Electrochemical and DFT studies of Terminalia bellerica fruit extract as an eco-friendly inhibitor for the corrosion of steel

It is well known that metal corrosion causes serious economy losses worldwide. One of the most effective ways to prevent corrosion is the continuous development of high-efficient and environment-friendly corrosion inhibitors. Among the widely used organic and inorganic corrosion inhibitors, plant extracts are top candidates due to their nontoxic nature. The present study reports a novel application of the methanolic extract of Terminalia bellerica fruits as an environment friendly corrosion inhibitor for steel in sulphuric acid medium. The phytochemicals of the extract, namely Ellagic, Gallic, and Malic acids, play a key role of the anti-corrosive behavior of the extract. The corrosion prevention activity was studied on the steel in 1 M H2SO4 using a variety of approaches including weight loss analysis (WL), scanning electron microscope (SEM), electrochemical impedance spectroscopy (EIS), density functional theory (DFT), natural bond orbital analysis (NBO), Fukui function and Monte Carlo simulations (MC). In 1 M H2SO4 solution, the maximum electrochemical inhibition efficiency of 91.79% was observed at 4000 mg/L concentration of the extract. The NBO analysis showed that the charge density of the double bonds and the oxygen atoms of carbonyl and hydroxyl groups of the phytochemicals lies on the top of the natural bond orbitals which promotes the anticorrosive properties of the investigated inhibitors. The surface coverage of steel was validated by SEM measurements. According to DFT studies, numerous nucleophilic regions were present in the active phytochemical constituents of the inhibitor, demonstrating their favorable nucleophilicity. The computed electronic structure of the phytochemicals revealed band gaps of 4.813, 5.444, and 7.562 eV for Ellagic, Gallic, and Malic acids respectively suggesting effective metal-inhibitor interactions. A good correlation between experimental and theoretical findings was addressed.


Preparation of the corrosive media
For the current experiment, we utilized a 1 M H 2 SO 4 solution that was made using AR grade sulphuric acid from Loba Chemie in double-distilled water.To get various extract concentrations, it was then further diluted.

Weight-loss measurement
Before every corrosion study, the 1 cm 2 steel coupons were polished with emery paper of various grades.The steel coupons were firstly weighed and then submerged in 1 M sulphuric acid with several inhibitor concentrations (1000, 2000, 3000, and 4000 mgL -1 ) for 24 h.The coupons of steel were taken out after being exposed to acidic media.Following acetone rinsing and drying of the coupons, the weight loss data were computed using the following equation 43,44 : W 0 − W i = W is the weight loss (mg), where w 0 and w i is the loss of weight without inhibitor and with involvement of inhibitors, respectively and θ is the surface coverage.

Theoretical models
Initial guesses of structures of Ellagic, Gallic, and Malic acids were prepared by ChemBioDraw Ultra 14.0 in 2D dimensions then a minimization (energy/geometry) was performed by Gaussian 09 revison-A.02-SMPpackage 50 at B3LYP/6-31 g(d,p) level [51][52][53] .The optimized parameters were reached after achieving the convergence criteria indicated by Gaussian 09: the maximum remaining force on an atom and the average root mean square (RMS) force on all atoms are below the tolerance threshold 45 × 10 −5 and 30 × 10 −5 Hartree, respectively as well as the maximum structural drift of one coordinate and RMS change over all structural parameters in the last two iterations are below 18 × 10 −4 and 12 × 10 −4 Å , respectively.Obtained optimized molecules representing local minima were sketched by Gauss view 6 and presented in Fig. 2 54 .
Vol.:(0123456789)  55 , therefore the DFT calculations were repeated using the Time-dependent density-functional theory (TD-DFT) method to calculate the lowest excited state energy and therefore correct the value of band gap energy E gap between Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO).Six energy states were included for this calculation at TD-B3LYP/6-31 g(d,p) following the procedure described by Ref. 55 .E HOMO andE LUMO as well as their corresponding reactivity descriptors were obtained as described by Ref. 56 .HOMO and LUMO surfaces with an iso value of 0.02 and density of 0.0004 were presented as transparent surfaces using the molecular orbital editor of Gauss view 6 57 .Natural bond orbitals (NBOs) were measured at B3LYP/6-31 g(d,p) level for selected sites of Ellagic, Gallic, and Malic acids.NBOs surfaces were created using the NBO Version 3.1 58 in Gaussian 09 software and plotted using the same isovalue of 0.02 and density of 0.0004 in order to compare them to Frontier Molecular Orbitals (FMOs).In addition, Fukui functions were calculated by addition of a positive and a negative charge to the neutral molecules and then re-optimizing it at B3LYP/6-31g (d,p).
Including water as a solvent, (2H + and SO 4 --) as corrosive medium (200 H 2 O, 20 H 3 O + , 10 SO 4 --), a Monte Carlo simulation had been used to get deeper details of the adsorption pattern for the Terminalia bellerica fruit extract phytochemical structures and their binding with the metal surface.The simulation was done using the Adsorption Locator module included in the Materials Studio 7.0 program 59 .All constituents within the structure were optimized using a COMPASS force field.Fe (1 1 0) unit cell with 11 layers of (11 × 11) atoms (under periodic boundary conditions with size 18.386 × 22.341 × 22.341 Å) and a vacuum slape of 30 Å which was employed to depict the steel surface.The electrostatic energy was determined using the Ewald summation technique, whereas the van der Waals energy was calculated utilizing the atom-based procedure 60 .

