Accepted Manuscript Adsorption and performance assessment of some imine derivatives as mild steel corrosion inhibitors in 1.0�M HCl solution by chemical, electrochemical and computational methods Emad A. Badr, M.A. Bedair, Samy M. Shaban PII: S0254-0584(18)30717-X DOI: 10.1016/j.matchemphys.2018.08.041 Reference: MAC 20884 To appear in: Materials Chemistry and Physics Received Date: 25 January 2018 Revised Date: 14 May 2018 Accepted Date: 19 August 2018 Please cite this article as: E.A. Badr, M.A. Bedair, S.M. Shaban, Adsorption and performance assessment of some imine derivatives as mild steel corrosion inhibitors in 1.0�M HCl solution by chemical, electrochemical and computational methods, Materials Chemistry and Physics (2018), doi: 10.1016/j.matchemphys.2018.08.041. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT RI PT Adsorption and performance assessment of some imine derivatives as mild steel corrosion inhibitors in 1.0 M HCl solution by chemical, electrochemical and computational methods. Emad A. Badr (a), M.A. Bedair (b,*) and Samy M. Shaban (a) SC (a) Petrochemical Department, Egyptian Petroleum Research Institute, Egypt. (b) Chemistry Department, Faculty of Science (Men’s Campus), Al-Azhar University, 11884, Egypt Abstract: This study provided a thermodynamic study of the adsorption process and the corrosion M AN U inhibition performance of three cationic surfactant based on imine surfactant corrosion inhibitor in 1.0 M HCl solution. The results showed that the tested imine surfactants inhibitors are promising because of their high inhibition efficiency at low concentrations and high temperatures. According to the obtained results, the adsorption behavior of the surfactant imine TE D inhibitors onto the mild steel surface follow Langmuir model isotherm. The potentiodyanamic polarization parameters showed that the surfactant imine inhibitors act as mixed type inhibitors. A reduction in the double layer capacitance and an increase in the charge transfer resistance are EP occurring as a result for the imine inhibitor adsorption. DFT, DMol3 and molecular dynamic simulations were also used for investigation of inhibitive and adsorption properties for the AC C studied compounds. Key words: imine cationic surfactants; Tafel Polarization; DFT; Electrochemical Impedance Spectroscopy; SEM; Molecular Dynamics. (*) Corresponding author Tel.: +20 1014134321. E-mail address: firstname.lastname@example.org, email@example.com firstname.lastname@example.org (Samy M.Shaban) 1 (M. A. Bedair) and ACCEPTED MANUSCRIPT 1. Introduction Mild steel considers the essential constructing material for vast of industries, so its protection RI PT from corrosion presents an essential case to save the safety, money and time. . In spite of the hydrochloric acid cause severe corrosion, it's used in many jobs like acid pickling, acid descaling, oil well acidizing and acid cleaning, consequently these jobs must be accompanied with an effective corrosion inhibitors for protecting the infrastructure [2-4]. The chemical SC corrosion inhibitor materials consider the most effective and economical method for controlling the metal dissolution, especially in petroleum production processes for protecting the pipeline, M AN U tanks, shipping pipeline lines, vessels, etc. [5, 6]. The chemical corrosion inhibitors are the materials which can be injected with the fluid phase in low concentration to achieve a good protection for the main constructing materials. The effective corrosion inhibitor should have high adsorption ability on the corroded surface which can be achieved electronic rich function groups TE D like heteroatoms (oxygen, sulfur, nitrogen, phosphorous and so….), unsaturated bonds and aromatic system, etc. which can form an intense electronic cloud [7, 8]. The Schiff base corrosion inhibitor compounds proved high efficiency in acidic medium, where nitrogen atom is EP capable to form coordinate-covalent bonds with metal surface by its unshared lone pairs of electrons; While the π-bond interact physically enhancing their adsorption affinity to the metal AC C surface [9-11]. The surfactant compounds are characterized by their high ability to adsorb at the interfaces due to their unique amphipathic structure, which consist of two opposing parts head and tail [12, 13]. The head is characterized by its high electronic rich, which is about set of some electronic rich functional group like carbonyl, double, imine group, nitrogen and oxygen, etc…, [14, 15]. A successive layer on the mild steel surface can be produced by the surfactant hydrocarbon which has the ability to isolate the corroded surface from the contact with 2 ACCEPTED MANUSCRIPT aggressive environments [16-18]. In addition the cationic surfactant is characterized by its biocidal activity which enhance their ability in petroleum sector . This research focused on preparing and evaluating the inhibition efficiency of the three imine RI PT compounds in the surfactant structure on the mild steel corrosion and using the 1 M HCl solution as an aggressive medium via weight loss tests, electrochemical experiments (polarization and impedance spectroscopy). The thermodynamic parameters governing the adsorption of inhibitor SC on the metal steel surface and the mechanism of adsorption were determined. Also, we are going to explain the inhibiting behavior of the studied compounds by means of DFT, DMol3 and M AN U molecular dynamic computational methods. 2. Materials and Experimental Methods 2.1. Preparation of corrosion inhibitors The amphipathic inhibitors were prepared as follows: TE D 2.1.1. Preparation of Schiff-base based on dimethoxybenzaldhyde: The Schiff base compound has been prepared through a condensation reaction between the 3, 4dimethoxybenzaldehyde and 2-dimethylamino ethylamine. In a typical procedure, 0.05 mole (4.4 ethylamine EP gm) from 2-dimethylamino was mixed with 0.05 mole from 3, 4- AC C dimethoxybenzaldehyde (8.3 gm) in a round flask 250 ml containing 80 ml absolute ethanol as a solvent. The reaction mixture was heated to reflux for 6 hrs. The solvent was evaporated and the obtained Schiff base was purified and crystallized using diethyl ether . 2.1.2. Preparation of cationic Schiff amphipathic corrosion inhibitor Equimolar from the prepared Schiff base (0.01 mol, 2.36 gm) from the first step was refluxed with equimolar from Octyl bromide (0.01 mol, 1.93 gm), Dodecyl bromide (0.01 mol, 2.49 gm) and Hexadecyl bromide (0.01 mol, 3.05 gm) separately in a round flask containing 90 ml from 3 ACCEPTED MANUSCRIPT the absolute ethanol as a solvent for 30 hours. The product was purified and recrystallized from diethyl ether, then filtrated and dried to obtain the synthesized cationic amphipathic inhibitors as clarified in Fig 1 . The prepared three amphipathic inhibitors named N-(2-(3,4bromide, N-(2-(3,4- RI PT dimethoxybenzylideneamino)ethyl)-N,N-dimethyloctan-1-ammonium dimethoxybenzylideneamino)ethyl)-N,N-dimethyldodecan-1-ammonium bromide and N-(2-(3,4- labeled as DMAOB, DMADB and DMAHB respectively. 