New Inhibitor Based on Hydrolyzed Keratin Peptides for Stainless Steel Corrosion in Physiological Serum: An Electrochemical and Thermodynamic Study

Reducing the impact of some biological fluids on bioimplants involves the control of surface characteristics by modeling the interface architecture and assembling ecofriendly thin films to retard corrosion. Therefore, a mixture of hydrolyzed keratin peptides (HKER) was investigated as a corrosion inhibitor for 304L stainless steel (SS) in physiological serum (PS), using electrochemical measurements associated with optical microscopy and atomic force microscopy (AFM). The tests, performed for various concentrations of the inhibitor at different temperatures, showed that the inhibition efficiency (IE) decreased with a rise in temperature and proportionally increased with the HKER concentration, reaching its maximum level, around 88%, at 25 °C, with a concentration of 40 g L−1 HKER in physiological serum. The experimental data best fitted the El-Awady adsorption model. The activation parameters (Ea, ∆Ha and ∆Sa) and the adsorption ones (∆Gads0, ∆Hads, ∆Sads) have highlighted a mixed action mechanism of HKER, revealing that physisorption prevails over chemisorption. AFM parameters, such as the average roughness (Ra), root-mean-square roughness (Rq) and maximum peak-to-valley height (Rp−v), confirmed HKER adsorption, indicating that a smoother surface of the 304L stainless steel was obtained when immersed in a PS-containing inhibitor, compared to the surface designed in blank solution, due to the development of a protective layer on the alloy surface.


Introduction
Numerous ways of reducing corrosion effects that induce changes in the characteristics and architecture of metal surfaces have been approached.Thus, the assembly of some protective coatings at the metal/environment interface, through the adsorption of natural or synthetic polymers on the metal surface, leads to the delay/blocking of corrosive processes.The polymer inhibitor action mechanism consists of the physical, chemical or mixed adsorption (covering both features) of macromolecules possessing numerous active centers.These determine the polymer's ability to interact with the metal surface, forming protective films and, thus, blocking the effects of metallic oxidation and corrosion processes, respectively [1][2][3].
The polymer inhibition efficiency depends on the coating uniformity and stability conferred by its nucleophilic character, involving the macromolecule's ability to donate electrons, the metal surface morphology, environmental composition and pH [1,4].
Both electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization were performed, using a standard electrochemical cell with three electrodes coupled to a potentiostat/galvanostat VoltaLab 40 (Radiometer Analytical SAS, Lyon, France) with Volta-Master 4 software (version 7.8.26338.3)(corrosion option), which allows the simultaneous evaluation of corrosion current density and corrosion rate (potentio-gravimetric method).The software specification indicates that the standards for electrochemical measurements are the ASTM-G3 [30] and ASTM-G5 [31] and CNC ASTM corrosion cell guidelines.
The working electrode was composed of a 304L stainless steel plate with an area of 1.0 cm 2 ; the auxiliary electrode was made from a platinum plate (with an area of 1.0 cm 2 ).The Ag/AgCl electrode was used as a reference.Before testing, the stainless steel plates were mechanically polished with emery paper, ultrasonically cleaned, degreased with acetone and dried in warm air.Additionally, a thermostatic heating device was used.The environment temperature from the electrochemical cell was continuously controlled with a specific thermometer.The electrochemical assembly was also reported in our previous studies [5][6][7][8]32].

Electrochemical Impedance Spectroscopy (EIS)
The electrochemical impedance spectroscopy analysis was carried out, at open circuit potential, after ten minutes from immersing the electrodes in the corrosive environment, in the frequency range of 10 5 Hz and 10 −1 Hz, with an AC perturbation signal of 10 mV.The Nyquist and Bode diagrams were recorded at temperatures of 25 • C and 45 • C, respectively, for 304L stainless steel (SS) immersed in physiological serum blank solution (SS/PS) and in physiological serum containing 30 mg L −1 inhibitor (SS/PS/30 mg L −1 HKER) and, respectively, 40 mg L −1 (SS/PS/40 mg L −1 HKER).

Potentiodynamic Polarization (PDP)
The potentiodynamic polarization analysis was carried out after EIS for the same solutions and temperatures, with a potential scan rate of 1.0 mV s −1 , in a potential range from −1.0 V to 1.0 V.The semi-logarithmic potentiodynamic curves were recorded across the entire potential range.The Tafel diagrams were processed in the interest area where the steel is active, namely, in the potential range of ±200 mV with respect to the corrosion potential values.In addition, to calculate the thermodynamic parameters of activation and adsorption, the corrosion rates were determined using the potentio-gravimetric method, in the potential range where the stainless steel is active, mentioned above, at four temperatures: 25 • C, 35 • C, 45 • C and 55 • C. SS was successively immersed in PS blank solution and PS containing the following HKER concentrations: 10 mg L −1 , 15 mg L −1 , 20 mg L −1 , 25 mg L −1 , 30 mg L −1 , 35 mg L −1 and 40 mg L −1 , further denoted: SS/PS (blank solution); SS/PS/10 mg L −1 HKER; SS/PS/15 mg L −1 HKER; SS/PS/20 mg L −1 HKER; SS/PS/25 mg L −1 HKER; SS/PS/30 mg L −1 HKER; SS/PS/35 mg L −1 HKER; SS/PS/40 mg L −1 HKER.Four sets of samples were prepared (one set for each temperature); each set contained eight plates made from 304L stainless steel, with an active area of 1.0 cm 2 ; the stages of processing, cleaning and drying were carried out; for each sample, the temperature was fixed in the corrosive environment; after 10 min of immersion, linear potentiometry with the potential scan rate of 1.0 mV s −1 .This was applied within a restricted potential range of ±500 mV with respect to the OCP; the potentiodynamic curves were processed as semi-logarithmic curves within the potential range of ± 200 mV on both sides of the corrosion potential; the software option for the calculation of corrosion parameters was accessed, and the corrosion rate (CR), expressed in µm year −1 , was revealed.

Surface Characterization
Optical microscopy and atomic force microscopy (AFM) were used to examine the 304L stainless steel surface morphology before and after corrosion in PS, both with and without HKER.

