The samples were cut in an L-shape for electrochemical and morphological analysis. The cut was performed using a hand guillotine. The test area was 1.0 cm², which was isolated with epoxy resin (Araldite^®).

For all investigations, the samples were wet sanded using silicon carbide sandpaper with grit sizes of 180, 220, 320, 500, 800, and 1200 mesh. The sanded samples were cleaned with 97% ethanol and dried in hot air. They were subsequently polished using Arotec^® 6 µm, 3 µm, 1 µm, and 1⁄4 µm diamond paste to obtain a scratch-free specular surface. The samples were sanded and polished using an Arotec^® polishing machine, the Aropol VV model.

The solutions used in the electrochemical tests (Potentiodynamic Polarization and Electrochemical Impedance Spectroscopy) for the analysis of the efficiency of the HEDP inhibitor were composed of a mixture of 3.5 wt% NaCl PA (Dinâmica, Indaiatuba, SP, Brazil), 1 mmol∙L⁻¹ Na₂S PA (Impex, Diadema, SP, Brazil) and 20, 30, 50, and 100 mg∙L⁻¹ HEDP (Polyorganic Technology, São Paulo, SP, Brazil). All the solutions were prepared using the ultrapure water (SARTORIUS mini Arium^® with a resistivity of 18.2 MΩ cm at 22˚C ± 3˚C).

The effects of calcium, zinc, and magnesium were investigated in a solution containing 3.5 wt% PA NaCl PA, 1 mmol∙L⁻¹ Na₂S PA, and 50 mg∙L⁻¹ HEDP, CaCl₂ PA (Dinâmica, Indaiatuba, SP, Brazil), ZnCl₂ (97%, Dinâmica, Indaiatuba, SP, Brazil), and MgCl₂ PA (Synth, Diadema,SP,Brazil) with concentrations ranged from 10 to 30 mg∙L⁻¹.

The pH of the solution was measured using the pocket-sized pH meter Isfetcom, S2K712 model. The pH of the solution in the absence of the inhibitor is 9.5, in the presence of the inhibitor (50 mg∙L⁻¹) 8.3, in the presence of calcium (10 mg∙L⁻¹) 5.9, in the presence of zinc (20 mg∙L⁻¹) 5.8 and in the presence of magnesium (10 mg∙L⁻¹) 6.4. The electrolytes were not stirred or heated. The temperature for all the measurements was 21˚C ± 3˚C. In order to obtain the real operation conditions, the oxygen dissolved in the solution was not removed.

The samples were prepared in bakelite phenolic resin by means of an Arotec^® automatic mounting press, Pre Mi model. Then, the samples were electrolyzed per 30 s, using a voltage of 6 V and in the presence of oxalic acid 10 wt%, according to ASTM A262-15 [27]. Microstructural characterizations by optical microscopy were performed using a Nikon Inverted Optical Microscope, Eclipse MA 200 model.

The microstructural characterizations of the samples under investigations were carried out using two different equipment: Scanning Electron Microscopy (SEM) coupled to the X-ray Dispersive Energy Spectrometer (EDS), Shimadzu^® SS550 model microscope with voltage acceleration of 25 kV; and the microscope from Zeizz^®, EVO I MA 10 model, and the Oxford Instruments model X-MaxN spectrometer. The data were obtained by AZtec 2.1a software. The voltage acceleration was 30 kV.

Electrochemical experiments were performed on an AUTOLAB 302 potentiostat/galvanostat equipped with Nova 2.1.1 software. A three-electrode cell configuration consisting of working electrode (1.0 cm² AISI 304 stainless steel samples), a carbon counter electrode with dimensions of 6.76 mm × 22.55 mm × 59.61 mm, and a saturated calomel reference electrode (SCE-Hg/Hg₂Cl₂) was used.

Open circuit potential (E_OC) was determined by employing a scan rate of 1 mV∙s⁻¹ over 3600 s. Potentiodynamic Polarization (PDP) measurements were carried out over a potential range of ±240 mV around the E_OC.