2.2. Solutions and Mild Steel SC dimethoxybenzylideneamino)ethyl)-N,N-dimethylhexadecan-1-ammonium bromide which are M AN U The used aggressive solution is 1.0 M HCl, which prepared by dilution of concentrated hydrochloric acid 37% using distilled water. The different concentrations ranged from (5x10-7 to 5x10-3 M) from the prepared amphipathic inhibitors (DMAOB, DMADB and DMAHB individually) were prepared. Stock solution 5x10-3 M from the surfactant were prepared using TE D 1.0 M HCl, then diluting it with 1.0 M HCl to obtain on the required doses. The tested mild steel was immersed in the prepared solutions. The used mild steel used in gravimetrical experiment and in electrochemical measurements is mild steel with a chemical composition (weight % ) C and the rest is Fe. EP (0.23%), Cr (0.05), Mo (0.01%), Mn (1.35%), P (0.017%), Ni (0.02%), Si (0.22%), S (0.01%), AC C 2.3. Corrosion Measurements The weight loss, electrochemical impedance spectroscopy and potentiodynamic polarization have been used for determining the ability of the synthesized Schiff base surfactant DMAOB, DMADB and DMAHB to inhibit corrosion of the mild steel in 1.0 M HCl. 2.3.1. Weight Loss Experiment 4 ACCEPTED MANUSCRIPT All the mild steel coupons which have been used during the weight loss experiments have the dimension of 6.0 cm x 3.0 cm x 0.4 cm. Each coupon was abraded with emery papers with different grades (400, 600, 1000 and 1200), then degreased with acetone before immersing in the RI PT specified solution. The experiment duration was 24 hours at the four different temperatures, which are 25, 40, 55 and 70oC using water bath of 0.2 oC accuracy. An analytical balance has been used for weighting the coupons before and after the experiment. Each experiment was M AN U 2.3.2. Electrochemical Measurements SC repeated and the average value was considered in the calculations [22, 23]. The Tafel and Nyquist curves have been obtained electrically at 25 ᴼC using voltalab 40 potentiostat PGZ 301. A three-electrode cell consisting from the working electrode (WE), platinum electrode, and saturated calomel reference electrode (SCE) has been used. The WE was TE D treated as it is outlined in the coupons, which used in weight loss and was left for 30 minutes in the tested solution before starting the experiment. The polarization experiment was conducted from -800 to -200 mV with scanting rate 0.2 mVs-1 [24, 25]. The electrochemical impedance EP measurements (Nyquist curves) have been carried out by changing the frequency from 100 kHz to 50 mHz with amplitude of 5 mV peak-to-peak . The exposed corroded area from the WE AC C is 0.7 cm2. 2.4. Scanning electron microscopy (SEM) The surface morphology has been examined after 24 h immersion of steel samples in the tested aggressive medium (1.0 M HCl) with and without the 5x10-3 M concentration of the tested Schiff base surfactant inhibitors using SEM techniques. The model of the instrument used for 5 ACCEPTED MANUSCRIPT scanning the samples is Quanta 250 FEG (Field Emission Gun) attached with EDX Unit (Energy Dispersive X-ray Analyses), magnification14x up to 1000000, accelerating voltage 30 K.V. RI PT 2.5. Computational calculations The computational calculations were performed using Gaussian 09  at DFT/B3LYP level using 6-31G + (d,p) basis set  and Materials Studio software version 7.0 (Accelrys Inc. USA) SC at DMol3 . The calculations were done on the cationic surfactants in gas phase and an aqueous phase. The self-consistent reaction field (SCRF) theory, with Tomasi’s polarized M AN U continuum model (PCM) was applied to perform DFT/B3LYP - 6-31G + (d,p) computations in solution. The eﬀect of solvent was considered in DMol3 calculations by including COSMO controls. In order to study the adsorption of the cationic surfactants on steel surface, molecular dynamic simulations were carried out. The Fe crystal was imported and cleaved along (110) plane and a slab of 15 Å was employed. The simulation box (22.90 Å×57.26 Å ×26.68 Å) and TE D COMPASS force field was used . EP 3. Results and Discussions: 3.1. Characterization the Structure of the Synthesized Schiff base Inhibitor: AC C The Chemical Structure of the synthesized Schiff base amphipathic inhibitors has been confirmed using FTIR and 1HNMR spectroscopy, as it is outlined in Supplement Figs. 1, 2. Supplement Fig. 1, represents the FTIR spectrum of the synthesized DMADB amphipathic inhibitor as a representative example, which show the appearance of a new azomethine group at 1640 cm-1 as a result of condensation reaction between the aldehyde and the amine ( carbonyl group and amino groups were disappeared). Some other bands are present confirming the 6 ACCEPTED MANUSCRIPT chemical structure of the synthesized amphipathic inhibitors like 2853.2, 2923, 1513, 1139 and 1023 cm-1 which refer to asymmetrical aliphatic CH, symmetrical aliphatic CH, aromatic C=C, RI PT C-O and C-N bond respectively. Supplement Fig. 2 represents the 1H-NMR spectrum data (δ ppm) of inhibitor DMADB as an example showing signals at: δ= 0.82 (t,3H, ـCH3); δ= 1.21 (m ,18H,( ـCH2)9CH3); δ=1.61 SC (m,2H, -CH2(CH2)9CH3); δ=2.47 (s,6H, -CH2N (CH3)2CH2-); δ=2.8 (t,2H,CH3(CH2)9CH2CH2N (CH3)2CH2-); δ=3.07 (t,2H,CH3(CH2)9CH2-CH2N (CH3)2CH2-CH2N=); δ=3.35 (s,6H, δ=7- 7.49 (m,3H, CH2N=CH- M AN U =CH-Ph(OCH3)2); δ=3.77 (t,2H,-CH2N=CH-Ph(OCH3)2); Ph(OCH3)2); δ=8.34 (s,1H, -N=CH -Ph(OCH3)2). 3.2. Weight loss measurements 3.2.1. Concentration influence TE D The corrosion rate (k), and the corrosion inhibition efficiencies (ηw) of the synthesized imine (Schiff base) surfactant inhibitors DMAOB , DMADB and DMAHB after 24 h of immersion at 25, 40, 55 and 70 ºC has been evaluated by the weight loss technique and calculated using EP equations 1 and 2 respectively [31, 32]. The experimental data have been listed in Table 1. (1) AC C = Where the expression ∆W correspond to the weight loss average of three parallel mild steel coupons immersed in protected or unprotected solution with different concentration of the imine amphipathic inhibitor, S corresponds to the total exposed area of the working electrode and finally t refer to the immersing time by hours. = × 100 = ᴼ ᴼ × 100 (2) 7 ACCEPTED MANUSCRIPT Where Wo and W represent the weight loss in the unprotected and protected mild steel coupon respectively. RI PT The experimental weight loss ∆W, and corrosion rate (k) values which depicted in Table 1, decrease with increasing the concentration of the imine surfactant derivatives DMAOB , DMADB and DMAHB, while inhibition efficiency and surface coverage were increased as it is SC obvious in Fig. 2. This might be owing to increasing the availability of electron donors (N), (O) and aromatic rings by increasing the concentration of inhibitor. Imine derivatives showed M AN U maximum inhibition efficiencies in 5.0 mM of DMAOB, DMADB and DMAHB inhibitors. Increasing the concentration of DMAOB, DMADB and DMAHB inhibitors lead to increasing the migration rate of the surfactant to the interface which permitting a higher accumulation of the prepared imine inhibitors at the interface. The electronic rich functional group located in the hydrophilic heads of DMAOB, DMADB and DMAHB are responsible for forming a 35]. TE D coordination bond with the vacant d-orbital through -C=N-, Nitrogen, and oxygen groups [33- EP 3.2.2. Temperature effect It is obvious from the dataset in Table 1 that the corrosion rate (k) increases with increasing the AC C solution temperature from 25 to 70 ᴼC. This can be ascribed to increasing the transfer rate of the aggressive ions with elevating the solution temperature. Fig.2. and Table 1, showed that the values of inhibition efficiency (ηw) (%), for each DMAOB , DMADB and DMAHB inhibitors increase with raising the temperature. Which give more insight for strong adsorption of the imine inhibitors on the mild steel surface which, enhanced by increasing the temperature, where some 8 ACCEPTED MANUSCRIPT chemical change occur, lead to forming a stronger bond between the DMAOB , DMADB and DMAHB inhibitors and the vacant d-orbital. [36, 37]. 