E ﬀ ective Interactions of Ag Nanoparticles on the Surface of SBA-15 in Performing Deep Desulfurization of Real Diesel Fuel

: SBA-15 materials as-synthesized and impregnated with Ag nanoparticles were applied to perform adsorptive desulfurization of real diesel fuel. High-angle annular dark-field scanning transmission electron microscopy and field-emission scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (HAADF-STEM-EDX and FESEM-EDX) and X-ray photoelectron spectroscopy (XPS) results confirmed that there is uniform distribution of Ag nanodomains on the surface and in the channels of a 2AgSBA-15 (2% Ag) sample. The interaction between sulfur compounds and adsorbent mainly occurred via π -complexation mechanisms, as observed via XPS and equilibrium data. The kinetic results for 2AgSBA-15 were better fitted to the pseudo-second-order model (R 2 > 0.9999), indicating that the determining step of the adsorptive process is chemisorption, whereas the equilibrium results were better fitted to the Langmuir model (R 2 > 0.9994), thus indicating that the adsorption occurs on the adsorbent surface monolayer with significant adsorption capacity (q m = 20.30 mgS / g), approximately two times greater than that observed for pure SBA-15. The mean desulfurization reached by the adsorbents was up to 86.8% for six recycling steps. The present study contributes by applying SBA-15 mesoporous material as-synthesized and modiﬁed with Ag and Ni in a cleaner alternative methodology for producing low-sulfur content diesel fuel by adsorptive desulfurization. X-ray photoelectron spectroscopy (XPS) as well as high-angle annular dark-ﬁeld scanning transmission electron microscopy and ﬁeld-emission scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (HAADF-STEM-EDX and FESEM-EDX) techniques were used to assess the e ﬃ ciency of the synthesis and impregnation steps. Diverse kinetic and equilibrium models were applied in order to evaluate the adsorption process, thus providing information and enabling employment of a lower cost method in comparison to the currently used process in petroleum reﬁneries.


