Facile Synthesis and Characterization of CeO2-Nanoparticle-Loaded Carboxymethyl Cellulose as Efficient Protective Films for Mild Steel: A Comparative Study of Experiential and Computational Findings

Corrosion is considered to be the most severe problem facing alloys and metals, one that causes potentially dangerous industrial issues such as the deterioration of buildings and machinery, and corrosion in factory tanks and pipelines in petroleum refineries, leading to limited lifetime and weak efficacy of such systems. In this work, novel CeO2-nanoparticle-loaded carboxymethyl cellulose (CMC) was successfully prepared by using a simple method. The structural configuration of the prepared CeO2-nanoparticle-loaded CMC was investigated by FE-SEM/EDX, TEM, FT-IR, and thermal analyses. The corrosion protection proficiency of uncoated and coated mild steel with CeO2-CMC systems in 1.0 M HCl solutions was studied by EOCP-time, EIS, and PDP tools. Moreover, the relationship between the structure of coating films and their corrosion protection was confirmed by DFT calculation and MC simulation. The obtained findings from the studied methods showed that the prepared CeO2-CMC-coated films reported high corrosion resistance. The protection capacity augmented with ceria presents an increase of up to 3% to achieve 98.4%. DFT calculation and MC simulation confirmed the influence of the chemical construction of coated films on its protection capacity, which was in accordance with the experimental results.


Introduction
Nanocomposite materials have emerged as a novel and superior alternative for numerous research and production objectives in recent years. Nanocomposites comprise heterogeneous films with chemically distinct phases or one phase isolated or embedded in another. There are either two separate crystalline phases, one crystalline and the other amorphous, or two distinct crystalline phases. In general, nanocomposite coatings consist of one host particle and another embedded homogeneously in it, one or both of which are nanoscale [1].
Nanocomposite coatings have unique mechanical, electronic, magnetic, and optical properties that make them useful and striking for a variety of engineering applications, including high-speed machining, tooling, optical devices, magnetic storage tools, and leaves, have shown that cellulose is a superb building component for superhydrophobic surfaces [41]. Cellulose is also appealing for industrial applications due to its low-cost, long-lasting material, with multilateral nanoparticles that allow for easy changes [42].
The present work aimed to prepare novel CeO 2 -nanoparticle-loaded carboxymethyl cellulose (CMC), and its corrosion resistance as coating films for mild steel in acidic chloride medium utilizing electrochemical methods including E cor -time, polarization plots (PD), and electrochemical impedance spectroscopy (EIS) was evaluated. The chemical structure and physical properties of the CeO 2 -CMC composite were also examined by field emission scanning electron microscopy (FESEM), transmission electron microscope (TEM), and thermal gravimetric analysis. Finally, DFT calculation and MC simulation were employed to elucidate the protection mechanism.

Preparation of CeO 2 -Nanoparticle-Loaded Carboxymethyl Cellulose (CeO 2 -CMC)
CeO 2 -CMC films were created by adding CeO 2 nanoparticles (CeO 2 NPs) to aqueous CMC. In the absence of light, a three-necked flask was swirled for two hours with a mixed solution of CMC (1.5 g%) and CeO 2 NPs (5 percent of CMC weight). In a Teflon petri dish, CeO 2 -CMC films with a thickness of 0.8 mm were cast over the course of 24 h at 60 • C. CeO 2 -CMC nanocomposite films were produced when the prepared film was desalted with deionized water and dried for 72 h at 50 • C.

Preparation of CeO 2 -CMC Coating Films
As substrate supplies, MS alloy samples with the following chemical formulations were applied: C (0.18%), Mn (0.08%), Cr (0.72%), Ni (0.01%), and Fe (remaining percent). These samples were gradually polished with emery papers No. 600-1800, degreased in ethanol, acetone, and bi-distilled H 2 O for 5.0 min each, and then dried by air. Using a dip-coating method, the MS alloy surface coating was structured. The electrode substrate was submerged in the sol for 2 min while being pulled out at a speed of 10 mm per minute. The specimen was dried out in an oven at 80 • C for 15 min after air-dehydrating it. In order to increase the coating thickness, the process from immersion to dehydration was repeated twice. Different CeO 2 % (1.0, 2.0, 3.0, 4.0, 5.0, and 6.0) were used to coat the samples.