Optical Microscopy
The optical microscopy images were acquired for the 304L stainless steel samples before corrosion (control sample-standard) and after the potentiodynamic polarization performed at 25 • C and 45 • C, respectively, as follows: SS corroded in PS without inhibitor; SS corroded in PS containing 30 mg L −1 HKER; SS corroded in PS containing 40 mg L −1 HKER.A metallographic microscope, EUROMEX, with a Canon camera and the included software was used, as reported in our previous studies [7].The following characteristics were used to collect all the examined images: eyepiece magnification power: 10; lens magnification power: 40; magnifying power of the microscope: 400.

Atomic Force Microscopy (AFM)
The surface morphology of the 304L stainless steel before and after electrochemical measurements, performed at 25 • C in PS both in the absence and presence of 30 mg L −1 and 40 mg L −1 HKER, were observed by non-contact mode atomic force microscopy, using the NC-AFM, PARK XE-100 SPM system.The cantilever had a nominal length of 125 mm, a nominal force constant of 40 N/m, and oscillation frequencies in the range of 275-373 kHz.The average roughness (R a ), root-mean-square roughness (R q ) and maximum peak-tovalley height (R p−v ) of the surfaces were estimated over the areas of 45 × 45 µm 2 .The devices were also described in our early studies [6,8].

Open Circuit Potential (OCP)
The open circuit potential variation for 304L stainless steel immersed in physiological serum, both in the absence and presence of HKER, at 25 • C and, respectively, 45 • C is presented in Figure 1.The open circuit potential variation for 304L stainless steel immersed in physiological serum, both in the absence and presence of HKER, at 25 °C and, respectively, 45 °C is presented in Figure 1.In the HKER presence, the potential moves in the positive direction, as its concentration increases, probably due to spontaneous adsorption of HKER molecules on the alloy surface.Therefore, a protective coating that interposes at the metal/environment interface, thus improving the system equilibrium, was formed, with the ionic transfer from the metal surface to the electrolyte and vice versa being delayed.
At 45 °C, in the presence of HKER, the potential stabilizes at more negative values compared to those recorded at 25 °C (Table 1), probably due to the fact that a higher temperature slightly facilitates the desorption process of HKER molecules.In the absence of HKER, at a temperature of 45 °C, the diffusion rate of the chemical species from the solution to the electrode surface increases compared to that at 25 °C, affecting more strongly the balance in the electric double layer and leading to an increase in the Cl − concentration at the steel/electrolyte interface.Therefore, the negative charge at the surface level is higher, inducing a displacement of the potential in the open circuit to a more negative value compared to that recorded at 25 °C.

