Thermodynamic Investigation and Study of Kinetics and Mass Transfer Mechanisms of Oily Wastewater Adsorption on UIO-66–MnFe₂O₄ as a Metal–Organic Framework (MOF)

Abstract

Hitherto, a considerable amount of research has been carried out to investigate the equilibrium condition of adsorption process; nevertheless, there is no comprehensive study to evaluate the surface adsorption properties of MOFs. Therefore, the adsorption mechanism and equilibrium capacity of MOFs have not been fully understood. Furthermore, the mass transfer mechanism is still unknown and so it is not possible to predict the adsorption process using MOFs. In this work, a new metal–organic framework (MOF) named UIO-66–MnFe₂O₄ was synthesized as an adsorbent for oily wastewater treatment. In this way the effects of temperature, amount of adsorbent, adsorption time, pH, and pollutant initial concentration were studied in the treatment of oily wastewater using the UIO-66-MnFe₂O₄ MOF through the adsorption process. Furthermore, to examine the process of surface adsorption, different adsorption kinetic models (pseudo-first-order, pseudo-second-order, and Elovich) have been performed for the removal of oily pollutants on MOF adsorbents and the surface adsorption mechanism has been discussed carefully. Moreover, to investigate the mass transfer mechanism of oily pollutants in the surface adsorption process, different mass transfer models (Weber and Morris, liquid film diffusion, and Bangham and Burt) have been investigated on porous adsorbents, and finally the mass transfer mechanism of the adsorption process has been proposed.

1. Introduction

With the expansion of urbanization and industrialization of human societies in the past few decades, many challenges have arisen, including global climate change [1], environmental pollution, and the reduction of natural resources [2]. Nowadays, the existence of serious and dangerous pollution in the environment has attracted a lot of attention [3]. One of these environmental concerns is oil pollution in water [4]. The presence of oily substances in water sources as potential pollutants can lead to damage to the aquatic ecosystem [5] and cause environmental hazards for humans and aquatic organisms [6]. The non-biodegradability [7], high toxicity, and chemical stability of these oily substances are obvious obstacles that have added to the previous concerns [8]. There are many strategies for modifying water pollution control, including decomposition [9,10], filtration [11], ion exchange [12], ionic liquid [13], and membrane process [14]; however, one of the most effective and cheapest methods of oil pollution treatment is the use of surface adsorption. During the last few decades, different high contact surface and high porosity materials have been used to remove environmental pollutants in the adsorption process, including bio-adsorbent material [15], carbon actives, zeolites, mesoporous silicas, and Metal–Organic Frameworks (MOFs) [16]. In recent years, MOFs have been commonly used to adsorb hazardous organic pollutants from wastewater owing to their high porosity and high specific area of the surface [17], which are the most important parameters of adsorbent selection [18].

The MOFs which are obtained by coordination bonds connecting to clusters/metal ions and organic ligands [19] have attracted much attention owing to their high porosity [20], high thermal [21] and chemical stability [22], and ability to adjust their structure and application [23,24,25].

During thermal decomposition, MOFs can be transformed into porous carbons, metal-based compounds in the form of oxides/carbides/phosphides and metal sulfides [26], which are important for adsorption [27] and storage applications [28]. The performance of these MOFs has already been studied in green projects such as the adsorption of carbon, the treatment of harmful gases [29], and the removal of oil pollutants from water [30]. Recently, the thermal conversion of MOFs into carbon-based materials and metal oxides in one-dimensional [31] and two-dimensional morphologies [32] have been well defined and have received much attention due to their special applications in the storage of gases [33]. In general, controlling the chemical synthesis procedure, such as starting chemicals (metal precursors and organic ligands) [34], synthesis conditions (temperature, pH value, concentration, etc.) [35], and synthesis method (hydrothermal method, microwave radiation, etc.), can easily adjust the MOF’s structure and properties [36].

In the process of surface adsorption, the most important factor in selecting an adsorbent is regeneration ability [37]. Among the different materials, there is a particular preference for MOFs due to their surface modifiability [38]. Among the improvements that can be made to surface interactions, electrostatic interactions are the most important [39].

MOF applications in water purification processes can be categorized into two major classes: (i) the treatment of organic substances such as pesticides [40], oil [41], dyes [42], and herbicides [43,44]; and (ii) the treatment of heavy metals [45]. In 2015, Li et al. [46] applied aluminum nitrate, aluminum oxide, alumina, and boehmite to synthesize MIL-53(Al) in order to perform dimethyl phthalate treatment. Moreover, Khan et al. [47] studied the adsorption of diethyl phthalate (DEP) and phthalic acid (PA) by ZIF-8, UiO-66(Zr) and NH2-UiO-66(Zr) MOFs. In 2021, Xue et al. [48] investigated the adsorption properties of porphyrinic Zr-MOF in the removal of water-soluble organic dyes.

Jing et al. [49] studied a synthesized hydrophobic hierarchical MOF (HZIF-8) as an adsorbent for oil in water emulsion; it showed extraordinary performance in oil adsorption. In 2019, Gao et al. [50] developed a strategy to synthesize the MOF-based materials and showed that synthesized MOFs contain an efficiently separate petroleum ether, toluene, chloroform, and n-hexane with high oil-in-water emulsion separation performance. The comparative study of MOFs based on the literature review was listed in

Table 1. The comparative study of MOFs based on the literature review.