Characterization Techniques
Field emission scanning electron microscopy (FESEM) complemented with EDAX (Jeol, Tokyo, Japan) with a voltage of around 20 kV was used to scan the morphological and chemical characteristics of CMC-CeO 2 . Additionally, a transmission electron microscope (TEM) and selected area electron analysis (SAED) in a Jeol-1230 electron microscope running at 200 KeV (JEOL, Peabody, MA 01960, USA) was applied to confirm the particle size of the prepared composite. After that, an FT-IR analysis was performed by using a spectrophotometer from BRUKER (Ettlingen 76275, Germany) which was applied to study function groups of the designed composite after and before CeO 2 incorporation within 4000-400 cm −1 . The thermal gravimetric analysis of the synthesized composite was performed by using TGA Instruments (New Castle, DE 19720, USA) for both CMC and CMC-CeO 2 composite and the temperature range was changed from 25 • C to 700 • C under a flow of oxygen at a rate of 10 • C/min. The studied CMC-CeO 2 composite has an organic component in addition to an oxide one, and these parts behave differently in terms of their thermal characteristics. Therefore, oxygen was applied as a flowing reagent to study this difference.

Corrosion Protection Measurements
All electrochemical investigations were implemented in an electrochemical cell containing 3-electrode systems of Ag/AgCl/KCl (sat) (silver/silver chloride), Pt-sheet, and the uncoated and coated MS specimens as reference, as counter electrode and working electrodes. EIS experiments were conducted to assess the corrosion protection of uncoated and Polymers 2022, 14, 3078 4 of 21 coated specimens in 15% HCl solution at 50 • C in 100 kHz to 1.0 Hz as a frequency range. A Potentiostat/Galvanostat/ZRA (Gamry 600, Warminster, PA, USA) instrument was used for EIS investigation. The EIS experiments were performed at 10 points/decade (scan frequency rate) with an open circuit potential (E OCP ) of 45 min, and the RMS signal was changed between 2.0 and 10.0 mV. PDP investigations were made to measure the corrosion protection proficiency of the uncoated and coated MS specimens. The PDP experiments were executed in the potential range of ±250 mV vs. E OCP at a scan rate of 0.2 mV/s. All tests were completed at least in duplicated specimens.

Computational Details
The energy optimization of the CeO 2 , CMC, and CeO 2 -CMC molecules was achieved in aqueous environments using DFT calculations with basis set BOP with ab initio, GGA method, and DNP 4.4 accomplished in the Dmol 3 module in Materials Studio V.7.0 program [43]. The outcomes achieved from DFT calculations involving the lowest unoccupied molecular orbital (LUMO), the highest occupied molecular orbital (HOMO), the gap energy (∆E), electronegativity (χ), hardness (η), global softness (σ), and number of electrons transferred (∆N), ∆E back-donation , and dipole moment (µ) were calculated as follows [44]: where ϕ is the function work of Fe (110), χ inh is the inhibitor electronegativity, and η Fe and η inh are the hardness of Fe (0 eV) and inhibitor, respectively. The most suitable adsorption arrangements of the CeO 2 -CMC molecule on the Fe (110) surface were achieved from MC simulations by employing the adsorption locator module in the Materials Studio V.7.0 program [45]. Primarily, the energy optimization of the adsorbate molecules was implemented via the COMPASS module [46]. Afterward, the adsorption of the CeO 2 -CMC, hydronium ions, Cl − ions, hydronium ions, and water molecules onto the surface of Fe(110) was executed in a simulation box (37.24 Å × 37.24 Å × 59.81 Å) [47].

