**3.2 Reaction rate determination**

The operational parameters during the kinetical experiments were 200 rpm and 30 °C. 0.01 g immobilized lipase preparation was added to the incubated homogeneous reaction mixture to initiate the enzymatic reaction. Samples in duplicates were taken from the reaction mixture regularly.

Experiments using substrate concentrations in the range of 0.4 - 6.0 and 0.2 - 2.0 mol/L of iamyl alcohol and oleic acid concentration, respectively, were carried out at 30 °C temperature, with an optimal initial 0.1 w/w % water content (determined earlier) (Koszorz et al., 2004) in n-heptane solvent. Progress curves: oleic acid consumptions as a function of time were measured.

From the data of progress curves the initial reaction rates were calculated by the Gregory-Newton method (Leskovac, 2003). The initial reaction rate data were modified taken into account the amount of enzyme used. Thus the reaction rate values were obtained as μmol/s.genzyme and summarised in Table 4.


Table 4. Intitial reaction rate data [μmol/s.genzyme ] using various oleic acid (cOA) and i-amyl alcohol concentrations (ciAA) (all the concentrations in mol/L)

#### **3.3 Effect of immobilization on the mass transfer**

Since immobilised enzyme preparation was used in the experiments, it was important to decide – before the detailed kinetical analysis – whether the reaction rates measured are the real values of enzymatic reaction or influenced significantly by the diffusion rates of the compounds (from the bulk phase to the solid particle and vice versa).

The reaction and the diffusion take place simultaneously and the rate limiting step is always the one which is slower. Using immobilised lipase preparations, rate of diffusion is usually not the limiting step (Letisse et al., 2003).

In our measurements Yadav-method (Yadav et al., 2003) was applied to determine the rate limiting step, using the Weisz-Prater criteria. This method is based on the calculation and comparison of the two relevant relaxation times. The ratio of the relaxation time of biocatalysis rate, tr and that of the diffusion rate, td shows which process should be considered as the limiting step.

The relaxation times can be defined as follows :

132 Food Industrial Processes – Methods and Equipment

It can be seen that the difference between the 4- and 5-parameter equations (Eqs. 4 and 6) is the KAB factor. Its influence is significant only in the case when concentrations of both substrates are very low. However, we do not plan to carry out measurements under these conditions, thus it is assumed that no significant difference will be experienced in the

The operational parameters during the kinetical experiments were 200 rpm and 30 °C. 0.01 g immobilized lipase preparation was added to the incubated homogeneous reaction mixture to initiate the enzymatic reaction. Samples in duplicates were taken from the reaction

Experiments using substrate concentrations in the range of 0.4 - 6.0 and 0.2 - 2.0 mol/L of iamyl alcohol and oleic acid concentration, respectively, were carried out at 30 °C temperature, with an optimal initial 0.1 w/w % water content (determined earlier) (Koszorz et al., 2004) in n-heptane solvent. Progress curves: oleic acid consumptions as a function of

From the data of progress curves the initial reaction rates were calculated by the Gregory-Newton method (Leskovac, 2003). The initial reaction rate data were modified taken into account the amount of enzyme used. Thus the reaction rate values were obtained as

0.2 4.90 5.13 5.45 5.57 3.50 0.5 7.91 7.91 8.26 7.13 7.31 1.0 9.68 12.56 12.80 9.69 10.80 1.5 11.25 15.15 18.45 15.30 13.72 2.0 9.78 14.46 17.65 14.50 14.31

Table 4. Intitial reaction rate data [μmol/s.genzyme ] using various oleic acid (cOA) and i-amyl

Since immobilised enzyme preparation was used in the experiments, it was important to decide – before the detailed kinetical analysis – whether the reaction rates measured are the real values of enzymatic reaction or influenced significantly by the diffusion rates of the

The reaction and the diffusion take place simultaneously and the rate limiting step is always the one which is slower. Using immobilised lipase preparations, rate of diffusion is usually

In our measurements Yadav-method (Yadav et al., 2003) was applied to determine the rate limiting step, using the Weisz-Prater criteria. This method is based on the calculation and

alcohol concentrations (ciAA) (all the concentrations in mol/L)

compounds (from the bulk phase to the solid particle and vice versa).