EIS measurements were carried out at three distinct potentials: E1 = corrosion potential (E_corr [V vs. SCE]), E2 = −0.3 [V vs. SCE] and E3 = 0.1 [V vs. SCE] at the frequency range from 100 kHz to 10 mHz, and the signal amplitude sine wave used was E_rms (root mean square) = 5 mV (p/p) with 10 points per logarithmic decade using “single sine” mode. The simulation of the obtained data was performed in EIS Spectrum Analyzer Software using the Newton algorithm and the amplitude function. The electrical equivalent circuit used in the fit was R_s(CPE − R_p) (see FigureS2 in the supplementary material), where R_s is the solution resistance, R_p is the polarization resistance, and CPE is the constant phase element and is related to capacitive characteristics of the system. Data were adjusted with errors below 10% and chi-square at 10⁻³. Chi-square ( r c 2 ) is determined according to Equation (1) [28], where Z ′ i is the real and Z ″ i is the imaginary impedance values obtained from the EIS experimental data; Z ′ i , calc is the real and Z ″ i , calc is the imaginary impedance values calculated at the fitting of the curve. This free software was obtained from the website: http://www.abc.chemistry.bsu.by/vi/analyser/ [28].

r c 2 = ∑ i = 1 N ( Z ′ i + Z ′ i , calc ) 2 − ( Z ″ i + Z ″ i , calc ) 2 ( Z ′ i ) 2 + ( Z ″ i ) 2 (1)

The inhibitor efficiency was calculated by Equation (2) [29], where η_E is the inhibitor efficiency, R_p is the polarization resistance in the presence of the inhibitor, and R ′ p is the polarization resistance in the absence of the inhibitor.

η E ( % ) = R p − R ′ p R p ∗ 100 (2)

Weight loss measurements were based on ASTM G31-72 [30]. The AISI 304 stainless steel samples were immersed in a 50 mL volume of the solutions that obtained the best result in the electrochemical tests for 3 months. After the soaking time, they were washed and treated for pickling. The steel pickling process was performed according to ASTM A380/A380M-17 [31] using a 20% v/v nitric acid solution. Following the pickling process, the samples were washed, dried, and weighed. The corrosion rate (C_R) was calculated according to Equation (3) [30], where K: constant (8.76 × 10⁴ mm∙year⁻¹); W: weight loss (g); A: sample area (cm²); T: immersion time (h); and D: sample density (8.0 g∙cm⁻³). The surface coverage (θ) and weight loss efficiency (η_m) calculations were performed according to Equations (4) and (5), respectively, where C_R0 is the corrosion rate in the absence of the inhibitor and C_RI is the corrosion rate in the presence of the inhibitor [32].

C R = K ∗ W A ∗ T ∗ D (3)

θ = C R 0 − C RI C R 0 (4)

η m ( % ) = C R 0 − C RI C R 0 ∗ 100 (5)

In the optical microscopy image of the AISI 304 stainless steel there is a microstructure of recrystallized austenite grains and annealing twins, which are characterized by parallel bands in contrast to the grains [33]. The inclusions are points susceptible to dissolution during corrosion and allow the formation of a corrosion cell within the metal and will act as an anode, cathode, or be inert, according to its potential [34] [35]. For these points, EDS analysis was performed and the spectra showed the presence of inclusions composed of Mn and S which favors the material corrosion process, as they are preferential sites for nucleation and pit growth [30] (see FigureS3 and FigureS4 in the supplementary material).

Potentiodynamic polarization curves for AISI 304 stainless steel in a solution containing 3.5 wt% NaCl, 1 mmol∙L⁻¹ Na₂S in the absence and presence of the HEDP inhibitor at concentrations of 20, 30, 50, and 100 mg∙L⁻¹ are shown in Figure 1. Figure 1(a) shows that the addition of the inhibitor favored a change of corrosion potential (E_corr) to more positive potentials, indicating that the HEDP inhibitor is an anodic type controlling the oxidation reaction. The same result was observed by Kármán et al. [17], Sekine et al. [19] and Salasi and Shahrabi [36] indicating that the complex is formed on the metallic surface on the anode sites.

The potentiodynamic polarization results shown in Figure 1 indicated that in the presence of the inhibitor there is a reduction in j_corr values up to the 50 mg∙L⁻¹ inhibitor concentration, suggesting a lower electron flow from the anodic region to the cathodic region and favoring greater protection of the material in the aggressive medium containing chloride and sulfide ions. On the other hand, an increase in j_corr is observed at a concentration of 100 mg∙L⁻¹, indicating an increase in the corrosion rate. According to Sekine et al. [19] the higher concentration of the inhibitor, culminate in an increase in the rate of corrosion, due to an excess of HEDP ions dissolved in the solution. The excess of HEDP leads to the formation of a soluble complex consisting of HEDP-iron capable of preventing passivation [20]. Thus, one can infer that, the best inhibitor concentration that favored greater corrosion inhibition is 50 mg∙L⁻¹.

