 280 °C. Initially, 1 μL of the sample was injected at
50 °C oven temperature and raised up to 250 °C with the rate of 17 °C min−1 and held
for 1 min. An internal standard method was used to determine the percent conversion
of acid using n-dodecane as an internal standard to calculate the standard relative
response of the detector.

Appl Biochem Biotechnol
Titrimetric Analysis
The change in concentration of acid during the reaction course was monitored by determining the
acid value of the samples using a standard titrimetric method reported in our previous work [46]. The
analysis was performed by transferring 0.10 to 0.20 g of the sample in a 50-cm3 conical flask. Ten
milliliters of neutralized ethanol was added to the flask, gently shaken to mix the contents in ethanol,
and titrated against the potassium hydroxide solution using phenolphthalein as an acid-base
indicator. The end point was determined by a change in color from colorless to slightly pink.
The progress of the reaction was measured on the basis of the determination of percent
conversion of the acid. The acid value was determined using the following formula:
56:1 Â N Â V
Acid value ¼
W
where N is the normality of KOH required to neutralize the acid, V is the volume of KOH in
milliliters required to neutralize the acid, and W is the weight of the sample in grams.
Determination of Enzymatic Activity
Enzyme assay was performed to determine the activity of the enzyme using the standard
protocol. The activity of free and immobilized CALB was assayed spectrophotometrically
with p-nitrophenyl acetate as a substrate [47]. The reaction mixture consisted of 2.0 cm3 of
buffer (1 g dm−3 gum arabic, 0.15 M NaCl, and 0.1 M sodium phosphate, pH 7.0) and 0.1 cm3
of 15 mmol dm−3 p-nitrophenyl acetate dissolved in 2-propanol. The mixture was prewarmed
at 40 °C, and then 100 mg of the enzyme was added. After 5 min of incubation, the reaction
was stopped by adding 2.0 cm3 of Marmur solution (chloroform/isoamyl alcohol, 24:1)
followed by centrifugation at 10,000 rpm for 5 min at 4 °C. The clear supernatant was taken
off and measured at 405 nm in a UV/Vis spectrophotometer. One enzyme unit is defined as the
amount of the enzyme that liberates 1 μmol of p-nitrophenol per min at pH 7.0 and 40 °C. The
activity of the enzyme used was found to be 10.653 U g−1.
Reusability Study of Enzyme
The reusability study was carried out to test the catalytic efficiency of the biocatalyst at the
optimum reaction conditions. After every cycle, the catalyst was recovered by simple filtration,
washed with acetone (5 mL × 2 mL), dried in an oven for 30 min at 40 °C, kept overnight in a
desiccator, and used for the next reaction cycle. The catalytic activity was determined after
every cycle by using the above mentioned procedure.
Determination of Kinetic Constant
The kinetics of esterification reaction of cinnamyl alcohol and butyric acid were done by
analyzing initial rates (determined by an initial slope method) at various acid and alcohol
concentrations. The data obtained was fitted with Michaelis–Menten kinetics with a ping-pong
bi-bi mechanism by a nonlinear regression (NLR) method using Microsoft Excel 2013. The
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
values of kinetic constants were calculated by using minimization of ∑ 1 þ MSRi2, where
MSRi is the mean square residual between theoretical and experimental data.
i

Appl Biochem Biotechnol
Results and Discussion
Effect of Enzyme Loading
Effect of enzyme loading on conversion of butyric acid was studied at different enzyme
concentrations ranging from 1 to 3% by keeping all other parameters constant. The results
obtained are represented in Fig. 1.
A significant change in the conversion was observed when enzyme concentration was
varied from 0.84 to 2% while with a further increase in enzyme concentration, the initial rate as
well as a total conversion of acid showed a marginal change. The increase in conversion can be
explained by an increase in acyl–enzyme complex formation due to increased catalytic sites at
higher enzyme loading. The saturation effect at elevated enzyme concentration was observed
due to a reduction in the formation of enzyme–substrate complexes due to the external mass
transfer limitations that arise from an excess of enzyme concentration. Also, due to the
reversible nature of the esterification reaction, the forward reaction becomes less dominant
after attaining the equilibrium conditions. The effect of enzyme concentration on conversion in
the case of enzymatic reactions was well reported and found to be in agreement with the
reported literature [22, 48]. As the conversion obtained at an enzyme concentration of 2 and
3% does not have any significant difference, 2% enzyme loading is considered to be optimum
and further experiments were carried out using the same enzyme loading.
Effect of Temperature Variation
Enzymes are very sensitive to temperature, and little fluctuation in reaction temperature above
optimum range may lead to enzyme deactivation resulting in lower enzyme activity [35]. The
90
80
70
60
50
40
30
20
10
0.84%
10
1%
15
2%
20
3%
0
0
5
25
Time (h)
Fig. 1 Effect of enzyme loading on percent conversion of butyric acid at a molar ratio of 1:2, reaction
temperature of 50 °C, and speed of agitation of 250 rpm

