# Biodiesel Production Using Palm Oil with a MOF-Lipase B Biocatalyst from Candida Antarctica: A Kinetic and Thermodynamic Study

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}Lipase, was achieved using ZIF-8 at 45 °C and an initial protein concentration of 1.20 mg·mL

^{−1}. The results obtained for the adsorption equilibrium studies allow us to infer that CALB was physically adsorbed on ZIF-8 while chemically adsorbed with MOF-199. It was determined that the adsorption between Lipase and the MOFs under study better fit the Sips isotherm model. The results of the kinetic studies show that adsorption kinetics follow the Elovich model for the two synthesized biocatalysts. This research shows that under the experimental conditions in which the studies were carried out, the adsorption processes are a function of the intraparticle and film diffusion models. According to the results, the prepared biocatalysts showed a high efficiency in the transesterification reaction to produce biodiesel, with methanol as a co-solvent medium. In this work, the catalytic studies for the imidazolate, ZIF-8, presented more catalytic activity when used with CALB. This system presented 95% biodiesel conversion, while the biocatalyst formed by MOF-199 and CALB generated a catalytic conversion percentage of 90%. Although both percentages are high, it should be noted that CALB-MOF-199 presented better reusability, which is due to chemical interactions.

## 1. Introduction

_{2}production [6,7,8]. To reduce the cost of biodiesel production by methanolysis [1,2,3,4], the process of biodiesel production by transesterification of oils catalyzed by lipases has begun to be used, a method that has been very interesting as unrefined oils can be used, generating fascinating results.

## 2. Results and Discussion

#### 2.1. MOFs Characterization

#### 2.1.1. Analysis of FTIR Results

^{−1}. The analysis shows that each one of the bands of the respective spectra starting with free MOF-199 (Figure 1a—line black) generally coincides with what has been reported by various authors in the specialized literature [28,29]. The following characteristic bands stand out from the spectrum: 1285 cm

^{−1}, which could be due to CO vibrations of BTC (benzene-1,3,5-tricarboxylate), and the bands at 1456 cm

^{−1}and 1340 cm

^{−1}, which could be due to the vibration and in-plane splitting of the C=O of BTC (benzene-1,3,5-tricarboxylate). Suppose one compares the FTIR of free MOF-199 with CALB-MOF-199. In that case, it is observed that there is a very marked band for the latter system, which some authors call “characteristic” at 1355 cm

^{−1}and assign it to the aromatic C-C stretching vibration of the BTC group of the carboxylate group.

^{−1}, at which point the intensity becomes more intense for CALB-MOF-199, clearly demonstrating the effect of lipase immobilization on the adsorbate. This allows us to confirm that the procedure carried out in the laboratory regarding the fixation of the Lipase on the MOF-199 was successful. The FTIRs presented in Figure 1b show the spectra of ZIF-8 free with Lipase adsorbed at 45 °C and 0.40 mg·mL

^{−1}of lipase loading. (CALB-ZIF-8). The results of the analysis were found to be in good agreement with those from previous studies [28,29]. The bands that lie towards approximately 440 cm

^{−1}can be assigned to vibrations of the Zn-N pair. Suppose the infrared spectrum is analyzed from left to right. In that case, certain acute vibrations will be found, in particular two bands of 770 cm

^{−1}and 1500 cm

^{−1}, which experts assign to the HMeIM ring, and some very small bands towards the weak 2800–3100 cm

^{−1}that surely correspond to the stretching and vibrations of aromatic and aliphatic CH of HmeIM [18,28]. The results of the analysis based on the FTIR presentation of the band show that they correspond to ZIF-8 in its hexahedral crystalline form together with adsorbed Lipase, as shown in the plots in Figure 1b.

#### 2.1.2. Analysis of X-ray Diffraction Analysis (XRD) Results

#### 2.1.3. Analysis of the Porosity and Surface Area Results

^{2}·g

^{−1}, 1733 m

^{2}·g

^{−1}, respectively.

^{3}·g

^{−1}, calculated by applying the Dubinin–Astakhov (DA) method for ZIF-8, while for MOF-199, it is 0.66 cm

^{3}·g

^{−1}. As mentioned, ZIF-8 is a microporous material with a BET-specific surface area of 1733 m

^{2}·g

^{−1}(relative pressure calculated from 0.009 to 0.02), while that of MOF-199 is 1750 m

^{2}·g

^{−1}.