Introduction
In recent years, research on the development of ordered mesoporous materials has been increasingly focused on their application in catalysis and mitigation of environmental pollutants, mainly by adsorption [1,2]. Some remarkable features such as highly ordered and uniform porous structure, large pore volume, high thermal stability, and the easy obtainment and modification have attracted the interest of many researchers to microporous and mesoporous silica-based materials, such as zeolites [3], SBA-15 [4], KIT-6 [5], MSU-S [6], and MCM-41 [7]. The N2 adsorption-desorption isotherms performed before and after Ag modification are shown in Figure 2, as well as the pore size distribution plot. The isotherms for both samples are classified as Type IV, characteristic of mesoporous materials according to the International Union of Pure and Applied Chemistry (IUPAC) classification, with an H1 hysteresis cycle, which indicates narrow and uniform pore size distribution [26][27][28]. The pore size distribution plot indicates that the adsorbents have uniform mesopore sizes with maximum distribution in the range of 87-95 Å. The incorporation of Ag species to the mesoporous support did not cause significant changes in the isotherm profile.
The textural parameters of SBA-15 and 2AgSBA-15 adsorbents are summarized in Table 1. The reduction in specific surface area and total pore volume in relation to the original material suggests that there was pore occlusion by the deposited Ag species [26,27,29].  Wide-angle XRD patterns (Figure 1b) only exhibit a wide peak centered at 2θ 22.5 • , which is attributed to the amorphous silica wall. The absence of peaks relative to the sample impregnated with silver (2AgSBA-15) may indicate that Ag species are highly dispersed and present high interaction with the mesoporous support. In addition, the size of these species may be below the equipment detection limit in the form of nanoparticles (<3 nm) [23][24][25].
The N 2 adsorption-desorption isotherms performed before and after Ag modification are shown in Figure 2, as well as the pore size distribution plot. The isotherms for both samples are classified as Type IV, characteristic of mesoporous materials according to the International Union of Pure and Applied Chemistry (IUPAC) classification, with an H1 hysteresis cycle, which indicates narrow and uniform pore size distribution [26][27][28]. The pore size distribution plot indicates that the adsorbents have uniform mesopore sizes with maximum distribution in the range of 87-95 Å. The incorporation of Ag species to the mesoporous support did not cause significant changes in the isotherm profile.
Catalysts 2020, 10, x FOR PEER REVIEW 3 of 20 silver (2AgSBA-15) may indicate that Ag species are highly dispersed and present high interaction with the mesoporous support. In addition, the size of these species may be below the equipment detection limit in the form of nanoparticles (<3 nm) [23][24][25]. The N2 adsorption-desorption isotherms performed before and after Ag modification are shown in Figure 2, as well as the pore size distribution plot. The isotherms for both samples are classified as Type IV, characteristic of mesoporous materials according to the International Union of Pure and Applied Chemistry (IUPAC) classification, with an H1 hysteresis cycle, which indicates narrow and uniform pore size distribution [26][27][28]. The pore size distribution plot indicates that the adsorbents have uniform mesopore sizes with maximum distribution in the range of 87-95 Å. The incorporation of Ag species to the mesoporous support did not cause significant changes in the isotherm profile.
The textural parameters of SBA-15 and 2AgSBA-15 adsorbents are summarized in Table 1. The reduction in specific surface area and total pore volume in relation to the original material suggests that there was pore occlusion by the deposited Ag species [26,27,29].   The textural parameters of SBA-15 and 2AgSBA-15 adsorbents are summarized in Table 1. The reduction in specific surface area and total pore volume in relation to the original material suggests that there was pore occlusion by the deposited Ag species [26,27,29]. HAADF-STEM images for pure SBA-15 (Figure 3a,b) confirm the well-ordered mesoporous hexagonal structure of the SBA-15 matrix [30][31][32]. As shown in Figure 3c, the structure of the original material was preserved after modification with Ag(I), which is in line with the previous characterization results. Some silver nanoparticle clusters can be observed ( Figure 3c); however, HAADF-STEM-EDX mapping images (Figure 3d) revealed uniform distribution of silver nanoparticles over the sustainable SBA-15 material.