Appl Biochem Biotechnol
effect of temperature variation on percentage conversion was studied in the temperature range
of 40–60 °C, and the results obtained are represented in Fig. 2. An increase in percent
conversion was observed with an increase in temperature from 40 to 50 °C, and a further
increase gives a slight increase in the conversion of the reaction. At higher reaction temper-
ature, the solubility of the substrates increases in the solvent favoring more diffusion of a
substrate molecule to the enzyme surface due to reducd mass transfer limitations of the system.
The increased diffusion of substrates favors the formation of more acyl–enzyme complexes
which directly influences the reaction rate as well as conversion profile of the reaction.
Although the rate of diffusion is proportional to the temperature, a marginal difference was
observed in the conversion obtained at 50 and 60 °C. Hence, 50 °C is considered as the
optimum reaction temperature. All the further reactions were carried out at the same
temperature.
Effect of Substrate Concentration on Reaction Kinetics
Reactions are carried out by keeping the concentration of one reactant constant while varying
the concentration of the other reactant. It was found that there is a significant influence of
substrate concentration on the conversion of butyric acid and also on the rate of reaction.
Initially, the butyric acid concentration was kept constant and the concentration of cinnamyl
alcohol was varied in the range of 1.84 to 7.36 mol dm−3 which was always in excess
compared to the concentration of acid. It was observed that with an increase in the concen-
tration of alcohol (Fig. 3), the initial reaction rate increases rapidly but, at higher reaction time,
the reaction rate gets reduced. It clearly shows the inhibition of enzyme with respect to alcohol
at higher concentrations. The increase in conversion with an increase in substrate concentration
was due to the increase in the formation of acyl–enzyme complex resulting in more product
formation. The enzyme inhibition at higher substrate concentrations leads to a decrease in the
90
80
70
60
50
40
30
20
40 °C
50 °C
60 °C
10
0
0
5
10
Time (h)
15
20
Fig. 2 Effect of reaction temperature on percent conversion of butyric acid at a molar ratio of 1:2, enzyme
loading of 2%, and speed of agitation of 250 rpm

Appl Biochem Biotechnol
90
80
70
60
50
40
30
20
10
0
1:01
1:02
1:03
1:04
0
5
10
15
20
25
Time (h)
Fig. 3 Effect of substrate concentration on percent conversion of butyric acid at a reaction temperature of 50 °C,
enzyme loading of 0.84%, and speed of agitation of 250 rpm
conversion. The reaction data shows that either single substrate or both the substrates can be
responsible for the inhibitory action of enzyme, reducing the progress of the reaction.
To investigate the inhibitory effect of both the substrates, experiments were carried out
individually by keeping one substrate constant and varying the concentration of the other. The
Lineweaver–Burk double reciprocal plot was studied with varying concentrations of alcohol at
constant acid concentration and by varying acid concentrations at constant alcohol concentra-
tion to determine the inhibitory effect of cinnamyl alcohol and butyric acid, respectively. The
results obtained are represented in Fig. 4a, b. From the Lineweaver–Burk plot, it is clear that
the reaction rate is substrate inhibited by both the substrates at higher substrate concentrations.
The inhibition effect of acid, as well as alcohol with the formation of the dead-end complex, is
well reported in the literature [2, 11].
The explanation of the mechanism using the random bi-bi mechanism is ruled out,
as enzymatic esterification reactions follow the formation of intermediate active acyl–
enzyme complex. In this study, the experimental findings were correlated and ex-
plained using a ping-pong bi-bi model, considering the inhibitory effect by both the
substrates.
The mechanism assumed to consist the following steps: the substrate butyric acid [A] binds
first to the enzyme [E] surface to form the acid–lipase complex [EA] which then, on
isomerization, forms the acyl–enzyme intermediate [E#] with the release of water [P] molecule.
In the second step, the cinnamyl alcohol [B] reacts to the acyl–enzyme binary complex to form
another complex [E#B], which, on isomerization, gives the enzyme–ester complex [EQ],
which finally gives ester [Q] and enzyme [E]. The dead-end inhibition complexes [E#A] and
[EB] are formed when the enzyme reacts with acid and alcohol, respectively. The general
schematic representation is illustrated in Fig. 5 [49].