SEM and TEM Analyses
The SEM images of CMC and the synthesized CMC-CeO 2 were studied at 75 KX as displayed in Figure 1A,B, respectively, in addition to TEM analysis, as shown in Figure 1C,D, at low and high magnification, respectively. For SEM analysis, the CMC image ( Figure 1A) has a homogeneous character without clear isolated particles. After incorporation of CeO 2 , the SEM surface image becomes heterogeneous, having different size particles which indicate the successful incorporation of CeO 2 onto the surface of CMC to design a CMC-CeO 2 composite. The observed particles in the SEM of CMC-CeO 2 were checked by TEM analysis at low and high magnifications ( Figure 1C,D, respectively). Nanoparticles could be seen in both TEM images, especially at high magnification. Another TEM image is shown in Figure 1E, and the network structure of the utilized polymer (CMC) can be seen, which confirms the morphology of CMC-CeO 2 . The SAED image shown in Figure 1F clarifies the amorphous/crystallinity of the prepared polymer/oxide material and the crystalline phase of the prepared polymer/oxide composite, which confirms the presence of crystalline oxide even after incorporating it into the amorphous organic (CMC) template. Thus, the   To investigate the chemical contents of the composite particles, EDX-SEM analysis was carried out for CMC and CMC-CeO 2 as shown in Figure 2A,B, respectively. For CMC before the incorporation of CeO 2 particles, the atomic percentages of O and C were detected at 58.99%, and 41.01%, respectively. After incorporation of the CeO 2 particles, the atomic percentages of O, C, and Ce were observed at 63.41%, 35.21%, and 1.38%, respectively. The decrease in carbon content, as well as increased oxygen content, indicates that the chemical content changed to include more oxide from CeO 2 incorporation. The mapping of C, O, and Ce was additionally studied for CMC and CMC-CeO 2 as described in Figure 3A-G. The increase in O content and decrease in carbon content could be observed and confirmed in elemental mapping as explained in EDX-SEM analysis. Furthermore, the map of the Ce element was clear and distributed and checked in a total survey ( Figure 3H). The total survey image indicates the successful incorporation of CeO 2 by the homogeneous distribution of Ce in addition to O. The oxygen content is higher than that of cerium because oxygen is existent in CMC polymer besides ceria. The SEM, TEM, EDX, and elemental mapping confirm the preparation of CMC-CeO 2 as a polymer/oxide composite.

FT-IR Analysis
The chemical bonds in CMC and the prepared CMC-CeO 2 composite were investigated using FT-IR analysis as shown in Figure 4A. Both materials (CMC and CMC-CeO 2 composite) mostly have the same chemical bonds which were indicated by the same locations of FT-IR peaks. The wide peak seen at 3320 cm −1 was ascribed to stretching vibration of OH stretching, while the peak at 2910 cm −1 referred to asymmetric CH 2 stretching. The peaks at 1590 and 1419 could belong to the vibration of the C = O, and tensile vibrations of -C-O-C-bonds [48]. A small peak at 506 cm −1 was found in the CMC-CeO 2 and not observed in CMC when using FT-IR, which could be due to the Ce-O vibration bond [49]; this is clarified in Figure 4B. In short, FT-IR spectroscopy confirms the chemical existence of CMC function groups in both CMC and CMC-CeO 2 composite in addition to a small peak related to the Ce-O bond in the case of CMC-CeO 2 .

Thermal Properties
TGA and its differential (dTG) analyses were studied for the CMC-CeO 2 composite and its components; CMC and CeO 2 are described in Figure 5. For CeO 2 , the loss of weight is negligible. It is observed at 3.5% and could be due to the expected thermal stability of metal oxide (CeO 2 ) up to 700 • C. In the case of the other investigated samples, CMC and CMC-CeO 2 , there are two clear exothermic peaks at 106 • C and 279 • C for CMC and a slight shift for CMC-CeO 2 . The exothermic peaks were seen at 99 • C and 297 • C in the case of CMC-CeO 2 . These exothermic peaks could be attributed to the evaporation of adsorbed water for the low-temperature peak (around 100 • C) and the decomposition of organic contents for the high-temperature peak (around 300 • C). The weight loss (%) of CMC, CeO 2 , and CeO 2 -CMC was found at 6.43%, 0.4%, and 5.33%, respectively, at 100 • C, which indicates the successful preparation of CeO 2 -CMC composite. Additionally, weight loss was found at 48.60% and 57.26% at 700 • C for CMC and CMC-CeO 2 , respectively. The difference between CMC and CMC-CeO 2 in weight loss and exothermic peak positions indicates the interaction between the polymer content (CMC) with the oxide part (CeO 2 ). This deduced interaction could provide higher thermal stability to the polymer contents, and so a shift to a higher temperature occurs.

OCP vs. Time and PDP Studies
It is widely acknowledged that the OCP of a corrosion process is a property utilized as a thermodynamic constraint of electrochemical process inclination in a corrosive medium [50]. The corrosion potential vs. time could be changed due to the progress of the passive layer, resistance, or oxidation [51]. Figure  potential in comparison with the blank MS, which confirms that the coated MS samples are in a passive situation and, accordingly, well protected from the acidic solutions [52]. In general, the primary positive potential for coated CeO 2 -CMC layers is related to the reduction-oxidation route in the CMC matrix. These results showed that the coated CeO 2 -CMC films supported the development of a stable passive film, possibly in a process comparable to anodic protection. This confirms that the coated CeO 2 -CMC layers increase MS corrosion protection by increasing the nobility of metal.