Measurements of weight reduction
Weight loss values, surface coverage and inhibitory effectiveness were determined and presented in Table 4 at varying concentrations of Terminalia bellerica extract at different environment temperatures.According to the information in the Table 4, by raising the extract's concentration, inhibition effectiveness increases (approached a maximum value of 83.38% at 4000 ppm and 298 K) while the corrosion rate decreased, which can also be inferred from the plot in Fig. 3.The corrosion rate was calculated using the following equation 61 : where K is the corrosion constant, W is the loss of weight after corrosion (mg), A is the total area of the coupon (cm 2 ), T is the corrosion time (h) and D coupon density (g/cm 3 ).This increase in inhibition effectiveness is only possible if electron-rich hereto atoms were adsorbed on the steel surface so that it retards the rate of metal corrosion in the abrasive medium 62,63 .
As the temperature ascending from 298 to 318 K, the rate of corrosion was raised which led to a decline in protection ability (Table 4, Fig. 3).Physical adsorption may be responsible for the decline in protective efficacy with raising temperature at all the evaluated doses.Due to desorption, the inhibitor molecules get detached from the steel substrate at elevated temperatures 43 .

Adsorption isotherm
The data calculated by weight loss analysis can be fitted to different isotherms to examine the adsorption characteristics 64 .The fitting results were collected for four different isotherms (Freundlich, Langmuir, Temkin and kinetic-thermodynamic models) in Table 5 65 .By plotting C/θ vs. log C, Eq. ( 6) can be employed to calculate the adsorption 66 : Where surface coverage is represented by θ, inhibitor concentration is depicted by C while K ads is the adsorption equilibrium constant.
The relationship between the concentrations of Terminalia bellerica extract and C/θ is depicted in Fig. 4. The resultant plot is linear, and the adsorption equilibrium constant (K ads ) can be measured by using the intercept.The corresponding K ads values are 0.0033, 0.0019 and 0.0018 ppm −1 at the temperatures 298 K, 308 K, and 318 K, respectively.
The following formula was used to determine the G • ads from the K ads values 67 : Where ΔG°a ds is the standard free energy of adsorption; R is the gas constant; T is the absolute temperature.The obtained values of G • ads , by using Eq. ( 7), are −20.37,−18.98 and −18.91 kJ mol −1 at the temperature of 298 K, 308 K, and 318 K, respectively.In general, values of ΔG 0 ads around −20 kJ/mol or more positive are indicative of the inhibitor's physisorption on the surface, likewise, values of −40 kJ/mol or more negative are indicative of the inhibitor's chemisorption on the steel surface 68 .Due to possible interaction between the abovementioned phytochemicals and the surface of the metal, they can be considered as effective corrosion inhibitor.The inhibitor layer prevents corrosion by obstructing the active sites upon the steel's surface and the physical adsorption is predominant.