Catalysts 2020, 10, x FOR PEER REVIEW 4 of 20  HAADF-STEM images for pure SBA-15 (Figure 3a,b) confirm the well-ordered mesoporous hexagonal structure of the SBA-15 matrix [30][31][32]. As shown in Figure 3c, the structure of the original material was preserved after modification with Ag(I), which is in line with the previous characterization results. Some silver nanoparticle clusters can be observed ( Figure 3c); however, The FESEM micrograph for the 2AgSBA-15 sample, illustrated in Figure 4a, revealed a uniform long-fiber shape morphology [33]. The mapping images (Figure 4b-d) show a homogeneous dispersion of Ag particles over the silica surface (O-Si-O), which is consistent with the HAADF-STEM-EDX results. The elemental composition of the 2AgSBA-15 sample obtained by EDX is depicted in Figure 4e.
Catalysts 2020, 10, x FOR PEER REVIEW 5 of 20 X-ray photoelectron spectroscopy (XPS) was used to evaluate the electronic properties of the surface species, including their oxidation states, binding energies, and the electronic atmosphere [34]. The XPS survey spectra of 2AgSBA-15 and 2AgSBA-15 S samples are depicted in Figure 5, which shows the sample before and after desulfurization, respectively. It is possible to observe the presence of Ag, O, Si, and C elements in both adsorbents. The presence of C is associated with the adventitious contamination. The photoemission peaks at 103.3 and 532.6 eV are assigned at Si 2p and O 1s of the silica in 2AgSBA-15 [24,35,36]. The presence of sulfur was not detected, probably due to its low surface concentration. The deconvoluted Ag 3d core level spectra for the 2AgSBA-15 sample before and after desulfurization are depicted in Figure 6. The deconvolutions reached significant correlation coefficient (R 2 > 0.998) and F values (>4308.8) with a low standard error (<13.78). The lower F value for the deconvolution of 2AgSBA-15 S is related to the higher noise presented in the spectra of the adsorbent after desulfurization, since a severe Savitzky-Golay smoothing was not used in order to maintain the real features of the data without overfitting. The Ag 3d5/2 -Ag 3d3/2 doublet at 367.8 and 373.8 eV, respectively (Figure 6a), is assigned to Ag(I) species chemically bonded to oxygen atoms, which may mainly occur by interactions with the silanol groups of SBA-15 (Ag-O-Si) [37], while the peaks at 369.2 eV and 374.9 eV are ascribed to metallic Ag sub-nanoparticles (<4 nm) widely dispersed over the support [38,39].
It can be seen that the binding energies increased after the desulfurization tests (Figure 6b), thus indicating a less negative charge of Ag species due to the electron transfer caused by π-backbonding complexation between these silver nanosites and the sulfur molecules (Ag-S-R, S-R = DBT) [40,41], which controls the chemisorption process. Furthermore, a small doublet related to a new Ag species X-ray photoelectron spectroscopy (XPS) was used to evaluate the electronic properties of the surface species, including their oxidation states, binding energies, and the electronic atmosphere [34]. The XPS survey spectra of 2AgSBA-15 and 2AgSBA-15 S samples are depicted in Figure 5, which shows the sample before and after desulfurization, respectively. It is possible to observe the presence of Ag, O, Si, and C elements in both adsorbents. The presence of C is associated with the adventitious contamination. The photoemission peaks at 103.3 and 532.6 eV are assigned at Si 2p and O 1s of the silica in 2AgSBA-15 [24,35,36]. The presence of sulfur was not detected, probably due to its low surface concentration. The deconvoluted Ag 3d core level spectra for the 2AgSBA-15 sample before and after desulfurization are depicted in Figure 6. The deconvolutions reached significant correlation coefficient (R 2 > 0.998) and F values (>4308.8) with a low standard error (<13.78). The lower F value for the deconvolution of 2AgSBA-15 S is related to the higher noise presented in the spectra of the adsorbent after desulfurization, since a severe Savitzky-Golay smoothing was not used in order to maintain the real features of the data without overfitting. The Ag 3d 5/2 -Ag 3d 3/2 doublet at 367.8 and 373.8 eV, respectively (Figure 6a), is assigned to Ag(I) species chemically bonded to oxygen atoms, which may mainly occur by interactions with the silanol groups of SBA-15 (Ag-O-Si) [37], while the peaks at 369.2 eV and 374.9 eV are ascribed to metallic Ag sub-nanoparticles (<4 nm) widely dispersed over the support [38,39].