FT-IR Analysis
The chemical bonds in CMC and the prepared CMC-CeO2 composite were investigated using FT-IR analysis as shown in Figure 4A. Both materials (CMC and CMC-CeO2 composite) mostly have the same chemical bonds which were indicated by the same locations of FT-IR peaks. The wide peak seen at 3320 cm −1 was ascribed to stretching vibration of OH stretching, while the peak at 2910 cm −1 referred to asymmetric CH2 stretching. The peaks at 1590 and 1419 could belong to the vibration of the C = O, and tensile vibrations of -C-O-C-bonds [48]. A small peak at 506 cm −1 was found in the CMC-CeO2 and not observed in CMC when using FT-IR, which could be due to the Ce-O vibration bond [49]; this is clarified in Figure 4B. In short, FT-IR spectroscopy confirms the chemical existence of CMC function groups in both CMC and CMC-CeO2 composite in addition to a small peak related to the Ce-O bond in the case of CMC-CeO2.

FT-IR Analysis
The chemical bonds in CMC and the prepared CMC-CeO2 composite were investigated using FT-IR analysis as shown in Figure 4A. Both materials (CMC and CMC-CeO2 composite) mostly have the same chemical bonds which were indicated by the same locations of FT-IR peaks. The wide peak seen at 3320 cm −1 was ascribed to stretching vibration of OH stretching, while the peak at 2910 cm −1 referred to asymmetric CH2 stretching. The peaks at 1590 and 1419 could belong to the vibration of the C = O, and tensile vibrations of -C-O-C-bonds [48]. A small peak at 506 cm −1 was found in the CMC-CeO2 and not observed in CMC when using FT-IR, which could be due to the Ce-O vibration bond [49]; this is clarified in Figure 4B. In short, FT-IR spectroscopy confirms the chemical existence of CMC function groups in both CMC and CMC-CeO2 composite in addition to a small peak related to the Ce-O bond in the case of CMC-CeO2.  The potentiodynamic polarization plots of the pristine MS and coated substrates with diverse ratio of % CeO 2 -CMC were completed after 50 min of immersion in molar hydrochloric acid at 323 K, as depicted in Figure 6B. It can be observed in Figure 6B that the anode and cathode branches were influenced as the % CeO 2 increased in the coating layers, which revealed that these layers block the anodic corrosion of the MS and the hydrogen evolution of cathodic reaction [53][54][55]. Furthermore, the anodic and cathodic divisions shift to smaller current densities in the case of coated layers, which causes a decrease in the wear-active centers [56][57][58].
CeO2, and CeO2-CMC was found at 6.43%, 0.4%, and 5.33%, respectively, at 100 °C, which indicates the successful preparation of CeO2-CMC composite. Additionally, weight loss was found at 48.60% and 57.26% at 700 °C for CMC and CMC-CeO2, respectively. The difference between CMC and CMC-CeO2 in weight loss and exothermic peak positions indicates the interaction between the polymer content (CMC) with the oxide part (CeO2). This deduced interaction could provide higher thermal stability to the polymer contents, and so a shift to a higher temperature occurs.

