Theoretical and experimental insights into the C-steel aqueous corrosion inhibition at elevated temperatures in 1.0 M HCl via multi-carbonyl Gemini cationic surfactants

: Despite corrosion being an inevitable process, researchers strive to con-trol corrosion. In this study, our goal was to prepare two amido Gemini cationic surfactants, LAPG and MAPG, each with di ﬀ erent alkyl chains and multiple carbonyl groups as rich electronic rich centers. We aimed to evaluate these surfactants as potential corrosion inhibitors for carbon steel (CS) in 1 M HCl at temperatures of 25 – 55 ± 0.1 ° C. In theoretical investigations, DFT parameters and Mont Carlo simulation were run to predict the adsorption a ﬃ nity and reactive sites of the LAPG and MAPG molecules. Their e ﬃ cacy was investigated experimentally considering weight loss and electrochemical techniques. The Tafel polarization revealed that at 0.1 mM of LAPG and MAPG, the corrosion current density ( i corr ) of CS was reduced to the lowest extent (75.56 and 53.82 μ A cm − 2 ) compared to 529.3 μ A cm − 2 in the absence of the inhibitors. EIS data suggests the enhancement of the thickness of the adsorbed layers of the studied compounds from the decrease of the double-layer capacitance C dl values. The Langmuir isotherm explained the adoption phenomena of these


Introduction
Many industrial applications use carbon steel (CS) as the main construction of their process due to its low cost, unique mechanical properties, and easy availability in the fabrication of vessels.Although carbon steel may be used in a variety of engineering fields, including oil and gas transportation, electricity production, desalination, food, and chemical and electrochemical industries, it is easy to be corroded in a variety of aggressive media, especially the acidic environments [1][2][3].Knowing that many processes use acid solutions such as descaling, cleaning, oil well acidification, and petrochemical processes, several techniques have been employed to monitor and inhibit the corrosion processes in these media [4,5].For example, several inhibitors are added in small quantities to slow the internal corrosion of industrial equipment (pipelines, storage tanks, etc.) [6,7].These inhibitors are chemicals that can be physisorbed and/or chemisorbed onto a metal surface, forming a protective barrier layer against metal corrosion in aggressive environments.Corrosion inhibitors are the most feasible mitigation method due to benefits such as low cost, high efficiency, eco-friendly and wide use in various fields.
Surfactants consider kind of organic materials that have two parts of different polarities in the same skeleton [8,9].The unique nature of the surfactant enhances their adsorption at the interface at CS/aggressive medium by constructing a protective film.The surfactant exhibited high corrosion inhibition efficiency, safety, ease of use, and low manufacturing cost [10,11].The hydrophilic portion of the surfactant molecules enhances their adsorption on metallic surfaces, inhibiting their active sites and protecting the surfaces against corrosion [12][13][14][15]; additionally, they reject the polar aqueous phase through aggregating and associating their hydrophobic tails group [16].Gemini surfactants is a kind surfactant with two amphiphilic moieties linked by a spacer group at or near two head groups.This unique structure render them with higher surface activity compared to individual surfactants [17,18].The Gemini surfactant have lower critical micelle concentrations (CMCs) and C 20 , better solubilizing abilities, greater wetting, foaming, and lime-soap dispersing properties, corrosion resistance, and stronger biological activities [19].Due to government and environmental precautions, eco-friendly surfactants will replace the conventional ones, therefore the Gemini surfactant is favorable than traditional one.
Introducing easily cleavable bonds, such as ester and amid bonds, into surfactants is one approach to improve biodegradability.Geo et al., for example, reported the synthesis of Gemini surfactants with an ester bond on the spacer unit based on 1,2-bis-chloroacetoxy-ethane, which had strong foaming and emulsifying properties [20].Surfactants containing ester linkages have been demonstrated to be biodegradable in numerous investigations [21][22][23][24].Many studies have revealed that amide Gemini surfactants are biodegradable and sensitive to chemical/enzymatic hydrolysis [25].Furthermore, the amide group improves the surfactants' physicochemical characteristics and enhances their performance [26].
Herein, we aimed to synthesize organic Gemini cationic surfactant having multiple functional groups that act as electronic rich functional groups for an enhanced corrosion inhibitor.We designated that Gemini cationic surfactants having multi-carbonyl as well as others groups a new surfactant structure for providing higher adsorption centers.Few papers in literature that handled that kind of Gemini cationic surfactant as corrosion inhibitors.We used two Gemini cationic surfactants (LAPG and MAPG) as corrosion inhibitors for CS in a highly acidic medium (1 M HCl) at room and elevated temperatures.We employed density functional theory (DFT) and Monte Carlo (MC) simulation approaches to determine the quantum chemical parameters of several surfactants and predict their adsorption behavior.We then examined the impact of these surfactants on electrochemical kinetics parameters using gravimetric and electrochemical test methods.Additionally, we conducted surface analysis studies using Atomic Force Microscopy (AFM) and X-ray photoelectron spectroscopy (XPS) to further understand the surfactants' effects.The novelty of this work is not only using these surfactants as corrosion inhibitors, which has never been done before, but their inhibition efficiencies increase as the temperature increases, which is an outstanding behavior.This differs from most corrosion inhibitors, whose functionality is based on their adsorption mechanism on metallic surfaces.Also, the thermodynamic parameters for the adsorption of these inhibitors have been calculated and reported.The adsorption was found to be chemical and followed the Langmuir adsorption isotherm.