Appl Biochem Biotechnol
14
12
10
8
a
6
4
2
0
0.1
0.2
0.3
0.4
0.5
0.6
1/CB (L mol-1)
14
13
12
11
10
9
b
8
7
6
5
4
0.10
0.20
0.30
0.40
0.50
0.60
1/CA (M-1)
Fig. 4 a The Lineweaver–Burk double reciprocal plot for different concentrations of cinnamyl alcohol (1.84–
7.36 M) at constant butyric acid concentration (1.84 M). b The Lineweaver–Burk double reciprocal plot for
different concentrations of butyric acid (1.84–7.36 M) at constant cinnamyl alcohol concentration (1.8 M)
Fig. 5 The general schematic representation of the ping-pong bi-bi mechanism with inhibition by both substrates

Appl Biochem Biotechnol
The results obtained in this study were validated with the kinetic expression for this mechanism.
The rate equation for the bisubstrate ping-pong bi-bi mechanism is represented by Eq. 1 [49]
Vmax½AŠ½BŠ
ꢀ
ꢁ
ꢀ
ꢁ
v ¼
ð1Þ
½BŠ
½AŠ
½AŠ½BŠ þ KMA½BŠ 1 þ
þ KMB½AŠ 1 þ
KiB
KiA
where v is the initial rate of the reaction, Vmax is the maximum velocity, [A] and [B] are the
initial concentrations of the two substrates, KMA is the Michaelis–Menten constant for
substrate [A], KMB is the Michaelis–Menten constant for substrate [B], KiA is the inhibition
constant for [A], and KiB is the inhibition constant for [B]. The values of the kinetic constants
were estimated by the nonlinear regression method using Microsoft Excel 2013 using mini-
mization of the sum of squares. The reaction rate data for esterification reaction was fitted with
the predicted data obtained by the ping-pong bi-bi mechanism. The experimental data was
further used to validate the kinetic model, and it is observed that the reaction follows a ping-
pong bi-bi mechanism with dead-end inhibition by butyric acid as well as cinnamyl alcohol.
Figure 6 represents the variation in initial rates plotted against the concentration of alcohol and
compared with the simulated rates predicted by the ping-pong bi-bi mechanism. The kinetic
parameters obtained using the initial reaction rate are summarized in Table 1. The values of
inhibition constants reveal that the inhibitory effect of cinnamyl alcohol is greater than the
inhibition effect observed by butyric acid. And, the greater value of the Michaelis constant
suggests that enzyme has the greater affinity towards the butyric acid over cinnamyl alcohol.
Effect of Mass Transfer
In a heterogeneous system containing immobilized enzyme as a catalyst, the reaction rate
might be affected by external or internal mass transfer limitations. The external mass transfer
limitations can be overcome by increasing the speed of agitation. Experiments were carried out
at the different speeds of agitation in the range of 150–450 rpm by keeping all the other
parameters constant, and the results obtained are depicted in Fig. 7.
6.00E-03
5.00E-03
4.00E-03
3.00E-03
2.00E-03
1.00E-03
Experimental
4.5
Predicted
5.5
0.00E+00
1.5
2.5
3.5
6.5
Concentration of alcohol (mol L-1)
Fig. 6 Comparison of experimental initial rates with simulated rates