_{2}isotherm at 77 K corresponds to the CALB-MOF-199 biocatalyst. This isotherm also has a type I isotherm characteristic corresponding to fundamentally microporous systems with a SBET that has decreased and is now 1400 m

^{2}·g

^{−1}, as well as a pore radius that is now 5.5 Å; when analyzing the results in Table 1, where the other textural parameters are reported, it is clear that these change when CALB is configured in MOF-199, and the values of each of its parameters decrease. It is worth noting here that the CALB-MOF-199 biocatalyst also exhibits a type I isotherm, which suggests that the basic framework of MOF-199 is conserved after CALB immobilization. Figure 3b—black—shows the isotherm obtained for the CALB-ZIF-8 biocatalyst. It behaves very similar to the free ZIF-8 isotherm (Figure 3a–grey), i.e., it is microporous with a type I isotherm according to IUPAC. In Table 1, it is again concluded, from the point of view of its textural characteristics, the parameters of this biocatalyst change when CALB is supported; the S

_{BET}now has a value of S

_{BET}1350 m

^{2}·g

^{−1}and the pore radius is 7.2 Å. The other textural parameters decrease due to the adsorption of CALB, as in the previous biocatalyst. To summarize the above information, it has been established that the reduction in the BET surface area when fixing the CALB on the two MOF’s may be due to the impregnation and/or blockage of the pores by the Lipase inside the MOF’s pores. This agrees with the reduction in the value of the parameters calculated through the models used. Additionally, maintaining the type of isotherm before and after fixing the CALB on the two MOFs confirms that their organo-metallic structure was not altered.

#### 2.1.4. Surface Morphology

#### 2.2. Lipase Adsorption Isotherms

^{2}correlation coefficient, which was used as a criterion to establish which model fits best and that describes the lipase adsorption on the MOFs, are presented in Table 2 for the two MOFs tested in this investigation. The experimental data q

_{e}(representing the lipase adsorption capacity on the MOF expressed as mg·g

^{−1}of the respective MOF) and C

_{e}(representing the lipase concentration at equilibrium expressed as mg·L

^{−1}) were fitted according to the models mentioned and explained in detail in Section 3.2.1 to understand the types of interactions and the mechanisms of Lipase adsorption on the surface of each MOF. To establish each of the fit parameters of the models, the Rosenbrock and quasi-Newton optimization method included in the Statistica

^{®}software v14 were used. Table 2 shows the parameters and coefficients obtained from the corresponding data for lipase adsorption, applying these models. The model that best describes the two biocatalysts was that of Sips, which was derived from the original model of the Langmuir isotherm, as described in Section 3.2.1 (where each of them was described in good detail, the models that were used in this investigation). This model is based on the premise that the adsorption process is presented in a monolayer throughout the mathematical development of said isotherm at high adsorbate concentrations for Langmuir-type modeling and is subsequently reduced to the form of the Freundlich isotherm model at low concentrations of adsorbate. As can be seen in the results reported in Table 2, the model that best fits the CALB-MOF-199 system at the different temperatures investigated is precisely that of Sips, considering that it presented the best R

^{2}compared with the other models applied. From a global point of view of the results, it can be seen that the parameters of each model (except for the Redlich–Peterson model) applied to the CALB-MOF-199 biocatalyst have an acceptable coincidence factor (R

^{2}).

^{−1}) for the hydrophilic surfaces, ZIF-8 and MOF-199, resulted in positive values, which confirmed the endothermic nature of the process. When ΔH° is less than 50 kJ·mol

^{−1}, adsorption is considered physisorption [36,37,38], as in the case of CALB-ZIF-8, while adsorption was chemisorption at values greater than 50 kJ·mol

^{−1}for CALB. -MOLF-199. The positive values for the entropic variable ΔS° for the CALB-MOF-199 and the CALB-ZIF-8 indicate the randomness in the solid–solution interface during the adsorption process, and a good affinity [28,37]. To explain these thermodynamic results, one must understand the forces of attraction. Adhesion of Lipase to ZIF-8 is by physical adsorption, while in the case of MOF-199, it is by chemical adsorption. In the first case, the attractive forces are mainly hydrophilic and Van der Waals forces, whereas they are chemical bonds in the second MOF. As the temperature increases, the adhesion of hydrophilic proteins to the hydrophilic surface of ZIF-8 compensates for the drop in Van der Waals forces [11,28,38]. However, in the case of MOF-199, the extent of chemisorption increased with increasing temperature, and enzyme binding increased [17] the adhesion of hydrophilic proteins to the hydrophilic surface of ZIF-8, which compensates for the drop in Van der Waals forces [11,28,38].

#### 2.3. Adsorption Kinetics

^{2}) as the adjustment criterion, where the kinetic model whose value is closest to 1, will be established as the one that gives a better explanation of the kinetic mechanism between CALB-MOF adsorption. The values corresponding to the parameters are found in Table 3 and Table 4. The results corresponding to the kinetics of PFO, PSO, and Elovich are shown in Table 3. From there, it is worth noting: (i) that for the PFO model, k

_{1}presents an inverse behavior concerning the concentrations of lipases tested; that is, when the concentration was increased, the value of k

_{1}decreased. Regarding temperature, Lipase, as a function of the temperature variable, increased in magnitude throughout the temperature study range; (ii) for the PSO kinetic model, the same phenomenon occurred; however, the magnitude is smaller for the k

_{s}. Some authors attribute this behavior to the tendency of Lipase to migrate from the solid phase to the bulk phase due to the effect of temperature [28,40]. It is worth mentioning that the R

^{2}are not close to 1, so the adsorption of Lipase on the MOFs is not well described through either of these two kinetic models: PFO or PSO.