In order to increase the efficiency of the corrosive process and favor a greater stabilization of the surface formed film, the effects of the addition of Ca²⁺, Zn²⁺, and Mg²⁺ in a solution containing 50 mg∙L⁻¹ HEDP were studied.

The addition of calcium in a solution containing chloride and sulfide ions did not produce a very significant effect when compared to a solution containing only 50 mg∙L⁻¹ HEDP, as shown in Figure1(b). The addition of this cation at a concentration of 10 mg∙L⁻¹ provided an increased inhibitory effect on AISI 304 stainless steel due to a slight lowering of j_corr value, as indicated in Figure1(b) and may be related to a greater blockage of active sites consisting of manganese sulfide, present in the sample before the potentiodynamic polarization tests (see the SEM-EDS analysis in the FigureS4 in the supplementary material). There is a slight decrease in the cathodic current density confirming that Ca²⁺ promotes the oxygen reduction reaction, this behavior was also verified by Karmán et al. [17].

Potentiodynamic polarization curves with the addition of zinc are shown in Figure 1(c). Through analyzing the PDP curves, it was observed that the addition of Zn²⁺ displaced the corrosion potential to low E_corr-values and decrease on j_corr when compared to the presence of 50 mg∙L⁻¹ HEDP. This behavior was also verified by Yan et al. [15] in a study performed on cold-rolled steel immersed in a medium containing 0.0082 mol∙L⁻¹ HEDP and 0.0082 mol∙L⁻¹ zinc nitrate and by Award [12] in a carbon steel study using a medium containing 0.003 mol∙L⁻¹ Cl⁻.

Figure 1(d) shows that the addition of magnesium did not cause a significant change in the 50 mg∙L⁻¹ HEDP PDP curves. It was found that on the three Mg

concentrations investigated, there was no substantial variation of E_corr. However, when comparing the cathodic and anodic polarization curves, one can verify a greater variation in the cathodic current density, when compared with the presence of 50 mg∙L⁻¹ HEDP, suggesting that this mixture acts mainly as a cathodic-type inhibitor [37]. The smallest j_corr was identified by the addition of 10 mg∙L⁻¹ Mg²⁺, indicating a greater blocking of the active sites and consequently a lower flow of electrons from the anodic region to the cathodic region. Smaller j_corr were observed with the addition of zinc and magnesium, suggesting that in the presence of these divalent cations a hydroxide film of these cations can be formed in the cathodic area and facilitates adsorption of the inhibitor in the anodic area.

The sample surface consists of metal and a protective film, which due to its chemical composition is generally not evenly distributed, thus resulting in discontinuities. The film is the cathode area and the discontinuities are the anodic area. Thus, the EIS analysis was performed on three distinct potentials: −0.3 [V vs. SCE], E_corr [V vs. SCE], and 0.1 [V vs. SCE]. Being that, two potentials far away to the E_corr (−0.3 [V vs. SCE] and 0.1 [V vs. SCE]) were performed to verify at which inhibitor concentrations the samples would present a more homogeneous film formation. Complex plane impedance (a, b, c) and Bode (d, e, f) plots obtained for the three distinct potentials are shown in Figure 2.

Complex plane impedance plots have the same shape as a single deformed semicircle for all the potentials investigated, indicating that the corrosion reaction in the AISI 304 stainless steel was controlled by the behavior of the double layer and the charge transfer process [38]. Moreover, it can see that the optimal inhibitor concentration to favor a surface containing a longer protective film was 100 mg∙L⁻¹ for the −0.3 [V vs. SCE] and 30 mg∙L⁻¹ for the others potentials (E_corr

[V vs. SCE], and 0.1 [V vs. SCE]). One could infer this due to higher Z_re-values observed. This fact indicates that at those concentrations, the inhibitor acted more effectively in the region most prone to the corrosive process such as inclusions, discontinuities, and grain boundaries, creating a protective barrier and making the surface more homogeneous. Increased semicircle inclination is associated with increased resistance to the charge transfer process from metal to electrolyte [37].