MOF Type	Surface Area (m2·g−1)	Pollutant	Removal (%)	Ref
Fe-BTC	877	Orange II	92	[51]
Ce(III)-doped UiO-67	1911	Methylene blue	95	[52]
In2S3/UiO-66(Zr)	148	tetracycline hydrochloride	85	[53]
HKUST-1 (CuBTC)	645	Oil	70	[54]
FMOF-1	723	cyclohexane	80	[55]
FMOF-1	723	n-hexane	50	[55]
FMOF-1	723	benzene	95	[55]
UiO-66-NH-C18	570	Oil	99	[56]
UiO-66-NH-C18	-	Various oils and organic solvents	67	[56]
UiO-66 onto Fe3O4 particles	652	2-nitroresorcinol	85	[57]
MOF-199	1876	Dibenzothiophene	76	[58]
Ni-based MOF	144	Different oil and organic compounds	95	[59]

.

On the other hand, designing a process and correlating a phenomenon are the most important parts of a process [26]. In fact, in order to better understand the process, mathematical modeling is a valuable tool that can be used to investigate operational parameters [35]. By developing a strong process model, the effect of the process’s parameters on its efficiency can be correlated [60]. Hitherto, considerable research has been carried out to investigate the equilibrium condition of the adsorption process; nevertheless, there is no comprehensive study to evaluate MOFs’ surface adsorption properties [61]. Therefore, the adsorption mechanism and equilibrium capacity of MOFs have not been fully understood [37]. Additionally, the mass transfer mechanism is still unknown and therefore it is not possible to predict the adsorption process using MOFs [62].

In this study, to correlate the process of surface adsorption, different adsorption kinetic models have been considered for the treatment of oily wastewater on MOF adsorbents. In this way, the measured experimental data have been correlated by different kinetic models and the correlations compared with each other. Finally, the surface adsorption mechanism has been discussed carefully. Moreover, to study the mass transfer mechanism of oily pollutants in the surface adsorption process, different mass transfer models on porous adsorbents have been investigated; then, the obtained experimental data have been correlated using the mass transfer models, and finally the mass transfer mechanism of the adsorption process has been proposed.

2. Materials and Methods

The synthesis of MnFe₂O₄ was carried out using the co-precipitation method [63], so that first 16.218 gm of FeCl₃·6H₂O was reacted with 5.937 gm of (MnCl)₂·4H₂O with a molar ratio of Fe:Mn = 2:1. In order to adjust the pH to the desired value, the NaOH solution (2M) was used. The solution was stirred at 85 ± 1 °C in an oven with nitrogen atmosphere. After changing the color of the solution, the precipitated MnFe₂O₄ was removed using a magnet. Then, the produced particles were washed twice using deionized water and dried using an oven at 95 °C for 12 h. Finally, the particles were heated to 560 ± 1 °C for 4 h in a furnace. The forming reaction of MnFe₂O₄ from MnCl₂ and FeCl₃ is as follows:

$$MnC{l}_2+2FeC{l}_3+8NaOH\stackrel{}{\to }MnF{e}_2{O}_4+8NaCl+4H_{2}O$$

(1)

For the synthesis of the final MOF, the pre-synthesized MnFe₂O₄ substance was added to the synthesized UIO-66 compound. In order to synthesize the UIO-66 initially 0.636 gm of ZrCl₄ salt and 0.408 gm of dicarboxylic benzene (H₂BDC) with 0.21 gm of previously obtained MnFe₂O₄ were dissolved in 300 gm of DMF solvent by a stirrer for 24 h. For chemical activation, the obtained solution was washed twice using dimethyl and placed in chloroform for 3 days, and the synthesized crystals were placed in an oven at a temperature of 200 ± 1 °C for 24 h, as mentioned elsewhere [64].

In order to obtain the adsorption experimental data, 35 mg of the obtained MOF was added to 150 mL of oil-in-water emulsion containing different initial concentrations of pollutant with continuous stirring in a dark place at different process conditions (temperature, pH, and adsorption time). The substances were analyzed using a UV spectrophotometer to measure the amount of residual pollutant in the sample [64,65].

The quality of the synthesized adsorbents in the treatment of oily wastewater was performed by producing a water–oil emulsion with a certain amount of gasoline. For the synthesis of the mentioned emulsion, first a certain amount of the pollutant was poured into double-distilled water and the desired emulsion was obtained using Tween80 as an emulsifier. The concentration of oil in the prepared feeds for different analysis was constant and was adjusted to 2000 mg/L (equivalent to 6400 ppm based on COD calculations). After adding Tween80 emulsifier to the system with a concentration of 100 mg/L, a high-speed homogenizer was applied to prepare an emulsion with high stability.

This homogenizing operation was performed for 30 min at 12,000 rpm. In order to measure the distribution of oil particle sizes in water, a DLS analysis (BeNano90) was performed. The synthesized oily wastewater particle sizes are shown in Figure 1.