3.3.1. Potentiodynamic polarization measurements: RI PT 3.3. Electrochemical measurements The obtained polarization curves for mild steel in 1.0 M HCl in the absence and presence of SC the synthesized imine surfactant inhibitors DMAOB, DMADB and DMAHB are shown in Fig.3 at 25 ᴼC. The addition of the synthesized imine surfactant inhibitors shifts the corrosion current M AN U density to lower values. This trend refers to decreasing the metal dissolution and retardation the hydrogen evolution as a result for the covering the corroded surface with the used DMAOB , DMADB and DMAHB imine surfactant inhibitors. The Polarization electrochemical parameters Ecorr (corrosion potential), Icorr (corrosion current density), βa and βc (anodic and TE D cathodic Tafel slopes), have been obtained by extrapolation of the obtained experimental tafel curves and were depicted in Table 2. The inhibition efficiency ( ) of DMAOB , DMADB and DMAHB imine surfactants acquired according to Eq. (3) × 100 = ° – ° × 100 EP % = (3) AC C Where iocorr and icorr are the corrosion current density of the uninhibited and inhibited mild steel with the DMAOB , DMADB and DMAHB imine surfactants inhibitors respectively. The experimental depicted data set in Table 2, refer to decreasing the icorr values with increasing the concentration of DMAOB, DMADB and DMAHB imine surfactants Fig. 3, hence the ηp increases Table 2. The decreasing icorr, give an insight on increasing the electrode surface covered area by DMAOB, DMADB and DMAHB imine inhibitors forming a protective layer. 9 ACCEPTED MANUSCRIPT Increasing the surfactant concentration, enhance their adsorption affinity to the interfaces and hence the covered area on the corroded mild steel is increasing. RI PT The negative shift in the corrosion potential of the three DMAOB, DMADB and DMAHB imine surfactants, not exceed 85 mV (vs. SCE), predicting that the three DMAOB, DMADB and DMAHB imine surfactants act as mixed-type inhibitors with a predominant cathodic inhibitor, SC i.e the synthesized cationic surfactant reduce the anodic dissolution of mild steel and at the same time it retards the cathodic hydrogen evolution reaction but the effect of DMAOB, DMADB and M AN U DMAHB surfactant on the cathodic hydrogen evolution reaction is more. The slight shift in the depicted anodic (βa) and cathodic (βc) Tafel in Table 2, refers to the DMAOB, DMADB and DMAHB imine surfactant inhibitors have an effect on the corrosion rate without changing the inhibition mechanism [38, 39]. Electrochemical Impedance Spectroscopy (EIS): TE D 3.3.2. Fig. 4 outlines the Nyquist plots for the used mild steel immersed in 1.0 M HCl containing different concentrations from DMAOB, DMADB and DMAHB imine surfactants inhibitors at 25 EP ᴼC. The equivalent circuit model used for fitting the obtained Nyquist plots is also presented in Fig. 4. The Fig. 4 outline increasing the radii of the obtained semi-circle with the plethora of the AC C DMAOB, DMADB and DMAHB imine inhibitor concentration as a result of increasing the protected surface area of the mild steel by the tested imine which act as a barrier between the mild steel and the aggressive medium, hence the corresponding inhibition efficiency increase [40, 41]. Double-layer capacitance (Cdl) values were calculated using the equation (4) Cdl = (Y0 Rct1-n)1/n (4) 10 ACCEPTED MANUSCRIPT Where Rct represent the charge transfer resistance, Y0 is CPE constant and n is CPE exponent. The experimental inhibition efficiency for DMAOB, DMADB and DMAHB imine inhibitors (ηz) have been calculated depending on the obtained Rct values according to equation (5) as follows = RI PT : 100 (5) SC Roct and Rct represent the charge transfer resistance of protected and unprotected solution with M AN U the synthesized DMAOB, DMADB and DMAHB imine inhibitors, respectively. The obtained electrochemical corrosion kinetic parameters Rct, Cdl and ηz (%)from the Nyquist plot were depicted in Table 3. The depicted values in the Table 3, declare that upon increasing the inhibitor concentration, the Rct increases while the corresponding (Cdl) decreases which lead to increasing the percentage inhibition efficiency. Decreasing Cdl with the plethora of the TE D DMAOB, DMADB and DMAHB concentration may be ascribed to decreasing the local dielectric constant and/or increasing the thickness of the formed electrical double layer by the EP imine surfactants inhibitors, which reflect their high adsorption ability on the metal/solution . Both Bode and phase angle plots of the synthesized imine surfactant inhibitors (DMAOB, AC C DMADB and DMAHB) are plotted in Fig. 5. The slopes of Bode impedance magnitude at an intermediate frequencies log |Z| vs. log f (S) and maximum phase angle (α°) values were depicted in the Table 3. The slopes of the Bode impedance magnitude at intermediate frequencies (S) and maximum phase angle values (α°) for an ideal capacitive behavior are −1 and −90° respectively. Inspection of the data revealed that the slopes are not equal to -1, which may be a result of frequency dispersion of interfacial impedance. It’s also clear that slopes (S) and 11 ACCEPTED MANUSCRIPT maximum phase angle values shifted toward −1 and −90° in the presence of the cationic surfactants as an indication of the capacitive behavior at intermediate frequencies. RI PT 3.4. Thermodynamic activation study: The temperature increasing has a great influence on the electrochemical processes rate, the adsorption equilibrium and kinetics. These thermodynamic activation functions were obtained $% & (6) M AN U = exp SC throughout Arrhenius and the transition-state equations (6, 7): Where R and A are the universal gas constant and the Arrhenius pre-exponential factor, respectively, while k is the experimental weight loss corrosion rate as depicted in Table 1 and T correspond to the absolute temperature (298, 313, 328, and 343 K). Fig. 6 exhibits the linear TE D relationship between log k of the synthesized DMAOB, DMADB and DMAHB imine inhibitor versus 1/T. The obtained straight lines are very close to 1, as an indication of following the Arrhenius equation and from the slope the apparent activation energy is obtained. The calculated EP activation energy values (Ea) are collected in Table 4, where the values of Ea of the three imine inhibitors DMAOB, DMADB and DMAHB were lower than blank. For example, the apparent AC C activation energies for the DMAOB, DMADB and DMAHB inhibitors at 5x10-3 M are equal to 30.38, 26.68 and 24.9 kJ/mol respectively, while the corresponding activation energy for the unprotected solution was equal to 43,14 kJ/mol. The lower values of Ea in the presence of the imine inhibitors (Table 4) can be interpreted as an indication of chemical adsorption [44, 45]. The activation standard enthalpy of (∆H*) and the activation entropy (∆S*) were calculated according to the transition state equation: 12 ACCEPTED MANUSCRIPT ) ln = *ln & +, - ∆ ∗ + 1− ∆3 ∗ & (7) Where h corresponds to Planck’s constant, R to the ideal gas constant and NA refers to RI PT Avogadro's number. The calculated ∆H* and ∆S* values were calculated according to the previous equation (7) and depicted in Table 4. Supplement Fig. 3 represents a relation between log k/T versus reciprocal of the absolute temperature of tested mild steel immersed in SC unprotected and protected aggressive solution with various dosages from the synthesized amphipathic imine inhibitors DMAOB, DMADB and DMAHB respectively. The obtained slope M AN U equal to (-∆ H*/2.303R) and the intersection is equal to [(log R/Nh) + (∆S*/2.303R)]. The positive signs of (∆H*) infer to the process of the mild steel dissolution is endothermic, which imply the difficulty of the mild steel corrosion in the protected solution with DMAOB, DMADB and DMAHB amphipathic inhibitor. The ∆S* values in case of unprotected and protected mild TE D steel synthesized imine inhibitors are negative (Table 4), which referring to more ordering are occurring, ongoing from reactant species to activated complex [46, 47]. 