^{2}that allows us to infer that the results for the biocatalysts can be interpreted using this model. However, it should be noted that the Elovich equation does not predict any defined mechanism. Still, it is interesting if one wishes to describe an adsorption process on highly heterogeneous adsorbents [28,29], as is the case of MOFs, in particular used here: MOF-199 and ZIF-8, whose structure, as demonstrated during the textural analysis, corresponds to a heterogeneous porous network. If the R

^{2}criterion is relaxed to examine the models, it can be seen, according to the R

^{2}values obtained and reported in Table 3, that R

^{2}, without being a value very close to 1, can be considered an acceptable value as a fit for the CALB-MOF-199 biocatalyst for the pseudo-second order model. This fact may be showing that the lipase adsorption on the MOF-199 structure can occur through a surface level exchange until the functional sites on the surface are fully occupied; after this occurs, the lipase molecules begin to diffuse into the MOF-199 network where additional interactions (such as inclusion complexes, hydrogen bonding, hydrogen phobic interactions) probably occur [40]. The PSO model assumes that each lipase molecule adsorbs to two adsorption sites, allowing a stable binuclear bond to form [28] for the pseudo-second order model. This fact may demonstrate that the lipase adsorption on the MOF-199 structure can occur through a surface level exchange until the functional sites on the surface are fully occupied; after this occurs, the lipase molecules begin to diffuse into the MOF-199 network where additional interactions (such as inclusion complexes, hydrogen bonding, hydrogen phobic interactions) probably occur [40,41,42].

_{id}, was found to increase with enzyme concentration due to increasing driving force, i.e., the concentration gradient [28]. In the initial stage of the adsorption process, film diffusion is an important step in rate control [10,11,12,13,14,15,28]. The intraparticle diffusion model suggested that mass transfer affects adsorption at lower concentrations [42]. The intraparticle diffusion constant, K

_{id}, was found to increase with enzyme concentration due to increasing driving force, i.e., the concentration gradient. The values of C (nm

^{2}·min

^{−1}) for the biocatalyst CALB-MOF-199 at low concentrations oscillate between 0.0077 and 0.0176 and at high concentrations between 0.084 and 0.097, while for CALB-ZIF-8 at low concentrations, it ranged between 0.0321 and 0.0349, and at high concentrations, it varied between 0.00443 and 0.0487. This behavior is very similar to that reported and widely explained in the literature by other authors [28].

#### 2.4. Transesterification Reaction and Operational Stability

## 3. Materials and Methods

#### 3.1. Reagents

#### 3.2. Batch Adsorption of Lipase onto Activated MOFs

^{−5}mbar. Subsequently, MOF-199 was activated at 125 °C for 6 h, while ZIF-8 was activated at 110 °C for 8 h. It should be noted that due to the heat treatment of MOF-199 to activate it, its color changed from light turquoise to dark blue (characteristic of copper, which is a metal in the center of the organic metal lattice). Before running the batch adsorption experiments, 0.23 g of the respective activated MOFs were taken, and 10 mL of phosphate buffer solution (pH 7.6) was added to the sealed glass vials [28]. The MOFs were then dispersed by sonication at an amplitude of 50 Hz for 15 min; then, the enzyme (CALB) was added to each. Next, 10 mL of the respective CALB Lipase solutions, at different concentrations, were added to the sealed vials and placed in a constantly stirred water bath at 300 rpm and different temperatures from 25 °C to 40 °C. The initial concentrations of enzymes in the mixtures ranged between 3.45 and 0.8570 mg·mL

^{−1}[28]. At regular intervals, 25 μL of the sample was withdrawn and filtered. Next, 200 μL of Bradford’s reagent [29] was added, and the optical density was measured at 595 nm using a microplate UV spectrophotometer (Multiskan GO, Leicestershire, UK). The enzyme concentration in the extracted samples was determined by comparing the optical density to a calibration curve prepared using serial dilutions of standard protein, albumin, and solution of known concentration. After 48 h, MOFs with immobilized Lipase (CALB) were collected by centrifugation at 9000 rpm and −4 °C for 15 min and washed twice with buffer solution [28]. The concentration of enzyme (CALB) remaining in the supernatant after 48 h was assumed to be an equilibrium concentration [28,29]. The respective MOF with the adsorbed Lipase, now called biocatalysts in this investigation, CALB-MOF-199 and CALB-ZIF-8, were lyophilized for further use. Enzyme immobilization efficiency (EIE) and immobilization capacity (q

_{m}) were determined using Equations (2) and (3), respectively [25,28]:

^{−1}) are the initial and final concentrations of the enzyme (CALB), respectively, q

_{m}(mg·g

^{−1}) is the capacity of the MOF, m (g) is the weight of the MOF, and V (mL) is the volume of the solution.

