Mathematical models predict corrosion inhibition

Mathematical models predict corrosion inhibition: Comparison

Please note this is a comparison between Version 20 by Evelin Gutiérrez and Version 19 by Evelin Gutiérrez.

The use of corrosion inhibitors is an important method to retard the process of metallic attack by corrosion. The construction of mathematical models from theoretical-computational and experimental data obtained for different molecules is one of the most attractive alternatives in the analysis of corrosion prevention, whose objective is to define those molecular characteristics that are common in high-performance corrosion inhibitors.

corrosion inhibition
organic inhibitors
theoretical studies
molecular descriptors
mathematical models

1. Introduction

Corrosion is defined as the destructive attack of a material by reaction with its environment. This process is a worldwide, significant problem because of the economic damage and safety loss it may lead to. The losses originating from corrosion can be categorized as direct and indirect, and the latter includes economic losses caused by plant shutdowns, efficiency reduction, costly maintenance, and contamination of products whose overall impact will ultimately require over-design. The direct losses include the cost of replacing corroded structures, fixing damaged machinery, and substituting some of its components.

Corrosion control can be achieved by recognizing and understanding the mechanisms associated with this process. It is possible to prevent corrosion by using corrosion-resistant materials and protective systems.

The selection of materials; which can be metallic, non-metallic or alloys, is a key factor in the prevention of corrosion processes, as well as the consideration of the temperature, the type of environment and the general conditions to which the material is subjected. In such selection, both the mechanical and physical analyses of the materials’ properties play a very important role. However, such selection is limited by the availability and cost of materials. This limitation forces the industry to resort to the corrosion protection offered by metallic or non-metallic coatings and anodic or cathodic processes for metal protection, as well as to carefully select the appropriate geometrical configurations to prevent corrosive conditions and to avoid the use of bimetallic couples, which can be responsible for favoring the corrosion process. Corrosion protection can also be achieved by promoting the formation of Ni and Cr protective barriers or by protecting a substrate (steel) with sacrificing materials such as Zn, Al or Cd ^[1].

The environments to which metals are exposed make them prone to corrosion. A less aggressive environment can be obtained by removing constituents that facilitate corrosion, modifying the temperature, dehumidifying the air, removing dissolved O₂ or solid particles, controlling the pH or adding corrosion inhibitors. The usage of inhibitors is one of the most practical methods for protection against corrosion in acidic, alkaline, saline, and other aggressive environments.

The following sections include:

The definition of a corrosion inhibitor and the structural characteristics associated with an inhibitor molecule; a brief mention is made of the techniques that allow evaluating the performance of corrosion inhibitors in the protection of metal surfaces exposed to aggressive environments.
The factors that increase the corrosion process and those that can be modified to prevent this phenomenon are briefly mentioned.
The most important data such as molecules and inhibition efficiencies obtained by different techniques and experimental conditions have been summarized, taking into account the functional group of greatest interest to the study authors. Information related to the descriptors used in the theoretical analysis of corrosion inhibitors has been collected.
Finally, a table has been generated with examples of some mathematical models obtained to evaluate corrosion inhibitor molecules, in which it is possible to observe the most common descriptors to predict the corrosion phenomenon.

2. Corrosion Inhibitors

Corrosion inhibitors are chemical substances that are added to aggressive environments in small concentrations to decrease the corrosion rate. These substances can react with either a metal surface or its surroundings providing protection to the surface, although it has been observed that corrosion inhibitors generally work by forming an adsorbed film. Corrosion inhibitors are an appropriate option for metal protection when these are exposed to aggressive media, such as, acidic solutions (widely employed for industrial cleaning), oil well acidification, and petrochemical processes ^[2]. Corrosion inhibitors can be introduced into the aggressive environment in a single application or continuously by gradual and controlled additions. The single addition is possible in static systems at low temperature and where friction is negligible. Gradual addition is necessary for systems where variation in flow and temperature degrade the integrity of the protective film formed on the metal surface, either by physisorption or chemisorption. The stability of the corrosion inhibitor films can be compromised by the concentration levels of the inhibitor in the medium ^[2]. Comparative studies performed to determine inhibition effects are generally performed without shaking. Therefore, the existence of a significant effect of immersion time on the quality of the formed film of an inhibitor is reasonable.

An important number of compounds have been used for the corrosion protection of metals exposed to aggressive media. Their effectiveness is associated to their chemical composition, molecular structure, alkyl chain length (or molecular volume), planarity, presence of lone pairs of electrons in heteroatoms (e.g., S, N, O, P), affinity for the metallic surface, dipole moment, presence of π-electrons (unsaturation or aromatic ring) and energy of frontier molecular orbitals. The efficiency (E%) of corrosion inhibitors is measured by applying the Equation (1) to experimental data obtained by techniques such as weight loss (WL), potentiodynamic polarization (PP), and electrochemical impedance spectroscopy (EIS):

\( E\% = \frac{{\left( {C{R_u} - C{R_i}} \right)}}{{C{R_u}}} \times 100 \). Equation (1)

where CR_u is the corrosion rate of the uninhibited system and CR_i is the rate of the inhibited system.