3. Adsorption Isotherm Models

The adsorption mechanism can be determined using isotherm models; in other words, the isotherms can be used to optimize the required adsorbent amount in a process. When the adsorbent is placed in contact with a pollutant, the concentration of the pollutant on the surface of the adsorbent increases until reaching thermodynamic equilibrium and then stabilizes at an equilibrium point, which is known as the adsorption isotherm and which is the primary basis for the design of adsorption systems. These equilibrium data can be applied to compare different adsorbents, as well as to design and optimize chemical processes [66]. To investigate the behavior of adsorbents in pollutant removal different adsorption models can be used, such as Langmuir (Lg), Freundlich (Fl), and Temkin (Tk) isotherms [67].

The Lg model was the first kinetically oriented theory presented for surface adsorption on a flat surface. In this theory, a continuous molecular mass transfer on the surface occurs so that the rate of accumulation of molecules on the surface remains equal to zero in the equilibrium state [68].

One of the assumptions used in the Lg model is that the surface adsorption energy is constant and has the same value in all sites. In other words, the adsorbent surface is assumed to be homogeneous. According to this model, each adsorption site can adsorb one molecule, at most.

The linear equation of Lg isotherm model is presented in Equation (2), where q_m is the maximum adsorption capacity, C_e is the concentration at equilibrium state, q_e is the equilibrium adsorbent concentration, and K_l is the Lg constant that is related to the strength of molecule adsorption on the adsorbent surface. Therefore, the larger K_l is, the more surface is covered with adsorbed molecules [69]. As can be seen from Equation (2), a linear plot of C_e/q_e versus C_e can be used to check the Lg model validity in terms of experimental data reproduction.

$$\frac{C_e}{q_e}=\frac{C_e}{q_m}+\frac{1}{K_l{q}_m}$$

(2)

To describe the equilibrium data, the Fl isotherm can also be applied; it is presented as Equation (3), where n and K_F are temperature-dependent constants of the Fl isotherm. As it can be understood from Equation (3), by plotting lnq_e in terms of lnC_e and calculating the intercept and the slope, the constants of the equation can be presented; consequently, n and K_F can be calculated [70].

$$\ln q_e=\frac{\ln C_e}{n}-\ln K_F$$

(3)

K_F represents the irreversibility of the process, and it is obvious that if n = 1 the Fl equation will be linear, and that the larger the n value the more the isotherm deviates from the linear state and will have a non-linear behavior [71]. In this model, it is assumed that the surface is non-uniform in terms of energy distribution, and the sites with equal surface energy are placed next to each other. It is also assumed that each molecule is adsorbed on just one site [68].

The linearized Tk isotherm is shown in Equation (4), where R is the universal gas constant, K_T and b are adjustable parameters, and T is the temperature. As it can be seen, the constants of the equation can be presented by plotting q_e in terms of lnC_e and calculating the intercept and the slope [68].

$$q_e=\frac{RT}{b}\left(\ln C_e+\ln K_T\right)$$

(4)

4. Kinetics

To correlate the surface adsorption process, some kinetic models have been developed by different researchers and have been applied to correlate the experimentally obtained data [72,73,74]. To investigate the kinetic adsorption mechanism, in this work, the pseudo-first-order (PFO), pseudo-second-order (PSO), and Elovich (ELO) models were applied. The pseudo-first-order kinetic model is based on physical adsorption; nevertheless, a chemical reaction is assumed in the pseudo-second order model [75].

The equation of the PFO model is given in Equation (5) and the PSO model is presented in Equation (6), where K₁ and K₂ are the constant coefficients of the PFO and the PSO models, respectively [76].

$$\log \left(q_e-q\right)=\log \left(c\right)-\frac{K_1}{2.303}$$

(5)

$$\frac{t}{q}=\frac{K_1}{K_2{q}_e^2}+\frac{1}{t\times q_e}$$

(6)

In kinetic process correlating, the oil adsorbent particles interact with the available active sites on the MOF adsorbent and form an unstable adsorbent–adsorbent complex, which subsequently becomes the final stable product [77]. Equation (7) describes the reaction mechanism of the mentioned phenomena, where M is the MOF adsorbent and S is the solute.

$$M+S\underset{k_2}{\overset{k_1}{\rightleftarrows }}M{S}^{*}\underset{k_4}{\overset{k_3}{\rightleftarrows }}MS$$

(7)

The reaction rate for MS*, which is an unstable intermediate complex, as well as the reversible reaction product, MS, are presented in Equations (8) and (9), where K₁, K₂, K₃ and K₄ are the rate constants for the reversible reactions [77].

$$\frac{d\left[M{S}^{*}\right]}{dt}=k_1\left[M\right]\left[S\right]-k_2\left[M{S}^{*}\right]-k_3\left[M{S}^{*}\right]+k_4\left[MS\right]$$

(8)

$$\frac{d\left[MS\right]}{dt}=k_3\left[M{S}^{*}\right]-k_4\left[MS\right]$$

(9)