_{e}(mg·g

^{−1})) and the equilibrium aqueous concentration of the protein (C

_{e}(mg·mL

^{−1})) and adjusting them to the linear form of the isotherm models. All the experiments were repeated three times, and the mean and average values were considered. The standard deviation of the mean values of the triple tests in all the experiments was less than 2%.

#### 3.2.1. Adsorption Models

#### 3.2.2. Adsorption Kinetics Models

#### 3.3. Biodiesel Production

^{−1}and 0.05 mg·mL

^{−1}, and the concentration of African palm oil changed in the range from 0.85 to 0.45 mg·mL

^{−1}. In the specialized literature, it has been assumed that biodiesel production is linear during the first 4 h; according to our experience it is preferable to assume this for 8 h, as we have found that linearity is not always reached in 4 h, and this can affect the final analysis of the results. The initial reaction rate in each condition was calculated by dividing the concentration of FAMEs after 8 h of reaction by 8 h.

#### 3.4. Gas Chromatography Analysis

^{−1}up to 230 °C (4 min); FID: 260 °C; hydrogen: 40 mL·min

^{−1}; air: 400 mL·min

^{−1}auxiliary gas (N

_{2}): 25 mL·min

^{−1}; injection: 1 µL. A 1 µL sample was injected into the column through a 0. 45 mm filter and compared to a calibration determined using a standard mix of FAMEs. The FAMEs production yield was determined using the following Equation (4) [28,45].

#### 3.5. MOF Characterization

_{BET}) was determined using the Brunauer-Emmet-Teller (BET) equation, and the total pore volume (V

_{total}) was calculated from the amount of N

_{2}adsorbed at a relative pressure of P/P

^{0}= 0.99. The size distribution of the mesopores was obtained using the DFT (Density Functional Theory) method. Before the analysis, the samples were degassed at 300 °C for 8 h. A Quantachrome sortometer, IQ2 (Boynton Beach, FL, USA), was used for this analysis. The hydrophobicity of MOF-199 and ZIF-8 was determined by the immersion of calorimetry measurements in benzene and water using a homemade immersion calorimeter.

## 4. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**DRX corresponding to MOFs: (

**a**) Free, Black-MOF-199 and Grey, CALB-MOF-199; (

**b**) Free, ZIF-8 and Grey, CALB-ZIF-8.

**Figure 3.**The N

_{2}adsorption–desorption isotherms: (

**a**) MOF-199 free and impregnated with Lipase Candida Antarctica (CALB-MOF-199); (

**b**) ZIF-8 free and impregnated with Lipase Candida Antarctica (CALB-ZIF-8).

**Figure 4.**SEM correspond to samples free and impregnated: (

**a**) MOF-199; (

**b**) CALB-MOF-199; (

**c**) ZIF-8; (

**d**) CALB-ZIF-8.

**Figure 5.**Comparison of experimental data and adsorption isotherms predicted for Lipase CALB on (

**a**) MOF-199 and (

**b**) ZIF-8: Adjusted to Freundlich, Langmuir, Sips, Redlich-Peterson (RP), Radke-Prausnitz and Toth. models, for the adsorption of CALB on MOF-199 and ZIF-8.

**Figure 6.**Results at fixed concentration at different temperatures for the Lipase-MOF system, at different temperatures: Adjusted to PFO, PSO and Elovich.

Samples | S_{BET} [m^{2}·g^{−1}] | DA (P/P^{0} < 0.1) | DFT (P/P^{0} 10^{−7} − 1) | ||||
---|---|---|---|---|---|---|---|

V_{mic} [cm^{3}·g^{−1}] | E_{o} [kJ·mol^{−1}] | n | Pore Radius [Å] | V_{P} [cm^{3}·g^{−1}] | Half PoreWidth [Å] | ||

MOF-199 | 1750 | 0.66 | 8.47 | 3.4 | 7.0 | 0.69 | 3.52 |

CAL-MOF-199 | 1400 | 0.54 | 8.21 | 3.1 | 5.5 | 0.55 | 2.70 |

ZIF-8 | 1733 | 0.88 | 4.47 | 3.4 | 8.6 | 0.65 | 4.63 |

CALB-ZIF-8 | 1350 | 0.73 | 4.12 | 2.9 | 7.2 | 0.59 | 4.00 |

**Table 2.**Adjustment parameters to the models of the Freundlich, Langmuir, Sips, Redlich-Peterson (RP), Radke-Prausnitz and Toth, for the adsorption of CALB on MOF-199 and ZIF-8.