Chemicals and solutions
1 M of hydrochloric acid was selected as an aggressive medium.It was prepared by diluting a concentrated HCl using bi-distilled water.Two amido Gemini surfactants with the chemical structure C-steel corrosion inhibition in Figure 1 have been formulated as previous work [27].The CS specimens used in our investigation have a composition of 0.2 % C, 0.6 % Mn, 0.05 % S, 0.04 % P, and 0.003 % Si while the rest is Fe.The used CS specimens of a dimension of 60 × 30 × 3 mm 3 were involved in the weight loss measurements.In contrast, the electrochemical measurements were conducted using a cylinder shape steel with 0.5 cm 2 as contacting surface area.

Quantum chemical study
The calculated parameters output from quantum chemical studies of the prepared amido Gemini cationic LAPG & MAPG surfactants predict the inclination of LAPG & MAPG to act as corrosion inhibitors for iron alloy.DMol3 module in Material studio 6.0 software has executed these theoretical studies using GGA with BOP method with a 3.5 DNP basis set as reported in our previous work [28,29].The probability of amido Gemini cationic LAPG & MAPG surfactants to be adsorbed over iron alloy is simulated via the adsorption locator module implemented in Ms6.0 software.Monte Carlo simulation (MC) process of LAPG & MAPG over Fe (110), the most stable plane of iron, in the presence of 500 H 2 O molecules, is running in simulation box 74.47 × 74.47 × 30.05 A. The simulated process options for LAPG & MAPG + 500 H 2 O/Fe (110) annealing were adjusted where the total annealing steps were 105,000 steps (7 cycles and 15,000 steps per cycle), geometry optimization of the whole system was done at smart algorithm with a medium level of convergence (energy 1 × 10 −3 kcal/mol and force 0.5 kcal/mol/A), and the summation method for electrostatic and Van der Waals was atom based with cut off distance 12.5 A.

Weight loss test method (WL)
The corrosion inhibition performance of the two Gemini cationic surfactants-based amido structures (LAPG and LAPG) had been investigated gravimetrically against the CS corrosion in aggressive HCl solution (1.0 M).The weight loss measurements were conducted at four different temperatures 25, 35, 45, and 55 ± 0.1 °C, in a water bath to control the temperature.Before starting each run, all coupon specimens were abraded using different grades of emery papers (400-2000), washed with distilled water, then acetone before drying.Each sample was weighed before and after immersing in the aggressive solution without and with different concentrations of LAPG and LAPG individually for 24 h using a highly precious digital balance.

Electrochemical techniques (ETs)
ETs, including electrochemical impedance spectroscopy (EIS) and potentiodynamic polarization (PDP), were performed via a 3-electrode system using a GAMRY 3000 potentiostat/galvanostat/ZRA (Warminster, PA, USA).For controlling the temperature, the ETs were done in a double-jacketed Pyrex cell attached to a Julabo F12 thermostat (GmbH, Seelbach, Germany).The working electrode is a disc of CS with a 0.5 cm 2 exposed area; a saturated calomel electrode (SCE) and a platinum wire were utilized as a reference and a counter electrode, respectively.The ETs were conducted after 30 min of immersion of the bare steel into 1 M HCl (see Figure S1).EIS measurements were studied in a frequency range of 100 kHz-0.1 Hz with a 10 mV AC amplitude.PDP curves were investigated within a potential window of −0.5 to 0.01 V versus the open circuit potential (OCP) with a scan rate of 0.167 mV/s.The LAPG and MAPG corrosion inhibitors were prepared with varying concentrations of 1 × 10 −6 , 5 × 10 −6 , 1 × 10 −5 , 5 × 10 −5 , and 1 × 10 −4 M in 1 M HCl to study their inhibition effect against CS corrosion.Each test was repeated twice, and the mean values were reported.