The intermediate complex compound, MS*, is an unstable molecule with a short lifetime which immediately turns into the MS as product. Due to the presence of an intermediary complex with a short lifetime, it can be assumed that the MS* concentration is negligible [76]. Therefore, the rate of the intermediary complex concentration must be zero according to Equation (10) [78]:

$$\frac{d\left[M{S}^{*}\right]}{dt}=k_1\left[M\right]\left[S\right]-k_2\left[M{S}^{*}\right]-k_3\left[M{S}^{*}\right]+k_4\left[MS\right]\approx 0$$

(10)

In surface adsorption, the initial concentration of the adsorbent (S₀) is equal to the total concentration of the active sites of the adsorbent (S) which are free; therefore, the site of the reacted complex, and the sites of the adsorbent which are occupied, can be related as Equation (11) [78].

$$\left[S_0\right]=\left[S\right]+\left[M{S}^{*}\right]+\left[MS\right]$$

(11)

As the occupied adsorbent sites do not become active adsorption sites without recovery and purification operations, the rate of the reverse reaction of K₄[MS] is insignificant in the operation of surface adsorption; in other words, the rate of the reverse reaction is almost zero [78]. Therefore, [MS*] can be rewritten as Equation (12), where α = (K₂ + K₃)/K₁.

$$\left[M{S}^{*}\right]=\frac{\left[M\right]}{\alpha +\left[M\right]}\left\{\left[S_0\right]-\left[MS\right]\right\}$$

(12)

Finally, the adsorption rate in the [MS] form is rewritten as Equation (13).

$$\frac{d\left[MS\right]}{dt}=k_3\frac{\left[M\right]}{\alpha +\left[M\right]}\left\{\left[S_0\right]-\left[MS\right]\right\}$$

(13)

For high concentrations of [M] and low concentrations of [MS], it can be found that [MS] = 0 and α + [M] = [M]; Therefore, the adsorption rate equation can be simplified as follows [78]:

$$\frac{d\left[MS\right]}{dt}=k_3\left[S_0\right]$$

(14)

One of the assumptions in the PSO model is that the surface adsorption is the rate-restricting step and the adsorbent is related to the active sites on the surface of the adsorbent which are free [79]. Based on Equation (15), when the solution concentration is low, the PSO kinetic model is associated with the surface adsorption phenomenon, where q_t, k_s2, and q_e are the adsorption capacity at t, the equilibrium rate constant, and the equilibrium adsorption capacity, respectively [78].

$$q_t=\frac{q_e^2·k_{s2}·t}{q_e·k_{s2}·t+1}$$

(15)

The ELO model can also be applied for the chemical adsorption phenomenon. The ELO model is shown in Equation (16), where α is the initial rate of the process of the surface adsorption and β is the constant of desorption [80].

$$q_t=\beta \ln \left(\alpha \beta \right)+\beta \ln \left(t\right)$$

(16)

5. Mass Transfer

The mass transfer study, as one of the most important phenomena in the process of the surface adsorption, is the key parameter in a deep understanding of adsorption. The surface adsorption of oily pollutants on the adsorbent can be described as a three-step process [81]:

(1)

Liquid Film Diffusion (LF) or Extra-Particle Diffusion model; where oil particles diffuse from the boundary layer of liquid film to the adsorbent surface.

(2)

Intra-Particle Diffusion model; where the diffusion of oil molecules occurs beneath the surface, inside the pores, or a combination of both.

(3)

Surface Chemical Reaction; where oil molecules are adsorbed by electrostatic interaction and hydrogen bonding.

As the third step is a very fast one in the surface adsorption process, among these three, the first and second steps can control the adsorption rate. It should be noted that these three steps play a role in the reaction mechanism separately or in combination [82].

As mentioned, in the LF (extra-particle diffusion) model, the oil molecules’ mass transfer from the liquid bulk to the adsorbent surface controls the rate; in the present study, due to the fact that increasing the stirring speed increases the solution agitation, and mixing between the adsorbent and the adsorbent in the discontinuous surface adsorption process, the thickness of the film boundary layer begins to decrease. As a result, the effect of extra-particle diffusion at high mixing rates can be ignored [83].

In the intra-particle diffusion model, which is also known as the Weber and Morris (WM) model, the mass transfer of oil particles to the inner part of the synthesized adsorbent is determined using the intra-particle diffusion coefficient [84]. The WM model is based on the second law of Fick’s mass transfer theory and is applied to investigate the mechanism of the surface mass transfer to the adsorbent pores. This model is expressed according to Equation (17) and is applied to measure the coefficient of diffusion inside the adsorbent pores [85].

$$\ln \left(1-\frac{q_t}{q_e}\right)=-k_{d}t$$

(17)

Usually, the diffusion of the particles inside the pores can control the adsorption process. In these situations, using the Bangham and Burt (BB) model can be useful [77]. It should be noted that using the BB model can be applied whether the surface adsorption is rate-controlled by diffusion inside the pores or not. This model is presented in Equation (18), where C_i is the initial concentration, q_t is the adsorption capacity at t, m is the adsorbent mass, and V is the solution volume. Moreover, k_b and α are the BB equation constants [86].