Electrochemical Impedance Spectroscopy (EIS)
Figures 2 and 3 display the Nyquist and Bode diagrams recorded in the frequency range from 10 5 Hz to 10 −1 Hz.The Nyquist plots obtained for 304L stainless steel immersed In the HKER presence, the potential moves in the positive direction, as its concentration increases, probably due to spontaneous adsorption of HKER molecules on the alloy surface.Therefore, a protective coating that interposes at the metal/environment interface, thus improving the system equilibrium, was formed, with the ionic transfer from the metal surface to the electrolyte and vice versa being delayed.
At 45 • C, in the presence of HKER, the potential stabilizes at more negative values compared to those recorded at 25 • C (Table 1), probably due to the fact that a higher temperature slightly facilitates the desorption process of HKER molecules.In the absence of HKER, at a temperature of 45 • C, the diffusion rate of the chemical species from the solution to the electrode surface increases compared to that at 25 • C, affecting more strongly the balance in the electric double layer and leading to an increase in the Cl − concentration at the steel/electrolyte interface.Therefore, the negative charge at the surface level is higher, inducing a displacement of the potential in the open circuit to a more negative value compared to that recorded at 25 • C.    2a,b.The capacitive loops are easily deviated from a semicircular shape due to surface defects and/or heterogeneities [20, [32][33][34] caused by the randomly agglomeration of chemical species at the metal/electrolyte interface.Moreover, for the same studied system, more extensive capacitive loops were recorded at 25 • C (Figure 2a) compared to those at 45 • C (Figure 2b).It can be observed (Figure 2a,b) that the diameters gradually increase with the inhibitor concentration, and, consequently, larger capacitive loops are highlighted due to the adsorption of an increasing number of HKER molecules on the alloy surface.Therefore, a protective layer that covers more and more extensive zones on the surface is formed, acting as a barrier at the metal/electrolyte interface, delaying corrosion by restricting the transfer of chemical species from the electrode to the electrolyte and vice versa, thus inducing an increase in charge transfer resistance (R ct ).On the other hand, the R ct decreases with the increase in temperature caused by, generally, an increase in the number of active sites (unprotected sample) or the desorption of peptides, leading to the appearance of additional free places on which the corrosion processes can be intensified.Consequently, at the same inhibitor concentration, R ct reaches higher levels at a low temperature, and, at both 25 • C and 45 • C, R ct increases with an increase in the HKER concentration, in agreement with the literature data [32,35].
in physiological serum with and without different concentrations of HKER at 25 °C and 45 °C, respectively, are shown in Figure 2a,b.The capacitive loops are easily deviated from a semicircular shape due to surface defects and/or heterogeneities [20,[32][33][34] caused by the randomly agglomeration of chemical species at the metal/electrolyte interface.Moreover, for the same studied system, more extensive capacitive loops were recorded at 25 °C (Figure 2a) compared to those at 45 °C (Figure 2b).It can be observed (Figure 2a,b) that the diameters gradually increase with the inhibitor concentration, and, consequently, larger capacitive loops are highlighted due to the adsorption of an increasing number of HKER molecules on the alloy surface.Therefore, a protective layer that covers more and more extensive zones on the surface is formed, acting as a barrier at the metal/electrolyte interface, delaying corrosion by restricting the transfer of chemical species from the electrode to the electrolyte and vice versa, thus inducing an increase in charge transfer resistance (Rct).On the other hand, the Rct decreases with the increase in temperature caused by, generally, an increase in the number of active sites (unprotected sample) or the desorption of peptides, leading to the appearance of additional free places on which the corrosion processes can be intensified.Consequently, at the same inhibitor concentration, Rct reaches higher levels at a low temperature, and, at both 25 °C and 45 °C, Rct increases with an increase in the HKER concentration, in agreement with the literature data [32,35].
The Nyquist diagram (Figure 2a,b) was evaluated by fitting the experimental data using the Randles equivalent circuit (inserted in Figure 2a), consisting of the charge transfer resistance (Rct) connected in parallel with the electrical double layer capacitance (Cdl), both of which are linked in series with the solution resistance (Rs).The intersection of the capacitive loop with the real axis at very low frequencies represents (Rct + Rs), and at high frequencies, it corresponds to the electrolyte resistance (Rs) [36][37][38][39].
where  represents the charge-transfer resistance obtained after the corrosion of 304L stainless steel in a physiological serum blank solution; Rct is the charge-transfer resistance of 304L of stainless steel corroded in physiological serum containing various HKER concentrations.
The inhibition efficiency (IE) and electrochemical parameters calculated from EIS are presented in Table 1.
The following conclusions can be deduced from Table 1: (i) Rct increases considerably with the increase in the HKER concentration, both at 25 °C and at 45 °C; (ii) the inhibition efficiency (IE) at 25 °C is higher than that obtained at 45 °C, probably due to the occurence of a more even and coherently organized upper layer, ensuring an effective inactivation of the active surface sites at a lower temperature; (iii) the decrease in Rs and Cdl, can be attributed to the ability of HKER molecules to replace pre-adsorbed molecules of water and/or other ions [32,35], such as chloride anions.
A similar equivalent circuit was used for 304L stainless steel corroded in hydrochloric acid solution, both in the absence and presence of a composite inhibitor based on polyvinyl alcohol and silver nanoparticles [6], when the inhibition efficiency reached the value of 81.7%.In addition, the anticorrosive performance of a vinyl butyral-co-vinyl alcohol-co-vinyl acetate-based copolymer (PVBA) on stainless steel corrosion was investigated in a sodium chloride solution, resulting in a moderate inhibition efficiency of 72 ± 2% and a polarization resistance of 4.52 kΩ cm 2 for SS in an uninhibited solution and of 15.1 kΩ cm 2 in the presence of PVBA.This was determined by fitting the experimental data in a similar equivalent circuit [8].
Analyzing the Bode impedance diagrams (Figure 3a,b), it can be seen that the impedance response at the frequency of 10 −1 Hz (log Freq = −1) follows the same trend as in the Niquist diagram.Thus, for the PS blank solution, logZ has the lowest values: 3.63 at 25 °C and 3.47 at 45 °C, respectively, which gradually increase to 4.53 (25 °C) and 4.21 (45 °C) for an HKER concentration of 40 g L −1 .
Thus, for the impedance (Z), almost similar values to (Rct + Rs) were identified, which confirms the validity of the equivalent circuit used to fit the experimental data [32].The Nyquist diagram (Figure 2a,b) was evaluated by fitting the experimental data using the Randles equivalent circuit (inserted in Figure 2a), consisting of the charge transfer resistance (R ct ) connected in parallel with the electrical double layer capacitance (C dl ), both of which are linked in series with the solution resistance (R s ).
The intersection of the capacitive loop with the real axis at very low frequencies represents (R ct + R s ), and at high frequencies, it corresponds to the electrolyte resistance (R s ) [36][37][38][39].
where R 0 ct represents the charge-transfer resistance obtained after the corrosion of 304L stainless steel in a physiological serum blank solution; R ct is the charge-transfer resistance of 304L of stainless steel corroded in physiological serum containing various HKER concentrations.
The inhibition efficiency (IE) and electrochemical parameters calculated from EIS are presented in Table 1.
The following conclusions can be deduced from Table 1: (i) R ct increases considerably with the increase in the HKER concentration, both at 25 • C and at 45 • C; (ii) the inhibition efficiency (IE) at 25 • C is higher than that obtained at 45 • C, probably due to the occurence of a more even and coherently organized upper layer, ensuring an effective inactivation of the active surface sites at a lower temperature; (iii) the decrease in R s and C dl , can be attributed to the ability of HKER molecules to replace pre-adsorbed molecules of water and/or other ions [32,35], such as chloride anions.
A similar equivalent circuit was used for 304L stainless steel corroded in hydrochloric acid solution, both in the absence and presence of a composite inhibitor based on polyvinyl alcohol and silver nanoparticles [6], when the inhibition efficiency reached the value of 81.7%.In addition, the anticorrosive performance of a vinyl butyral-co-vinyl alcohol-covinyl acetate-based copolymer (PVBA) on stainless steel corrosion was investigated in a sodium chloride solution, resulting in a moderate inhibition efficiency of 72 ± 2% and a polarization resistance of 4.52 kΩ cm 2 for SS in an uninhibited solution and of 15.1 kΩ cm 2 in the presence of PVBA.This was determined by fitting the experimental data in a similar equivalent circuit [8].
Figure 3 shows the Bode impedance diagrams (Figure 3a Thus, for the impedance (Z), almost similar values to (R ct + R s ) were identified, which confirms the validity of the equivalent circuit used to fit the experimental data [32].
From the Bode phase diagrams (Figure 3a',b'), it can be seen that, in the presence of the HKER inhibitor, at 25 • C (Figure 3a'), an extensive phase angle maximum, centered around −79 degrees, was recorded, reaching very close values to that obtained for the physiological serum blank solution.
At 45 • C (Figure 3b'), the HKER presence leads to the phase angle maximum shifting to lower values, from −72 (PS) to around −80 (PS/HKER), more or less hypothetically attributed to the change in the surface film configuration, which can be disturbed by the temperature increase.