Surface analysis (AFM & XPS)
An atomic force microscope (AFM, Asylum Research MFP-3D, Santa Barbara, CA, USA) was used to (i) study the surface topography of CS after 24 h exposure in inhibitor-free HCl, and after LAPG and MAPG optimum concentration addition was added and to (ii) measure the surface roughness.The CS surface treated with 1 × 10 −4 MAPG has been examined using X-ray photoelectron spectroscopy (XPS).XPS was performed using an Al-Kα excitation source and operating at a constant 1486.7 eV.The analyzer energy mode was 10 mA for the target current, 50 eV for the pass energy, and 2.4 nm s −1 for sputtering speed.The angle between the sample and the ion gun was 30°.The uncertainty in binding energy was 0.1 eV C1s peak at 284.6 eV was observed for all the obtained spectra.The spectral simulation for the peaks from experiments was obtained using Kratos Advantage software, where the XPS standard spectral line data were derived from the XPS manual.
3 Results and discussions

Quantum chemical study
The collected snapshots presented in Figure 2 display the most stable distributed atomic structure of amido Gemini cationic LAPG & MAPG surfactants in space (optimized geometry structure), frontier molecular orbitals, electrostatic potential mapping, and electron density distribution over the LAPG & MAPG structures.The electron density distributed over the quaternary nitrogen and bromide atoms in the highest occupied molecular orbitals (HOMO) indicates the probability of LAPG & MAPG adsorption via electron donation to the empty outer orbital of iron (3d), and electrostatic attraction with the charged iron surface make the studied LAPG & MAPG coming closer to the iron surface.Also, the electron cloud distributed over ester, amid, and phenyl groups in the lowest unoccupied molecular orbitals (LUMO) allows the electron back-donation transfer from the outer fulfilled orbitals (4s and 3d) of iron to the antibonding molecular orbital (π*) of LAPG & MAPG.The electron donation and receiving process gives the prepared LAPG & MAPG a high propensity to be preferable corrosion inhibition ability for iron.Electrostatic potential maps for LAPG & MAPG certain the HOMO and LUMO point of view.The regions with red color pointed to high electron density, while the blue one indicates low electron density.These regions (red and blue) are considered adsorption centers.The electron density over the long aliphatic chains gives LAPG & MAPG probability to form a dense and more compacted adsorbed layer over the iron surface [30][31][32].The numerical analysis of DFT parameters based on energy values of HOMO and LUMO calculated according to the following equations and recorded in Table 1: where: energy gap (ΔE gap ), global hardness (η) and softness (σ), electronegativity (χ), electron back-donation (ΔE back-d ), the fraction of transferred electron (ΔN) and Work function (φ) of Fe (110) plan is 4.82 eV [33,34].
According to the data recorded in Table 1, the values of E HOMO , E LUMO , and ΔE gap, for both studied compounds LAPG & MAPG indicate that they may have adsorption propensity compared to the previously published compounds [27].The electron donation and acceptance are related to the E HOMO and E LUMO values, respectively.It can be noticed that E HOMO follows the order MAPG > LAPG.This indicates that MAPG has a high affinity to donate to the empty 3d orbital electron compared to LAPG and, in turn, has a high probability for adsorption affinity over the CS surface.On the other side, MAPG has a lower value (high negative) of E LUMO compared to LAPG, indicating the high acquiring affinity to the liberated electron from fulfilled 3d or/and 4S orbitals of iron also helps the adsorption process perform efficiently via the backdonation process.The adsorption activity of MAPG & LAPG is related to the energy difference between HOMO and LUMO (ΔE gap ).The lower ΔE gap value is, the higher reactivity and tendency of adsorption are.According to the data recorded in Table 1, the adsorption performance of MAPG over CS is more energetically favored than LAPG.Also, the adsorption probability of studied compounds can be predicted from softness and hardness points of view.Soft molecules have a high reactivity tendency (low ΔE gap ) and, in turn, a high electron-donating ability.The MAPG and LAPG are soft molecules relative to the published molecules, but MAPG is more reactive than LAPG [35].The numerical value of the dipole moment parameter gives insight into the probability of tested compounds accumulating and forming a protective layer  shielding the metallic surface from the offensive action of corrosive media.As we reported elsewhere, lowering dipole moment values encourages the accumulation of the tested molecules over the CS surface [36].So, MAPG has an accumulation affinity higher than LAPG.This predicts the adsorption superiority of MAPG over the LAPG and is in touch with the previous discussion of quantum descriptors.An adsorption phenomenon involves sharing electrons between synthesized compounds and metal surfaces.This can be discussed based on ΔN and E back−donat.

← values recorded in
Table 1 according to Gomez theory [37].Based on ΔN value, the electrons can transfer to the metal in case of ΔN > 0 (positive) or vice versa when ΔN < 0 (negative) [34].The electron transfer process is related to the value of electronegativity (χ); the lower the electronegativity, the higher the electron transfer.The data in Table 1 confirm the capabilities of both compounds to transfer electrons to the CS surface.The MAPG has a higher positive ΔN value than LAPG, which will support the corrosion inhibition ranking prospected.Also, E back−donat.