$$\log \log \left(\frac{C_i}{C_i-q_{t}m}\right)=\log \left(\frac{k_{b}m}{2.303\hspace{0.33em}V}\right)+\alpha ·\log (t)$$

(18)

6. Results and Discussion

6.1. Characterization

Figure 2 shows the X-ray diffraction (XRD) for the MnFe₂O₄, UIO-66, and the synthesized UIO-66–MnFe₂O₄ metal–organic frameworks (MOFs), which was performed in order to investigate the structure of the obtained adsorbent. The MnFe₂O₄ peaks in the range of 30 to 45 (at 2θ = 31, 36, 43, and 58) prove the formation of MnFe₂O₄. The peaks in the range of 5 to 10 (at 2θ = 6 and 8) show the presence of UIO-66. The FTIR analysis results are displayed in Figure 3. The peaks at 1551 cm⁻¹ and 1453 cm⁻¹ show carbon–oxygen bonds and the peaks at 1251 cm⁻¹ indicate the benzene structure in UIO-66.

The BET surface area analysis and porosimeter system (China, TMAX-3H-2000PS1) equipment was utilized to measure the surface area and the porosity of the obtained samples. The values of 783 m²/gm and 1061 m²/gm were obtained using BET for the surface area of the obtained UIO-66-MnFe₂O₄ MOF samples and UIO-66, respectively. The porosity was measured as 87% using the nitrogen adsorption–desorption isotherm at a temperature of 77 °C.

To analyze the surface of the obtained adsorbent, a scanning electron microscope (SEM, FEI Altura 810) was utilized. Figure 4 shows the SEM image of the UIO-66–MnFe₂O₄ microcrystal adsorbent surface. The EDX spectrum of the synthesized adsorbent sample is presented in

Table 2. The EDX spectrum of the synthesized adsorbent sample.

Sample	C	O	Cl	Fe	Zn	Zr	Mn
ZnFe2O4	-	14.6	-	57.3	29.1	-	23.1
Uio-66	39.2	30.3	2.1	0.42	-	27.1	46
UIO-66-MnFe2O4	14.6	34.8	4.2	31.8	6.6	8.2	54.1

. The results show that the particle sizes of UIO-66–MnFe₂O₄ MOF crystals vary from 8 to 23 μm.

6.2. Pollutant Initial Concentration Effect

In order to measure the initial concentration effect of the oil pollutant and its capacity in adsorption on the synthesized adsorbent, the amount of the oil pollutant initial concentration from 200 to 2000 (mol/L) was examined. The experimentally obtained data of the effect of the initial concentration of oil pollution according to the percentage of pollution treatment are depicted in Figure 5.

As can be seen from Figure 5, a high amount of oil pollution can be adsorbed by using a small amount of adsorbent. It should be considered that the high concentration of the pollutant in the solution may saturate the adsorbent-free sites. By increasing the concentration of pollution from a certain limit, it can be seen that the treatment percentage decreases, which can be attributed to the decrease in the effective adsorbed surface due to the active site saturation [87,88]. It should be mentioned that this change is extremely small and can be observed in a small amount with very accurate measurements; Therefore, the analyses show that the mutual effect between the initial concentration of the pollution and the desired adsorbent is significant; therefore, the change of the pollution initial concentration has a remarkable effect on the process of surface adsorption in terms of pollutant removal percentage [89].

The previously mentioned kinetic equations were evaluated using the experimentally obtained data for pollutant adsorption by the synthesized adsorbent. The PFO, PSO, and ELO model parameters in various concentrations from 200 to 2000 mg/L are shown in

Table 3. The correlated parameters of different kinetic models of the surface adsorption process in concentrations from 200 to 2000 mg/L.

Model	Parameters	200 mg/L	400 mg/L	1000 mg/L	1500 mg/L	2000 mg/L
pseudo-first-order	Kl (min−1)	1.62	1.87	1.93	2.09	2.17
	qm (mg/g)	93	182	255	297	344
	R2	0.998	0.993	0.987	0.979	0.991
pseudo-second-order	K2 (g/mg min)	0.13	0.13	0.18	0.21	0.24
	q (mg/g)	206	268	345	393	457
	R2	0.732	0.762	0.818	0.733	0.740
Elovich	α	121	144	184	208	249
	β	0.014	0.024	0.035	0.042	0.051
	R2	0.963	0.955	0.948	0.952	0.987

.

Figure 6 shows the correlation diagram of the PFO, PSO, and ELO models with the experimentally obtained data. As can be seen, the PFO model with an average of R² = 0.989 has the most agreement with the experimentally obtained data and is closer to the y = x line. It is worth noting that the average R² for the PSO and ELO models is 0.757 and 0.961, respectively.

The WM, LF, and BB mass transfer models for the process of surface adsorption of oil molecules in different concentrations from 200 to 2000 mg/L on the adsorbent are shown in the

Table 4. The correlated parameters of different mass transfer models of the surface adsorption process in different concentrations from 200 to 2000 mg/L.