Model | Parameters | CALB-ZIF-8 | ||
---|---|---|---|---|

25 °C | 30 °C | 40 °C | ||

Langmuir | q_{max} (mg·g^{−1}) | 27.64 | 32.12 | 36.78 |

K_{L} (mg^{−1}·g^{−1}) | 7875 | 8034 | 8934 | |

R^{2} | 0.9789 | 0.9789 | 0.9834 | |

R_{L} | 0.015 | 0.019 | 0.021 | |

Freundlich | K_{F} (mg·g^{−1}) (L·mg^{−1}) 1/n | 6845 | 7987 | 8005 |

1/n | 0.301 | 0.312 | 0.379 | |

R^{2} | 0.9843 | 0.9834 | 0.9856 | |

Sips | q_{max} (mg·g^{−1}) | 30.79 | 38.57 | 41.07 |

K_{s} (L·mg^{−1}) | 0.3487 | 0.2394 | 0.2065 | |

n_{s} | 0.8943 | 0.8631 | 0.8304 | |

R^{2} | 0.9993 | 0.9989 | 0.9985 | |

Redlich-Peterson (RP) | K_{R} (L·g^{−1}) | 0.894 | 1765 | 1898 |

a_{R} (L·mg^{−1}) | 0.398 | 0.299 | 0.272 | |

β | 0.865 | 0.887 | 0.898 | |

R^{2} | 0.9587 | 0.9698 | 0.9456 | |

Radke Prausnitz | q_{mRP} (mg·g^{−1}) | 27.98 | 29.67 | 30.73 |

K_{RP} (L·mg^{−1}) | 0.078 | 0.086 | 0.094 | |

m_{RP} | 1087 | 1435 | 1754 | |

R^{2} | 0.9876 | 0.9798 | 0.9895 | |

Toth | q_{mT} (mg·g^{−1}) | 28.54 | 33.88 | 35.67 |

K_{T} | 0.354 | 0.185 | 0.234 | |

m_{T} | 0.786 | 0.804 | 0.847 | |

R^{2} | 0.9876 | 0.9910 | 0.9854 |

T (°C) | C_{o} | q_{e} (mg·g^{−1}) | Pseudo-First Order | Pseudo-Second Order | Elovich Model | ||||
---|---|---|---|---|---|---|---|---|---|

k_{1} (min^{−1}) | R^{2} | k_{2} (g/mg·min) | R^{2} | α (m/g/min) | 1/β (mg/g) | R^{2} | |||