Monte Carlo simulations (MCs)
MC simulation has a significant role in simplifying and visualizing the adsorption of the under-studied compounds over the most stable plan of ion crystal Fe (110).This helps in predicting the inhibition affinity of specific compounds.The optimized geometric configurations and the orientations of the under-investigation compounds over Fe (110) are obtained from the simulated annealing process at certain adjusted conditions, as represented in Figure 3.The inspection of Figure 3(a) and (b) reflects the capabilities of both compounds to be adsorbed on the plane of Fe (110) because their active adsorption centers (HOMO & LUMO) are oriented flat over (as seen from top views) and parallel to (from side views) the Fe (110) surface.These orientations make the donor-acceptor interaction take place efficiently, and the exposed metallic surface area becomes most diminutive as possible.The output calculated data of MC recorded in Table 2 can be summarized as follow: i.The large negative adsorption energy values for the tested compounds with Fe (110) predict their strong and spontaneous adsorption affinity [39].ii.The absolute values of E ads for MAPG & LAPG suggest that MAPG has more favorable adsorption efficacy than LAPG.iii.The tested cationic compounds have an affinity to replace the adsorption water molecules from the CS surface and form a stable barrier adsorption film saving the CS from the severity of surrounding media as their E ads values are higher than water adsorption energy [37,40].
It is evident that DFT and MC indices recorded in Tables 1 and 2 suggest the understudied cationic surfactant compounds (MAPG & LAPG) have a high probability of being adsorbed firmly over iron surface via hetero atoms of ester amid and quaternary ammonium salt groups and π-electrons of phenyl groups.And this makes the prepared compounds have high potential applications as corrosion inhibitors.

Gravimetric analysis
The corrosion inhibition efficiency (η w ) & the surface coverage (θ) conducted by the synthesized amido Gemini cationic (LAPG & MAPG) surfactant-inhibitors have been investigated by weight loss technique according to Equations ( 7) and ( 8) [41]: where CR and CR o refer to the corrosion rate of CS immersed in the aggressive 1.0 M HCl with different concentrations of the LAPG and MAPG and without, respectively.The t = 24 h as immersion time.The CR assigned, based on Equation ( 8), W and S to steel loss in mg and the exposed steel surface area in cm 2 .Table 3 shows the η w and CR of steel corrosion in the absence and presence of different concentrations of the LAPG and MAPG amido Gemini surfactant-inhibitors at 25, 35, 45, & 55 °C.As the inhibitor concentration increases, the weight loss of the CS specimen also decreases, confirming the steel protection.Reducing weight loss and, subsequently, the CR refers to adsorption of the prepared amido Gemini surfactant on surfactants on the steel surface.The adsorption of LAPG and MAPG on the surface leads to forming of a protective layer that isolates the steel surface and the aggressive solution.Increasing the inhibitor concentration led to increasing the amount of the LAPG and MAPG adsorbed on the steel surface, hence increasing the θ and so enhancing the steel protection η w .Additionally, the weight loss results in Table 3 clarify the potential impact of the hydrophobic surfactant tail on the inhibition efficiency performance.
Increasing the hydrophobic tail length led to an increase in steel inhibition efficiency.For an instant, the ղ w of LAPG, and MAPG at 25 °C, are equal to 88.01 and 90.1 % at the concentration of 1 × 10 −4 M, respectively Table 3.As clarified previously, their adsorption affinity on the surfaces increases with the elongation of the surfactant tail [9,42].Subsequently, the surfactant tail controls the adsorption of the surfactant inhibitor on the surface, increasing the surface coverage & inhibition efficiency [43,44].Increasing the solution temperature that contains the synthesized LAPG, and MAPG Surfactant inhibitor, the corresponding η w increases as clarified from the experimental results depicted in the Table 3.The behavior of increasing η w of the LAPG, and MAPG solution with raising the solution temperature reflects their chemical adsorption on the steel surface.Increasing solution temperature induces some chemical structure change that promotes electron densities of the active centers, subsequently enhancing the adsorption on the corroded steel surface [45][46][47].
The two positively ammonium-charged centers of the LAPG and MAPG amido Gemini cationic surfactant electrostatically interact with the negative center generated on the steel surface dipped in the aggressive acidic medium [48].The Arrhenius-type plot was conducted according to Equation (9) to determine the apparent activation energy (E a ) to elucidate the corrosion kinetics.
Weight loss (mg) where the k corresponds to the corrosion rate, A is the Arrhenius constant, T is Kelvin temperature, and R corresponds to the gas constant [49].The synthesized amido Gemini cationic surfactants LAPG and MAPG followed the Arrhenius plot, as shown in Figure 4a, with high regression coefficient.The E a was extracted from the Arrhenius line slope that equals (−E a /R).The E a inspected in Table 4 in the presence of the synthesized amido Gemini cationic surfactants LAPG and MAPG are lower than in their absence (Blank solution), which reflects the chemisorption nature of the synthesized LAPG and MAPG inhibitors on the carbon steel surface [49,50].The activation entropy (ΔS*) and Enthalpy (ΔH*) were extracted from transition state theory (Equation ( 10)) [51] ln