The effect of calcium is verified in Figure 3 in the complex plane impedance plots obtained at −0.3 [V vs. SCE] (a), E_corr [V vs. SCE] (b), and 0.1 [V vs. SCE] (c). These results show that the addition of a lower calcium concentration (10 mg∙L⁻¹) ensures a greater Z_re range and, consequently, a higher R_p value. This observation is in agreement with the results found in the PDP technique and

indicates that there has been a change in the kinetics of the corrosive process due to the formation of a protective film [39].

The adsorption of the inhibitor on the metal surface is influenced by pH. Zenobi et al. [40] perform in-situ ATR-FTIR spectroscopy of HEDP in aqueous solution and observed a similar spectrum at pH 9.0 and 8.0, only the PO 3 2 − specie is protonated and, therefore, the phosphonic groups have different symmetry. At pH 7.0, bands of HPO 3 − appear, in addition to the bands of PO 3 2 − . At pH 6.0 and 5.0 the spectra show the same bands found for pH 7.0, however, at pH 6.0 there is a decrease in the bands corresponding to the PO 3 2 − species and an increase in the HPO 3 − , POH and P=O bands. At pH 5.0, there was an increase in the intensity of the bands of the protonated species.

The pH measured for the absence of the inhibitor was 9.5 and for the addition of 50 mg∙L⁻¹ HEDP, 8.3. The addition of 10 mg∙L⁻¹ Ca²⁺, which provided the best electrochemical results, shifted the pH to the value of 5.9. The adsorption of the inhibitor occurs by the union of the ligand with the divalent cation in the PO 3 2 − species [29], however, in the pH range from 8.0 to 9.0, only the PO 3 2 − specie is deprotonated [40], making the adsorption difficult. With the decrease in pH, with the addition of Ca²⁺, in the range of 6.0 - 5.0, there is a reduction of the PO 3 2 − bands and the appearance of new bands [40] it is suggested that in this concentration there was an increase of protective film, due to a greater transport of the inhibitor to the metal surface.

According to Deluchat et al. [16] HEDP has the ability to complex with Ca²⁺ in a pH range of 5.5 - 7.0. However, in the same pH-range, it has a greater affinity for Fe²⁺. This indicates that Ca²⁺ facilitated the transport of HEDP to the metal surface, but did not favor the formation of a hydroxide film with protective characteristics. If one takes into account that the corrosion process occurs much more pronounced in an acidic environment, the change in pH observed from basic pH to acidic pH, the system became much more aggressive, however, when observing that even at this acidic pH the inhibitor acted to protect the specimen by inhibiting the corrosive process. In this way, one can infer that the inhibition efficiency is much greater in the presence of inhibitor than without the inhibitor.

Figure 4 shows the effect of a zinc addition on the complex plane impedance plots at −0.3 [V vs. SCE] (a), E_corr [V vs. SCE] (b), and 0.1 [V vs. SCE] (c). At potential −0.3 [V vs. SCE] (Figure 4(a)), it is observed that the addition of Zn did not contribute to the formation a protective film because it observed the larger deformed semicircle at 50 mg∙L⁻¹ HEDP concentration in the absence of zinc cations. At E_corr [V vs. SCE] (Figure 4(b)), the addition of Zn was positive for the protection of the steel surface from the attack of chloride and sulfide ions present in the solution. This was confirmed by an increase in deformed semicircle diameter at 10 mg∙L⁻¹ and 20 mg∙L⁻¹ concentrations. A study by Miao, Wang, and Hu [29] suggest that in the presence of Zn²⁺ in a bulk solution, HEDP-Zn²⁺ complexes are formed and diffused to the steel surface where it is converted to HEDP-Fe²⁺. HEDP-Fe²⁺ is adsorbed to the anodic region according to Equation

(6). Zn²⁺ reacts with OH⁻ from the cathodic reaction (Equation (7)) and forms zinc hydroxide (equation (8)) which is adsorbed to the cathodic region and has protective characteristics. Reznik et al. [41] also found a better result for the addition of 20 mg∙L⁻¹ Zn²⁺, in a work with the 1020 carbon steel, immersed in a medium containing 30 mg∙L⁻¹ Cl⁻ and 50 mg∙L⁻¹ HEDP and concluded that the addition of Zn²⁺ was conducive to a greater formation of Zn(OH)₂ and its deposition on cathodic sites, delaying the corrosive process.

The pH found for the presence of Zn²⁺ is similar to that found for Ca²⁺. ([Zn²⁺] = 20 mg∙L⁻¹, the pH = 5.8). In the range of pH from 5.5 to 7.0, the Zn²⁺ ions can complex with HEDP, it already is verified by Deluchut et al. [16] that Zn²⁺ has a greater affinity to this inhibitor. This fact justifies greater protection for AISI 304 stainless steel in the presence of zinc, due to the formation and adsorption of a Zn(OH)₂ film on cathodic sites.