3.5. Adsorption isotherm model EP The adsorption isotherm calculations performed to present description about the inhibition AC C mechanism throughout the adsorption nature of the synthesized imine derivatives DMAOB, DMADB and DMAHB on the mild steel surface at the four tested temperatures. The experimental weight loss surface coverage (θ) values (Table 1) have been considered fitting the different adsorption isotherm models. The most fitted adsorption isotherm was Langmuir isotherm through equation 8: 4 5 =7 6 89: +; (8) 13 ACCEPTED MANUSCRIPT Where Kads is the adsorption equilibrium constant while C refer to the inhibitor concentration. Fig. 7 present a relation between C/θ versus C for the prepared imine inhibitors DMAOB, DMADB and DMAHB. The obtained correlation factors (R2) for the obtained straight lines are RI PT very close to 1 as an indication for obey the Langmuir equation 8. The obtained slopes, which depicted in Table 5 are greater than 1 indicating that each imine inhibitor DMAOB, DMADB and DMAHB occupy more than one adsorption center on the mild steel surface which is not SC matching with the postulates of the Langmuir theory. Consequently, the adsorption of the synthesized DMAOB, DMADB and DMAHB imine inhibitors can be expressed through the new 4 5 = < 789: M AN U modified Langmuir isotherm (Villamil isotherm), as described in equation 9 [22, 49]: + =; (9) The slope is equal to n which resemble to the number of the adsorbed water molecules displaced TE D from the corroded mild steel surface. The equilibrium constant Kads for the DMAOB, DMADB and DMAHB imine inhibitors at the four tested temperatures 25, 40, 55 and 70oC have been determined from the intercept. The adsorption heat (∆Hoads) was calculated according to the van't 389: & + CD=EFG=F (10) AC C >=?@AB = EP Hoff equation 10: The calculated standard free energy of adsorption (∆Goads) and standard adsorption entropy (∆Soads) for DMAOB, DMADB and DMAHB imine inhibitors were calculated throughout the equations 11 and 12: J HI@AB = −KL>=55.5?@AB (11) The value of 55.5 is the water molar concentration in the solution. 14 ACCEPTED MANUSCRIPT J HO@AB = P 389: & P Q89: (12) All the calculated thermodynamic parameters ∆Goads, ∆Hoads and ∆Soads have been depicted in RI PT Table 5. The ∆Goads values are negative referring that the adsorption of DMAOB, DMADB and DMAHB imine inhibitor on the metal surface is a spontaneous in nature. On analyzing the data in Table 5, we disclose that the adsorption of DMAOB, DMADB and DMAHB on the tested SC mild steel surface is a mixture between physical and chemical as outlined from the ∆Goads values which ranged from -37.08 to -46.17 kJ mol−1. In presence of DMAHB imine inhibitor, the ∆Goads M AN U value is equal to 46.17 kJ mol-1 at temperature 70 ᴼC. These findings may confirm that the upon raising the solution temperature, some chemical change takes place in the imine inhibitor in 1.0 M HCl solution leading to a typical of chemical adsorption on the mild steel surface [49, 50]. The ∆Hᴼads values of DMAOB, DMADB and DMAHB imine inhibitors depicted in Table 5, is TE D positive referring that their adsorption on the mild steel surface is an endothermic process. While their ∆Soads values depicted Table 5 carry a positive sign, referring that the endothermic adsorption process is accompanied by an increase of entropy, which controls the DMAOB, EP DMADB and DMAHB imine adsorption on the mild steel surface . AC C 3.6. Scanning electron microscopy The surface morphology of the mild steel samples rinsed in 1.0M HCl solutions unprotected and protected with 5x10-3 M from the DMAOB, DMADB and DMAHB imine inhibitors at the 25 ᴼC are shown in Fig .8. We can notice that the surface morphology of the steel sample kept immersed in 1.0 M HCl solution for 24 h without adding any inhibitor was extremely damaged as a result of highly significant corrosion. On the contrary, in case of the protected mild steel with DMAOB, DMADB and DMAHB imine inhibitors, the mild steel surface becomes 15 ACCEPTED MANUSCRIPT smoother, reflecting a considerable prevention of the corrosion rate. This improvement in the surface morphology is a result of the formation of a good protective layer from the DMAOB, RI PT DMADB and DMAHB inhibitor on the mild steel surface. The results of EDX spectra in Fig .8 shows that the abraded mild steel surface immersed in HCl without adding any inhibitor presents the characteristic peaks of the elements constituting mild SC mild steel sample and the corrosive medium (Fe, O and Cl) ascribed to general corrosion in hydrochloric acid. While, for solutions containing surfactant inhibitors, the EDX spectra showed M AN U an additional peak characteristic for the existence of (N) and absence of (Cl) peak. This data indicates that surfactant inhibitors (DMAOB, DMADB and DMAHB) have the ability to adsorb on the mild steel surface with percentage contents listed in Table 6. 3.7. Computational calculations TE D Geometric and electronic structures of the cationic surfactants in the gas phase and aqueous phase are calculated by the optimization all structure parameters; bond lengths, bond angles and dihedral angles to the lowest energy. The optimization energy curves by DMol3 method are EP shown in Supplement Fig. 4. The optimized structures, frontier molecular orbitals (HOMO and LUMO), electrostatic potential and Mulliken atomic charges obtained from DFT calculations in AC C the gas phase are shown in Fig .9. The structure parameters obtained from the calculation are listed in Table 7. 3.7.1. Atomic bond distance The calculations of geometrical structures of the cationic surfactants using DFT/ B3LYP/6-31+G (d,p) showed that the bond distance within the aromatic ring moiety vary from 1.38 to 1.42 Å 16 ACCEPTED MANUSCRIPT which is characteristic for conjugated system . For the substituted two methoxy groups on ring, the O-Ar bond distance 1.35- 1.37 Ȧ and O-CH3 bond distance 1.43- 1.44 Ȧ. The two methyl groups attached to the nitrogen atom that bears positive charge, the N-CH3 bond distance 1.50 – RI PT 1.52 Ȧ (sp3 hybridization). The azo methane group N=CH bond showed a short bond distance 1.27 - 1.28 Å (formation of a double bond, sp2 hybridization). The aliphatic hydrocarbon chain showed the longest bond length with values equal to 1.52- 1. 