Appl Biochem Biotechnol
Table 1 Kinetic parameters for the esterification reactions of butyric acid with cinnamyl alcohol
Parameter
Value
V
max (mol h−1
)
K
mA (mol dm−3
)
K
mB (mol dm−3
)
K
iA (mol dm−3
)
K
iB (mol dm−3
)
SSE
0.0072
0.0004
0.1549
0.1263
0.0001
1.2E−08
It can be seen that there is external mass transfer limitations in a heterogeneous system. As
the speed of agitation increases the overall reaction conversion increases up to certain level and
a further increase leads to a decrease in percent conversion. Here, a difference in the rate of
reaction and conversion obtained at 250 and 350 rpm was very low which indicates that the
external mass transfer resistance is negligible after 250 rpm. The decrease is possibly due to
breakage of enzyme bonding with the immobilized surface resulting in the loss of enzymatic
activity. The evaluation of diffusional mass transfer and internal diffusivity coefficient was
done by using theoretical calculations to determine the controlling mechanism.
In the case of enzyme immobilized on the spherical porous beads, it is necessary to determine the
effect of external diffusional mass transfer at the surface of the catalyst and the internal diffusional
mass transfer through the pores of the catalyst. The effect of external mass transfer on the rate of the
reaction was determined at 250 rpm with the help of the dimensionless Damköhler number (Da) and
the external effectiveness number (η) represented by Eqs. 2 and 3 respectively [50].
″
Vmax
Da ¼
ð2Þ
Ksl⋅½AŠ
b
observed reaction rate
η ¼
ð3Þ
reaction rate obtained without external mass transfer limitations
where Vmax″ is the maximum reaction rate per unit surface area of biocatalyst (mol dm−2 s−1), Ksl is
the solid–liquid mass transfer coefficient, and [A]b is the concentration of butyric acid in bulk.
90
80
70
60
50
No stirring
40
150 rpm
30
250 rpm
20
350 rpm
10
450 rpm
0
0
2
4
6
8
10
12
14
Time (h)
Fig. 7 Effect of speed of agitation on percent conversion of butyric acid at a molar ratio of 1:2, reaction
temperature of 50 °C, and enzyme loading of 2%

Appl Biochem Biotechnol
Many authors calculated the solid–liquid mass transfer coefficient by considering the
limiting value of the Sherwood number, Sh = 2, which is generally used for the non-agitated
system (natural convection), but in the given agitated system, a more accurate solid–liquid
mass transfer coefficient was determined according to Eq. 4 [51].
ꢂ
ꢃ
2
3
1=4
P
⋅μ
VL
Ksl ⋅Sc2=3 ¼ 0:13
ð4Þ
4
5
ρ2
where Sc is the Schmidt number, P is the power intake (W), ρ is the density of the continuous
phase (kg m−3), VL is the total volume of the solution (cm3), and μ is the dynamic fluid
viscosity (mPa s−1).
The terms involved in the above equation was calculated with the help of some reported
equations (Eqs. 5–9) for shake flask with some modifications in average energy dissipation
and modified power number correlations [52, 53].
P
VL
¼ ε⋅ρ
ð5Þ
0
ε ¼ Ne ⋅n3⋅d5⋅VL
ð6Þ
ð7Þ
−2=3
Ne0 ¼ 70⋅Re−1 þ 25⋅Re−0:6 þ 1:5⋅Re−0:2
n⋅d2⋅ρ
μ
Re ¼
ð8Þ
μ
Sc ¼
ð9Þ
ρ⋅D
where ε is the average energy dissipation rate (W kg−1), Ne′ is the modified power number, n is
the speed of agitation (rps), d is the diameter of the impeller (m), Re is the Reynolds number,
and D is the diffusivity of cinnamic acid (cm2 s−1).
The diffusion coefficient of solute in n-hexane was calculated with the help of Wilke–
Chang equation modified and generalized in terms of latent heat of vaporization by Sitaraman
et al. [54]. The generalized form of Wilke–Chang equation is represented in Eq. 1.
ꢀ
ꢁ
0:93
Ms1=2⋅Ls1=3⋅T
η⋅Vm0:5⋅L0:3
D ¼ 5:4 Â 10−8
ð10Þ
where Ms is the molar mass of the solvent, Ls is the latent heat of vaporization of solvent at
normal boiling point (cal g−1), Vm is the molecular volume (m3 mol−1), L is the latent heat of
vaporization of solute at normal boiling point (cal g−1), and T is the temperature (K).
The surface area of the biocatalyst needed for the calculation of the maximum rate of
reaction per unit surface area of the catalyst was 116.72 m2 g−1 (provided by Fermenta
Biotech, Ltd., Mumbai). By calculating all the factors associated in Eqs. 4–10, the value of
Damköhler number and external effectiveness factor can be calculated from Eqs. 2 and 3. The
value of Damköhler number is found to be 5.49 × 10−11. If the value Da 1, the external
diffusional mass transfer has a negligible effect on the given system [50]. Hence, it was
confirmed that the rate of the reported system is not influenced by any external diffusive mass