Figure 4b, with an intercept of log( R N
) and a slope of ( ΔH * R ), that is used for calculating the corresponding ΔS* and ΔH*, respectively, as depicted in Table 4.The calculated positive values of ΔH* refer to the endothermic nature of the corrosion process [52].The determined ΔS* values in the presence and LAPG, and MAPG inhibitors, Table 4, are negative, suggesting that the activated complex (rate-determining step) is an association rather than dissociation, i.e., more order conducted ongoing from reactant to activate complex [53][54][55].
To investigate the adsorption behavior of the synthesized LAPG, and MAPG surfactants on the steel surface under the examined corrosion conditions, we performed several adsorption isotherms based on the θ values obtained from the weight loss experiment, such as Freundlich and Temkin (see Figure S2, Tables S1 and S2) while, Langmuir isotherm was the more fitted one.Our results, as shown in Table 5 and Figure 5, indicate that the Langmuir isotherm (Equation ( 11)) accurately describes the adsorption of the investigated inhibitors, with a high correlation coefficient (R 2 ) ∼ 0.999.
The K ads (adsorption equilibrium constant) values have been extracted (Table 5) from the intercept of the Langmuir curve, which reflects the strong adsorption of all synthesized LAPG and MAPG surfactant inhibitors on the steel surfaces.We observed increasing the K ads as a function of increasing the solution temperature and the length of the surfactant tail, which matches their inhibition performance depicted in Table 3.This trend refers to the chemical adsorption mechanism of the LAPG and MAPG surfactant on the surface of the CS [56,57].The adsorption-free energy change (ΔG o ads ) regarding the prepared amido Gemini cationic LAPG and MAPG surfactant inhibitors was calculated according to Gibbs equation (Equation ( 12)) [58,59]: The adsorption heat change (ΔH o ads ) is extracted from the slope of Van't Hoff equation (Equation ( 13)), R is gas constant, and T is the temperature in Kelvin [60]:  The standard adsorption entropy (ΔS o ads ) is calculated based on Equation ( 14) [52,61]: ΔG ads °= ΔH ads °− TΔS ads °( 14) The thermodynamic parameters ΔG ads °, ΔH ads °, and ΔS ads °of LAPG and MAPG inhibitors were depicted in Table 5.The calculated ΔG°a ds values range from −43.55 to −49.78 kJ mol −1 , which give insight into the affinity of the synthesized LAPG, and MAPG surfactant to adsorb chemically on the steel surface under the examined condition of acidity and temperature conditions.The chemical adsorption by the LAPG and MAPG surfactant involves electron transfer from their active centers to the vacant 3d-orbital of iron under inspected temperatures 25-70 °C with, generating a coordination bond [62].The positive values of the ΔH o ads describe the endothermic nature of the process of LAPG and MAPG surfactant adsorption.The positive sign of ΔS o ads values (Table 5) reflects more disorder due to replacing more than one H 2 O molecule due to the LAPG and MAPG surfactant adsorption on CS surface [63].
The amido Gemini LAPG and MAPG surfactants under investigation contain numerous active adsorption centers that facilitate their adsorption onto the steel surface and promote their effectiveness as a corrosion inhibitor.Various functional groups, such as oxygen, nitrogen, C-O, C=C, C=O, and an aromatic structure, have been identified to enhance the adsorption process.The positively charged ammonium group can electrostatically interact with the cathodic sites that form on the surface of mild steel exposed to corrosive solutions.Additionally, the two hydrophobic tails of the synthesized inhibitors form a protective layer that insulates the contact between the steel surface and the aggressive medium.