OCP vs. Time and PDP Studies
It is widely acknowledged that the OCP of a corrosion process is a property utilized as a thermodynamic constraint of electrochemical process inclination in a corrosive medium [50]. The corrosion potential vs. time could be changed due to the progress of the passive layer, resistance, or oxidation [51]. Figure 6A reveals the change in OCP with time in a molar HCl solution for pristine MS and coated samples with the various percentages of CeO2-CMC at 323 K. All coated samples at the preliminary time of immersion had further positive potential in comparison with the blank MS, which confirms that the coated MS samples are in a passive situation and, accordingly, well protected from the acidic solutions [52]. In general, the primary positive potential for coated CeO2-CMC layers is related to the reduction-oxidation route in the CMC matrix. These results showed that the coated CeO2-CMC films supported the development of a stable passive film, possibly in a process comparable to anodic protection. This confirms that the coated CeO2-CMC layers increase MS corrosion protection by increasing the nobility of metal. The coated and uncoated parameter values, such as corrosion potential (E cor ), corrosion current density (i cor ), and anodic and cathodic Tafel slopes (β a , β c ), shown in Table 1 were ascertained by extrapolating Tafel slopes to the corrosion potential. The values of protection capability (η/%) were computed by determining the i cor , from the coated (i c cor ) and uncoated (i 0 cor ) by the following equation [59][60][61][62]: As shown in Table 1, the values of E cor in the presence of coatings films do not show obvious change, indicating that these films prevent both anodic corrosion and hydrogen evolution cathodic reactions, i.e., an increase in corrosion resistance. After the inclusion of ceria NPS in the CMC matrix, the MS surface shows a lower i cor , signifying a decline in the rate of corrosion of the CeO 2 -CMC coated samples. That is, the ceria NP-loaded carboxymethyl cellulose coatings provide enhanced corrosion resistance for the MS interface in a molar hydrochloric acid medium. Predominantly, 3.0%CeO 2 -CMC and 4.0%CeO 2 -CMC coating films display the lowest i cor among all the samples, indicating the extreme effectiveness of this layer, due to its uniform surface structure. The reserved protection properties can be ascribed to the thick surface structure and enriched adhesion after ceria are embedded in the CMC matrix, consequently decreasing the corrosive Clion permeation. The values of cathodic and anodic Tafel slopes (β a and β c ) in the case of coated samples were found to be greater than in the case of uncoated MS, suggesting that the ceria-CMC coating films change the hydrogen evolution reaction mechanism [63][64][65][66]. Furthermore, β c values are also found to be lower than the analogous β a .
The findings presented in Table 1 show a remarkable decrease in values of i cor in the presence of CeO 2 NPs in the CMC matrix compared with the coated surface with CMC alone, and this decrease is overcome by increasing the percentage of CeO 2 NPs up to 3%, then there is an upsurge. The values of i cor decrease in the following order: uncoated MS (765.3 µA cm −2 ) > pristine CMC coating (278.6 µA cm −2 ) > 1.0%CeO 2 coating (179.1 µA cm −2 ) > 2.0%CeO 2 coating (79.6 µA cm −2 ) > 3.0%CeO 2 coating (28.3 µA cm −2 ) < 4.0%CeO 2 coating (44.4 µA cm −2 ) < 5.0%CeO 2 coating (56.6 µA cm −2 ) < 10.0%CeO 2 coating (107.9 µA cm −2 ). This suggests that ceria-CMC reduces the MS corrosion rate. The decline in i cor values in the presence of CeO 2 embedded in the CMC matrix can be attributed to the impeding of the efficient centers present on the MS substrate [67]. The highest protection capacity of~96.3% was documented in the case of the 3.0%CeO 2 -CMC-coated layer. The MS substrate coated with CeO 2 -CMC revealed reputable corrosion protection, which might be due to the well-intentioned dispersion of ceria in the CMC matrix. The use of a CeO 2 -embedded CMC matrix enhances the barrier features due to greater crosslinking of the CeO 2 -CMC composite. Ultimately, the existence of CeO 2 NPs embedded in the CMC structure decreases the pores available for H 2 O absorption and eliminates conductive paths in the coating film, inventing its barrier characteristics.