Model	Parameters	200 mg/L	400 mg/L	1000 mg/L	1500 mg/L	2000 mg/L
Weber and Morris	C	67	152	216	341	426
	Ki (mg/g min0.5)	15.3	18.6	19.1	20.2	21.6
	R2	0.927	0.912	0.914	0.939	0.892
liquid film diffusion	C	−0.322	−0.396	−0.492	−0.548	−0.672
	Kd (S−1)	0.012	0.015	0.019	0.026	0.038
	R2	0.944	0.923	0.897	0.917	0.920
Bangham and Burt	A	0.589	0.483	0.327	0.306	0.245
	kb (mL/g L)	0.254	0.342	0.488	0.563	0.633
	R2	0.994	0.895	0.980	0.925	0.936

.

In order to investigate the mechanism of the adsorption, three different adsorption isotherm models, Fl, Lg, and Tk isotherms, were correlated and the parameters of the isotherms were determined using the linearized experimental data. The isotherm parameters are available in

Table 5. The correlated parameters of Lg, Fl, and Tk isotherms for oil removal in different concentrations from 200 to 2000 mg/L.

Model	Parameters	200 mg/L	400 mg/L	1000 mg/L	1500 mg/L	2000 mg/L
Langmuir	Kl × 10−4 (dm3/mg)	7.678	4.416	1.490	0.998	2.189
	qm× 104	9.66	8.577	6.360	4.224	3.046
	R2	0.999	0.994	0.997	0.989	0.998
Freundlich	KF × 10−2 (dm3/g)	4.869	1.823	1.775	6.25	15.221
	n	10.2	4.01	3.42	4.56	7.79
	R2	0.712	0.722	0.912	0.923	0.974
Temkin	KT × 10−8 (dm3/g)	4.229	2.050	0.009	0.025	0.109
	b× 10−7	2.988	0.361	2.442	4.123	10.260
	R2	0.692	0.752	0.912	0.922	0.947

.

Figure 7 shows the initial concentration effect on the adsorption of Pollutant wastewater. All cases show a decrease in removal efficiency with an increase in temperature, which can be attributed to the fact that the adsorption process is an exothermic reaction.

6.3. pH Effect

The most important of the parameters that can strongly influence the adsorption procedure is the pH of the wastewater solution because it has a remarkable effect on the ionization and the surface charge of the adsorbent [90]. The experimental data in Figure 8 show the effect of the pH value on adsorption.

To determine the pH’s effect on the process of adsorption, the adsorption process was performed at pH = 2 to 10. It was found that at low or high pH values the rate of adsorption is low. In other words, the pH value has an optimum level in the adsorption rate as pH = 6. This phenomenon can be attributed to the fact that varying the pH value of the sample can improve the surface characteristics, which increases the capacity of adsorption [91].

Table 6. The correlated parameters of different kinetic models of the surface adsorption process at different pH values from 2 to 10.

Model	Parameters	pH = 2	pH = 4	pH = 6	pH = 8	pH = 10
pseudo-first-order	Kl (min−1)	2.53	2.77	2.98	3.19	3.35
	qm (mg/g)	72	91	128	136	159
	R2	0.996	0.994	0.997	0.986	0.983
pseudo-second-order	K2 (g/mg min)	0.09	0.11	0.17	0.19	0.22
	q (mg/g)	159	186	203	246	293
	R2	0.786	0.862	0.718	0.782	0.803
Elovich	α	98	103	167	186	204
	Β	0.009	0.013	0.024	0.031	0.043
	R2	0.971	0.962	0.903	0.950	0.899

shows the correlated parameters of the ELO, PSO, and PFO kinetic models using the obtained experimental data. As can be understood, the PFO model with an average of R² = 0.990 has the closest agreement with the experimentally obtained data. It is worth noting that the average R² for PSO and ELO models is 0.790 and 0.937, respectively.

The WM, LF, and BB mass transfer models for the process of surface adsorption of oil molecules on the adsorbent are shown in the

Table 7. The correlated parameters of different mass transfer models of the adsorption process at different pH values from 2 to 10.

Model	Parameters	pH = 2	pH = 4	pH = 6	pH = 8	pH = 10
Weber and Morris	C	73	92	109	125	186
	Ki (mg/g min0.5)	10.9	17.3	21.5	23.2	29.5
	R2	0.938	0.921	0.969	0.941	0.920
liquid film diffusion	C	−0.022	−0.160	−0.264	−0.389	−0.497
	Kd (S−1)	0.018	0.018	0.022	0.029	0.032
	R2	0.934	0.933	0.907	0.924	0.892
Bangham and Burt	A	0.452	0.363	0.323	0.266	0.235
	kb (mL/g L)	0.123	0.233	0.348	0.463	0.566
	R2	0.983	0.865	0.903	0.903	0.966

at different pH values. As can be understood, all the WM, LF, and BB models have almost the same R² value as 0.937, 0.918, and 0.924, respectively.

Three different isotherm models of adsorption processes, i.e., the Tk, Fl, and Lg isotherms, were also applied to correlate the adsorption; in this manner, the parameters of isotherm models were determined through the linearized experimentally obtained data at different pH values, as presented in

Table 8. The correlated parameters of the Lg, Fl, and Tk isotherms for oil removal from wastewater.