Activation parameter
Figure 5a demonstrates a linear relationship between ln (CR) and 1/T, from which E a can be figured out.Using Eq. ( 8), E a can be calculated and with accordance to the Arrhenius law, E a varies as temperature rises, which accelerates metal corrosion.
When an inhibitor was added, E a (Table 6) was increased from 32.69 to 58.19 kJ/mol, demonstrating the physical adsorption of the inhibitor onto the metal surface 69 .Due to the development of a protective layer over the exposed steel surface, activation energy has therefore increased, suggesting that dissolved steel has been reduced.

Adsorption parameter for entropy and enthalpy
The following equation has been used to evaluate the entropy and enthalpy of adsorption: In this formula, N a , h, ∆H a, and ∆S a are Avogadro's number, Planck constant, standard activation enthalpy and standard activation entropy, respectively.
By using graph ln (CR/T) versus /T, as shown in Fig. 5b, the ∆H a and ∆S a parameters have been determined and illustrated in Table 6.It can be inferred, the metal is very well protected because a corrosion-preventing energy barrier is maintained, as demonstrated by the fact that H a is greater when there an inhibitor used (54.46 kJ/mol) compared to solution without inhibitor (29.50 kJ/mol).The inhibitor adsorption leads to a rise in the corrosion reaction's enthalpy (+ ve, endothermic).The introduction of the inhibitor produced an entropy value of -21.02 J/mol/K as opposed to the blank solution having entropy of −93.96J/mol/K.

Potentiodynamic polarization (PDP) study
In the corrosive solvent with various extract concentrations, Fig. 6 clearly demonstrates the anodic and cathodic polarization responses of steel coupons, while Table 7 enlists the related corrosion outcomes and inhibition efficiencies.www.nature.com/scientificreports/According to the Tafel curves, the anodic and cathodic section current density is decreasing in the presence of the Terminalia bellerica extract.This behavior demonstrate that the inhibitor has the ability to suppress the cathodic hydrogen evolution as well as anodic metal oxidation 70 .The anodic as well as cathodic Tafel graphs (βa and βc) with the Terminalia bellerica extract has been changed with certain concentrations which show that the inhibitor affects the cathode hydrogen gas evolution and also interfering with the anode iron dissolving process 71 .Thus, in a solution of 1 M H 2 SO 4 , the Terminalia bellerica extract regulates both cathodic and anodic corrosion reactions 72,73 .This should indicate that adding more Terminalia bellerica extract prevents the steel corrosion process.According to Table 7, the corrosion current density reduces as Terminalia bellerica extract concentration increases 74 .At a concentration of 4000 mg/L, the lowest corrosion current density is 2.610 -4 A/cm 2 and the best inhibition efficiency showed 91.03%.In addition, Table 7 demonstrates a decline in the corrosion rate in the presence of extract; all this is due to the adsorption capacity of the extract on the surface of the metal which provides remarkable resistance against metal dissolution.

Electrochemical impedance spectroscopy
The resulting Nyquist as well as Bode diagrams are displayed in Fig. 7a, b, and resulted findings are shown in Table 8. Figure 7a also, shows the circuit which was employed in this study.From Fig. 7a, the diameter of the capacitive loops increased when the extract was added compared to that one without extract, indicating that this additive significantly slowed down the dissolution of steel 75,76 .The profiles of the spectra seem similar, and the semicircular form suggests that the corrosion mechanism was not affected by the presence or absence of the plant extract 77 .The outcomes of Table 8 indicate that increasing the inhibitor concentration while it reaches the highest efficiency at 4000 ppm increases the value of charge transfer resistance and inhibition efficiency.According to the Bode angle diagram, just after introduction of the inhibitor, the establishment of a protective layer on the surface, causes the curves to widen while moving to the left (toward smaller frequencies).In this study, R ct values increase with rise in inhibitor concentrations, which indicates that the extract from Terminalia bellerica is easily absorbable on the steel's surface, with a highest efficiency of 91.95% at a concentration of 4000 mg/L being observed.A presence of non-ideal capacitor can be indicated by the slightly flattened semi-circles that result from the electrode flaws and/or surface reactions 78 .In an analogous circuit, the capacitive element's variations are represented by a constant phase element (CPE).The variation of the capacitor behavior for a CPE is represented by a value of 0 < n < 1 (n = 1 represents a pure capacitor) 72,73 .For n, a value of around 0.8 was found in this study as shown in Table 8.