EIS studies
To clarify the steel kinetic processes and the surface features of M-steel, the EIS investigation was conducted on uncoated and coated M-steel in hydrochloric acid solution. The Nyquist (A), Bode (B), and Bode phase (C) diagram 1.0 M HCl solution for MS and coated with various values of %CeO 2 -CMC at 50 • C are represented in Figure 7A-C respectively. The Nyquist diagram ( Figure 7A) in the case of pristine MS bare shows a single capacitive loop (one semicircle), which is ascribed to the corrosion process of charge-transfer. Nevertheless, in the case of coated MS surfaces with different values of %CeO 2 -CMC nanocomposites, two capacitive loops are discerned as shown in Figure 7A. At relatively high-frequency (HF) areas, the inductive-loop can be clarified as the coating film capacitance (Q coat , CPE coat ) and the resistance of coating film (R c ) [49]. However, at low frequency (LF), the capacitive-loop areas might be attributed to the polarization-resistance (R p ) in parallel with the capacitance of the double layer (Q dl , CPE dl ) [50]. The occurrence of double capacitive loops for coated surfaces has been recorded previously [51,52]. The capacitive loops are not precise semicircles and are depressed to some degree. This is associated with the frequency dispersion effect as a result of the roughness and inhomogeneity of the metal surface.
The diameter of Nyquist plots in the case of all coated layers with different ceria percentages was larger than that of the uncoated MS surface. This suggests that the %CeO 2 -CMC-coated films create a protective layer on the steel interface, consequently increasing the impedance of corrosion by the metal surface. This diameter of the semicircle increases with increasing the CeO 2 percent in the coating structure until 3%CeO 2 then declines to 10%CeO 2 (Table 2), which indicates that the steel protection is directly dependent on ceria percent. The coated layers of %CeO 2 -CMC designed the protective adsorbed films on the metal surface by forming a robust bond among N atoms in the CeO 2 -CMC film and the metal substrate. These layers are designed on the metal interface and proficiently block it from the corrosive chloride ions [68]. The Bode impedance modulus ( Figure 7B) shows linear portions at middle frequencies, and the linearity is further evident in the case of the coated films, implying greater slopes than the uncoated metal [69]. In order to fit the EIS data, the equivalent circuit (EEC) was used as depicted in Figure 7D (uncoated (DI) and coated (DII)). The model utilized to fitting the EIS findings contains constant phase-element (CPE); R e (solution resistance); polarization resistance (R p ) (R p = R L (layer resistance) + R ct (charge transfer resistance)), i.e., a simple Randles EEC accompanied by C c (coating pseudo-capacitance); and R po (electrical pore resistance) in the presence of coated films. The calculated electrochemical parameters such as R p , R po , CPE, and n were fitted by using the Z-View program and are listed in Table 2. The protection proficiencies (%η e ) were calculated from the following equation [70]: where θ is the surface coverage part; R 0 p and R c p describe polarization resistances in the case of uncoated and coated substrates, respectively. To provide a more accurate fitting, CPE was calculated rather than the pure capacitance element; the double-layer is created by the film on the metal surface functioning as CPE [71]. The impedance of CPE is estimated from the following equation [71]: where Y 0 represents the magnitude of CPE, ω is angular frequency, j is the √ −1, and n represents the phase shift. The lower value of n ( Table 2) for uncoated MS reflects the surface heterogeneity caused by the steel's roughening surface due to corrosion. Nonetheless, in the presence of films coated with CeO 2 -CMC, the n values were increased, signifying declining heterogeneity of surface due to the structure of combined ceria and CMC-coated films. In addition, the R po values were found to increase with the ceria content up to 3%, after which they decreased. The highest R po value was attained for the sample coated with 3%CeO 2 -CMC film, confirming that this is the minimal porous coating film (Table 2).
A considerable increase in the R p was noticed in the presence of the coated films compared with the uncoated sample ( Table 2). The R p increases with increasing the ceria percent in the CMC matrix, resulting in enhanced coating protection. This phenomenon is due to the structure of coated films on the metal surface. The characteristic structures of ceria nanoparticles prevent the corrosive ions from infiltrating the metal surface and increase the resistance of coating corrosion, consequently impeding more charge and mass transfer. As shown in Table 2, the η e /% and R p order of diverse coating layers throughout the entire inspection method is as follows: 3.0%CeO 2 -CMC (98.4%) > 4.0%CeO 2 -CMC (98.1%) > 5.0%CeO 2 -CMC (98.0%) > 10.0%CeO 2 -CMC (97.7%) > 2.0%CeO 2 -CMC (97.2%) > 1.0%CeO 2 -CMC (95.8%).
The values of CPE for the blank and coated samples are presented in Table 2. The CPE values for coated films decrease in comparison with the uncoated surface because of the protection efficacy improvement provided by the CeO 2 -CMC films. The greater value of R p with a smaller CPE value shows the superior corrosion impedance of the prepared coating layers [72]. It could be detected that the CPE values dropped from 123.61 µΩ −1 s n cm −2 to 45. 24, 34.65, 21.37, 24.34, 26.89, and 31.23 µΩ −1 s n cm −2 in the presence of coated films with 1.0%CeO 2 -CMC, 2.0%CeO 2 -CMC, 3.0%CeO 2 -CMC, 4.0%CeO 2 -CMC, 5.0%CeO 2 -CMC, and 10.0%CeO 2 -CMC. This decrease in CPE values is ascribed to the augmentation in the thickness of the electrical double-layer and/or the decrease in local-dielectric constant, indicating that ceria-CMC composite decreases the corrosion rate by steady adsorption at the metal/solution interface [73]. The improvement in R p is consistent with the increase in R po and decrease in CPE values of the coating films, confirming the anticorrosion capability of the prepared films. The steadiness of the coated layers is due to the robust adsorption of CMC active centers on the metal surface through the contribution of lone electron pairs of oxygen atoms to the empty d-orbital of Fe ions to form a coated layer of CMC molecules that operates by ceria NPs on the electrode substrate, as shown in Figure 8.       Figure 9 presents an energy diagram of the Frontier molecular orbitals (FMO) for CMC and CeO 2 -CMC molecules, and the associated theoretical parameters are listed in Table 3. It is evident that the HOMO level for CeO 2 -CMC molecule was situated on the nitrogen and oxygen atoms, as shown in Figure 9, which are desired sites for electrophilic attacks on the MS surface. Furthermore, the ∆E (energy gap) is a decisive parameter to boost the corrosion protection capability of the inhibitor molecule, i.e., it enhances as the ∆E value is reduced [74]. As shown in Table 3, the CeO 2 -CMC molecule has a smaller ∆E value (0.18 eV) than CeO 2 and CMC molecules, which develops the great tendency of CeO 2 -CMC molecules to be adsorbed onto the steel interface.  Figure 9 presents an energy diagram of the Frontier molecular orbitals (FMO) for CMC and CeO2-CMC molecules, and the associated theoretical parameters are listed in Table 3. It is evident that the HOMO level for CeO2-CMC molecule was situated on the nitrogen and oxygen atoms, as shown in Figure 9, which are desired sites for electrophilic attacks on the MS surface. Furthermore, the ΔE (energy gap) is a decisive parameter to boost the corrosion protection capability of the inhibitor molecule, i.e., it enhances as the ΔE value is reduced [74]. As shown in Table 3, the CeO2-CMC molecule has a smaller ΔE value (0.18 eV) than CeO2 and CMC molecules, which develops the great tendency of CeO2-CMC molecules to be adsorbed onto the steel interface.    Usually, corrosion inhibitors have low electronegativity (χ), indicating the inhibitors' aptitude for electron provision to the metal surface [70]. However, high electronegativity (χ) indicates an inhibitor's ability to receive the electron from steel interface atoms (i.e., back-donation) and create a powerful bond with the MS surface [75]. The electronegativity of CeO 2 , CMC, and CeO 2 -CMC molecules are moderately high (about 5) as shown in Table 1, revealing the back-donation propensity of the CeO 2 , CMC, and CeO 2 -CMC molecules to create a durable bond with the MS surface.