Model	Parameters	pH = 2	pH = 4	pH = 6	pH = 8	pH = 10
Langmuir	Kl × 10−4 (dm3/mg)	5.654	2.154	6.578	4.552	7.332
	qm× 104	8.245	6.321	5.321	6.568	8.318
	R2	0.999	0.995	0.999	0.996	0.998
Freundlich	KF × 10−2 (dm3/g)	2.654	3.553	2.852	4.546	5.476
	n	3.23	5.34	6.32	9.47	4.57
	R2	0.753	0.763	0.785	0.836	0.783
Temkin	KT × 10−8 (dm3/g)	3.656	3.987	5.632	1.689	6.632
	b × 10−7	0.622	3.648	4.856	1.685	9.861
	R2	0.563	0.706	0.765	0.862	0.725

.

6.4. Adsorption Time Effect

The time of contact to reach the equilibrium state depends on the structure and the characteristics of the adsorbent [92]. To investigate the effect of the contact time on the adsorbent, a period of 200 min was considered for the experiments. As can be seen from Figure 9, the rate of the adsorption process is very high in the first contact, which can be attributed to the high specific surface and active areas of the adsorbent.

As can be understood from Figure 9, the process of adsorption in terms of adsorption rate can be considered in two steps. In the first, adsorption is achieved in a short time period with a high adsorption rate, while in the second, the adsorption process is achieved in a longer time period with a lower adsorption rate [93]. The high adsorption rate in the first step is because of the presence of more free sites on the adsorbent surface, which are quickly filled by the adsorbed substance.

6.5. Effect of Adsorbent Amount

To investigate the effect of the adsorbent amount on the process of adsorption, different amounts of adsorbent were exposed to the pollutant. Figure 10 shows the effect of the amount of adsorbent on the treatment of oil impurities in the wastewater [94]. As can be seen from Figure 10, it is clear that a low amount of adsorbent is unable to remove the pollutant completely, which is related to the number of available active sites; however, by increasing the adsorbent amount, 100% of pollutant adsorption can be achieved.

The correlated parameters of the PSO, ELO, and PFO kinetic models are listed in

Table 9. The correlated parameters of different kinetic models of the surface adsorption process in different adsorption amounts.

Model	Parameters	10 mg	20 mg	50 mg	100 mg	200 mg
pseudo-first-order	Kl (min−1)	2.44	2.52	2.97	3.29	3.36
	qm (mg/g)	79	106	143	198	263
	R2	0.998	0.982	0.976	0.993	0.999
pseudo-second-order	K2 (g/mg min)	0.16	0.18	0.23	0.30	0.41
	q (mg/g)	186	193	211	236	249
	R2	0.703	0.774	0.728	0.863	0.806
Elovich	α	93	103	169	193	204
	β	0.012	0.019	0.026	0.039	0.051
	R2	0.979	0.998	0.987	0.996	0.990

. As can be understood, the PFO model with an average of R² = 0.989 has the closest agreement with the experimentally obtained data and is closer to the x = y line (see Figure 11). It is worth noting that the average R² for PSO and ELO models is 0.775 and 0.990, respectively.

The correlated parameters of the WM, LF, and BB models for the process of surface adsorption of oil molecules on the adsorbent are presented in the

Table 10. The correlated parameters of different mass transfer models of the surface adsorption process in different adsorbent amounts.

Model	Parameters	10 mg	20 mg	50 mg	100 mg	200 mg
Weber and Morris	C	76	96	128	193	218
	Ki (mg/g min0.5)	18.4	21.2	26.8	35.3	48.7
	R2	0.973	0.962	0.979	0.992	0.966
Liquid film diffusion	C	−0.255	−0.309	−0.326	−0.394	−0.413
	Kd (S−1)	0.005	0.006	0.011	0.022	0.031
	R2	0.977	0.963	0.989	0.966	0.893
Bangham and Burt	A	0.952	0.752	0.692	0.439	0.266
	kb (mL/g L)	0.152	0.185	0.263	0.465	0.522
	R2	0.997	0.932	0.909	0.988	0.949

.

Three different adsorption isotherm models, Fl, Tk, and Lg isotherms, were used to correlate the adsorption process; the correlated isotherm parameters that were determined through the linearized experimentally obtained data are listed in

Table 11. The correlated parameters of Lg, Fl, and Tk isotherms for the removal of oil from wastewater.

Model	Parameters	10 mg	20 mg	50 mg	100 mg	200 mg
Langmuir	Kl × 10−4 (dm3/mg)	12.523	11.845	9.143	8.842	4.543
	qm× 104	16.652	14.316	11.533	8.233	7.654
	R2	0.999	0.998	0.993	0.993	0.998
Freundlich	KF × 10−2 (dm3/g)	8.320	6.312	3.623	9.361	5.646
	N	9.25	8.78	4.33	9.45	6.44
	R2	0.836	0.899	0.928	0.852	0.879
Temkin	KT × 10−8 (dm3/g)	3.564	9.143	7.414	8.966	6.966
	b × 10−7	4.652	6.545	6.422	4.987	9.920
	R2	0.799	0.908	0.896	0.966	0.948

.