Appl Biochem Biotechnol
transfer limitations. Also, as the concentration of acid in the reaction mass is nearly equal to the
concentration at the surface of the catalyst, the external effectiveness factor tended to 1. It also
implies that the rate is not limited by external mass transfer [50]. Hydrodynamic parameters of
the batch reactor for esterification reaction are represented in Table 2.
Internal diffusional mass transfer was theoretically evaluated through the observable Thiele
modulus (ϕ) represented in Eq. 11 [50].
ꢀ ꢁ
2
νobs
R
3
ϕ ¼
:
ð11Þ
Deff ⋅½AŠ
0
εp
τ
Deff ¼ D⋅
ð12Þ
where Vobs is the observable reaction rate per unit mass of biocatalyst (mol mg−1 s−1), R is the
particle radius (m), Deff is the effective diffusivity (cm2 s−1), [A]0 is the initial concentration of
butyric acid, τ is the tortuosity factor of enzyme, and εp is the particle porosity.
Values for the ratio of particle porosity versus tortuosity factor, and bulk density of Fermase
CALB 10000 were 0.25 and 0.453 g cm−3. The value of observable Thiele modulus was found
to be 1.01 × 10−9. For the values of ϕ ≤0.3, the internal effectiveness factor approaches 1 [50]
and there is a negligible effect of internal diffusional mass transfer on reaction rate. The
obtained values are in correlation with the internal effectiveness factor which indicates that
internal diffusional mass transfer resistance had no significant effect on the reaction rate of the
system. Considering overall diffusion limited mass transfer, it can be concluded that the rate of
reaction is only governed by enzyme kinetics, via ping-pong bi-bi mechanism.
Enzyme Reusability
Enzyme reusability was studied by performing th esterification reaction at optimum reaction
conditions, which includes enzyme loading 2%, temperature 50°C, molar ratio 1:2, and speed
of agitation 250 rpm. The percent conversion was calculated by considering the conversion of
the first cycle as 100%. The results obtained are represented in Fig. 8. The marginal change in
percent conversion was observed after four consecutive cycles. The conversion was decreased
from 88.4 to 75.84% after the 4th cycle. The decrease in conversion might be due to the loss of
enzymatic activity during the reaction course.
Table 2 Hydrodynamic parameters for the esterification reaction of butyric acid with cinnamyl alcohol
Hydrodynamic parameter
Value
ρ, kg m−3
d, m
655
0.02
n, rps
5.83
VL, m−3
μ, Pa s−1
Da, m2 s−1
ε, W kg−1
Re
17.13 × 10−6
3.15 × 10−3
5.49 × 10−11
1.539
48,518
Ne′
Sc
0.2133
6.881 × 10−3
1008.4147
1.6938 × 10−5
P/VL, W m−3
Ksl, m s−1

Appl Biochem Biotechnol
100
95
90
85
80
75
1
2
3
4
5
Number of cycles
Fig. 8 Effect of reusability of catalyst on percent conversion of butyric acid at a molar ratio of 1:2, reaction
temperature of 50 °C, enzyme loading of 2%, and speed of agitation of 250 rpm. The conversion for the first
cycle (88.4%) is considered as a 100% to determine the relative conversion for subsequent cycles after 10 h
Conclusion
The current study investigated the immobilized enzyme (Fermase CALB 10000) catalyzed
synthesis of cinnamyl butyrate by esterification of butyric acid and cinnamyl alcohol in
hexane. This study also illustrated the effects of various reaction parameters on the reaction
progress, and the parameters are optimized using a basic single factor at a time method. It was
observed that the molar ratio of acid to alcohol of 1:2, enzyme loading of 2%, reaction
temperature of 50 °C, and speed of agitation of 250 rpm are found to be the optimum for
the maximum conversion. The kinetic model for esterification reaction was developed and
fitted based on the experimental initial rate data, and the kinetic parameters were determined.
Based on the findings in this study, it was proved that the esterification reaction follows the
ping-pong bi-bi mechanism with dead-end inhibition by both cinnamyl alcohol and butyric
acid at higher concentrations. The diffusional mass transfer limitations were studied, and it was
found that internal as well as external mass transfer limitations do not play any significant role
in the given esterification reaction and the reaction is mainly governed by enzyme kinetics.
Acknowledgements The authors are thankful to the UGC-GREEN TECH and UGC-CAS for providing the
financial assistance and to the Fermenta Biotech Ltd., Thane, Mumbai, for providing the gift sample of Fermase
CALB 10000.
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