Computational Calculations (DFT)
Additionally, softness (σ) and hardness (η) are important indicators to assess the stability and reactivity of the inhibitor molecule, i.e., soft molecules have protection proficiency greater than that of hard molecules through the effortless transfer of electrons to the steel interface, forming an adsorbed layer that can be considered as an effective corrosion inhibitor [71]. As shown in Table 3, the CeO 2 -CMC molecule has a larger σ value (11.24) and lower η value (0.09) than CMC molecules, while the CeO 2 molecule has a low σ value (0.30) and high η value (3.39), indicating the low electron contribution capability of CeO 2 molecules in contrast with CeO 2 -CMC molecules, which have an efficient contribution of electrons to the steel surface and excellent protection capability.
Furthermore, the electron-donating or accepting capacity of the inhibitor molecule can be clarified by the fraction of electron transfer and ∆E back-donation . As follows, if the ∆N values are more than 0, the electron transfer is probable from inhibitor to MS interface atoms, whereas, if the ∆N values are less than 0 zero, the electron transfer is possible from metal atoms to inhibitor molecule (i.e., back-donation) [72]. As shown in Table 3, the ∆N value for the CeO 2 @-CMC molecule is above zero (10.14) and higher than CeO 2 and CMC molecules, revealing that the CeO 2 -CMC molecule is proficient in providing electrons to the MS surface. In addition, the ∆E back-donation will be < 0 when η > 0, the electron will be transmitted to a molecule, followed by a back-donation from the molecule, and this is energetically desired [76]. In Table 3, the value of ∆E back-donation for CeO 2 , CMC, and CeO 2 -CMC molecules are negative, which reveals that back-donation is favored for CeO 2 , CMC, and CeO 2 -CMC molecules and constructs a sturdy bond [77].
Similarly, the dipole moment is an imperative index that designates the corrosion protection capability of the inhibitor molecule [73]. Thus, the upsurge in dipole moment provides enhanced distortion energy, and augmentation in the adsorption of the inhibitor molecule on the MS surface implies a reinforcement in corrosion protection proficiency [78]. As shown in Table 3, the CeO 2 -CMC molecule has a greater dipole moment value (18.56 debye) than CeO 2 and CMC molecules, which strengthens the additional proclivity for the CeO 2 -CMC molecule to be adsorbed onto the MS interface and improves the protection. Lastly, the protection proficiency of the CeO 2 -CMC molecule for corrosion of the MS surface is correlated with its molecular surface area. The corrosion protection capability improved as the molecular area was enhanced because of the increase in MS surface area shielded with adsorbed inhibitor molecules [79]. As shown in Table 3, the CeO 2 -CMC molecule had a greater molecular surface area (2741.52 Å 2 ) than CeO 2 and CMC molecules, which boosts the corrosion protection proficiency of the CeO 2 -CMC molecule. The theoretical outcomes are in accordance with the experimental findings.