Potentiodynamic Polarization
The potentiodynamic polarization was performed on 304L stainless steel electrode in PS both with and without two HKER concentrations at 25 • C and 45 • C, respectively, in the potential range of −1.0 and 1.0 V.The semi-logarithmic curves were recorded and displayed in Figure 4.Both at 25 • C (Figure 4a) and at 45 • C (Figure 4b), in the presence of HKER, the polarization curves shifted in the positive direction, indicating lower current density areas, and, consequently, the corrosion potential (E corr ) moved to higher values compared to that recorded in the PS blank solution.
the current density suddenly drops, which can be associated with the damage and relocation of the passive surface layer, up to 0.12 V. Beyond 0.12 V, the steel is reactivated by entering the trans-passivation zone.Consequently, in the anodic field, the polarization curves present three distinctive zones: (a) the active area, where the current densities increase directly proportional to the potentials, being accompanied by iron oxidation; (b) the passive zone, where the current density remains approximately constant, and the potential increases; (c) the trans-passive zone, where the steel is reactivated, the anodic dissolution of the iron being followed by the oxidation of nickel and chromium, which are part of the alloy.At both temperatures, the cathodic process is influenced to a lesser extent by HKER presence, indicating that it acts as a mixed inhibitor, predominantly anodic.As shown in Figure 4a, at 25 • C, a characteristic plateau, located at a lower current density, is observed in the presence of 30 mg L −1 HKER, compared to that recorded in the PS blank solution.This is due to the development of a protective surface layer by inhibitor adsorption, providing the substrate with a higher stability compared to that of the layer formed in the PS blank solution.Over 0.3 V, the current density sharply increases, indicating a SS trans-passivation process caused by HKER desorption from its surface.
At a concentration of 40 mg L −1 HKER, beyond 0.3 V, the current density exhibits a slower increase compared to the previous one.This is due to the fact that more active sites on the steel surface are occupied by HKER-adsorbed molecules, and fewer free microzones are formed and, therefore, corrosion processes take place less intensively.At 45 • C (Figure 4b), at a potential of −0.1 V, there is an alteration of the passive plateau, when the current density suddenly drops, which can be associated with the damage and relocation of the passive surface layer, up to 0.12 V. Beyond 0.12 V, the steel is reactivated by entering the trans-passivation zone.Consequently, in the anodic field, the polarization curves present three distinctive zones: (a) the active area, where the current densities increase directly proportional to the potentials, being accompanied by iron oxidation; (b) the passive zone, where the current density remains approximately constant, and the potential increases; (c) the trans-passive zone, where the steel is reactivated, the anodic dissolution of the iron being followed by the oxidation of nickel and chromium, which are part of the alloy.At both temperatures, the cathodic process is influenced to a lesser extent by HKER presence, indicating that it acts as a mixed inhibitor, predominantly anodic.
In order to elucidate the HKER effect on 304L stainless steel corrosion, taking into consideration its susceptibility zone in physiological serum, the semi-logarithmic polarization curves recorded at both 25 • C and 45 • C, respectively, are comparatively presented for the alloy activity zone, where iron preferentially oxidizes (Figure 5).In order to elucidate the HKER effect on 304L stainless steel corrosion, taking into consideration its susceptibility zone in physiological serum, the semi-logarithmic polarization curves recorded at both 25 °C and 45 °C, respectively, are comparatively presented for the alloy activity zone, where iron preferentially oxidizes (Figure 5).It is mentioned that the corrosion current density (icorr) is difficult to determine in the passive or trans-passive zones.For this reason, the change in electrochemical parameters is identified in the active zone for the Tafel segments located at potentials higher than 52 mV than the corrosion potential (Ecorr) for the anodic field and lower than −52 mV for the cathodic one, respectively.
The main similarities between the polarization curves consist of the following: (i) both in the absence and in the presence of the inhibitor, the corrosion potentials (Ecorr) recorded at 45 °C shift in the negative direction compared to those at 25 °C, and the polarization curves are located in higher current areas; (ii) the corrosion current density (icorr) was determined at the intersection of the Tafel segments extrapolated to the corrosion potential, reaching lower values at 25 °C than at 45 °C.
Certain details for the corrosion current density calculation will be provided below.Equation (2) shows that the corrosion process rate is described by the two terms: the anodic and cathodic ones.This allows for the graphical determination of the main corrosion parameter, icorr, by plotting semilogarithmic polarization curves both for the anodic and for the cathodic processes, as shown in Figure 5.In the potential range, where a single partial reaction (anodic or cathodic) predominates, the polarization curve is linear (Tafel line) for pure electron transfer reactions.
According to electrochemical kinetics, to determine the anodic Tafel equation, the conditions η ≥ 52 mV and E >> Ecorr are imposed, when the cathodic term exp − → 0 and Equation (2) become as follows (3): It is mentioned that the corrosion current density (i corr ) is difficult to determine in the passive or trans-passive zones.For this reason, the change in electrochemical parameters is identified in the active zone for the Tafel segments located at potentials higher than 52 mV than the corrosion potential (E corr ) for the anodic field and lower than −52 mV for the cathodic one, respectively.
The main similarities between the polarization curves consist of the following: (i) both in the absence and in the presence of the inhibitor, the corrosion potentials (E corr ) recorded at 45 • C shift in the negative direction compared to those at 25 • C, and the polarization curves are located in higher current areas; (ii) the corrosion current density (i corr ) was determined at the intersection of the Tafel segments extrapolated to the corrosion potential, reaching lower values at 25 • C than at 45 • C.
Certain details for the corrosion current density calculation will be provided below.Equation (2) shows that the corrosion process rate is described by the two terms: the anodic and cathodic ones.This allows for the graphical determination of the main corrosion parameter, i corr , by plotting semilogarithmic polarization curves both for the anodic and for the cathodic processes, as shown in Figure 5.In the potential range, where a single partial reaction (anodic or cathodic) predominates, the polarization curve is linear (Tafel line) for pure electron transfer reactions.
According to electrochemical kinetics, to determine the anodic Tafel equation, the conditions η ≥ 52 mV and E >> E corr are imposed, when the cathodic term exp − zFβη RT → 0 and Equation (2) become as follows (3): For the cathodic domain, when η ≤ −52 mV and E << E corr , the anodic term exp zFαη RT → 0 .Thus, Equation (2) can be written according to Expression (4).
Successively, by logarithmization, applying a correction factor of 2.303, and rearranging the terms, the Tafel equations for both the anodic and cathodic processes are obtained, as the Expressions ( 5) and ( 6) show.
By solving the system of Equations ( 5) and ( 6), the coordinates of the intersection points of the Tafel lines are obtained, from which E corr and logi corr are computed.The anodic (b a ) and cathodic (b c ) Tafel slopes are calculated according to Equations ( 7) and ( 8).
Additionally, the potentio-gravimetric method was simultaneously applied, by converting the corrosion current density (i corr ) to the corrosion rate (CR), according to Equation (9) [7,32].