**3.3 Effect of immobilization on the mass transfer** 

not the limiting step (Letisse et al., 2003).

0.4 1.0 2.0 4.0 6.0

modelling results obtained by using the two systems.

μmol/s.genzyme and summarised in Table 4.

**3.2 Reaction rate determination** 

mixture regularly.

time were measured.

CiAA

COA

$$t\_{\text{-}} \frac{\mathbf{C}\_{\text{0}}}{r(\mathbf{C}\_{\text{0}})} \text{ and } \ t = \frac{D}{\text{(}k\text{)}^2} \tag{7}$$

Oleic acid – having slower diffusivity – was chosen for the calculations and the highest reaction rate-substrate concentration value-pair was taken from Table 4. Thus tr was calculate as:

$$t\_{\prime} = \frac{\mathbf{C}\_{0}}{r(\mathbf{C}\_{0})} = \mathbf{2}^{5}\mathbf{s} \tag{8}$$

Diffusion constant (D) of oleic acid in n-heptane was determined according to Shibel (Perry, 1969):

$$D = k \frac{T}{\eta \nu V\_\* \mathcal{Y}} \tag{9}$$

VS molar volume density was estimated from its critical volume (Vc):

$$V\_s = 0.285 V\_\odot^{1.048} \tag{10}$$

Vc of oleic acid is 1152 cm3/mol, thus Vs is obtained as 460 cm3/g. In this way D diffusion coefficient is calculated as 1.61x 10-5 cm2/s.

The mass transfer coefficient can be calculated – based on the Sherwood number – from the diffusion coefficient and the particle size:

$$k\_{\rm sl.} = \mathcal{D}D \int d\_{\rm k} \tag{11}$$

The average diameter of Novozyme 435 immobilised lipase preparation is 0.06 cm, thus the value of the mass transfer coefficient is 5.3x 10-4 cm/s.

The relaxation time for the diffusion is calculated as:

$$t\_d = \frac{D}{\left(k\_{\rm sl}\right)^2} = \frac{1,61.10^{-5} \left\lfloor cm^2 \right/s \right\rfloor}{\left(5,3^\* \cdot 10^{-4} \left\lfloor cm \right/s \right)^2} = 55,9s \tag{12}$$

Comparing the values of tr and td it can be concluded that diffusion rate is three order of magnitude higher than the reaction rate, thus the rates measured in the enzymatic process can be considered as the real reaction rates.

#### **3.4 Kinetical analysis**

In Fig. 5a the initial reaction rates are presented as a function of oleic acid (substrate 1) concentration, while in Fig. 5b the same data are shown as a function of i-amyl alcohol (substrate 2) concentration. It can be clearly seen that the i-amyl alcohol has a considerably and oleic acid a slight inhibition effect on the enzymatic reaction.

on the experimental data. In the calculation a variation of simplex method was applied, namely the Nielder-Niemand method (Bailey, 1986), which is more sensitive for the initial values of the parameters and slower than the original simplex method, but it provides more

Since the method is sensitive for the initial values of the parameters, a two-step method was elaborated. In the first step the values of kinetic parameters were estimated by a special programme, applying a simplified model (Luzenc4 programme) with no inhibition, using the experimental data. Thus the instability of the method was eliminated. The estimated kinetic parameters obtained were then used as initial parameters for the extended kinetic model. Having checked the kinetic results by comparing the experimental data, the program either refused the results and started another circle - modifying one or more parameters

During the procedure programme was run on data belonging to only one acid concentration, otherwise divergence occurred. In this way the parameters were obtained for every acid concentration, which were used in a final run of the programme, where errors

In Table 3 values of the parameters determined are summarized. It can be seen from the value of r2, that the four-parameter model (taking into account the inhibitions, as well) described better the kinetics of enzymatic i-amyl oleate synthesis than the three-parameter

> Four-parameter model

Five-parameter model

129

according to the Nielder-Niemand method - or accepted the results and presented.