Electrochemical impedance spectroscopy (EIS)
EIS technique has been utilized to investigate the electrode/electrolyte interactions and estimate their different corrosion mechanisms [64].Figure 7 represents a simple one-time constant equivalent circuit commonly used to explain a uniform corrosion hypothesis.The elements of equivalent circuits are solution-resistant (R s ), charge transfer resistance (R ct ) and constant phase element of charge transfer process (CPE).It is worth mentioning that the double layer between the charged metal surface and the solution concerns an electrical capacitor.The capacitance of the double layer (C dl ) replaced by CPE.Because the non-ideal behavior of capacitance can be attributed to the roughness of the electrode interface or/and a non-uniform surface coverage or current distribution or corrosion rate.
The CPE is derived from the equation below [65,66]: where Z Q is the impedance for CPE (Ω cm −2 ); Y 0 is the CPE constant as it is equal to the admittance of the system at unity (µs n Ω −1 cm −2 ); j is equal to (−1) 1/2 , w is the angular frequency (rad s −1 ), and the value of n ranges between 0 and 1.When n = 1, the CPE becomes equivalent to an ideal capacitor, and when n = 0, the CPE becomes equivalent to a resistor.The double-layer capacitance (C dl ) can be calculated using the equation below: Figure 6 represents Nyquist and bode plots to display the behavior of CS immersed in acidic solutions treated and untreated with selected concentrations from the prepared corrosion inhibitors (LAPG, MAPG) at room temperature.The inspection of the Nyquist plot in Figure 6(a) and (c) reflects that the addition of the different inhibitors has no significant effect on the semicircular shape of EIS response curves except their diameter values.This means that the CS corrosion reaction mechanism is still unchanged and controlled by the charge transfer process [67,68].The diameter of the capacitive loop in the Nyquist diagram is incremented with the inhibitors' addition, the absolute value of impedance Z mod at lower frequency region in bode plot is raised to higher value and the phase angle at intermediate frequency area is shifted toward the more negative value.These observations may be related to the inhibition action of LAPG and MAPG compounds for CS corrosion, as their structures are enriched with the adsorption centers [69].It can be observed that the capacitive loop looks like the depressed semicircle, and the calculated line slope of the Bode plot and phase angle values at the intermediate frequency region deviate from −1 to −90°, respectively, as reported in Table 6.This can be referred to as the frequency dispersion effect and the non-homogenous CS surface [70].
The electrochemical Impedance fitted parameters (R s , R ct , n, Y o , C dl , CPE) and the calculated surface coverage (θ) and inhibition efficiency IE EIS % using equations are listed in Table 7.
Table : The slopes of the Bode impedance magnitude plots and the maximum phase angles (S) at definite frequency.IE EIS % = θ × 100 (18) Table 7 shows that increasing the concentration of the different corrosion inhibitors enhances the numerical values of R ct while suppressing the C dl values.These may be due to the adsorption action of high electron density groups (oxygen atoms, quaternary nitrogen atoms, and amide groups) found in LAPG and MAPG and the long chain alkyl groups that increase the stability of adsorption film formed over CS.Adsorption of the synthesized compounds over the CS surface decreases the metal substrate's direct contact with the offensive action of HCl by replacing the adsorbed water and aggressive anions that lead to a decrease in the CPE values and increase the thickness of protective layer formed according to Helmholtz model.
where δ ads is the adsorbed layer thickness of the corrosion inhibitor, ε o is the permittivity of air, ε is the local dielectric constant, and A is the electrode surface area.This equation shows that C dl is inversely proportional to δ ads i.e., the decrease of the C dl value is attributed to the growth of the adsorbed film of corrosion inhibitor as its concentration increases in solution.It is evident from Table 7, n values are in the range of 0.723-0.892,representative non-ideal capacitive actions.Also, in the blank solution C dl value of CS is more than that for an inhibited solution.The increment in corrosion inhibitors concentration reduces C dl value.The decline in C dl causes the regular replacements of water molecules via inhibitor molecule adsorption at CS/solution interface.The EIS reported parameters ended the ranking of the understudied cationic surfactants as LAPG < MAPG that coheres to the WL order.
Table : EIS parameters for the corrosion of carbon steel in . M HCl in the absence and presence of varied concentrations of LAPG, and MAPG surfactants at room temperature.