6.6. Temperature Effect

Figure 12 shows the effect of temperature on the percentage of adsorption treatment of oil impurities in the wastewater. As can be seen from Figure 12, it is clear that at very low temperatures adsorption is also low and that it can be increased by increasing the temperature [95].

The correlated parameters of the ELO, PSO, and PFO kinetic models are shown in

Table 12. The correlated parameters of different kinetic models of the surface adsorption process at different temperatures from 5 to 40 °C.

Model	Parameters	T = 5 °C	T = 10 °C	T = 20 °C	T = 30 °C	T = 40 °C
pseudo-first-order	Kl (min−1)	4.49	4.65	6.30	8.54	9.93
	qm (mg/g)	91	125	169	209	255
	R2	0.998	0.992	0.996	0.994	0.999
pseudo-second-order	K2 (g/mg min)	0.11	0.14	0.15	0.19	0.26
	q (mg/g)	196	239	264	309	362
	R2	0.983	0.836	0.921	0.893	0.966
Elovich	α	46	83	109	127	161
	β	0.029	0.046	0.068	0.093	0.153
	R2	0.989	0.998	0.999	0.996	0.995

. As can be understood, the PFO model with an average of R² = 0.996 has the closest agreement with the experimentally obtained data and is closer to the x = y line (see Figure 13). It is worth noting that the average R² for the PSO and ELO models is 0.920 and 0.995, respectively.

The different mass transfer models (WM, LF, and BB) for the process of surface adsorption of oil molecules on the adsorbent are shown in

Table 13. The correlated parameters of different mass transfer models of surface adsorption process at different temperatures from 5 to 40 °C.

Model	Parameters	T = 5 °C	T = 10 °C	T = 20 °C	T = 30 °C	T = 40 °C
Weber and Morris	C	64	75	92	113	129
	Ki (mg/g min0.5)	11.3	15.5	19.2	26.5	38.1
	R2	0.993	0.998	0.999	0.992	0.989
Liquid film diffusion	C	−0.349	−0.482	−0.561	−0.693	−0.816
	Kd (S−1)	0.011	0.013	0.020	0.029	0.037
	R2	0.996	0.993	0.982	0.994	0.899
Bangham and Burt	A	0.622	0.519	0.487	0.406	0.333
	kb (mL/g L)	0.073	0.121	0.199	0.263	0.305
	R2	0.998	0.999	0.983	0.996	0.989

.

The parameters of Tk, Fl, and Lg isotherms were correlated using the linearized experimentally obtained data. The isotherm parameters are presented in

Table 14. The correlated parameters of Lg, Fl, and Tk isotherms for the removal of oil from wastewater at different temperatures from 5 to 40 °C.

Model	Parameters	T = 5 °C	T = 10 °C	T = 20 °C	T = 30 °C	T = 40 °C
Langmuir	Kl × 10−4 (dm3/mg)	14.852	13.654	11.653	9.662	7.422
	qm× 104	18.655	17.669	13.488	11.356	7.778
	R2	0.997	0.996	0.999	0.994	0.998
Freundlich	KF × 10−2 (dm3/g)	6.666	4.985	3.565	2.350	0.471
	n	8.54	6.55	5.63	3.12	2.39
	R2	0.993	0.965	0.945	0.975	0.929
Temkin	KT × 10−8 (dm3/g)	5.623	8.875	3.445	7.356	11.396
	b × 10−7	6.680	6.125	6.235	8.468	7.692
	R2	0.999	0.982	0.968	0.996	0.982

.

7. Conclusions

Hitherto, a considerable amount of research has been carried out to investigate the equilibrium condition of the adsorption process; nevertheless, there is no comprehensive study to evaluate the surface adsorption properties of MOFs. Therefore, the adsorption mechanism and equilibrium capacity of MOFs have not been fully understood. Moreover, the mass transfer mechanism is still unknown and therefore it is not possible to predict the process using MOFs. In this work, the UIO-66–MnFe₂O₄ MOF was synthesized as a novel high-performance metal–organic framework adsorbent, and its applications in oily wastewater treatment were studied. The study was performed in four phases, experimental, thermodynamic, kinetic, and mass transfer.

To correlate the process of surface adsorption, different adsorption kinetic models have been applied for the treatment of oil pollutant on MOF adsorbents. Finally, the surface adsorption mechanism has been discussed carefully. Moreover, the mass transfer mechanism of oily pollutants in the surface adsorption process has been investigated using different mass transfer models on porous adsorbents; then, the experimentally obtained data have been correlated with different models of mass transfer, and finally the mass transfer mechanism of the process has been presented. In this way the effects of temperature, amount of adsorbent, adsorption time, pH, and pollutant initial concentration have been studied in the treatment of oily wastewater in the experimental phase. This work is the first step in the analysis of mass transfer and the kinetics of the process of surface adsorption, which can be used to predict the properties of the adsorbent and the process of surface adsorption. In the future, with the expansion of mass transfer and kinetic models and the simultaneous investigation of these two phenomena, it is suggested that the possibility of predicting the adsorption process in other MOFs be investigated.