MC Simulations
MC simulations were designed to discern the adsorption of the inhibitor molecule onto the MS surface, and provide information about the protection mechanism. Thus, Figure 10 shows the most suitable adsorption conformations for the CeO 2 -CMC molecule on the MS interface in acidic medium which is displayed in a nearly flat arrangement, suggesting an improvement in the adsorption and highest surface coverage [80]. The evaluated results for the adsorption energies from the MC simulations are listed in Table 4. As seen in Table 4, the CeO 2 -CMC molecule has a high negative adsorption energy value of −2868.29 kcal mol −1 , which indicates energetic adsorption of CeO 2 -CMC molecule onto the MS interface, generating a durable adsorbed film and shielding the MS surface from the corrosion. These outcomes are in accordance with the experimental results [81]. From Table 4, it is obvious that the adsorption energy value for CeO 2 -CMC molecule for the pre-geometry optimization step, i.e., unrelaxed (−2168.86 kcal mol −1 ) is highly negative and for the post-geometry optimization step, i.e., relaxed (−699.42 kcal mol −1 ) it is also negative, confirming a high protection proficiency for the CeO 2 -CMC molecule.
The dEads/dNi values reveal the metal/adsorbates adsorption energy if one of the ad-sorbed species has been excluded [45]. The dEads/dNi value for the CeO2-CMC molecule (−372.13 kcal mol −1 ) is more negative than the dEads/dNi values for hydronium ions, chloride ions, and water molecules, which are −31.07, −61.07, and −15.26 kcal mol −1 , respectively. Therefore, a more forceful adsorption of the CeO2-CMC molecule than hydronium ions, chloride ions, and water molecules enhances the exchange of hydronium ions, chloride ions, and water molecules by the CeO2-CMC molecule. Thus, the CeO2-CMC molecules are forcefully adsorbed onto the MS surface and create an efficient adsorbed protective layer, which shields the MS surface from corrosion, as confirmed by both experimental and computational studies.

Final Equilibrium Configurations
Side View   The dE ads /dN i values reveal the metal/adsorbates adsorption energy if one of the adsorbed species has been excluded [45]. The dE ads /dN i value for the CeO 2 -CMC molecule (−372.13 kcal mol −1 ) is more negative than the dE ads /dN i values for hydronium ions, chloride ions, and water molecules, which are −31.07, −61.07, and −15.26 kcal mol −1 , respectively. Therefore, a more forceful adsorption of the CeO 2 -CMC molecule than hydronium ions, chloride ions, and water molecules enhances the exchange of hydronium ions, chloride ions, and water molecules by the CeO 2 -CMC molecule. Thus, the CeO2-CMC molecules are forcefully adsorbed onto the MS surface and create an efficient adsorbed protective layer, which shields the MS surface from corrosion, as confirmed by both experimental and computational studies.

Conclusions
In this study, CeO 2 -nanoparticle-loaded carboxymethyl cellulose was prepared, and its structure was categorized through FT-IR, TEM, FE-SEM/EDX, and thermal analysis. The SEM, TEM, EDX, and elemental mapping confirm the formation of CMC-CeO 2 as a polymer/oxide composite. This prepared nanocomposite showed higher thermal stability. For the first time, CeO 2 -CMC composite with different CeO 2 ratios displayed superior protective performance as a coating film for MS in HCl solutions. The protection capabilities of the as-prepared CeO 2 -CMC composites by electrochemical approaches followed the order of 3.0%CeO 2 -CMC (98.4%) > 4.0%CeO 2 -CMC (98.1%) > 5.0%CeO 2 -CMC (98.0%) > 10.0%CeO 2 -CMC (97.7%) > 2.0%CeO 2 -CMC (97.2%) > 1.0%CeO 2 -CMC (95.8%). The findings of the DFT calculations and MC simulations showed that coated films were robustly adsorbed onto the metal substrate, and theoretical parameters involving E HOMO , E LUMO , and ∆E were in agreement with the empirical data, which help elucidate the mechanism of adsorption of the CeO 2 -CMC composite onto metal surfaces. Consequently, CeO 2 -CMC composite is clearly a suitable eco-friendly coating film for MS corrosion in the pickling process.