Potentiodynamic polarization (PDP)
Figure 8 displays the electrochemical cathodic/anodic polarization of CS immersed in 1 M HCl in the absence and the presence of different concentrations of LAPG and MAPG corrosion inhibitors, respectively, under static conditions at room temperature.
Figure 8 shows that LAPG and MAPG corrosion inhibitors have no significant effect on the reaction mechanism of CS versus 1.0 M HCl, which saves the blank counterpart's polarization curves.The addition of LAPG and MAPG forces the CS polarization curve parts (cathodic and anodic) to be shifted toward the region of low corrosion rate compared to that of blank one, which indicates the inhibition ability of the prepared compounds (LAPG and MAPG) [71].
The extrapolation of i-v curves at Tafel regions gives rise to parameters used to evaluate the tested corrosion inhibitors and predict the reaction mechanism at the CS/HCl interface.These parameters: corrosion potential (E corr ), corrosion current density (i corr ), Tafel slopes (β c and β a ), polarization resistance (R P ) are collected in Table 8.The polarization resistance can be derived using the Stern-Geary equation Assuming that the whole surface of the CS is uniformly attacked, and no localized corrosion is detected, the corrosion rate could be derived from the equation below.
corrosion rate (mpy where i corr is the corrosion current density (A cm −2 ), 10 is a dimension change factor, M is the iron atomic weight (g mol −1 ), 3.15 × 10 7 is the number of seconds in one year, F is the Faraday constant, n is the number of transferred electrons per metal atom, d is the density of iron.The calculated inhibition efficiency percentage (IE Pot %) are functions of i corr according to the equations: where the uninhibited and inhibited corrosion current densities are represented by i corr °and i corr , respectively.The E corr of CS in the presence of LAPG and MAPG fluctuated around that of blank by ±20 mV at varied concentrations.This means that the difference in CS potential in the absence and presence of the different studied corrosion inhibitors (LAPG and MAPG) and their concentrations are within the range of ±85 mV.This is reverted into the adsorbed molecules, which mask both anodic and cathodic reactions that take place at CS active centers (Fe → Fe +2 + 2e − (anod) and 2e − + 2H + → H 2↑ (cathod)).So, both corrosion inhibitors are classified as mixed corrosion inhibitors [72].Intriguingly, adding LAPG and MAPG inhibitors leads to the suppression the i corr of CS to 75.56 and 53.82 μA cm −2 , respectively, compared to blank counterpart 590 μA cm −2 and rise the inhibition efficacy to 85.72 and 89.83 %.These are returned into the high electron density centers presented in their chemical structure, forming a compact adsorbed film over the CS surface [73,74].This formed protective film increases the surface coverage (θ) up to 0.8572 and 0.8983, making the CS corrosion reaction hard to occur.Moreover, the CS polarization resistance (Rct) value is enhanced in the presence of LAPG and MAPG up to 407 and 510 Ω cm 2 , respectively.This confirms the resistance stability of adsorbed inhibitors to form a barrier film that shields the CS surface away from the offensive action of hydrochloric acid media [75].The PDP parameters arrange the performance of LGPA and MGPA like WL and EIS and comparing the tested inhibitors with their Gemini surfactants counterparts, showed a noticeable inhibition efficiency better than the other published materials at similar conditions (see Table S3).

Surface analysis studies 3.6.1 AFM analysis
The three-dimensional AFM technique has become one of the favorite choices for exploring surface topography at nano and micro levels.It is also a powerful method for elucidating the efficiency of the corrosion inhibitor at the metal/solution interface.The AFM technique provides sufficient images for quantitative analysis with nanoscale as it could explain the interaction mechanism between the steel surface and the other additives in the aggressive media.The surface roughness of carbon steel can be determined by the mean roughness factor (Ra).The R a values show that the roughness of the metal surface immersed in 1.0 M HCl is around 132 nm.However, adding 0.0001 M of LAPG and MAPG corrosion inhibitor reduced the Ra to 16 and 8 nm respectively due to forming an adsorbed protective layer which shifted to reduce the surface roughness [43,76].Height profile graphs further support these results in Figure 9.

XPS analysis
The XPS analysis was utilized to identify the passivation layer formed on CS after immersion in 1.0 M HCl in the presence of 0.0001 M of MAPG corrosion inhibitor.The analysis revealed the presence of C1s, N1s, O1s, and Fe2p signals, as seen in Figure S3.The decomposition of each signal provides valuable information on the chemical environment of each element and, consequently, on changes in the chemical composition of the carbon steel surface, as shown in Figure 10.The carbon C1s signal presents four peaks at 285; 286.69; 287.85, and 288.77eV, respectively assigned to the carbon atoms of the groups (C-C and C-H), (C-N), (C=O) and (C-O), all belonging to the corrosion inhibitor.The deconvolution of the N1s signal provides three components, respectively at 399.50, 398.34, and 400.99 eV, related to the different types of nitrogen in the corrosion inhibitor (-N=, -N-, and N + ).The decomposition of the iron Fe2p signal essentially allows identifying any bonds between the metal substrate and the corrosion inhibitor.This deconvolution shows that iron exists in several forms: Fe-N at 707.10 eV, Fe 3 O 4 at 708.45 eV, FeO at 709.80 eV, and FeOOH at 711.15 eV.Also, the deconvolution of the O1s signal gives rise to four peaks at 529.79; 530; 531.40, and 532.40 eV, respectively, corresponding to the same groups combining oxygen to iron, observed in the case of the Fe 2p signal: Fe 2 O 3 and FeOOH.It can be concluded that the passivation layer is formed of oxides, hydroxides, and the adsorbed corrosion inhibitor.