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Catalysts 2020, 10, x FOR PEER REVIEW 6 of 20 emerged at 371.4 eV and 377.1 eV, which were previously ascribed in the literature as "anomalous chemical shifts" present in XPS spectra of sulfur containing Ag molecules [42]. Thus, the recorded XPS data proved that the Ag species on the SBA-15 surface are able to drive the organosulfur adsorption by chemisorption processes, thus enhancing the desulfurization performance. The Ag MNN Auger lines were also recorded; however, these signals are very noisy and presented low intensity due to the low silver content, and therefore are not helpful for studying the chemical states of silver.

Adsorption Kinetics
Pseudo-first-order, pseudo-second-order, Elovich, intraparticle diffusion, and Boyd's filmdiffusion kinetic models were used to test the experimental data and evaluate the controlling mechanism of the sulfur adsorption process. The fitting for the kinetic data of the studied adsorbents depicted in Table 2   It can be seen that the binding energies increased after the desulfurization tests (Figure 6b), thus indicating a less negative charge of Ag species due to the electron transfer caused by π-backbonding complexation between these silver nanosites and the sulfur molecules (Ag-S-R, S-R = DBT) [40,41], which controls the chemisorption process. Furthermore, a small doublet related to a new Ag species emerged at 371.4 eV and 377.1 eV, which were previously ascribed in the literature as "anomalous chemical shifts" present in XPS spectra of sulfur containing Ag molecules [42]. Thus, the recorded XPS data proved that the Ag species on the SBA-15 surface are able to drive the organosulfur adsorption by chemisorption processes, thus enhancing the desulfurization performance.
The Ag MNN Auger lines were also recorded; however, these signals are very noisy and presented low intensity due to the low silver content, and therefore are not helpful for studying the chemical states of silver.

Adsorption Kinetics
Pseudo-first-order, pseudo-second-order, Elovich, intraparticle diffusion, and Boyd's film-diffusion kinetic models were used to test the experimental data and evaluate the controlling mechanism of the sulfur adsorption process. The fitting for the kinetic data of the studied adsorbents depicted in Table 2 and Figures 7 and 8 summarize the estimated parameters and the determination coefficients (R 2 ) of the models. The plot of the amount of sulfur adsorbed per time for 2AgSBA-15 and AgSBA-15 is depicted in Figure S3 of the Supplementary Materials. The pseudo-first-order model did not present satisfactory fitting to the studied data, with a low R 2 value (R 2 < 0.8904) and a large discrepancy between the calculated and experimental maximum adsorption capacities (q e ), thus limiting its applicability. The experimental results of the studied adsorbents were better adjusted to the pseudo-second-order model, as can be seen in Figures 7 and 8 and  Table 2, since the determination coefficient was near 1 (R 2 > 0.9999). Moreover, the differences between the experimental and calculated q e values were lower than those obtained by the pseudo-first-order model. This kinetic model indicated that the rate-determining step is chemisorption, which involves valence forces through sharing or exchanging electrons between adsorbent/adsorbate [43]. It is notable that the 2AgSBA-15 data presented a higher fit to this model than the pure material, since the interactions between the transition metal active sites and the adsorbate, such as π-complexation, are considerably stronger than the predominant van der Waals forces present in the SBA-15 support [44]. The Elovich equations were also evaluated, but they were not able to fit the experimental data (R 2 > 0.7601). Finally, the influence of diffusion and the mechanism which controls mass-transfer resistance on the adsorption rate were assessed by the intraparticle diffusion and Boyd's film-diffusion models. The SBA-15 and 2AgSBA-15 adsorbents did not present a good fit to the intraparticle diffusion model (R 2 > 0.606). The fact that none of the regression lines passed through the origin (Figures 7 and 8) imply that the intraparticle diffusion may not be the only rate-determining step, and suggest the occurrence of additional processes involved in the adsorption mechanism [45]. The positive C constant value suggests fast adsorption of sulfur compounds [46]. However, the 2AgSBA-15 data could be fitted to the Boyd's film diffusion (R 2 > 0.9034), and the plot not being linear (Figure 8)

Adsorption Equilibrium Isotherms
Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich (D-R) isotherms were applied to evaluate the relation between adsorbate/adsorbent when the adsorption process reaches equilibrium at different initial concentrations, as depicted in Figure 9. The parameters and R 2 of the isotherm models (Table 3) for the studied adsorbents reveal that the Ag sites on SBA-15 provided high adsorptive capacity to the material, as seen in the qm values. Finally, the influence of diffusion and the mechanism which controls mass-transfer resistance on the adsorption rate were assessed by the intraparticle diffusion and Boyd's film-diffusion models. The SBA-15 and 2AgSBA-15 adsorbents did not present a good fit to the intraparticle diffusion model (R 2 > 0.606). The fact that none of the regression lines passed through the origin (Figures 7 and 8) imply that the intraparticle diffusion may not be the only rate-determining step, and suggest the occurrence of additional processes involved in the adsorption mechanism [45]. The positive C constant value suggests fast adsorption of sulfur compounds [46]. However, the 2AgSBA-15 data could be fitted to the Boyd's film diffusion (R 2 > 0.9034), and the plot not being linear (Figure 8) suggests that the pore diffusion is not the rate-controlling step mechanism [47], further indicating that significantly strong chemical interactions are the main forces which govern the adsorptive desulfurization over 2AgSBA-15.