HEDP-Zn 2 + + Fe ( s ) ⇄ HEDP-Fe 2 + + Zn 2 + ( aq ) (6)

O 2 ( g ) + 2H 2 O ( l ) + 4e − ⇄ 4OH − ( aq ) (7)

Zn 2 + ( aq ) + 2OH − ( aq ) ⇄ Zn ( OH ) 2 ( aq ) (8)

Finally, at potential 0.1 [V vs. SCE] (Figure 4(c)), it is shown that for all Zn concentrations there was an increase in deformed semicircle diameters, demonstrating that this element favors stabilization of the protective film adsorbed to the cathodic region.

Figure 5 shows the effect of magnesium addition in the complex plane impedance

plots obtained at the potential −0.3 [V vs. SCE] (a), E_corr [V vs. SCE] (b) and 0.1 [V vs. SCE] (c). It is observed that the addition of magnesium results in a behavior similar to that of the addition of zinc, since both the cations, at the same potential −0.3 [V vs. SCE], do not indicate contribute to the formation of the protective film. Besides, it was observed that magnesium at 10 mg∙L⁻¹ and 20 mg∙L⁻¹, favors the stabilization of the protective film due to a larger deformed semicircle at the E_corr [V vs. SCE] and at the potential 0.1 [V vs. SCE]. The increase of the deformed semicircle indicates a greater inhibition of the corrosive process induced by the presence of the inhibitor [42]. The increase in semicircle inclination may be linked to the formation of an HEDP-Mg²⁺ complex in bulk solution which is transported to the material surface where it is converted to HEDP-Fe²⁺ (Equation (9)) and adsorbed in the anodic region. Mg²⁺ reacts with OH⁻ from the cathodic reaction (Equation (7)) and forms magnesium hydroxide (Equation (10)), which is adsorbed to the cathodic region. According to the EIS-results obtained, it suggests that the film is formed by magnesium hydroxide has protective characteristics. At 10 mg∙L⁻¹ Mg²⁺ concentration, the pH of the solution was 6.4, indicating that the formation of the protective film consisting of Mg(OH)₂ occurs at a pH value higher than that found for the presence of Ca²⁺ and Zn²⁺.

HEDP-Mg 2 + + Fe ( s ) ⇄ HEDP-Fe 2 + + Mg 2 + ( aq ) (9)

Mg 2 + ( aq ) + 2OH − ( aq ) ⇄ Mg ( OH ) 2 ( aq ) (10)

Bode plot (Figure2(d)) shows that the addition of the inhibitor favored an increase in phase angle. At concentrations of 30, 50, and 100 mg∙L⁻¹ of HEDP, this value remained constant at approximately −68.0˚. When analyzing the Bode plots, in the absence of the inhibitor a greater frequency widening is found suggesting a surface covered by a more uniform protective film [43]. This larger widening is due to the presence of Ni found in the EDS spectra (FigureS4(b) in the supplementary material), which guarantees greater resistance to the corrosive process in austenitic stainless steel [4]. According to Sekine et al. [19], on AISI 304 stainless steel a film is formed on the metal surface consisting of Ni, Cr and the HEDP inhibitor. In Bode plot (Figure2(e)), the maximum phase angle achieved was −76.0˚ (30 mg∙L⁻¹). Phase angles closer to −90.0˚ indicate an increased inhibition of the corrosive process due to higher adsorption of inhibitor molecules on the metal surface [44].

Bode plot (Figure 2(f)) indicates that the maximum phase angle reached was −77.3˚ (30 mg∙L⁻¹). Compared with the results obtained in the −0.3 [V vs. SCE] and on the corrosion potential, an increase of the maximum phase angle is evidence, indicating that the addition of the inhibitor contributed to a more capacitive behavior of the steel. Bode plots in the presence of calcium revealed that the addition of this element does not favor stabilization of the formed film due to a phase angle increasing from −73.0˚ (−0.3 [V vs. SCE]) to −77.04˚ (E_corr [V vs. SCE]) and its subsequent decay to −73.2˚ (0.1 [V vs. SCE]) (see Figures 3(d)-(f)).