54 Å (saturated C-C single bond, SC sp3 hybridization). M AN U 3.7.2. Atomic charges Electric charges in the cationic surfactants are responsible for the polarity of the molecules and so electrostatic interactions with metal surface. The electronic charges are important for physicochemical properties of the cationic surfactants and its intermolecular interactions. It’s TE D well known that the more negative the calculated charge, the greater is the ability of the cationic surfactant molecule to donate its electrons to mild steel surface and so the its inhibition efficiency increased. There are many methods for calculating the partial atomic charges like EP Mulliken and natural population analysis. AC C 184.108.40.206. Mulliken population analysis The calculated Mulliken charges prove the presence of more than one active center . The data showed that the tetravalent N atom has a high negative charge in all cationic surfactants with values equal to -0.546, -0.548 and -0.546 e for DMAOB, DMADB and DMAHB respectively, using DFT/B3LYP/6-31G+ (d,p) method due to the electron donating ability of the two adjacent methyl groups. It is also found that two O atoms have a high negative charge with values from -0.36 to -0.37 e, using DFT/B3LYP/6-31G+(d,p) method and with values from 17 ACCEPTED MANUSCRIPT 0.42 to -0.45 e using DMol3 method. The N atom of azo methane group has also high negative charge with values -0.28 e, in Dmol3 method. The presence of negative charges on carbon atoms of the aromatic ring moiety and delocalization of electrons is good evidence that the conjugating RI PT system of the aromatic ring has the ability to donate π electrons to the mild steel surface, acting also as an active center for the adsorption process. The total negative charge on the cationic surfactants was calculated. The data show that TNC has values -6.20, -7.277 and -8.424 for SC DMAOB, DMADB and DMAHB respectively in the gas phase and values -6.248, -7.306 and 8.426 for DMAOB, DMADB and DMAHB respectively in the aqueous phase using M AN U DFT/B3LYP/6-31G+(d,p) method. From the view of TNC the order of inhibition efficiency will be DMAHB > DMADB > DMAOB which is the same ranking obtained from experimental results. TE D 220.127.116.11. Natural Bonding Orbital NBO analysis is done to provide information about the electron distribution of the molecular orbitals, electron delocalization within the molecule and atomic charge distribution. According to EP NBO analysis for DMAOB molecule as an example, the -CH=N- bonding orbital has σ bond occupancy of 1.98938 electrons resulting from the overlap of sp1.98 (33.57% s, 66.33% p, 0.10% AC C d) hybrid on C with sp1.44 (40.95% s, 58.99% p, 0.06% d) hybrid on N atom and π bond occupancy of 1.94600 electrons resulting from the overlap of sp 99.99 14.74 d (0.01 % s, 99.80 % p, 0.18 % d) hybrid on C with sp99.99d7.65 (0.02% s, 99.83% p, 0.15% d) hybrid on N atom. The atomic charge distributions for the cationic surfactant structures were examined through natural population analysis (NPA) as a result of NBO calculation . The data of NPA charges showed that hetero atoms (two N atoms and two O atoms), carbon atoms of the aromatic ring and aliphatic chain carbon atoms bears negative charges. O atom exhibit the maximum negative 18 ACCEPTED MANUSCRIPT charge value (-0.56 e) but the tetravalent N atom exhibit the minimum negative charge value (0.34 e). The N atom of azo methane group has value from -0.52 to -0.54 e and the aliphatic side chain carbon atoms have value of – 0.46 e. TNC by NBO method has been also calculated and RI PT showed the values of -8.386, -10.734 and -12.678 for DMAOB, DMADB and DMAHB respectively in the gas phase and values of -8.893, -10.759 and -12.707 for DMAOB, DMADB and DMAHB respectively in the aqueous phase using DFT/B3LYP/6-31G+(d,p). It’s clear that SC TNC increases by the same order of increasing inhibition efficiency. M AN U 18.104.22.168. Active sites by Fukui analysis Local reactivity, structure–activity relationship of the cationic surfactant molecules with the mild steel surface can be understood by means of condensed Fukui functions (CFF) . It’s useful for prediction the inhibitor atomic sites on which nucleophilic and electrophilic interaction can TE D be occurred. The nucleophilic f + and electrophilic f - Fukui indices were calculated using the finite difference approximation as follows . EP f + = q (N + 1) – q (N) f - = q (N) – q (N - 1) (13) (14) AC C Where q (N + 1), q (N) and q (N – 1) represent charge values of atom for anion, neutral, and cation, respectively. The data of the Fukui indices for nucleophilic and electrophilic sites of DMAOB, DMADB and DMAHB are listed in Table 8. In case of the electrophilic attack the highest values are observed in O7 (0.115, 0.110 and 0.100), O8 (0.059, 0.062 and 0.066), N12 (0.050, 0.058 and 0.064) and the C atoms of the aromatic ring, which are the most which are the most reactive sites for the investigated cationic surfactants. The presences of the methyl groups 19 ACCEPTED MANUSCRIPT adjacent to O atoms in these cationic surfactants enhance their electron donation to the mild steel surface. The most susceptible sites for nucleophilic attack are present in C11 (0.088, 0.119 and 0.125), C10 (0.120 for DMAOB), and N12 (0.085 and 0.079 for DMADB and DMAHB RI PT respectively). 3.7.3. Global reactivity descriptors SC It’s known that chemical interactions are either electrostatic (polar) or orbital (covalent). Forming of any chemical bond is due to transition of electrons which is a result of interaction M AN U between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of reacting species . HOMO can be considered as the sites of donating electrons while LUMO is the sites of accepting electrons between the inhibitors and metal surfaces. Perfect inhibitors not only donate electrons to the empty d- orbitals of metal surface, but also can TE D accept electrons from metal leading to the formation of a back donation bond. According to previous results, the higher is the value of EHOMO of the inhibitor, the easier is its offering electrons to the metal surface and the greater is its inhibition efficiency. On the other hand, the EP lower is the value of ELUMO of the inhibitor; the easier is its ability to accept electrons from the metal surface and the greater is its inhibition efficiency . The results from the Fig. 9 indicate AC C that the HOMO and LUMO orbitals are largely distributed throughout the aromatic ring, the two OCH3 groups and CH=N- group. According to data in Table 7, the calculated values of EHOMO for the investigated cationic surfactants in gas and aqueous phases by DFT/B3LYP/6-31G+ (d,p) and DMol3 methods showed that increasing values of EHOMO, are consistent with the same order obtained from experimental results (DMAHB > DMADB > DMAOB). However, from the data obtained for ELUMO in gas phase and aqueous phase showed that there is no clear relation between the trend in the experimentally determined corrosion inhibition efficiency and ELUMO. 20 ACCEPTED MANUSCRIPT The HOMO–LUMO separation energy gap is considered as an important stability factor and function of reactivity of the investigated compounds towards adsorption on metal surface. Low values of ∆E indicate high reactivity and so high inhibition efficiency. It was shown from Table RI PT 7 in the aqueous phase that DMAHB has the lowest ∆E with values equal to 4.4896 and 3.2332 eV in DFT/B3LYP/6-31G+ (d,p) and DMol3 methods, respectively, which means that it is the highest reactivity in the aqueous phase and accordingly the highest inhibition efficiency. It was SC also found that DMAOB has the highest ∆E in the aqueous phase with value equal to 4.5779 eV in DFT/B3LYP/6-31+G(d,p) method, which means that it has the lowest reactivity and M AN U accordingly the lowest inhibition efficiency. 