Inhibition mechanism
The adsorption mechanism of organic compounds at metal/solution interfaces depends on more than one factor.We cannot ignore or specify one of them due to the complex nature of the adsorption process.These factors are the chemical structure of the inhibitor and the charge distribution overall in its structure in addition to the nature or/and charge of the steel surface [77].Generally, corroded iron surface in HCl solution carries -Ve charge due to the electrostatic adsorption of Cl − ions on the steel surface (FeCl − ) ads .
So, we suggest the LAPG and MAPG adsorption follow one of these pathways or all of them: 1. Positive centers (quaternary nitrogen atoms or protonated oxygen atoms) attract physically with the negatively CS-charged centers according to [78]: +4 ] ads (25) This complex attracts CS-charged surface, blocking the active centers of CS from reacting with HCl. 4. The aforementioned 1 and 3 pathways make the LAPG and MAPG compound come closer to the surface of CS and form a compact protected layer to shield the CS surface from the HCl contact. 5. Electron sharing between the electron-rich function groups in LAPG and MAPG compounds and the vacant 3d-orbital CS based on the donor-acceptor interaction concept forms a chemisorbed protective layer over the CS surface.

Conclusions
In this study, we investigated the use of Gemini cationic surfactants containing multiple carbonyl groups and different hydrophobic tails as corrosion inhibitors for CS in 1 M HCl at temperatures ranging from 25 to 55 ± 0.1 °C.The surfactants demonstrated high corrosion inhibition efficiency for CS, as confirmed through both theoretical and laboratory investigations using WL, EIS, and PDP techniques.DFT and MCs calculated parameters predict the high adsorption inclination of LAPG and MAPG compounds over the CS surface.According to MCs, MAPG with 14 carbon as hydrophobic tail has a more spontaneous adsorption capability than LAPG with lower hydrophobic tail, outlining the significant role of the hydrophobic tail in control the corrosion inhibition efficiency.WL data show that the LAPG and MAPG decrease the CS corrosion rate to a high extent as their concentration increases at different temperatures.For the adsorption or/and thermodynamic activation parameters, both LAPG and MAPG surfactants exhibited a chemically adsorbed passive film that impedes CS corrosion reaction.The LAPG and MAPG follow the Langmuir adsorption isotherm model.The electrochemical data (Tafel and EIS) are in good coherence with each other and the WL data.E corr slightly shifted negatively, indicating that LAPG and MAPG are mixed types.They prevent both the anodic and cathodic processes.i corr decreases with rising LAPG and MAPG concentrations as well increasing the surfactant tail.These compounds addition leads to a rise in R ct and a drop in Y°.And thus, lead to diminishing the contact surface area subjected to the offensive action of HCl.AFM and XPS confirms the protective layer formation over CS from the reduction of CS surface roughness.

Figure 1 :
Figure 1: The chemical structure for the two as-synthesized amide Gemini cationic surfactants.

Figure 4 :
Figure 4: Arrhenius plots (a, b) and transition state plots (c, d) for carbon steel dissolution in absence and presence of different concentrations from LAPG, MAPG.

Figure 5 :
Figure 5: Langmuir isotherm adsorption model by the synthesized amido Gemini cationic surfactant (a) LAPG, and (b) MAPG on the steel surface at different temperatures.

Figure 6 :
Figure 6: EIS Nyquist and Bode plots for the corrosion of carbon steel in 1.0 M HCl in the absence and presence of varied concentrations for (a, b) LAPG and (c, d) MAPG corrosion inhibitors at room temperature.

Figure 7 :
Figure 7: The equivalent circuit utilized for analyzing the measured EIS data.

Figure 8 :
Figure 8: Potentiodynamic polarization curves for the corrosion of carbon steel in 1.0 M HCl in the absence and presence of varied concentrations for (a) LAPG and (b) MAPG corrosion inhibitors at room temperature.

Figure 9 :
Figure 9: AFM images and height profile graphs for steel surface after immersion in 1.0 M HCl solution for 24 h in absence and presence of inhibitor at room temperature.

Figure 10 :
Figure 10: High resolution XPS spectrum of (a) nitrogen, (b) iron, (c) carbon and (d) oxygen atoms on the steel surface after immersion in 1.0 M HCl solution for 24 h in the presence of 0.0001 M of MAPG corrosion inhibitor at room temperature.

Table  :
Quantum chemical parameters of the investigated LAPG, and MAPG surfactant compounds.

Table  :
Corrosion rate, surface coverage and percentage inhibition efficiency for carbon steel in different concentrations of LAPG, and MAPG surfactants at different temperatures.

Table  :
Activation parameters values of carbon steel in . M HCl of different concentrations of the synthesized LAPG, and MAPG surfactants inhibitors.

Table  :
Thermodynamic parameters from Langmuir adsorption isotherm on carbon steel surface in . M HCl in presence of LAPG, and MAPG surfactants.