Adsorption Equilibrium Isotherms
Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich (D-R) isotherms were applied to evaluate the relation between adsorbate/adsorbent when the adsorption process reaches equilibrium at different initial concentrations, as depicted in Figure 9. The parameters and R 2 of the isotherm models (Table 3) for the studied adsorbents reveal that the Ag sites on SBA-15 provided high adsorptive capacity to the material, as seen in the q m values.  The Langmuir, Freundlich, and Temkin models showed a good fit to the adsorption equilibrium data of all the studied adsorbents. However, the equilibrium results did not fit the D-R model (R 2 < 0.5066). Moreover, the good fit of the Langmuir model (R 2 > 0.9909) to the equilibrium data of all the adsorbents suggests monolayer adsorption on the adsorbent surface with a finite number of sites [48]. The 0 < RL < 1 obtained for these materials indicates favorable adsorption of S-compounds [45]. It was possible to observe an increment in the maximum adsorption capacity of S-compounds (from 10.62 mg/g to 20.30 mg/g) of 2AgSBA-15, indicating the occurrence of chemisorption mechanisms such as π-complexation in the process [41]. The Freundlich isotherm model presented the second-best fit to the experimental data for SBA-15 ( Figure 9a) and 2AgSBA-15 ( Figure 9b) (R 2 > 0.9412), and indicates a favorable adsorption process in heterogeneous systems or multilayer adsorption (Freundlich, 1906). For instance, the n values higher than 1 obtained for 2AgSBA-15 suggest that the adsorptive desulfurization was a favorable process [49]. Regarding the Temkin model, there is a linear decrease of the adsorption heat in the adsorbate molecules when the adsorbent layer is covered, thus suggesting maximum uniform energy distribution over the adsorbents' surface [45], which can be considered for both adsorbents (R 2 > 0.9169). The adsorptive capacity of the 2AgSBA-15 sample is superior or similar when compared to other materials applied in fuel desulfurization, as shown in Table 4.  The Langmuir, Freundlich, and Temkin models showed a good fit to the adsorption equilibrium data of all the studied adsorbents. However, the equilibrium results did not fit the D-R model (R 2 < 0.5066). Moreover, the good fit of the Langmuir model (R 2 > 0.9909) to the equilibrium data of all the adsorbents suggests monolayer adsorption on the adsorbent surface with a finite number of sites [48]. The 0 < R L < 1 obtained for these materials indicates favorable adsorption of S-compounds [45]. It was possible to observe an increment in the maximum adsorption capacity of S-compounds (from 10.62 mg/g to 20.30 mg/g) of 2AgSBA-15, indicating the occurrence of chemisorption mechanisms such as π-complexation in the process [41]. The Freundlich isotherm model presented the second-best fit to the experimental data for SBA-15 ( Figure 9a) and 2AgSBA-15 (Figure 9b) (R 2 > 0.9412), and indicates a favorable adsorption process in heterogeneous systems or multilayer adsorption (Freundlich, 1906). For instance, the n values higher than 1 obtained for 2AgSBA-15 suggest that the adsorptive desulfurization was a favorable process [49]. Regarding the Temkin model, there is a linear decrease of the adsorption heat in the adsorbate molecules when the adsorbent layer is covered, thus suggesting maximum uniform energy distribution over the adsorbents' surface [45], which can be considered for both adsorbents (R 2 > 0.9169). The adsorptive capacity of the 2AgSBA-15 sample is superior or similar when compared to other materials applied in fuel desulfurization, as shown in Table 4.  (5)).
The molecular components of model diesel are smaller when compared to those in real diesel, as well as their respective critical diameters [58]. Thus, the best way to evaluate the adsorption capacity of an adsorbent is by performing desulfurization tests with real diesel. For effective adsorption of large molecules, the pore size of the adsorbent should not only be, at a minimum, larger than the critical diameter of the adsorbate, but should also be sufficiently large to reduce diffusional resistance during adsorption [59]. Both the SBA-15 and 2AgSBA-15 materials presented satisfactory reuse rates with a low decrease in sulfur adsorption after six regeneration cycles with the solvent mixture, thus indicating significant organosulfur removal by the adsorbents for many recycling steps, as shown in Figure 10. The main organosulfur components of real diesel and their critical diameters are depicted in Tables S1 and S2 of the Supplementary Material, respectively.