where z is the number of electrons interchangeable in the process; i corr is the corrosion current density (A m −2 ); A represents iron atomic mass (g mol −1 ); F is Faraday's constant (A h); ρ is iron density (kg m −3 ); 24 and 365 are multiplication factors for hours and days, respectively; 1000 and 10 6 and are the correction factors for the density unit, from kg m −3 to g m −3 , and the transformation factor for the CR unit from meters (m) to µm, respectively.The gravimetric corrosion index, (k g g m −2 h −1 ) will be determined according to the CR values by applying Equation (10) [41].
The polarization resistance (R p ) was determined using the Stern-Geary Equation (11) [42]: where i corr is the corrosion current density (A cm −2 ) and b a and b c are the anodic and cathodic Tafel slopes (V dec −1 ).The electrochemical parameters, namely the corrosion potential (E corr ) and corrosion current density (i corr ), as well as their conversion to corrosion rate (CR) and polarization resistance (R p ), were computed using VoltaMaster 4 software.The electrochemical parameters, k g , CR and IE are listed in Table 2.
The average inhibition efficiency (IE m ) was calculated as the arithmetic mean of the inhibition efficiencies obtained according to Equations ( 12)-( 14).Analyzing the potentiodynamic polarization data displayed in Table 2, the following conclusions are noted: (i) at both temperatures, i corr , k g and CR decreased, while R p and IE increased with an increasing HKER concentration; (ii) inhibition efficiency reached the highest level (IE m = 88.5%) at 25 • C and 40 mg L −1 HKER; (iii) at 45 • C, for the same inhibitor concentration, i corr , k g and CR increases, and R p and IE m decreases compared to the values obtained at 25 • C, probably due to the fact that partial HKER desorption is relatively favored by a temperature increase; at 45 • C, IE m reaches the value of 80.6%, approximately 8% lower than that calculated at 25 • C; (iv) the results are in full agreement with those obtained from the EIS.
where A is the Arrhenius pre-exponential factor, T is the absolute temperature (K) and R is the universal gas constant (8.31 J mol −1 K −1 ).
where T 1 = 25  16) and ( 17) and after rearranging the terms, the activation energy expression (E a ) is obtained (18).
The activation energy varies as follows: The activation energy, E a , of stainless steel immersed in a PS blank solution has a lower value than that determined in PS containing HKER, suggesting a good adsorption of the inhibitor [47] on the alloy surface.However, it does not reach the required threshold of 80 kJ mol −1 , which involves chemical adsorption [47].It has also been reported that a higher E a value in the presence of an inhibitor, compared to that of the blank solution, usually indicates physisorption [42,48].Consequently, HKER acts through a physical adsorption mechanism or through a mixed mechanism, where physisorption prevails over chemisorption.
To confirm the activation energy evolution, the corrosion rate was determined using the potentio-gravimetric method under similar conditions to those previously applied, for various HKER concentrations, such as 10 mg L −1 ; 15 mg L −1 ; 20 mg L −1 ; 25 mg L −1 ; 30 mg L −1 ; 35 mg L −1 ; 40 mg L −1 , and at four temperatures, namely, 25  3.As can be seen, the corrosion rate decreases with an increasing inhibitor concentration and a decrease of temperature.Thus, to determine the activation energy from Equation ( 8), lnk g = f (1/T) was plotted, obtaining straight lines with slopes of −E a /R, and the intersection with the y-axis representing lnA, the linearity coefficient R 2 being close to unity.
Figure 6 shows the Arrhenius diagram and the equations related to the straight lines drawn for the HKER studied concentrations.By deriving the equations inserted in Figure 6, the slope (dy/dx) equal to −Ea/R is obtained, from which E a , listed in Table 4, is determined from Equation (19).
Polymers 2024, 16, x FOR PEER REVIEW 13 of 25 Inspecting the data from Table 4, it can be seen that Ea gradually increases with an increased inhibitor concentration, starting with 25 mg L −1 HKER in physiological serum.The HKER concentrationʹs impact on Ea values indicates that a complex compound has been formed between the inhibitor molecules and cations from the stainless steel surface [48].At concentrations lower than 25 mg L −1 HKER, the activation energy reached values almost similar to those obtained for stainless steel corroded in a physiological serum  Inspecting the data from Table 4, it can be seen that E a gradually increases with an increased inhibitor concentration, starting with 25 mg L −1 HKER in physiological serum.The HKER concentration's impact on E a values indicates that a complex compound has been formed between the inhibitor molecules and cations from the stainless steel surface [48].At concentrations lower than 25 mg L −1 HKER, the activation energy reached values almost similar to those obtained for stainless steel corroded in a physiological serum blank solution.Thus, the same energy barrier intervenes in the corrosion process, suggesting that an insufficient HKER concentration leads to the occurrence of numerous active surface sites on which the corrosion process similarly continues, as in the physiological serum blank solution.
On the other hand, the Arrhenius pre-exponential factor (A) progressively decreases as the HKER concentration increases, reaching the lowest value for the SS/PS/20 mg L −1 HKER system.At HKER concentrations higher than 20 mg L −1 , the Arrhenius factor (A) significantly rises, suggesting an enhancement in the frequency of collisions between the inhibitor molecules and the alloy surface and, therefore, an increased number of adsorbed water molecules are replaced by HKER molecules.
Moreover, for an E a graphically calculated (Figure 6), values close to those determined from Equation (18) were obtained, for inhibitor concentrations of 30 mg L −1 and 40 mg L −1 , showing the Arrhenius model's validity applied on corrosion inhibition of 304L stainless steel in PS, both in the absence and presence of the HKER inhibitor.
As an alternative to the Arrhenius model, the transition-state equation will be applied for HKER concentrations varying from 25 mg L −1 to 40 mg L −1 .The linearized form of the transition-state equation is given by Expression (20) [42,[47][48][49]: where ∆H a (kJ mol −1 ) is the enthalpy of activation and ∆S a (J mol −1 K −1 ) is the entropy of activation, respectively; k g is the corrosion rate, expressed as the gravimetric corrosion index, h is Planck's constant, 6.626 × 10 −34 J s; N is Avogadro's number, 6.023 × 10 23 mol −1 ; T is the absolute temperature (K); R is the universal gas constant (8.31 J mol −1 K −1 ).
Figure 7 shows the plot of ln(k g /T) as a function of 1/T, when straight lines were obtained, with the slopes representing −∆H a /R.From the ln(k g /T)-axis intercepts, [ln(R/h•N) + ∆S a /R] values were calculated and are given in Table 4. Consequently, using the Equations inserted in Figure 7, ∆H a and ∆S a were computed, with relations (21) and (22).
The negative activation entropy (ΔSa) values indicate that, in the determining stage of the reaction rate, the activated complex constitutes more of an association step than a The positive values of ∆H a gradually increase with an increased HKER concentration, from 21.91 kJ mol −1 (SS/PS) to 39.95 (SS/PS/40 mg L −1 HKER), revealing an endothermic dissolution process of stainless steel [42,49].The decline in corrosion rate of 304L stainless steel is mainly controlled by the activation thermodynamic parameters [47].
The negative activation entropy (∆S a ) values indicate that, in the determining stage of the reaction rate, the activated complex constitutes more of an association step than a dissociation one, meaning that, on passing from reactants to the activated complex, a decrease in disorderliness takes place [42,47,48].
The increase of ∆S a from −183.91 J mol −1 K −1 to −143.33 J mol −1 K −1 (from higher to lower negative values), observed with an increased HKER concentration, shows an increase in disorder occurring during HKER adsorption, which is probably due to the replacement of other adsorbed chemical species (water, Cl − ) on the stainless steel surface by the inhibitor molecules [47].