CALB-MOF-199 | |||||||||

25 | 1.2 | 21.34 | 0.0165 | 0.865 | 0.0087 | 0.916 | 3.456 | 2.154 | 0.967 |

0.9 | 18.89 | 0.0189 | 0.856 | 0.0122 | 0.903 | 3.165 | 2.078 | 0.974 | |

0.6 | 16.56 | 0.0216 | 0.810 | 0.0146 | 0.892 | 2.678 | 1.896 | 0.962 | |

0.3 | 15.74 | 0.0365 | 0.845 | 0.0245 | 0.898 | 2.345 | 1.654 | 0.981 | |

30 | 1.2 | 23.34 | 0.0254 | 0.798 | 0.0076 | 0.912 | 3.765 | 3.154 | 0.943 |

0.9 | 19.65 | 0.0278 | 0.795 | 0.0116 | 0.943 | 3.376 | 2.986 | 0.967 | |

0.6 | 18.67 | 0.0306 | 0.795 | 0.0116 | 0.943 | 3.376 | 2.986 | 0.967 | |

0.3 | 17.56 | 0.0389 | 0.812 | 0.0213 | 0.904 | 2.896 | 1.967 | 0.987 | |

40 | 1.2 | 26.34 | 0.0345 | 0.797 | 0.0063 | 0.934 | 5.875 | 4.034 | 0.978 |

0.9 | 21.96 | 0.0374 | 0.807 | 0.0104 | 0.921 | 4.965 | 3.871 | 0.985 | |

0.6 | 18.26 | 0.0387 | 0.804 | 0.0124 | 0.912 | 4.762 | 2.987 | 0.976 | |

0.3 | 17.32 | 0.0402 | 0.808 | 0.0202 | 0.899 | 3.986 | 2.487 | 0.956 | |

CALB-ZIF-8 | |||||||||

25 | 1.2 | 19.45 | 0.0168 | 0.832 | 0.0058 | 0.934 | 3.876 | 2.376 | 0.919 |

0.9 | 17.87 | 0.0176 | 0.834 | 0.158 | 0.925 | 3.653 | 2.267 | 0.921 | |

0.6 | 15.12 | 0.0201 | 0.810 | 0.0187 | 0.932 | 3.521 | 2.056 | 0.937 | |

0.3 | 14.76 | 0.0304 | 0.786 | 0.0289 | 0.912 | 3.312 | 1.965 | 0.934 | |

30 | 1.2 | 22.52 | 0.0215 | 0.734 | 0.0046 | 0.906 | 3.985 | 3.452 | 0.923 |

0.9 | 18.31 | 0.0287 | 0.782 | 0.0164 | 0.909 | 4.763 | 3.296 | 0.965 | |

0.6 | 17.10 | 0.0300 | 0.796 | 0.0174 | 0.934 | 4.965 | 3.038 | 0.965 | |

0.3 | 16.23 | 0.0321 | 0.895 | 0.0265 | 0.901 | 5.098 | 2.896 | 0.976 | |

40 | 1.2 | 23.33 | 0.275 | 0.876 | 0.0032 | 0.921 | 6.231 | 4.342 | 0.934 |

0.9 | 20.05 | 0.0295 | 0.854 | 0.0153 | 0.902 | 5.865 | 4.106 | 0.976 | |

0.6 | 19.56 | 0.0312 | 0.845 | 0.0166 | 0.943 | 5.321 | 3.892 | 0.947 | |

0.3 | 18.45 | 0.0355 | 0.807 | 0.0243 | 0.931 | 5.031 | 3.753 | 0.967 |

T (°C) | C_{o} | q_{e} (mg·g^{−1}) | Intraparticle Diffusion (IPD) | |||
---|---|---|---|---|---|---|

K_{pi1} | K_{pi2} | C_{i} (nm^{2}·min^{−1}) | R^{2} | |||

CALB-MOF-199 | ||||||

25 | 1.2 | 21.34 | 12.98 | 10.67 | 0.0076 | 0.997 |

0.9 | 18.89 | 10.64 | 9.65 | 0.0087 | 0.994 | |

0.6 | 16.56 | 9.96 | 8.45 | 0.0245 | 0.998 | |

0.3 | 15.74 | 9.65 | 7.85 | 0.0287 | 0.994 | |

30 | 1.2 | 23.34 | 13.98 | 12.92 | 0.0121 | 0.992 |

0.9 | 19.65 | 11.43 | 11.65 | 0.0189 | 0.998 | |

0.6 | 18.67 | 10.07 | 9.87 | 0.0256 | 0.998 | |

0.3 | 17.56 | 9.87 | 8.94 | 0.0298 | 0.999 | |

40 | 1.2 | 22.76 | 14.43 | 13.32 | 0.0132 | 0.994 |

0.9 | 21.96 | 13.21 | 12.02 | 0.0143 | 0.992 | |

0.6 | 18.26 | 12.76 | 11.98 | 0.0321 | 0.997 | |

0.3 | 17.56 | 11.07 | 10.65 | 0.0346 | 0.998 | |

CALB-ZIF-8 | ||||||

25 | 1.2 | 19.45 | 13.12 | 12.34 | 0.0084 | 0.997 |

0.9 | 17.87 | 12.32 | 11.64 | 0.0097 | 0.996 | |

0.6 | 15.12 | 11.45 | 10.65 | 0.0256 | 0.994 | |

0.3 | 14.76 | 11.02 | 9.87 | 0.0297 | 0.993 | |

30 | 1.2 | 22.52 | 14.21 | 13.76 | 0.0136 | 0.997 |

0.9 | 18.31 | 13.77 | 12.86 | 0.0198 | 0.994 | |

0.6 | 17.10 | 12.87 | 11.98 | 0.0287 | 0.993 | |

0.3 | 16.23 | 12.22 | 10.76 | 0.0318 | 0.996 | |

40 | 1.2 | 23.33 | 14.87 | 14.34 | 0.0146 | 0.997 |

0.9 | 20.05 | 13.03 | 13.21 | 0.0177 | 0.993 | |

0.6 | 19.56 | 11.82 | 12.54 | 0.0443 | 0.996 | |

0.3 | 18.45 | 11.02 | 11.43 | 0.0487 | 0.997 |

Adsorption Models | Description |
---|---|

Langmuir |
$$qe={q}_{max}*\frac{{K}_{L}{C}_{e}}{{1+K}_{L}{C}_{e}}\text{\hspace{1em}\hspace{1em}\hspace{1em}}\frac{{C}_{e}}{{q}_{e}}=\frac{1}{{q}_{max}}{C}_{e}+\frac{1}{{K}_{L}{q}_{max}}$$
This isotherm is based on three assumptions: adsorption is limited to the monolayer coverage, all surface sites are equal, and the ability of a molecule to be adsorbed at a given site is independent of its occupancy of neighboring sites [44,45,46]. |