Vm (μmol/s g) 23.5 30.8 29.9 KA (mol/L) 0.86 0.65 0.55 KB (mol/L) 0.19 0.58 0.53 KiB (mol/L) - 3.2 2.7 KAB (mol/L) - - 0.055 r2 (-) 0.952 0.975 0.975 ARE\* (%) 12,2 3,1 2,8

However, the five-parameter model is not more accurate than the four-parameter one (value of r2 is the same), therefore it is not reasonable to use the more complicated model This theory evaluated using F-statistics (Bates, 1988) used significance level was P=0.05, as the result shows the 3 parameter model was significance different then the 4 and 5 parameters model while the 4 parameter and 5 parameters model are not significantly different. The results of the modelling were intended to compare with other literature data, however no similar results were found in published materials. Either the substrates of the esterification, or the enzyme applied were different, thus the parameters were not

accurate final results.

were minimised.

Parameters Three-parameter

Table 5. Parameters of the kinetical models

possible to compare.

model

model.

Fig. 5. Initial reaction rates as a (a) function of oleic-acid concentration at different i-amyl alcohol concentrations; (b) a function of i-amyl alcohol concentration at different oleic acid concentrations in mol/L

In the first step of the kinetic analysis the traditional linearization (graphical) methods were applied. Reciprocal data of the initial rates were plotted against the reciprocal data of the initial substrate concentrations (both) (Figs. 6a and 6b). It can be seen that in Fig. 6b in lower substrate concentrations the lines are parallel, implying ping-pong bi-bi mechanism. However, in higher substrate concentrations the lines steeply keep upwards to the ordinate, which means that inhibition (by the alcohol compound) occurred. Thus the kinetic parameters can not be determined graphically and the mechanism of inhibitions can not be doubtlessly decided.

Fig. 6. (a) and (b) Lineweaver-Burk linearization of the reaction rate – substrate concentration data

Ping-ping bi-bi kinetic models having 3 (eq. 3), 4 (eq. 4.) and 5 (eq. 6.) parameters were used for the description of the enzymatic esterification and the parameters were calculated based

Fig. 5. Initial reaction rates as a (a) function of oleic-acid concentration at different i-amyl alcohol concentrations; (b) a function of i-amyl alcohol concentration at different oleic acid

In the first step of the kinetic analysis the traditional linearization (graphical) methods were applied. Reciprocal data of the initial rates were plotted against the reciprocal data of the initial substrate concentrations (both) (Figs. 6a and 6b). It can be seen that in Fig. 6b in lower substrate concentrations the lines are parallel, implying ping-pong bi-bi mechanism. However, in higher substrate concentrations the lines steeply keep upwards to the ordinate, which means that inhibition (by the alcohol compound) occurred. Thus the kinetic parameters can not be determined graphically and the mechanism of inhibitions can not be

Fig. 6. (a) and (b) Lineweaver-Burk linearization of the reaction rate – substrate

Ping-ping bi-bi kinetic models having 3 (eq. 3), 4 (eq. 4.) and 5 (eq. 6.) parameters were used for the description of the enzymatic esterification and the parameters were calculated based

concentrations in mol/L

doubtlessly decided.

concentration data

on the experimental data. In the calculation a variation of simplex method was applied, namely the Nielder-Niemand method (Bailey, 1986), which is more sensitive for the initial values of the parameters and slower than the original simplex method, but it provides more accurate final results.