Adsorption Isotherm Approach. Calculation of Adsorption Parameters
First, the degree of 304L stainless steel surface coverage (θ = IE/100) was determined using Equation (23).For concentrations lower than 25 mg L −1 HKER, the corrosion rate decreased with an increase in inhibitor concentration and a decrease in temperature, but the surface coverage degree varied randomly (Table 5) due to an insufficient inhibitor concentration, leading to the formation of a discontinuous and dispersed protective film on the metal surface.At concentrations higher than 25 mg L −1 , θ increased consistently with the inhibitor concentration and decreased with an increase in temperature for the same concentration of HKER.
The most well-known way to quantitatively reproduce an inhibitor's adsorption on the metal surface is represented by fitting the experimental data with a certain suitable adsorption model, obtaining regression coefficients (R 2 ) very close to unity.Therefore, Langmuir and Freundlich adsorption isotherms were firstly applied for the HKER adsorption on the 304L stainless steel surface, using their linearized forms represented by Equations ( 24) and (25), respectively [32,48].
logθ = nlogC + logK ads (25) θ is the surface coverage degree; K ads is the adsorption-desorption equilibrium constant; C represents the inhibitor concentration; n represents a Freundlich factor.The Langmuir and Freundlich plots are displayed in Figure 8.It can be seen that the Langmuir isotherm (Figure 8, Langmuir) is unsuitable for the linearization of the experimental data and implicitly for HKER adsorption on the stainless steel surface.The Freundlich isotherm (Figure 8, Freundlich) does not accurately represent an adsorption model for HKER at temperatures of 298 K and 308 K, respectively, the regression coefficients (R 2 ) being lower than 0.99.In the following, the Temkin isotherm and El-Awady's adsorption model will be comparatively presented using their respective linear expressions, represented by Equation (26) (Temkin) [32,51,52] and Equation ( 27) (El-Awady) [32,53], respectively.
where f represents a positive factor that characterizes the surface heterogeneity [32,50,51,54]; y is the number of water molecules replaced by one inhibitor molecule [53]; Kads is the adsorption-desorption equilibrium constant; C represents the inhibitor concentration.
where f represents a positive factor that characterizes the surface heterogeneity [32,50,51,54]; y is the number of water molecules replaced by one inhibitor molecule [53]; K ads is the adsorption-desorption equilibrium constant; C represents the inhibitor concentration.As can be seen from Equation (26), by plotting θ = f [ln(C−HKER)], straight lines are obtained, with the slope equal to 1/f and the intercept equal to [(1/f )lnK ads ], from which K ads is easily deduced [32,51,52].By analogy, using Equation (27), from the plot of log θ 1−θ = f (logC), straight lines are obtained, with y-slopes and intercept equal to logK.K ads is computed according to Equation (28) [53].Both models are presented in Figure 9.
where f represents a positive factor that characterizes the surface heterogeneity [32,50,51,54]; y is the number of water molecules replaced by one inhibitor molecule [53]; Kads is the adsorption-desorption equilibrium constant; C represents the inhibitor concentration.
As can be seen from Equation (26), by plotting θ = f [ln(C−HKER)], straight lines are obtained, with the slope equal to 1/f and the intercept equal to [(1/f)lnKads], from which Kads is easily deduced [32,51,52].By analogy, using Equation (27), from the plot of  = f(logC), straight lines are obtained, with y-slopes and intercept equal to logK.Kads is computed according to Equation (28) [53].Both models are presented in Figure 9.As shown in Figure 9, the experimental data obey both adsorption models, except at the temperature of 308 K, for which the coefficient R 2 reaches a lower value of 0.9792.As shown in Figure 9, the experimental data obey both adsorption models, except at the temperature of 308 K, for which the coefficient R 2 reaches a lower value of 0.9792.Therefore, the El-Awady model provides a slightly improved fitting of the experimental data, constituting a priority option for HKER adsorption on the steel surface, in relation to the Temkin isotherm.
where R is the universal constant of gases (8.31 J mol −1 K −1 ), T is the temperature and 55.5 is the value of the molar concentration of water in the solution.
In this study, the adsorption-desorption equilibrium constant (K ads ) is expressed in L g −1 .Thus, the concentration of water in the solution must be considered in g L −1 , meaning 55.5 mol × 18.015283 g mol −1 ≈ 1000 g L −1 [56].Equation ( 29) can be written as Equation (30) [56].
∆G o ads = −RTln(1000•K ads ) The values of ∆G o ads and R 2 are listed in Table 6.It is observed that relatively close values were obtained for ∆G o ads , revealing a spontaneous adsorption process, and the physical adsorption prevails over the chemical one.10a From Figure 10b From Figure 10a From Figure 10b 298  10a From Figure 10b From Figure 10a From Figure 10b 298 The adsorption parameters, enthalpy (∆H o ads , kJ mol −1 ) and entropy (∆S o ads , J mol −1 K −1 ), were be calculated using Equations ( 31) and ( 32) [42]: Figure 10a displays the plot of lnK ads = f(1/T) for HKER adsorption on the stainless steel surface.From the slope of the straight line (−∆H o ads /R), adsorption enthalpy (∆H 0 ads ) was calculated, and from the intercept [(∆S o ads /R) − ln(1000)], adsorption entropy was determined.Figure 10b represents the ∆G 0 ads linear variation over temperature, where the slope is associated with −∆S o ads (kJ mol −1 K −1 ) and the intercept with ∆H o ads (kJ mol −1 ).As Table 6 shows, by applying the two methods of calculation, very close values were obtained for the enthalpy and entropy of adsorption, confirming the validity of the proposed adsorption model.Furthermore, from Figure 10a, it can be observed that the adsorption parameters (∆H o ads and ∆S o ads ) were obtained with a lower linearity coefficient (R 2 = 0.9642) when K ads was calculated from El-Awady's model, compared to 0.9965 when K ads was determined from the Temkin isotherm.However, the plot of ∆G 0 ads = f(T) for both models shows a high R 2 value (0.9989).For the determination of K ads , the El-Awady model offers a higher degree of confidence, with R 2 ranging between 0.9889 and 0.9995, compared to the Temkin isotherm when R 2 falls below 0.98.Accordingly, further comments will refer to the results obtained from the El-Awady's adsorption model.
As shown in Table 6, the negative and closely related values for ∆G o ads were obtained, slightly decreasing from −26.5 kJ mol L −1 at 298 K to −28.7 kJ mol L −1 at 328 K, which indicates the stability of the protective layer [47,48] and the spontaneous adsorption of HKER [42,47,48] on the stainless steel surface, involving an endothermic process [47].The values of ∆G 0 ads did not reach the threshold of −40 kJ mol −1 imposed for chemical adsorption and, also, the degree of surface coverage (θ) and the inhibition efficiency (IE), respectively, decreased with an increase in the temperature, indicating that HKER acts through a predominantly physical adsorption mechanism [47].
The negative value of ∆H o ads can suggest either physisorption, chemisorption or a mixture of both types of adsorption [42].The positive value of ∆S o ads can result from the replacement process of water molecules adsorbed on the metal surface with inhibitor molecules, leading to an increase in the disorder of the adsorption process [42].
Another study reported that for three newly synthesized dipeptide Schiff bases formed by the condensation glycyl-l-tyrosine and indole-3-carboxaldehyde (GTI), the same aldehyde and glycyl-glycine (GGI), or glycyl-l-glutamine (GGMI), relatively close values of ∆G o ads were calculated, being investigated as corrosion inhibitors for mild steel in a 1.0 mol L −1 HCl solution.Thus, for GGI, ∆G o ads slightly decreased from −33.26 kJ mol −1 to −36.56 kJ mol −1 in the temperature range between 293 K and 323 K, whereas for the other two, in the same temperature range, similar slight variations of the ∆G o ads values were obtained, from −33.78 kJ mol −1 to −36.28 kJ mol −1 (GGMI) and from to −34.73 kJ mol −1 to −36.6 kJ mol −1 (GTI), respectively.Similar to HKER, the ∆G o ads value slightly declined with increasing temperature [57].The differences between the values are caused by substrate type and the environment composition.A natural polymer (okra pectin) has been reported as a corrosion inhibitor for 304 stainless steel (304 SS) in a 1.0 mol L −1 HCl solution [56].The ∆G o ads values between −23 kJ mol −1 and −24 kJ mol −1 were obtained, in the temperature range from 25 to 50 • C [56].Additionally, for the corrosion inhibition of low-carbon steel using albumin, ∆G o ads reached a value lower than −20 kJ mol −1 , demonstrating the spontaneity of the adsorption process and the predominant mechanism of physisorption [58].Consequently, our study falls within the limits reported by certain authors for adsorption parameters and the HKER action mechanism.