Analysis of phytochemicals
The phytochemicals found in the Terminalia bellerica extract are further described in Table 9.

Wagner's test
The extract was treated with Wagner's reagent.The development of a brownish-reddish precipitate hints the presence of alkaloids 79 .

Mayer's test
Solution was tested for alkaloids using Mayer's reagent.Presence of alkaloids revealed by yellow color in the solution 79 .   .

Test for quinones
Upon addition of one mL of the extract in H 2 SO 4 , a color change is observed accordingly the existence of quinones is verified 82 .

Test for coumarin
To about 2 ml of the extract, a few drops of an alcoholic NaOH solution were added.The appearance of a yellow color is an evidence that coumarin exists 82 .

Test for sugars
Fehling solution test for sugars Both the Fehling solutions A and B were combined in a one-to-one ratio and then boiled for 1 min.About 1 ml of an extract was taken from that mixture and then heated for 5 to 10 min in the water bath.When yellowish or brick red precipitates first appeared, The presence of carbohydrates is confirmed 79,80 .
UV visible spectroscopy UV spectra of Terminalia bellerica extracts were analyzed before and after corrosion.The acidic medium having an inhibitor, while the steel was not yet submerged, showed a significantly high absorbance, as shown by the spectra.This was compared to that of the abrasive medium in which the steel was submerged for 24 h, as shown in Fig. 8.When the steel specimen was soaked in the corrosive media containing an inhibitor, a complex between the surface of the steel and the inhibitor was formed.It is clear that the various phytochemicals of the inhibitor have formed a protective layer after being adsorbed to the metal 83 .

Scanning electron microscope (SEM)
The morphological changes to the cleaned steel surfaces after a 24-h immersion in 1M H 2 SO 4 with or without extract are illustrated in Fig. 9.It can be observed from Fig. 9a that the polished metal surface was not homogeneous and had a few flaws that might serve as corrosion points.Figure 9b shows a very rough surface caused by the rapid and powerful corrosion processes that took place during the immersion of steel in blank H 2 SO 4 .Accordingly a protective layer on the steel's surface was created by adding an inhibitor to 1 M H 2 SO 4 , thereby reducing the extent of surface damage caused by corrosion (see Fig. 9c) 84 .The surface roughness measured in the presence of Terminalia bellerica extract was 23.27 nm.From the values of roughens, it is evident that a protective layer was developed on the metal's surface 85 .