It was exposed that the corrosive process of steel in a medium containing HEDP, chloride, sulfide, and Zn²⁺ ions involved only a time constant. There was also a widening of range the frequency at intermediate frequencies. The impedance at intermediate frequencies reflects the contribution of capacitance [15] indicating that the formation of a protective film with greater homogeneity occurred, creating a barrier to the corrosive process. Film stabilization is confirmed by increasing the phase angle from −73.6˚ (−0.3 [V vs. SCE]—Figure 4(d)) to −77.1˚ (0.1 [V vs. SCE]—Figure 4(f)) at concentration of 20 mg∙L⁻¹ Zn²⁺. Phase angles close to −90.0˚ suggests a more capacitive system and occur in response to increase inhibitor adsorption on the metal surface. At 0.1 [V vs. SCE], the maximum phase angle was displaced to lower frequencies, indicating that the corrosive process was softened [39].

Figure 5 also shows Bode plots at −0.3 [V vs. SCE] (d), E_corr [V vs. SCE] (e), and 0.1 [V vs. SCE] (f) in a medium containing chloride, sulfide, and HEDP inhibitor in the presence and absence of magnesium. It was shown that for all investigated concentrations a single peak was identified, demonstrating that the corrosive process of AISI 304 stainless steel in these conditions is influenced by the charge transfer process and capacitance of the electrical double layer [45]. As verified for the presence of Zn, the stabilization of the film on the AISI 304 stainless steel surface in the presence of Mg is confirmed by the phase angle increase from −71.9˚ (−0.3 [V vs. SCE]—Figure 5(d)) to −78.3˚ (0.1 [V vs. SCE]—Figure 5(f)), indicating an adsorption of the inhibitor molecule on the metal surface.

The impedance plots were analyzed by the equivalent electrical circuit described in FigureS2 in the supplementary material and the results are shown in Table 1. The capacitance of the electrical double layer (C_dl) was calculated according to equation 11 [46].

C dl = [ C P E ( R s − 1 + R p − 1 ) n − 1 ] 1 / n (11)

As shown in Table 1 (−0.3 [V vs. SCE]), R_p values increased with the addition of the inhibitor. This fact suggests the formation of a thicker film on the metal surface, which minimizes localized corrosion by the penetration of chloride and sulfide ions. In parameter n and the CPE values, no significant variation was observed indicating that the corrosion mechanism at this potential is controlled by the charge transfer process [23]. Thus, it is indicated that at potentials below the corrosion potential the presence of the HEDP inhibitor provided the formation of a more uniform and adherent protective film, indicating greater protection for dissolution of the AISI 304 stainless steel at higher potentials. The maximum inhibitor efficiency (n_E = 43.8%) achieved was [HEDP] = 100 mg∙L⁻¹.

At E_corr [V vs. SCE], the addition of the inhibitor generated an increase in R_p values. This increase was observed at concentrations of 30 mg∙L⁻¹ and 50 mg∙L⁻¹ and is associated to the adsorption of the molecule on the material surface [39]. There is also a decrease in C_dl values, which may be related to a reduction in the

dielectric constant and/or an increase in the thickness of the electrical double layer. The approximation of parameter n close to 1.0 indicates that the electrical double layer formed on the metal surface resembles a pure capacitor [47].

At 0.1 [V vs. SCE], an increase in charge transfer resistance values (R_p-values) up to a concentration of 30 mg∙L⁻¹ is observed, reaching a value of 9.06 × 10³ Ω cm² (and n_E = 32.4%). This fact may be related to the presence of Ni in the chemical composition of AISI 304 stainless steel as responsible for the repassivation process of regions of the ruptured protective film. A higher adsorption of the inhibitor on the surface of the steel at concentration of 50 mg∙L⁻¹ HEDP + 10 mg∙L⁻¹ Ca²⁺ is confirmed by the decrease in CPE, C_dl, and an increase in n at E_corr [V vs. SCE] which means a reduction of the exposed steel area and consequently a thicker electrical double layer [9]. The destabilization of the film is sustained by the increase of the CPE and C_dl value at 0.1 [V vs. SCE].