Freundilch |
$$qe={K}_{F}{C}_{e}^{1/n}\text{\hspace{1em}\hspace{1em}\hspace{1em}}log{q}_{e}={\mathrm{log}K}_{F}+\frac{1}{n}\mathrm{l}\mathrm{o}\mathrm{g}{C}_{e}$$
The Freundlich Isotherm is a widely used empirical equation for describing adsorption equilibrium. The plot of log q _{e} against log C_{e} has a slope with the value of 1/n, and the intercept is K_{F}. log K_{F} is equivalent to log q_{e} when C_{e} = 1. However, in another case, when 1/n, the KF value depends on the units in which q_{e} and C_{e} are expressed $\ne 1$.On average, a favorable adsorption Freundlich constant, n, is between 1 and 10. Increasing n implies a greater interaction between adsorbate and adsorbent, while 1/n = 1 indicates linear adsorption leading to higher adsorption energies, identical for all sites [47,48,49]. |

Toth |
$$qe={q}_{max}\ast \frac{{b}_{T}{C}_{e}}{{{(1+({B}_{T}{C}_{e})}^{{n}_{T}})}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${n}_{T}$}\right.}}$$
This isotherm is derived from the potential theory. The Toth equation has proven to be a valuable tool in describing adsorption for heterogeneous systems. A quasi-Gaussian asymmetric energy distribution with the left side broadened is assumed, i.e., most adsorption sites have less energy than the mean value [50,51,52,53]. |

Redlich-Peterson |
$$qe=\frac{{K}_{RP}{C}_{e}}{{1+a}_{RP}{C}_{e}^{\beta}}$$
Redlich-Paterson is an empirical equation, designated as the “three parameter equation”, capable of representing adsorption at equilibrium over a wide range of concentrations. Redlich and Peterson incorporate the features of the Langmuir and Freundlich isotherms into a single equation. Frequently applied in homogeneous or heterogeneous adsorption processes. There are two limiting behaviors, i.e., the Langmuir form and Henry’s law form [54]. $\beta =1,\beta =0$ |

Sips |
$${q}_{e}={q}_{m}\ast \frac{{K}_{s}{C}_{e}^{\beta s}}{{a}_{s}{C}_{e}^{\beta s}}\text{\hspace{1em}\hspace{1em}\hspace{1em}}{\beta}_{s}ln{C}_{e}=-ln\left(\frac{{K}_{s}}{{q}_{e}}\right)+ln\left({a}_{s}\right)$$
The Sips isotherm combines the Langmuir and Freundlich isotherms and is given the above general equation (left-hand side). Here K _{s} is the constant of the Sips isotherm model (L·g^{−1}), 𝛽_{𝑠} is the Sips isotherm exponent, and 𝑎𝑠 is the constant of the Sips isotherm model (L·g^{−1}). The above right-hand paragraph also gives the linearized form [55]. This model is suitable for predicting adsorption on heterogeneous surfaces, thus avoiding the limitation that normally occurs during increasing adsorbate concentration, normally associated with the Freundlich model [55]. Therefore, this model reduces to the Freundlich model at low adsorbate concentrations, but at high adsorbate concentrations it predicts the Langmuir model (monolayer adsorption). The parameters of the Sips isotherm are a function of the pH, temperature, and concentration +, and isotherm constants differ by linearization and non-linear regression [55]. |

Radke Prausnitz |
$$qe\frac{{q}_{MRP}{K}_{RP}{C}_{e}}{{(1+{K}_{PR}{C}_{e})}^{MRP}}$$
The Radke-Prausnitz isotherm model has several important properties that make it very useful in adsorption at low adsorbate concentrations [56]. The previous expression gives the isotherm. In this equation, q _{mrp} is the maximum Radke-Prausnitz adsorption capacity (mg·g^{−1}), K_{PR} is the Radke-Prausnitz equilibrium constant, and MRP is the exponent of the Radke-Prausnitz model. At a low adsorbate concentration, this model isotherm reduces to a linear isotherm, while at a high adsorbate concentration, it becomes the Freundlich isotherm, and when M_{PR} = 0, it becomes the Langmuir isotherm. Another important feature of this isotherm is that it fits a wide range of adsorbate concentrations well. In this Radke-Prausnitz model, the model parameters are obtained by non-linear statistical fitting of experimental data [57]. |

Kinetic Models | Description |
---|---|

Pseudo-First Order (Lagergren’s model) | The model given by Langergren is defined as
$$\frac{dq}{dt}={k}_{1}({q}_{e}-q)$$
Integrating the equation concerning the boundary conditions q = 0 at = 0 and q = q _{e} at = t, we obtain
$$\mathrm{log}({q}_{e}-q)=\mathrm{log}({q}_{e})-\frac{{k}_{1}}{2303}t$$
where k _{1} is the Lagergren adsorption rate constant (min^{−1}); q_{t} and q_{e} are the amounts adsorbed at a time t and equilibrium, respectively, t in (min). The plot of log(q_{e} − q_{t}) as a function of time; the intercept is log q_{e} and the slope is k_{1} [58]. |