Global reactivity
Organic molecules usually show good reactivity toward metallic surfaces or metal ions because they are rich in π-electrons and lone pairs of hetero atoms 86 .Such loosely tight electrons with low ionization potentials are easily reallocated in the vicinity of d-orbitals of common transition metals 87,88 .This donating behavior of organic molecules can be evaluated by calculating the global reactivity descriptors including ionization potential, electronegativity, chemical harness, electron affinity etc. (Table 10) in addition to the band gap between the HOMO and LUMO (Fig. 11).However, the B3LYP method underestimates the HOMO eigen value by average absolute error of 3.10 eV according to Zhang and Musgrave et.al. 55 .Although it cannot be predicted about the LUMO eigen value that agrees with the recorded electron affinities; therefore, a calculated accurate band gap is a challenge.Nevertheless, the estimated band gap using timedependent (TD) B3LYP is fairly accurate.Therefore, a correction to the eigen value of HOMO could be used with the TD band gap for accurate estimation of LUMO and hence an accurate prediction for the reactivity descriptors.Correction of HOMO eigen value is carried out using the formula: −HOMO corr = A + B(−HOMO cal ) where A = 1.42 and B = 1.20; correlation parameters of B3LYP functional 55 .Then, an accurate value of LUMO is obtained using the formula: LUMO = HOMO + E gap .The band gap E gap calculated by TD-B3LYP for Ellagic, Gal- lic and Malic acids are 4.813, 5.444 and 7.562 eV, respectively (Table 10 and Fig. 11).Because the HOMO and LUMO wave functions of a moderate-sized band gap are easily combined, the molecule is quickly polarized and requires less energy to be excited 56,89 .Therefore, the calculated low energy gaps promote the reactivity of these molecules toward the metal surface and hence their ability as corrosion inhibition candidates in the following order Ellagic > Gallic > Malic acid.Table 10.Calculated electronic reactivity indices for ellagic, gallic and malic acids.a All parameters in eV except ΔN is dimensionless quantity.b All values are corrected according to the procedure in Ref. 55 .10).These low orbitals eigen values indicate that the electrons occupying these orbitals need few electron volts of energy to be ionized (i.e.: + 8.723, + 8.603, and + 10.219 eV for Ellagic, Gallic, and Malic acid, respectively) and hence can be easily shared into the metal surface.As expected, the HOMOs are mainly localized on the π-system of the carbonyl group and phenyl ring in both Ellagic and Gallic acids and on the carbonyl group and bonds including covalently attached oxygen atoms (Fig. 11).Moreover, the chemical hardness for the studied molecules was estimated as suggested by R. G. Pearson in "chemical hardness" 56 .Pearson suggested that in molecules where the HOMO is filled with electrons, the electronegativity divides the band gap into two parts and the addition of these parts gives the chemical hardness.Having low chemical hardness 2.407, 2.723, and 3.781 (Table 10) for Ellagic, Gallic, and Malic acid, respectively indicates that they are good candidates for strong and efficient interactions with the metal surface.Furthermore, the mutual tendency of charge transfer between two interacting entities, in this case, inhibitor and metal surface, could be calculated as follows 90 :

Ellagic
where χ and η are electronegativity and chemical hardness, respectively.The predicted ΔN for the Ellagic, Gallic, and Malic acid are 0.288, 0.308, and 0.228, respectively (Table 10) revealing the good tendency of these molecules to mutually share electrons with the metal surface.Overall, global reactivity indices suggest a feasible mutual inhibitor-metal interactions between Ellagic, Gallic, and Malic acid and mild steel nominating them for effective corrosion suppression and explaining their recorded electrochemical high inhibition efficiency.

Natural bond orbital analysis
The results of NBO analysis are summarized in Tables 11, 12 and 13 for molecules of Ellagic, Gallic, and Malic acid, respectively.
The Tables list natural bond orbitals at expected inhibitor-metal interactions in descending order according to their energies along with their type of bonding, electron occupancy, energy, hybridization, and percent of s and p characters.Moreover, the surface densities of these orbitals are plotted in Table S1 to Table S3 with the same descending order.Analyzing NBOs allows us to determine the importance of individual sites of a molecule to come into interaction with the steel surface.In other words, NBOs order is an order of donating ability of the electron density involved in an interaction.The results in Table 11 show that the electron density of Ellagic acid molecule can be shared into the metal surface in the following order: LP The plots in (Table S1 to S3) show the source orbitals for these NBOs; for example, bonding orbital LP(2)O 27 originates from HOMO of the Ellagic acid molecule.In other words, the HOMO of the Ellagic acid molecule is localized on the lone pair of the O 27 atom and it is easier to interact with the steel surface than the other NBOs.In this order, the electronic density of BD ( 2