The non-contribution of the protective film formation (−0.3 [V vs. SCE]) in the presence of zinc is confirmed by the increase in C_dl and the decrease in R_p values at E_corr [V vs. SCE], there is a decrease in C_dl and an increase in parameter n at concentrations of 10 and 20 mg∙L⁻¹ confirming what was observed in the PDP results (Figure 1(c)). A decrease in C_dl-values was also observed by Felhósi et al. [48], indicating formation of protective film on the metal surface. Film stabilization is supported by a more capacitive behavior due to an increase in the value of n reaching the value of 0.880 (0.1 [V vs. SCE]). In the same potential (0.1 [V vs. SCE]) but the presence of 20 mg∙L⁻¹ of Zn²⁺, a higher R_p value was obtained showing that a protective film consisting of Zn(OH)₂ occurred on the metal/solution interface making to harder pit development [49]. Through analyzing the parameters obtained in the three distinct potentials under study, possible adsorption of Mg(OH)₂ in the cathodic region is observed due to a slight lowering of C_dl. The characteristic of Mg to promote the stabilization of the protective film is confirmed by decrease in C_dl-values and an increase of parameter n for the addition of 10 mg∙L⁻¹ at 0.1 [V vs. SCE]. This fact is linked to the substitution of molecules of water adsorbed on the metal surface by inhibitory molecules, suggesting an increasing thickness of the electrical double layer and reducing the active area of the AISI 304 stainless steel [50] [51].

Figure6 shows the influence of the addition of Ca, Zn, and Mg elements in a solution containing 50 mg∙L⁻¹ HEDP on the AISI 304 stainless steel surface after open circuit potential measurements. It is observed that in the absence of divalent cations, the deposition of NaCl crystals on the metal surface was verified and the corrosion product is justified by the presence of Fe and Cl in the EDS spectra (FigureS5 in the supplementary material) and the elemental mapping (FigureS6 in the supplementary material). Fe²⁺ ions from the oxidation reaction (Equation 12) reacts with chloride ions (Cl⁻) present in the medium and forms FeCl_2(s) as shown in equation 13. The formation of this solid in aqueous solution

favors the reduction of the solution’s pH providing acceleration of the corrosive process [52]. The product formed around the pit is composed of Fe(OH)₂ (Equation (14)) and the product formed inside the pit is composed of FeCl₂ [53]. However, the inhibitor adsorption is observed on the metal surface due to the presence of Fe and C (FigureS5 and FigureS6 in the supplementary material) [54], indicating that possibly there was a decrease in the rate of oxygen reduction and/or iron dissolution reactions.

Fe ( s ) ⇄ Fe 2 + ( aq ) + 2e − (12)

Fe 2 + ( aq ) + 2Cl − ( aq ) ⇄ FeCl 2 ( s ) (13)

FeCl 2 ( s ) + 2H 2 O ( l ) ⇄ Fe ( OH ) 2 ( s ) + 2H + ( aq ) + 2Cl − ( aq ) (14)

EDS analysis of the samples immersed in a solution containing the divalent cations showed that the presence of Cl⁻ species was not verified, suggesting that the inhibitor favored a barrier for chloride ion penetrations (FigureS6(b), FigureS7(b), and FigureS8(b) in the supplementary material). The non-stabilizing characteristic of the protective film, guaranteed by the presence of Ca²⁺ cations, is justified by a lower intensity signal from C in the EDS spectra (FigureS6(a) in the supplementary material). For the presence of Zn²⁺, a signal from C similar to the presence of 50 mg∙L⁻¹ HEDP was found (FigureS7(a) in the supplementary material). A higher inhibitory behavior on film stabilization with the presence of Mg²⁺ is supported by the presence of a higher intensity signal from C (FigureS8(a) in the supplementary material), suggesting the formation of a more homogeneous barrier with greater protective features against corrosive attacks.

Table 2 shows the corrosion rate (C_R), surface coverage, and inhibitor efficiency (η_m). From the results obtained it is clear that the efficiency of the inhibitor is increased with the addition of divalent cations, corroborated with the results obtained by electrochemical tests (PDP and EIS data). The presence of Zn²⁺ favored a maximum efficiency (η_m = 85.2%) followed by Mg²⁺ (η_m = 70.4%). This result is in agreement with that observed in the EIS test, where at the E_corr in the presence of Zn²⁺ culminated in higher resistance to the corrosive process. A higher weight loss value obtained by the addition of Ca²⁺ implies that this cation is not responsible for the stabilization of the protective film. Comparing the

efficiency values obtained in the EIS technique (Table 1) and by weight loss (Table 2) a significant difference in the values is observed. Lower values found in the EIS-results may be related to the presence of iron oxide on the metal surface, which it could not observe in the weight loss because the samples were subjected to pickling treatment.