Optical Microscopy
The microscopic images of 304L stainless steel, before and after potentiodynamic polarization, carried out in PS both with and without two concentrations of HKER, are displayed in Figure 11.The control sample surface shows a characteristic morphology of the stainless steel surface before potentiodynamic polarization (Figure 11a).The microscopic images from Figure 11b (SS/PS, 25 • C) and Figure 11c (SS/PS, 45 • C) show that, after the electrochemical measurements, the alloy surface was coated with large corrosion spots, which changed its appearance, this change being more nuanced at 45 • C (Figure 11c) than at 25 • C (Figure 11b).mechanism of physisorption [58].Consequently, our study falls within the limits reported by certain authors for adsorption parameters and the HKER action mechanism.

Optical Microscopy
The microscopic images of 304L stainless steel, before and after potentiodynamic polarization, carried out in PS both with and without two concentrations of HKER, are displayed in Figure 11.The control sample surface shows a characteristic morphology of the stainless steel surface before potentiodynamic polarization (Figure 11a).The microscopic images from Figure 11b (SS/PS, 25 °C) and Figure 11c (SS/PS, 45 °C) show that, after the electrochemical measurements, the alloy surface was coated with large corrosion spots, which changed its appearance, this change being more nuanced at 45 °C (Figure 11c) than at 25 °C (Figure 11b).
Moreover, some fractions of the surface retain the morphology of the standard, indicating that the passive layer formed during electrochemical measurements (Figure 3) is not completely damaged during the trans-passivation range (Figure 3), providing a protective effect to the stainless steel surface, especially at 25 °C (Figure 11b).

Figure 1 .
Figure 1.The OCP diagrams of 304L stainless steel in physiological serum, in the presence and absence of HKER: (a) at 25 °C; (b) at 45 °C.

Figure 1 .
Figure 1.The OCP diagrams of 304L stainless steel in physiological serum, in the presence and absence of HKER: (a) at 25 • C; (b) at 45 • C.

Figure 2 .
Figure 2. Nyquist plots recorded for 304L stainless steel immersed in physiological serum, both in the presence and absence of HKER: (a) at 25 °C; (b) at 45 °C.