Reagents
The following reagents were used: hydrochloric acid (HCl, 37%

Synthesis of SBA-15 Material
The SBA-15 mesoporous material used in this study was obtained according to the methodology described in the literature [60], with modifications consisting of functionalizing the adsorbents with Ag(I) and Ni(II) salts. The adapted method for SBA-15 hydrothermal synthesis starts with the addition of TEOS and the triblock copolymer to 2 mol L −1 HCl aqueous solution, followed by stirring the emerged mixture for 3 h at 40 • C. Next, TEOS was added dropwise (TEOS/P123 = 2.0 w/w) and the obtained polymer-TEOS mixture was stirred for 24 h under the same conditions. The gel (molar composition of 0.00034 P123: 0.021 TEOS: 1.974 HCl: 0.834 H 2 O) was transferred to a sealed Teflon autoclave container (Metaquímica, Jaraguá do Sul, SC, Brazil) and kept at 110 • C for a period of 48 h. The final product was filtered, washed with 50 mL of ethanol/water (1:1) solution, and dried for 12 h at 100 • C. SBA-15 was calcined at 600 • C for 285 min at a rate of 2 • C min −1 .

Adsorbents' Characterization
X-ray diffraction (XRD) patterns of the adsorbents were collected on a Bruker D2 Phaser equipment (Bruker AXS, Madison, WI, USA) using CuKα radiation (λ = 1.5406 Å) at the 2θ ranges of 0-5 • and 5-90 • , with 30 kV filament, 10 mA current, Ni filter, and a LYNXEYE detector. Nitrogen adsorption/desorption isotherms at 77 K were used to determine the textural parameters of the adsorbents in a Quantachrome Nova apparatus (Boynton Beach, FL, USA). The specific surface area (S BET ) was calculated using the Brunauer-Emmett-Teller (BET) equation and the pore size and volume were determined, respectively, by applying the Barrett-Joyner-Halenda (BJH) method to the desorption branch of the N 2 isotherm at P/P 0 = 0.996.
Scanning transmission electron microscopy (STEM) analysis and mapping data were recorded in a Helios Nanolab 650 instrument (FEI, Brno, Czech Republic) with a high-angle annular dark-field (HAADF) detector, at 200 kV and 200 nA. The microanalysis was carried out with an energy-dispersive X-ray (EDX) spectroscopy Super-X system (FEI, Brno, Czech Republic) provided with four X-ray detectors and an extreme field emission gun (X-FEG) beam. The morphology of the catalysts was evaluated by scanning electron microscopy (SEM) with field emission gun (FEG) images obtained by a SEM-FEG AURIGA microscope from ZEISS (Carl Zeiss, Oberkochen, BW, Germany) coupled to a Bruker Xflash Detector 410-M energy-dispersive X-ray (EDX) apparatus (Bruker AXS+, Madison, WI, USA). X-ray photoelectron spectroscopy (XPS) was performed by a Physical Electronics PHI 5700 spectrometer (Physical Electronics, Inc., Chanhassen, MN, USA) with non-monochromatic Al Kα radiation (95.2 W, 15 kV, and 1486.6 eV) and a multi-channel detector. High-resolution spectra were recorded at a take-off angle of 45 • using a concentric hemispherical analyzer operating in constant-pass-energy mode at 29.35 eV, using a 720 µm diameter analysis area. C1s peaks were used as an internal standard calibration peak at 284.8 eV using the Multipak (version 9.6.0.15) software program (Physical Electronics, Inc., Chanhassen, MN, USA). Ag3d spectra were subsequently deconvoluted using PeakFit 4.12 software (Systat Software, Inc., Berkshire, UK) by applying Savitzky-Golay filter smoothing (<20%), linear baseline, and Gaussian curves for iterative peak fitting in order to more accurately determine the binding energies of different element core levels.