Local reactivity
While global reactivity explores the tendency of a molecular entity to be involved in chemical change, local reactivity figures out the sites within this entity to react with another one.For a molecule contacting metal surface and suppress corrosion reaction, it is worthy to have electron rich regions more than electron-poor ones.These regions could be explored using a calculated molecular electrostatic potential (MEP) map shown in Fig. 12.
In such map, electron-rich sites having low electrostatic potential are designated with red color and electronpoor sites are blue colored while sites with green color indicate moderate charge density content.The mapped surfaces presented in Fig. 12 show that the distribution of the colors follows the order: green > blue > red.The existence of wide areas with moderate electron density is common in organic molecules; however, maps of Ellagic, Gallic, and Malic molecules are characterized by electron-rich regions much more than electron poor-regions.The red regions are localized around carbonyl groups which agree with the order of the NBOs where HOMOs are corresponding to the lone pairs of oxygen atoms of the carbonyl groups suggesting that these groups have the priority to contact the metal surface.
Although the localization of electronic density over a particular site indicates its tendency to contact metal surface, which is useful, the magnitude of this conduct cannot be estimated from the MEP map.The magnitude of a particular site to be either nucleophile or electrophile could be determined using Fukui functions.In this procedure, the neutral molecule is charged by either a negative or a positive charge than the second derivative of energy is probed, for each atom, with respect to number of electrons and the external potential owing while molecules approaching each other as follows: A good approximation to solve this equation is to use "condensed" Fukui functions on an atom-by-atom basis 91 : Where f − k and f + k are electrophilic and nucleophilic Fukui indices, respectively and q k is the atomic charge.We used Hirshfeld charges since it is corrected to bond orders and is much accurate for molecules having singledouble bonds in conjugations.We listed the predicted Fukui indices for the Ellagic, Gallic, and Malic molecules in Table 14 according to the descending order of electrophilic Fukui function since it is of more interest for inhibitor-metal interactions.
Some good information can be inferred from Table 14, for example, in Ellagic acid, the oxygen atoms of carbonyl groups carry the highest (f − k = 0.073) electrophilic Fukui indices (O 28 and O 27 ) while those of hydroxyl groups carry lower indices ranging between 0.024 and 0.035 and those involved in the carbon skeleton are of the lowest electrophilic sites (Table 14).The same trend applies to oxygen atoms of Gallic acid; however, the presence of conjugation within the carbon rings provides stronger electrophilic sites than those of oxygen atoms.Finally, the Malic acid has the lowest electrophilic Fukui indices, though its carbonyl is much electrophilic than the corresponding carbonyl of Gallic acid which could be attributed to the conjugation of the latter with the phenyl ring.

Monte Carlo simulations
The modeling at the molecular level was done for the adsorption of Terminalia bellerica Fruit Extract (Ellagic, Gallic, and Malic acid) on steel (or Fe (1 1 0)) in the gas phase and the aqueous phase.Figure 13 displays the most stable configurations of the adsorbed Terminalia bellerica Fruit Extract modeled using MC in the aqueous phase settings.Figure 13 shows the close contact between Terminalia bellerica Fruit Extract constituents and the steel surface.This confirms their ability to compete with water and the corrosive ions in adsorption and so enhance protection 92 .It is noteworthy findings of the MC support the DFT investigation, which showed that the Ellagic structure has a high reactivity (completely flat and parallel adsorption) compared to Gallic and Malic acid, which are partially flat adsorbed.This may be used to support the inhibitory performance of the studied structures.( 11) Table 15 displays the binding energy and the different forms of the adsorption energy values for the Ellagic, Gallic, and Malic acid molecules.The spontaneous tendencies of Terminalia bellerica Fruit Extract constituents for adsorption are confirmed by negative adsorption energies values 93 .This is due to the numerous active adsorption sites found on the extract molecules.Based on the binding energy values, Ellagic has the highest binding energy followed by Gallic and Malic acid.This arrangement supports the outcomes of the DFT computation.

Corrosion inhibition mechanism by the extract of Terminalia bellerica on steel
A corrosion reaction consists of two electrochemical reactions: oxidation on the anode and reduction on the cathode.
When the electrons of the heteroatoms donate electrons to the empty orbital of the metal, a coordinate bond is formed 94 .
In 1 M sulfuric acid, steel corrosion can be reduced using phytochemicals present in Terminalia bellerica extract.These phytochemicals have a variety of functional groups, like carbonyl, hydroxyl, and carboxylic acids, as well as double bonds.Figure 14 illustrates how the lone pair of heteroatoms and the multiple bonds found in the phytochemicals form a coordinate bond.It is the inhibitory activity of the plant extract on the metal surface that leads to blocking of the active site.