3 bFigure 2 .
Figure 2. Nyquist plots recorded for 304L stainless steel immersed in physiological serum, both in the presence and absence of HKER: (a) at 25 • C; (b) at 45 • C.
,b) and Bode phase diagrams (Figure 3a',b') at 25 • C (Figure 3a,a') and 45 • C (Figure 3b,b').Analyzing the Bode impedance diagrams (Figure 3a,b), it can be seen that the impedance response at the frequency of 10 −1 Hz (log Freq = −1) follows the same trend as in the Niquist diagram.Thus, for the PS blank solution, logZ has the lowest values: 3.63 at 25 • C and 3.47 at 45 • C, respectively, which gradually increase to 4.53 (25 • C) and 4.21 (45 • C) for an HKER concentration of 40 g L −1 .

Figure 4 .
Figure 4. Semi-logarithmic curves recorded in a potential range between −1.0 V and 1.0 V for 304L of stainless steel corroded in physiological serum, both in the presence and absence of HKER: (a) at 25 • C; (b) at 45 • C.

Polymers 2024 ,
16, 669 9 of 24 of stainless steel corroded in physiological serum, both in the presence and absence of HKER: (a) at 25 °C; (b) at 45 °C.

Figure 5 .
Figure 5. Semi−logarithmic curves recorded for 304L of stainless steel activity field to calculate corrosion current density in physiological serum, in the presence and absence of HKER, at 25 °C and 45 °C, respectively: (a) in physiological serum in the absence of HKER; (b) in physiological serum containing 30 mg L −1 HKER; (c) in physiological serum containing 40 mg L −1 HKER.

Figure 5 .
Figure 5. Semi−logarithmic curves recorded for 304L of stainless steel activity field to calculate corrosion current density in physiological serum, in the presence and absence of HKER, at 25 • C and 45 • C, respectively: (a) in physiological serum in the absence of HKER; (b) in physiological serum containing 30 mg L −1 HKER; (c) in physiological serum containing 40 mg L −1 HKER.

Figure 6 .
Figure 6.Arrhenius diagram obtained for 304L stainless steel corroded in physiological serum both in the absence and presence of different HKER concentrations.

8 Figure 6 .
Figure 6.Arrhenius diagram obtained for 304L stainless steel corroded in physiological serum both in the absence and presence of different HKER concentrations.

Figure 7 .Table 4 .
Figure 7. Transition state diagram obtained for 304L stainless steel corroded in physiological serum both in the absence and presence of different HKER concentrations.

Figure 7 .
Figure 7. Transition state diagram obtained for 304L stainless steel corroded in physiological serum both in the absence and presence of different HKER concentrations.

Figure 8 .
Figure 8. Langmuir and Freundlich diagrams obtained for HKER adsorption on 304L stainless steel surface physiological serum, at different temperatures.

Figure 9 .
Figure 9. Temkin and El-Awady's models obtained for HKER adsorption on 304L stainless steel surface in physiological serum, at different temperatures.

Figure 9 .
Figure 9. Temkin and El-Awady's models obtained for HKER adsorption on 304L stainless steel surface in physiological serum, at different temperatures.

Figure 10 .
Figure 10.The determination of adsorption parameters (∆H o ads and ∆S o ads ) for 304L stainless steel corroded in physiological serum containing various HKER concentrations, (a) the plot of lnK ads = f(1/T), (b) ∆G 0 ads linear variation over T.

Figure 11 .
Figure 11.Optical microscopy images acquired for 304L stainless steel surface: (a) before corrosion (control sample); (b) after corrosion in PS blank solution, at 25 °C; (c) after corrosion in PS blank solution, at 45 °C; (d) after corrosion in PS containing 30 mg L −1 HKER, at 25 °C; (e) after corrosion, in PS containing 30 mg L −1 HKER, at 45 °C; (f) after corrosion in PS containing 40 mg L −1 HKER, at 25 °C; (g) after corrosion in PS containing 40 mg L −1 HKER, at 45 °C.In Figure11d-g, the microscopic images are completely different compared to those presented above, showing less pronounced disturbances of the surface layer morphology.Figure11e(SS/PS/30 mg L −1 HKER, 45 °C) and Figure11g(SS/PS/40 mg L −1 HKER, 45 °C) display a more damaged appearance of the surface than the corresponding ones at 25 °C (Figure11d,f), highlighting that the increase in temperature causes a slightly desorption of the inhibitor.

Table 1 .
Inhibition efficiency and EIS parameters obtained from EIS for 304L stainless steel immersed in physiological serum with and without HKER at 25 °C and 45 °C, respectively.

Table 1 .
Inhibition efficiency and EIS parameters obtained from EIS for 304L stainless steel immersed in physiological serum with and without HKER at 25 • C and 45 • C, respectively.

Sample OCP/mV vs. Ag/AgCl 45 • C Nyquist Parameters Bode Parameters IE/ % R s / Ω cm 2 R ct / kΩ cm 2 C dl / µF cm −2 log Z/ Ω cm 2 Z/ kΩ cm 2 Phase/ Degrees
Hz to 10 −1 Hz.The Nyquist plots obtained for 304L stainless steel immersed in physiological serum with and without different concentrations of HKER at 25 • C and 45 • C, respectively, are shown in Figure

Table 2 .
Inhibition efficiency, corrosion rate and electrochemical parameters obtained from the potentiodynamic polarization for 304L stainless steel corroded in physiological serum both with and without HKER, at 25 • C and 45 • C, respectively.
• C and T 2 = 45 • C; k g1 and k g2 represent the gravimetric corrosion indices at 25 • C and 45 • C, respectively.By subtracting Equations ( • C, 35 • C, 45 • C and 55 • C. The data are centralized in Table

Table 3 .
Corrosion rate expressed in µm year −1 (CR) and in g m −2 h −1 (k g ) determined by potentiogravimetric method for 304L stainless steel corroded in physiological serum, both in the absence and presence of various HKER concentrations, at 25 • C, 35 • C, 45 • C and 55 • C.

Table 4 .
Activation parameters of 304L stainless steel corrosion in physiological serum, both in the absence and presence of different concentrations of HKER.

Table 5 .
The degree of surface coverage (θ) of 304L stainless steel by HKER adsorption, at different temperatures.

Table 6 .
Adsorption parameters of HKER on 304L stainless steel, obtained from Temkin isotherm and Awady's model in physiological serum in various conditions, at different temperatures./kJ mol −1    /J mol −1 K

Table 6 .
Adsorption parameters of HKER on 304L stainless steel, obtained from Temkin isotherm and Awady's model in physiological serum in various conditions, at different temperatures.