Since the method is sensitive for the initial values of the parameters, a two-step method was elaborated. In the first step the values of kinetic parameters were estimated by a special programme, applying a simplified model (Luzenc4 programme) with no inhibition, using the experimental data. Thus the instability of the method was eliminated. The estimated kinetic parameters obtained were then used as initial parameters for the extended kinetic model. Having checked the kinetic results by comparing the experimental data, the program either refused the results and started another circle - modifying one or more parameters according to the Nielder-Niemand method - or accepted the results and presented.

During the procedure programme was run on data belonging to only one acid concentration, otherwise divergence occurred. In this way the parameters were obtained for every acid concentration, which were used in a final run of the programme, where errors were minimised.

In Table 3 values of the parameters determined are summarized. It can be seen from the value of r2, that the four-parameter model (taking into account the inhibitions, as well) described better the kinetics of enzymatic i-amyl oleate synthesis than the three-parameter model.


Table 5. Parameters of the kinetical models

However, the five-parameter model is not more accurate than the four-parameter one (value of r2 is the same), therefore it is not reasonable to use the more complicated model This theory evaluated using F-statistics (Bates, 1988) used significance level was P=0.05, as the result shows the 3 parameter model was significance different then the 4 and 5 parameters model while the 4 parameter and 5 parameters model are not significantly different. The results of the modelling were intended to compare with other literature data, however no similar results were found in published materials. Either the substrates of the esterification, or the enzyme applied were different, thus the parameters were not possible to compare.

ionic liquids (Cyphos-105 and Cyphos-110) were mixed with the substrates, so they were not investigated further. Henceforth the reactions were carried out at 50 °C, the ester yield was followed by GC and the decreasing oleic acid concentration using titrimetry. The percentage esterification was calculated from the values obtained for the blank and the test samples. The further phosphonium-type ionic liquids, Cyphos-201 and Cyphos-104 without

131

Time [h] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Fig. 7. Oleate ester concentration in case of using different phosphonium-type ionic liquids

For imidazolium-cation containing ionic liquids literary data show that these types of ionic liquids are the most suitable for esterification, transesterification reactions (Moniruzzaman at al., 2010). Both investigated imidazolium-type ionic liquids were successfully applied in earlier experiments, where natural aroma esters production was the aim. In case of [bmim]BF4 there were no significant differences in the detected oleate concentration if enzyme was added or not. For [bmim]PF6 - without the presence of the enzyme only negligible product formation was observed, in the presence of enzyme, higher concentrations were achieved than in the experiments where n-hexane was used as

Therefore for further investigations this ionic liquid was chosen. In case of ionic liquids for water solubility cations are responsible. Comparing the same cation having [bmim]BF4 and [bmim]PF6 shows that while the first not miscible with water, the later has an unlimited solubility in water. Thus, the hydrophilic [bmim]BF4 ionic liquid often distracts the absorbed water layer from the surface of the enzyme which should be necessary for the active conformation. Therefore the enzyme is deactivated (van Rantwijk & Sheldon, 2007). Further

The optimal parameters of the batch production were determinated using experimental design software application. In doing so Statistica 8.0 program was applied. Based on earlier studies substrate molar ratio, amount of enzyme and ionic liquid were chosen as key factors. Each factor was prepared in two levels: -1 for low level and +1 for high level.

advance that in case of using [bmim]PF6 side-reactions were not observed.

the presence of enzyme greatly catalyze the process as it shown on Fig. 7.

Cyphos 201 Cyphos 201+enzyme Cyphos 104 Cyphos 104+enzyme

Concentration [mmol/g]

(reaction time: 180 min)

**4.3 Acid/alcohol molar ratio** 

solvent.

Kinetic model for description of the enzymatic esterification of oleic acid and i-amyl alcohol was – according to our best knowledge – elaborated and presented in the first time in literature. The model is based on the ping-pong bi-bi mechanism and not only product, but substrate inhibition is taken into account, as well. The model fitted well to the experimental data (checked by r2 values), though the measurements covered an extremely wide concentration range.