3.7.4. Electronegativity and global electrophilicty The absolute electronegativity (χ) can be calculated from the energy of the HOMO and the TE D LUMO by the following equations . Ionization energy (I) = -EHOMO, Electron affinity (A) = -ELUMO RST U (16) EP χ= (15) It’s well-known from Sanderson’s electronegativity equalization principle that the electrons will AC C flow from molecules that had lower electronegativity values for that with higher electronegativity values until the chemical potential becomes equalized . So the perfect inhibitor is the one that has low electronegativity and so higher values of the electronegativity gap between metal and inhibitor, offering electrons to flow to metal surface. The calculated (χ) data in Table 7 show that the values of electronegativity vary by the order DMAHB < DMADB < DMAOB either in the gas phase or in an aqueous phase. The calculated values of 21 ACCEPTED MANUSCRIPT electronegativity emphasize the same inhibition efficiency trend obtained from experimental results. RI PT Electrophilicity (ω) can be defined as the ability of chemical molecules to gain electrons. It can be calculated from chemical potential (µ) and global hardness (η) by the following equations . (17) U VW UX (18) M AN U ω= R T SC µ = - χ, η = So a good electrophile possesses high values of ω and a good nucleophile possesses low values of ω. Weak electrophile (strong nucleophile) will show high inhibition efficiency. Examination of the calculated data of ω in Table 7 showed that, if ω was decisive for the inhibitor properties, TE D the order of the investigated cationic surfactants should be DMAHB < DMADB < DMAOB ;( ω). All The calculations either in gas phase or in aqueous phase indicate that DMAHB ( highest inhibition efficiency) has the lowest ω in the all methods with values equal to 9.227, 3.452, EP 13.747 and 4.981 eV, then DMADB ( ranks 2nd in inhibition efficiency) with values equal to 9.233, 3.459, 13.783 and 4.994 eV, and DMAOB ( ranks 3rd in inhibition efficiency ) has the AC C highest ω with values equal to 9.248, 3.465, 14.021 and 5.008 eV in DFT/B3LYP/6-31+G (d,p) gas phase, DFT/B3LYP/6-31+G (d,p) aqueous phase, DMol3 gas phase and DMol3 aqueous phase methods, respectively. 3.7.5. Molecular volume and dipole moment In the presence of adsorption centers, molecular volume is a very effective quantum factor that contributes to inhibition efficiency. By increasing the molecular volume of the inhibitor 22 ACCEPTED MANUSCRIPT molecules, the surface covered of metal increases and so inhibition efficiency. The calculated values of molecular volume by DFT/B3LYP/6-31+G (d,p) are shown in Table 7. It’s clear from the data that DMAHB has the highest volume by values 426.366 cm3/mol in gas phase and RI PT 430.351cm3/mol in aqueous phase. The ranking of the investigated cationic surfactants according to their molecular volume is the same one obtained from experimental inhibition efficiency SC (DMAHB > DMADB > DMAOB). There’s a lack in literature either dipole moment (DM) can be utilized in estimating the corrosion M AN U inhibition properties of chemical species or not. Some research papers indicated that a clear correlation between DM and inhibition efficiency is not found [61, 62]. On the other hand other research papers indicated that corrosion inhibition efficiency can be stimulated by increasing the value of DM [63, 64]. Our calculated data reveal that a higher value of DM corresponds with higher inhibition efficiency. DMAHB has the highest value of DM (20.399 debye, TE D DFT/B3LYP/6-31+G (d,p) in the gas phase) among the three investigated cationic surfactants, while DMAOB that has the lowest inhibition efficiency, possess a DM value of 1.177 debye EP (DFT/B3LYP/6-31+G (d,p) in the gas phase). 3.7.6. Electron transfer electron back-donation AC C We can calculate the fraction of electrons transferred from cationic surfactant molecules to the mild steel surface using the equation ; ∆N = Z[\ Z]^_ (19) U(a[\Sa]^_) By application of the theoretical value, χFe = 7 eV/mol and value of η Fe = 0 eV/mol for iron (steel). ∆N doesn’t give precise values express the actual number of electrons transferred but it 23 ACCEPTED MANUSCRIPT expresses the tendency of the inhibitor molecules to provide the metal surface with its electrons. Lukovits et al.  proposed that, the corrosion inhibition ability improved by increasing electron donating ability if <3.6. The calculated data of ∆N have the ranking DMAHB > RI PT DMADB > DMAOB. As highest values of ∆N refers to DMAHB with highest inhibition efficiency while smallest values of ∆N refer to DMAOB with lowest inhibition efficiency. SC The donation of electrons back from metal to inhibitor molecules may control the binding of surfactant molecules to metal surface. Gomez et al  related the back donation energy (∆EBackby the hardness of the inhibitor molecules (η) for a charge transfer model, if the both M AN U donation) processes of electron donation and electron back donation occur by the equation; X ∆EBack-donation = - c (20) The negative values of ∆EBack-donation indicate that the electron follows from metal to inhibitor is TE D favorable. The increase in the ∆EBack-donation may lead to strong adsorption and so high inhibition efficiency. ∆EBack-donation values for the cationic surfactants molecules are -0.53632, -0.53625 and the gas phase. EP -0.53612 eV for DMAHB, DMADB and DMAOB respectively by DFT/B3LYP/6-31+G (d,p) in AC C 3.7.7. Molecular dynamic simulation MD simulations were performed to get a better understanding for the interaction process between the cationic surfactant molecules and steel surface. Supplement Fig. 5 presents a typical energy profile plot for DMAHB surfactant molecule on Fe (110) surface at the simulation process. The lowest energy adsorption configurations of DMAHB, DMADB and DMAOB on the Fe (110) interface are shown in Fig. 10. It’s clear from Fig. 10 that all cationic surfactant molecules can 24 ACCEPTED MANUSCRIPT adsorb on steel surface. The adsorption of the surfactants occur side by side (the surfactant molecules parallel to steel surface) which leads to more surface coverage and so high inhibition efficiency. The adsorption occurs mainly through π electrons of the aromatic ring, lone pairs of RI PT electrons of the two O-CH3 groups, the two nitrogen atoms and so the aliphatic hydrocarbon chain. The calculated adsorption energy by its different forms (total adsorption, rigid adsorption, and deformation energies) and so binding energy are listed in Table 9. The data in Table 9 show SC that the cationic surfactants possess negative adsorption energy indicating the spontaneous nature of the adsorption process. The binding energy values of the cationic surfactants are 317.074, M AN U 278.967 and 237.638kcal/mol for DMAHB, DMADB and DMAOB respectively. The order of binding energy confirms the order of laboratory findings. Radial distribution functions of Fe (110) - surfactant structures, g(r), were also calculated and plotted in Fig. 11. The peaks in the g(r)~r plot within 3.5 Å represent chemical adsorption, TE D otherwise that located outside 3.5 Å represent columbic and Van der Waals attraction . Our data indicated that, the length between the cationic surfactant molecules and Fe (110) surface is steel surfaces. EP about 2.49 Å so chemical bonds can be occurred between the cationic surfactant molecules and AC C 4. Conclusion From the chemical, electrochemical and computational data obtained throughout the paper, we can conclude that: 1- The prepared three cationic surfactants (DMAOB, DMADB and DMAHB) act as successful corrosion inhibitors for steel in 1 M HCl solution. 2- Their inhibition effects increase with increases in both concentration and temperature. 