Preliminary Adsorption Tests
High-sulfur content diesel fuel S1800 (real diesel with 1800 mg kg −1 sulfur) from Clara Camarão Potiguar Refinery (Guamaré/RN, Brazil) was used to evaluate the adsorption processes. The sulfur removal capacity of the adsorbents was analyzed by a preliminary test performed in glass columns (0.61 cm × 30.0 cm) with downward flow. Each adsorbent was placed in the column up to 9.0 cm in height (approximately 0.5 g of material), and 5.0 mL of diesel (constant volume) was subsequently added. Aliquots of 0.3 mL were collected from the bottom of the columns, and the sulfur content was measured in a total sulfur analyzer ultraviolet fluorescence (UVF) Antek Multitek spectrometer (PAC, L.P, Houston, TX, USA) according to ASTM D5453 methodology.

Adsorption Study
The S-compounds' removal from diesel was performed using the finite bath method, in which 0.3 g of the adsorbent and 8.0 mL of diesel fuel were mixed and stirred at 100 rpm in a shaker apparatus (Solab, SL 180/DT, Piracicaba, SP, Brazil). Solutions containing different sulfur concentrations were applied in each test. The adsorbents were separated by centrifugation (15 min, 150 rpm) and the residual sulfur content in the supernatant was quantified by UVF spectroscopy. The sulfur adsorption capacity at equilibrium (q e ) of each adsorbent was calculated using Equation (1) ( Table 5).
The adsorption equilibrium was evaluated by fitting the experimental adsorption data to Langmuir, Freundlich, Temkin, and D-R mathematical models in order to predict the equilibrium parameters and explain the adsorbent/adsorbate system. The Langmuir model (Equation (7)) describes specific homogenous sites and is applied in a monolayer adsorption process. The dimensionless constant, commonly known as a separation factor (R L ) and proposed by Weber and Chakravorti, is presented in Equation (8). The Freundlich isotherm describes a heterogeneous system and can be applied to an adsorption of multiple layers with non-uniform distribution of the adsorption heat by the linear equation (Equation (9)) [21,[61][62][63]. The Temkin isotherm suggests that the adsorption heat of the adsorbed molecules decreases linearly with the layer coverage due to the effects of indirect adsorbent/adsorbate interaction. The model can be expressed according to Equation (10). The Dubinin-Radushkevich (D-R) isotherm does not assume a homogeneous surface or constant adsorption potential. The linear form of the D-R isotherm model can be represented by the following (Equation (11)) [46,64]. The equations used in this work are described in Table 5. Origin 2019b software (OriginLab, Northampton, MA, USA) was used to adjust the linearized equations of the models for calculating the equilibrium parameters.