Conclusion
1.The weight reduction method, potentiodynamic polarization study, and DFT were used to assess the corrosion resistance of steel immersed in H 2 SO 4 in the absence of Terminalia bellerica extract and in presence of extract.2. The addition of a fruit extract from Terminalia bellerica seems to increase the effectiveness of corrosion inhibition.3. It has been found that at a concentration of 4000 ppm, the inhibitory efficacy was 91.79%.4. The potentiodynamic polarization investigation shows that when the concentration of Terminalia bellerica extracts raises, the corrosion current density decreases.5.The various phytochemicals found in the extract have an impact on the inhibition's potency.6.As the inhibitor concentration is increased, the inhibition efficiency improves.www.nature.com/scientificreports/ 7.According to the NBO study, Ellagic acid has a stronger inhibitory efficiency due to the low energy gaps that may promote the reactivity of these molecules toward the metal surface.8.As a result of the Langmuir adsorption isotherm, SEM, and AFM, the adsorption process has been identified as the mechanism that prevents corrosion.

Figure 3 .
Figure 3. Corrosion inhibition efficiency of Terminalia bellerica extract at different concentrations.

Figure 5 .
Figure 5. Arrhenius plots and Transition state plots for steel dissolution with and without different concentrations of Terminalia bellerica in 1.0 M H 2 SO 4 solution.

Figure 6 .
Figure 6.Tafel polarization curves in 1 M H 2 SO 4 without and with various concentrations of Terminalia bellerica extract.

Figure 7 .
Figure 7. Nyquist (a) and Bode plots (b), and equivalent circuit of constant phase element (CPE) for steel in 1 M H 2 SO 4 without and with various concentrations of Terminalia bellerica extract at 298 K.

Figure 8 .
Figure 8. UV spectrum of Terminalia bellerica extract before and after the corrosion inhibition performance.

Figure 13 .
Figure 13.Side and top views of the most appropriate configuration for adsorption of neutral molecules on Fe (110) Surface obtained by MC simulations in the aqueous solution.

Table 2 .
Corrosion inhibition efficiency of some plants. S.

Table 3 .
Composition of the studied steel coupons.

Table 4 .
Weight loss data of inhibition efficiency and surface coverage of Terminalia bellerica in 1 M H 2 SO 4.

Table 5 .
Adsorption isotherms models of the Terminalia bellerica with values of R 2 , slopes, intercepts, and thermodynamic parameters (K ads and ΔG o ads ) by using data obtained from WL measurements.

Table 6 .
Activation parameters of dissolution reaction of steel in 1 M H 2 SO 4 with at different concentrations of Terminalia bellerica.

Table 7 .
Potentiodynamic polarization parameters for steel dissolution without and with various concentrations of extract.

Table 8 .
Electrochemical parameters calculated from EIS measurements on mild steel electrode in 1.0 M H 2 SO 4 solutions without and with various concentrations of Terminalia bellerica at 298 K. R s solution resistance, R ct charge transfer resistant, Y 0 , n constants of phase elements, C dl double layer capacitance, S slopes of the Bode impedance magnitude at intermediate frequencies, α° maximum phase angle values, θ surface coverage, η z inhibition efficiency.

Table 9 .
Phytochemical analysis of Terminalia bellerica extract.Test for saponinsFive milliliters of water and five milliliters of filtrate are mixed vigorously.The development of steady foam is a clue that saponins are present.

Table 12
while corresponding orbital densities from HOMO to HOMO-9 are listed in TableS2.Moreover, NBOs of Malic acid show donating behavior following the order: LP(2)O 16 > LP(2) O 10 > LP(2)O 12 > LP(2)O 14 > BD(2)C 9 -O 16 > BD(1)C 1 -H 2 .It is worth noticing that the number of donating sites follows the order Ellagic > Gallic > Malic which in turn favors the adhering of metal surface in the same order.

Table 15 .
The outputs and descriptors calculated by the Monte Carlo simulation for adsorption of ellagic, gallic and malic acid molecules on Fe (110).*All quantities are in (k cal mol −1 ).