25 ACCEPTED MANUSCRIPT 3- Tafel polarization curves proved that DMAOB, DMADB and DMAHB act as mixed-type inhibitors. due to chemisorption and follows the Langmuir model. 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Xu, W. Li, J. Colloid Interface Sci., 472 (2016) 52.  S. Martinez, Mater. Chem. Phys. 77 (2002) 97. TE D  I. Lukovits, E. Kalman, F. Zucchi, Corrosion. 57 (2001) 3.  B. Gomez, N.V. Likhanova, M.A. Dominguez-Aguilar, R. Martinez-Palou, R. Vela, J. Gasquez, J .Phy. Chem B. 110 (2006) 8928-894. AC C EP  J.P. Zeng, J.Y. Zhang, X.D. Gong, Comput. Theor. Chem., 963 (2011) 110. 30 ACCEPTED MANUSCRIPT Table 1 Corrosion rate, surface coverage and percentage inhibition efficiency of the mild steel in 1.0 HCl of synthesized surfactants (DMAOB , DMADB and DMAHB) at different temperatures. CR, (mg cm-2h-1) ηw θ (%) ----- 0.9110 ----- ----- 5x10-3 0.0611 0.8285 82.85 0.1282 0.8593 85.93 5x10-4 0.0879 0.7533 75.33 0.1752 0.8077 80.77 5x10-5 0.1081 0.6965 69.65 0.2124 0.7668 76.68 5x10-6 0.1251 0.6488 64.88 0.2636 0.7106 5x10-7 0.1572 0.5585 55.85 0.3178 5x10-3 0.0560 0.8428 84.28 0.1177 0.0779 0.7813 78.13 0.1576 0.8270 0.0959 0.7307 73.07 0.1912 0.1164 0.6732 67.32 0.2348 0.1384 0.6113 61.13 0.0452 0.8730 87.30 0.0609 0.8290 0.0836 5x10 -4 5x10 -5 5x10 -6 5x10 -7 5x10 -4 5x10 -5 5x10 -6 5x10 -7 θ 70 oC ηw CR, (mg cm-2h-1) θ (%) ηw (%) ----- ----- 3.4054 ----- ----- 0.2212 0.8914 89.14 0.3004 0.9118 91.18 0.3194 0.8432 84.32 0.4706 0.8618 86.18 0.3989 0.8041 80.41 0.6083 0.8214 82.14 71.06 0.5138 0.7477 74.77 0.7529 0.7789 77.89 0.6511 65.11 0.6449 0.6833 68.33 0.9812 0.7119 71.19 0.8708 87.08 0.2041 0.8998 89.98 0.2480 0.9272 92.72 82.70 0.2860 0.8596 85.96 0.3837 0.8873 88.73 0.7901 79.01 0.3454 0.8303 83.03 0.5055 0.8516 85.16 0.7423 74.23 0.4431 0.7824 78.24 0.6645 0.8049 80.49 0.6857 68.57 0.5544 0.7277 72.77 0.8377 0.7540 75.40 0.0918 0.8992 89.92 0.1281 0.9371 93.71 0.1730 0.9492 94.92 82.90 0.1270 0.8606 86.06 0.2027 0.9004 90.04 0.2711 0.9204 92.04 0.7653 76.53 0.1721 0.8111 81.11 0.2816 0.8617 86.17 0.4068 0.8805 88.05 0.1036 0.7090 70.90 0.2264 0.7515 75.15 0.3843 0.8112 81.12 0.5525 0.8378 83.78 0.1260 0.6462 64.62 0.2625 0.7119 71.19 0.5034 0.7528 75.28 0.7115 0.7911 79.11 0.2863 2.0361 SC ----- CR, (mg cm-2h-1) M AN U 0.3561 RI PT ηw (%) 0 5x10-3 DMAHB θ θ 55 oC TE D DMADB CR, CR, (mg cm-2h-1) 40 oC EP DMAOB 25 oC AC C Inhibitor Inhibitor Conc. (M) 1 ACCEPTED MANUSCRIPT Table 2 Potentiodynamic polarization parameters of corrosion of the mild steel in 1.0M HCl of synthesized cationic surfactants at 25oC at scanning rate 0.2 mV s-1. DMADB βc mA cm-2 mV dec-1 mV dec-1 -496 0.2488 176.7 -159.3 ----- ----- 5x10-3 -534.7 0.0494 169.2 -198.10 0.8014 80.14 -4 5x10 -526.8 0.0612 173.6 -182.40 0.7540 75.40 5x10-5 -507.2 0.0797 135.3 -156.80 0.6797 67.97 -6 5x10 5x10-7 -514 -501.8 0.0905 0.1111 153 148.2 -154.30 -157.30 0.6363 0.5535 63.63 55.35 5x10-3 -528.20 0.0462 174.7 -189.10 0.8145 81.45 -4 5x10 -523.10 0.0572 117.9 -332.00 0.7699 76.99 5x10-5 -508.80 0.0715 161.4 -142.70 0.7127 71.27 -6 5x10 5x10-7 -502.90 -516.50 0.0807 0.0919 157.7 157.4 -201.60 -162.50 0.6755 0.6308 67.55 63.08 5x10-3 5x10-4 -538.9 -530.6 0.0391 0.0507 164.9 200.6 -163.90 -178.40 0.8428 0.7961 84.28 79.61 5x10-5 -524.8 0.0563 176.5 -196.70 0.7738 77.38 5x10-6 -506.7 0.0716 135.5 -155.50 0.7121 71.21 0.0847 182.6 200.40 0.6593 65.93 EP DMAHB 0.00 βa -7 -515.6 AC C 5x10 2 % RI PT Ө SC M AN U DMAOB (SCE) Icorr mV TE D Inhibitor name Ecorr Conc. of inhibitor (M) ACCEPTED MANUSCRIPT Table 3 EIS parameters, slopes of the Bode impedance magnitude at intermediate frequencies (S) and maximum phase angle values (α°) for corrosion of steel in 1.0 M HCl in the absence and ηz % -0.528 -0.599 -0.681 -58.92 -60.87 -59.39 ----0.833 0.750 ----83.37 75.02 119.80 -0.682 -68.24 0.697 69.78 112.88 -0.651 -62.93 0.647 64.78 0.8372 169.82 -0.613 -65.64 0.548 54.81 270.8 0.7284 147.87 -0.647 -58.8 0.849 84.95 467.8 458.3 0.7735 225.75 -0.585 -55.2 0.799 79.96 1.415 403.7 150.9 0.7044 67.123 -0.560 -59.71 0.767 76.78 12.47 265.8 258.0 0.7988 115.08 -0.489 -49.96 0.647 64.74 1.969 238.4 530.7 0.7755 259.03 -0.640 -61.01 0.606 60.68 1.440 701.4 181.1 0.6932 72.662 -0.613 -57.03 0.866 86.63 1.001 466.9 100.2 0.7968 45.889 -0.716 -67.02 0.799 79.92 1.003 427.7 156.1 0.7222 55.112 -0.632 -58.22 0.780 78.08 3.797 334.0 280.8 0.7143 108.96 -0.517 -55.59 0.719 71.94 357.1 0.7422 156.52 -0.492 -54.49 0.640 64.03 1.581 1.381 4.593 93.72 563.8 375.2 530.7 340.3 289.9 0.8071 0.7254 0.7933 1.442 310.2 199.9 0.8445 1.371 266.1 228.6 0.7987 1.568 207.4 292.8 1.377 622.9 11.97 5x10 -4 5x10 -5 -6 5x10 5x10-7 5x10 -3 5x10 -4 5x10-5 -6 5x10 5x10-7 3.677 -2 s cm ) 260.6 n Cdl (µF cm-2) 259.03 182.15 162.63 M AN U 5x10 -3 (µ Ω Yo -1 n TE D 5x10 5x10-7 Rct (Rp) (Ω cm2) 3 S SC 0.00 5x10-3 5x10-4 5x10-5 -6 RI PT θ Rs (Ru) (Ω cm2) EP DMAHB DMADB DMAOB blank αo o ( ) Conc (M ). AC C Inhibitor name presence of different concentrations of the prepared cationic surfactants at 25oC. ACCEPTED MANUSCRIPT Table 4 Activation parameters values of the mild steel in 1.0M HCl of different concentrations of the synthesized inhibitors. Conc. of inhibitor (M) Ea (kJ mol-1) Linear regression coefficient ∆H* (kJ mol-1) ∆S* (J mol-1 K-1) Blank 0.00 43.14 0.9927 40.48 -117.22 5x10-3 5x10-4 5x10-5 5x10-6 5x10-7 30.38 32.07 33.06 34.47 35.26 0.9807 0.9935 0.9961 0.9904 0.9941 27.73 29.41 30.40 31.81 32.61 -174.51 -166.13 -161.22 -155.09 -150.70 5x10-3 5x10-4 5x10-5 5x10-6 5x10-7 28.68 30.68 31.76 33.36 34.49 0.9603 0.9826 0.9929 0.9942 0.9937 26.03 28.02 29.10 30.70 31.84 -180.75 -171.60 -166.45 -159.52 -154.25 5x10-3 5x10-4 5x10-5 5x10-6 5x10-7 24.90 28.26 29.86 31.65 33.31 0.9678 0.9755 0.988 0.9842 0.9874 22.24 25.60 27.20 29.00 30.65 -195.26 -181.58 -173.75 -165.84 -158.87 DMADB AC C EP TE D DMAHB SC M AN U DMAOB RI PT Inhibitor name 4 ACCEPTED MANUSCRIPT Table 5 Thermodynamic parameters from Villamil adsorption isotherm of the mild steel surface in 1.0M HCl containing different concentrations of the synthesized inhibitors at different temperatures. M kJ mol -1 1.20 0.9999 5.64 -37.08 40 1.16 0.9999 9.12 -40.19 55 1.12 1.10 25 1.18 1.15 40 55 25 55 0.9999 0.9999 -42.51 -44.51 kJ mol -1 12.02 KJ mol-1 K-1 0.1647 0.1667 0.1662 0.1647 -37.69 -40.71 13.16 13.87 -43.12 -45.24 0.9999 10.33 12.84 -38.58 -41.08 1.07 0.9999 15.17 -43.51 0.1676 1.05 0.9999 19.23 -46.17 0.1680 1.14 1.11 0.9999 0.9999 0.9999 0.9999 AC C EP 70 10.54 10.75 TE D 40 0.9999 ∆Sads 7.23 11.11 1.11 1.08 70 DMAHB -1 25 70 DMADB R ∆Hads RI PT DMAOB C Slope ∆Gads SC Name o Kads x10-5 2 M AN U Inhibitor Temp. 5 0.1675 0.1691 12.24 11.48 0.1687 0.1675 0.1679 0.1679 ACCEPTED MANUSCRIPT Table6. Quantitative analysis for steel surface after 24 hr immersion in 1.0 M HCl in the presence and absence of the prepared surfactant inhibitors obtained from EDX. Blank (HCl- Fe) DMAOB - Fe DMADB - Fe DMAHB - Fe Element Mass % Atom % Mass % 2.73 1.58 ----5.07 90.62 100 3.58 6.14 ----14.75 75.53 100 ----4.12 0.65 2.19 93.05 100 ----15.65 2.11 6.23 76.01 100 ----- 100 M AN U TE D EP 6 Mass % Atom % ----- ----- ----- 6.48 3.13 6.09 84.29 1.60 0.77 1.46 96.17 6.67 2.76 4.55 86.03 100 100 100 SC 1.58 0.89 1.98 95.55 Atom % RI PT Atom % AC C Cl C N O Fe Total Mass % ACCEPTED MANUSCRIPT EHOMO ELUMO ∆E ∆E back donation DM TNC (e) T.E. 3 M.V. cm /mol (eV) (eV) (eV) (eV) (D) (eV) Mulliken ∆N (eV-1) (eV) (eV) (e) ∆N max (e) η IE* (eV) (%) -29427.8 290.941 -6.200 -8.386 0.46631 9.248 6.298 0.163 2.936 2.1444 83.37 DMADB -8.4386 -4.148 4.2900 -0.53625 9.969 -33704.0 376.846 -7.277 -10.734 0.46619 9.233 6.293 0.164 2.934 2.1450 84.95 DMAHB -8.4373 -4.146 4.2905 -0.53632 20.399 -37980.2 426.366 -8.424 -12.678 0.46613 9.227 6.292 0.165 2.932 2.1452 86.63 DMAOB -6.2721 -1.6942 4.5779 -0.57225 2.106 -29429.7 278.011 -6.248 -8.893 0.43687 3.465 3.983 0.658 1.740 2.2889 83.37 DMADB -6.2297 -1.6933 4.5363 -0.56705 9.536 -33705.8 333.363 -7.306 -10.759 0.4408 3.459 3.961 0.669 DMAHB -6.1816 -1.6920 4.4896 -0.5612 20.039 -37982.0 430.351 -8.426 -12.707 0.4454 3.452 3.936 0.682 1.746 2.2681 84.95 1.753 2.2448 86.63 M AN U 4.2889 -0.53612 1.177 Hirshfeld -7.5632 -4.8263 2.7368 -0.34211 1.8732 -28869.2 ------ -7.259 -1.0728 0.7307 14.021 6.194 0.2941 4.526 1.3684 83.37 DMADB -7.7175 -4.8518 2.8656 -0.35821 9.0466 -7.7204 -4.8478 2.8726 -0.35908 19.399 -33047.9 ------ -8.542 -1.2919 0.6979 13.783 6.285 0.2496 4.386 1.4328 84.95 -37226.5 ------ -10.035 -1.5257 0.6962 13.747 6.284 0.2492 4.375 1.4363 86.63 DMAOB EP Mulliken DMAOB -5.6455 -2.4080 3.2374 -0.40468 1.5191 -28869.2 ------ -7.461 -1.1506 0.61776 5.008 4.026 0.9183 2.487 1.618 83.37 DMADB -5.6416 -2.4024 3.2391 -0.40490 10.022 -33047.9 ------ -8.301 -1.3741 0.61743 4.994 4.022 0.9193 2.483 1.619 84.95 DMAHB -5.6298 -2.3965 3.2332 -0.40416 20.355 -37226.5 ------ -10.508 -1.6146 0.61856 4.981 4.013 0.9237 2.482 1.616 86.63 DMAHB AC C gas phase X -8.4420 -4.153 DMol3 aqueous phase ω DMAOB TE D aqueous phase gas phase DFT/B3LYP/6-31G+(d,p) NBO σ SC Molecule RI PT Table 7The calculated quantum chemical parameters in eV for the investigated inhibitors at DFT/B3LYP/6-31G+(d,p) and DMol3 in gas phase and in aqueous phase. 7 ACCEPTED MANUSCRIPT Table 8 The Fukui functions of studied inhibitors, calculated by DMol3 method at GGA function with BOP/DNP basis set DMADB DMAHB f- f+ f- f+ 0.042 0.023 0.051 0.013 0.042 0.033 0.115 0.059 -0.043 -0.036 0.018 0.05 -0.024 -0.004 -0.002 0.002 -0.005 -0.01 -0.004 -0.003 -0.002 -0.002 -0.002 -0.002 -0.001 0.015 0.037 -0.022 0.051 0.021 0.021 0.04 -0.026 -0.032 0.12 0.088 -0.037 -0.007 -0.009 -0.002 -0.014 -0.014 -0.006 -0.004 -0.003 -0.003 -0.002 -0.003 -0.002 0.015 0.045 0.027 0.04 0.017 0.036 0.039 0.110 0.062 -0.053 -0.045 0.018 0.058 -0.027 0.001 -0.002 0.004 -0.008 -0.008 0.01 -0.003 -0.003 -0.001 -0.002 -0.001 -0.002 -0.001 -0.001 -0.001 0.000 0.065 0.014 0.044 -0.018 0.049 0.02 0.013 0.04 -0.015 -0.024 0.119 0.085 -0.034 -0.012 -0.009 -0.004 -0.004 -0.016 -0.027 -0.004 -0.003 -0.003 -0.001 -0.002 -0.001 -0.001 -0.001 -0.001 -0.001 0.054 0.025 0.039 0.038 0.018 0.06 0.100 0.066 -0.047 -0.04 0.01 0.064 -0.023 0.001 0.003 0.003 -0.014 -0.006 0.01 -0.003 -0.001 -0.002 -0.002 -0.003 -0.005 -0.007 -0.009 -0.011 -0.012 -0.012 -0.013 -0.011 -0.010 0.065 0.014 0.044 -0.023 0.058 0.015 0.011 0.036 -0.01 -0.021 0.125 0.079 -0.032 -0.014 -0.013 -0.004 0.002 -0.015 -0.026 -0.005 -0.005 -0.005 -0.003 -0.003 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 -0.001 TE D M AN U SC RI PT f+ EP C ( 1) C ( 2) C ( 3) C ( 4) C ( 5) C ( 6) O ( 7) O ( 8) C ( 9) C ( 10) C ( 11) N ( 12) C ( 13) C ( 14) N ( 15) C ( 16) C ( 17) C ( 18) C ( 19) C ( 20) C ( 21) C ( 22) C ( 23) C ( 24) C ( 25) C ( 26) C ( 27) C ( 28) C ( 29) C ( 30) C ( 31) C ( 32) C ( 33) DMAOB f- AC C 2 Aliphatic chain N(CH3) C=N-C-C (O – CH3)2 Aromatic ring atom 8 ACCEPTED MANUSCRIPT Table 9 The outputs and descriptors calculated by the Molecular dynamic simulation for adsorption of DMAHB, DMADB and DMAOB on Fe (110) (in kcal/ mol). DMAOB -323.710 -274.338 -221.233 -317.074 -278.967 -237.638 -288.494 -253.537 -216.390 SC -28.579 RI PT DMADB -25.429 -21.247 -317.074 -278.967 -237.638 317.074 278.967 237.638 86.63 84.95 83.37 AC C EP TE D Total energy (kcalmol-1) Adsorption energy (kcalmol-1) Rigid adsorption energy (kcalmol-1) Deformation energy (kcalmol-1) (dEads/dNi) (kcalmol-1) Binding energy (kcalmol-1) IE* (%) DMAHB M AN U inhibitor 9 AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig. 1: The synthetic route for the three tested amphipathic inhibitors. TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig.2: Variation of corrosion rate and so inhibition efficiency against logarithm C of the AC C EP prepared amphipathic inhibitors using weight loss method at different temperatures. AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig.3. Potentiodynamic polarization curves for the corrosion of mild steel in 1.0 M HCl in the absence and presence of different concentrations of DMAOB, DMADB and DMAHB. M AN U SC RI PT ACCEPTED MANUSCRIPT AC C EP TE D Fig. 4. Nyquist plots for the mild steel in 1.0 M HCl in the absence and presence of different concentrations of surfactants (a) for DMAOB, (b) for DMADB and (c) for DMAHB at 25oC and (d) the equivalent circuit model used to fit the EIS data. AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig. 5. Bode and phase angle plots of impedance spectra for the mild steel in 1.0 M HCl in the absence and presence of different concentrations of surfactants (a) for DMAOB, (b) for DMADB and (c) for DMAHB) at 25 oC. AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig. 6 Arrhenius plots (log k vs. 1/T) for steel dissolution in the absence and the presence of different concentrations of DMAOB, DMADB and DMAHB in 1.0 M HCl solution. AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig. 7. Langmuir isotherm adsorption model of the mild steel surface of compound DMAOB, DMADB and DMAHB in 1.0 M HCl at different temperatures. AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig.8. SEM images and EDX spectra of the mild steel in 1 M HCl after 24 h immersion without inhibitor (blank) and with the surfactant inhibitors. AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig.9. The optimized structures, frontier molecular orbitals (HOMO and LUMO), electrostatic potential and Mulliken atomic charges obtained from DFT calculations in the gas phase. AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig.10. Top and side views of the most stable low energy configurations for the adsorption of the three cationic surfactants on Fe (110) interface obtained using Molecular dynamic simulations. AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Fig. 11. Radial distribution functions of the three cationic surfactants on Fe (110) surface. M AN U SC RI PT ACCEPTED MANUSCRIPT AC C EP TE D Supplement Fig. 1: IR spectrum of N-(2-((3,4-dimethoxybenzylidene)amino)ethyl)-N,Ndimethyldodecan-1- ammonium bromide (DMADB). M AN U SC RI PT ACCEPTED MANUSCRIPT AC C EP TE D Supplement Fig. 2: 1H-NMR spectrum of N-(2-((3,4-dimethoxybenzylidene)amino)ethyl)-N,Ndimethyldodecan-1-ammonium bromide (DMADB). AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT Supplement Fig. 3 Transition state plots of the mild steel dissolution in the absence and the presence of different concentrations of DMAOB, DMADB and DMAHB in 1.0 M HCl solution. TE D M AN U SC RI PT ACCEPTED MANUSCRIPT AC C EP Supplement Fig. 4. Optimization energy curves for the cationic surfactants in gas phase and aqueous phase obtained from DMol3 M AN U SC RI PT ACCEPTED MANUSCRIPT AC C EP TE D Supplement Fig. 5. The typical energy profile for the adsorption of DMAHB on Fe (110) surface obtained using Molecular dynamic simulations. ACCEPTED MANUSCRIPT • Three surfactants were synthesized and characterized by FTIR and 1HNMR. • The adsorption of these compounds is chemical adsorption and obeys Langmuir adsorption isotherm. Calculated quantum chemical parameters showed a good correlation with inhibition RI PT • AC C EP TE D M AN U SC efficiencies.