Pseudo-Second Order | The pseudo second order equation based on equilibrium adsorption is expressed as:
$$\frac{dq}{dt}={k}_{2}{({q}_{e}-q)}^{2}$$
Separating the variables in the above equation, we obtain
$$\frac{dq}{{({q}_{e}-q)}^{2}}={k}_{2}dt$$
Integrating this equation with respect to the boundary conditions q = 0 at = 0 and q = q _{e} at = t, we obtain:
$$\frac{t}{q}=\frac{1}{{k}_{2}{q}_{e}^{2}}+\frac{1}{{q}_{e}}t$$
where k _{2} is the pseudo second order rate constant (g·mg^{−1}·min^{−1}); q_{t} and q_{e} are the amounts adsorbed at time t and equilibrium, respectively. The line graph of t/q_{t} as a function of time has 1/q_{e} as the slope and 1/k_{2} as the intercept. This rate constant is used to calculate the initial adsorption rate, h (mg·g^{−1}·min^{−1}), where q_{e} is the equilibrium adsorption capacity, k_{2} (mg·g^{−1}·min^{−1}) is determined experimentally from the slope e intercept of the t/q plot versus t [59]. ${q}_{e}^{2}$ |

Intraparticle model (Weber-Morris) | Kinetic models do not identify the diffusion mechanism. The intraparticle diffusion model based on the theory proposed by Weber and Morris establishes a common empirical relationship in most adsorption processes since it varies proportionally with t^{1/2} more than with the contact time t. According to this theory, we have:
$${q}_{t}={k}_{pi}{t}^{1/2}+{C}_{i}$$
where k _{pi} (mg·g^{−1}·min^{−1/2}), the speed parameter for each stage, is obtained from the line q_{t} versus t^{1/2} slope. C_{i} is the intercept of stage i, giving an idea of the thickness of the boundary layer. If intraparticle diffusion occurs, q_{t} versus t^{1/2} will be linear; if the graph passes through the origin, then the rate-limiting process is only due to intraparticle diffusion. Otherwise, another mechanism is involved along with intraparticle diffusion. In intraparticle diffusion plots, stage I is due to flash adsorption or external surface adsorption, where the adsorbate travels to the external surface of the adsorbent. In stage II, a gradual adsorption occurs where intraparticle diffusion is the rate limiting; that is, the adsorbate travels inside the pores of the adsorbent. In some cases, a stage III represents the final equilibrium where the intraparticle diffusion begins to decrease due to the low concentration of adsorbate; adsorption occurs inside the adsorbent [60]. |

Elovich model | This model is useful to understand chemisorption in an adsorption process (developed by Zeldowitsch). It makes it possible to predict the diffusion of mass and surface, a system’s activation, and deactivation energy. Although this model was initially used only for gaseous systems, its use was later extended to processes in aqueous solutions. The model assumes that the solute adsorption rate decreases exponentially as the amount of solute adsorbed increases.
$$\frac{{dq}_{t}}{dt}=\alpha {exp}^{-\beta qt}$$
Since q _{t} ≈ 0, ≈ α is the initial adsorption rate (mg/g·min), and β is the desorption constant. Integrating and applying the limits for t (0, t) and q_{t} 0; q_{t}, the Elovich model can be linearized as: $\frac{{dq}_{t}}{dt}$
$$qt=\frac{1}{\beta}ln\left[t+\frac{1}{\alpha \beta}\right]-\frac{1}{\beta}ln\left(\alpha \beta \right)$$
when the system approaches equilibrium, t ≫ 1/αβ, the previous equation becomes:
$${q}_{t}=\frac{1}{\beta}ln\left[\alpha \beta \right]+\frac{1}{\beta}lnt$$
The graph of q _{t} versus at will help to establish the nature of the adsorption on the heterogeneous surface of the adsorbent, whether it is chemisorption or not [61]. |

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Giraldo, L.; Gómez-Granados, F.; Moreno-Piraján, J.C.
Biodiesel Production Using Palm Oil with a MOF-Lipase B Biocatalyst from Candida Antarctica: A Kinetic and Thermodynamic Study. *Int. J. Mol. Sci.* **2023**, *24*, 10741.
https://doi.org/10.3390/ijms241310741

**AMA Style**

Giraldo L, Gómez-Granados F, Moreno-Piraján JC.
Biodiesel Production Using Palm Oil with a MOF-Lipase B Biocatalyst from Candida Antarctica: A Kinetic and Thermodynamic Study. *International Journal of Molecular Sciences*. 2023; 24(13):10741.
https://doi.org/10.3390/ijms241310741

**Chicago/Turabian Style**

Giraldo, Liliana, Fernando Gómez-Granados, and Juan Carlos Moreno-Piraján.
2023. "Biodiesel Production Using Palm Oil with a MOF-Lipase B Biocatalyst from Candida Antarctica: A Kinetic and Thermodynamic Study" *International Journal of Molecular Sciences* 24, no. 13: 10741.
https://doi.org/10.3390/ijms241310741