Equation
Parameter Unity Adsorption capacity 1 q e , 2 V, 3 Ci, 4 Ce and 5 M AD mg/g, L, mg/L, mg/L and g (1) Equations and parameters of the kinetic models

Equation Parameter Unity
Pseudo-first-order log(q e − q t ) = logq e − k 1 t

Equation Parameter Unity
Langmuir model C e q e = 1 q max K L + C e q max 4 C e , 1 q e , 15 q max and 16 K L g/L, mg/g, mg/g and L/g (7) R L = 1/(1 + K L C 0 ) 16 K L and 17 C 0 L/g and mg/L (8) Freundlich model log q e = logk f + 1 n logC e 1 q e, 4 C e , 18 K F and 19 n mg/g, g/L, L/g and Const.
(9) Temkin model q e = βlnK t + βlnC e 1 q e , 20 β, 21 K t and 4 C e mg/g, J/mol, L/g and g/L (10) 23 T, 4 Ce, 1 q e , 25 q s , 26 β and 27 E J/mol, J/mol K, K, g/L, mg/g, mg/g, mol 2 /kJ 2 and kJ/mol (11) . 1 Amount of sulfur adsorbed at the equilibrium. 2 Diesel solution volume. 3 Initial sulfur content in the fuel. 4 Sulfur content in the fuel at equilibrium. 5 Adsorbent mass. 6 Amount of sulfur adsorbed at a time t. 7 Time. 8 Constant of the pseudo-first-order model. 9 Constant of the pseudo-second-order model. 10 Constant of the intraparticle diffusion model. 11 Constant of the Elovich equation. 12 Desorption constant. 13 Boyd's constant. 14 Fractional attainment of equilibrium at a time t. 15 Constant expressing the maximum absorption of the adsorbate. 16 Langmuir constant. 17 Initial concentration of the analytes. 18 Adsorption capacity. 19 Constants of Freundlich. 20 Adsorption heat. 21 Equilibrium binding constant. 22 Universal gas constant. 23 Temperature. 24 Polanyi potential. 25 Adsorption capacity. 26 Constant for the mean free energy. 27 Mean adsorption energy.

Recycling Tests
The regeneration methodology was adapted from Sales et al. (2019) [9]. One gram (1 g) of SBA-15 and 2AgSBA-15 residual adsorbents collected from the desulfurization tests was packed in apparatuses formed by a 10 mm × 50 cm (diameter and height, respectively) glass column. The adsorbents were individually added up to 8 cm of fixed bed height. Then, 30 mL of the mixture containing acetone/chloroform/hexane were added in a 3:4:3 ratio, being defined after preliminary tests for the desorption of organic sulfur compounds. After eluting the solution, the adsorbents were washed and heated to about 343 K for 1 h. The regeneration efficiency was determined for 6 cycles by a ratio between the percentage of sulfur removal reached in the first adsorption test and the percentage of sulfur removal reached by the regenerated adsorbent.

Conclusions
Characterization results were elucidated for the SBA-15 material, confirming the synthesis success. Modification with Ag(I) did not alter the morphology of the support. Preliminary desulfurization tests using the SBA-15 indicated better adsorption performance of the 2AgSBA-15 sample in comparison to the Ni-impregnated materials. HAADF-STEM-EDX and FESEM-EDX showed that there was uniform distribution of silver nanoparticles on the 2AgSBA-15 surface. The deconvoluted XPS spectra of 2AgSBA-15 before and after desulfurization revealed an interaction between the Ag(I) and metallic Ag sites and the sulfur molecules via π-complexation, thus controlling the chemisorption process suggested by the kinetic and equilibrium results, which were better fitted to the pseudo-second-order and Langmuir models, respectively.
The R L separation factor (0 < R L < 1) indicated that the adsorption of S-compounds on the surface of 2AgSBA-15 was favorable. In addition, the incorporation of Ag nanosites onto the SBA-15 support increased the adsorption capacity by approximately two times. Thus, the 2AgSBA-15 material presented high efficiency for the adsorptive desulfurization of real diesel samples and is able to be employed as a complementary method to the HDS method. The 2AgSBA-15 adsorbent presented a satisfactory regeneration after a total of six sulfur adsorption cycles enabled the reuse of this material for many times.