The mechanisms through which corrosion inhibitors can be bounded to the metal or the metal oxide surface may be physisorption, chemisorption, complexation or precipitation. The film formed by corrosion inhibitors prevents the access of oxygen to the cathode and the diffusion of hydrogen away from it, or simply inhibits metal dissolution (anodic inhibitors). Inhibition efficiency can be altered by modifying the system parameters such as pH, temperature, metal composition, type of inhibitor and molecular structure of the corrosion inhibitor ^[3]. An important factor associated with the corrosion process is surface roughness. The increase in the surface roughness of alloys (magnesium, titanium-based), stainless steels, copper, and aluminum increases the pitting susceptibility and the corrosion rate ^[4].

Corrosion inhibitors can act by stimulating anodic or cathodic polarization, reducing the transport of ions towards the metallic surface and increasing the electrical resistance of a metallic material. These compounds can be classified according to their functionality (anodic, cathodic, organic and precipitation-inducing inhibitors). Anodic inhibitors are molecules that cause a large anodic shift of the corrosion potential and by this means they are able to generate the passivation of the metal surface. On the other hand, cathodic inhibitors either slow the cathodic reaction or selectively precipitate on cathodic areas increasing the surface impedance and reducing the diffusion of species. Some cathodic inhibitors may precipitate as oxides building a protective layer on the metallic surface. Organic inhibitors can be classified as another type of inhibitor. These substances can be associated with anodic and cathodic effects; they generally protect the metallic surface by creating a film whose function consists in isolating the metal from corrosion. Finally, precipitation-inducing inhibitors are compounds responsible for the formation of precipitates on the metallic surface which protect it from the corrosion process . In the study of amino acids carried out by Aouniti et al. ^[3], it was demonstrated by the analysis of cathodic and anodic potentiodynamic polarisation curves, that these compounds act as cathodic inhibiting only the cathodic process. In the analysis, before recording the cathodic polarisation curves, the electrode was polarised at −800 mV/SCE (saturated calomel electrode) for 10 min, while for the anodic curves, the potential electrode was swept from its corrosion potential (maintained 30 min) to positive values. No changes were observed in the anodic curves.

The phosphonate derivatives evaluated by Benabdellah et al. ^[4] are also cathodic inhibitors that cause a decrease in current density and do not modify the characteristics in the anodic domain. In the study, the slopes of cathodic Tafel lines and the corrosion potential remain almost constant which reveals that the mechanism of reduction of hydrogen ion is not affected by the presence of inhibitor. An important number of corrosion inhibitors act as mixed inhibitors blocking the cathodic reaction sites (hydrogen evolution) and anodic reaction sites (metal dissolution) on the metallic surface ^[5].

There are also mixed inhibitors with the most significant anodic effect, which can be observed in the change of the slopes of anodic Tafel lines and the displacement of corrosion potential towards positive values compared with not protected surfaces. Among these, hydantoin ^[6], pyrimidine ^[7], and Schiff base compounds ^[8] are also reported. Film-forming compounds are precipitation-inducing inhibitors. Precipitation inhibitors act on both the anodic and cathodic sites indirectly by blocking the metal surface, examples include silicates and phosphate ^[9]. As has been previously mentioned, inhibitors often act by adsorbing themselves on a metallic surface preventing the corrosive attack through the formed film. The adsorption of corrosion inhibitors depends on the charge of the corrosion inhibitor and the charge of the metallic surface, as well as the temperature and pressure involved in the process. Many researchers have mentioned that compounds containing nitrogen, oxygen and sulphur atoms give rise to a high inhibition efficiency in acidic media ^[10] ^[11] ^[12]. Most organic substances containing at least one functional group that can serve as a potential reaction centre for adsorption on a metallic surface can be probed as a corrosion inhibitor ^[13].

Corrosion protection as a result of a film formation process is mainly associated with sorption processes. The organic compounds adsorbed on a metal surface replace the pre-adsorbed water molecules and prevent the dissolution of the metallic surface, reducing the interaction between the metal surface and corrosive electrolytes ^[14].

Ehteshamzadeh et al. ^[8] described the interaction processes of organic corrosion inhibitors and a metallic surface through four mechanisms: (a) electrostatic interaction between a negatively charged surface, which is a result of the (Cl⁻) anions adsorbed on iron and the positive charge of the inhibitor in HCl media, (b) interaction of the unshared electron pairs of the corrosion inhibitor with the metallic surface, (c) interaction of p-electrons with the metal and (d) the combination of types a-c. The adsorption process can be named physisorption only when electrostatic forces between ionic charges or dipoles on the adsorbed species and an electric charge at the metal/solution interface are involved. This adsorption mechanism has low values of adsorption heat and it is stable only at low temperatures. The adsorption process can also occur through chemisorption, which involves charge sharing or charge transfer from the corrosion inhibitor to the metal surface forming a coordinate-type bond. Chemisorption is associated with a higher adsorption energy than physical adsorption, therefore the established bond will be stable at higher temperatures ^[15] ^[16] ^[17].

Among the compounds proposed as corrosion inhibitors we find: N-containing heterocyclic organic molecules such as imidazole, benzimidazole, bis-benzimidazoles, amine, Schiff base compounds and alkaloids (e.g., papaverine, strychnine, quinine, and nicotine); S-containing compounds that comprise sulphonamides-which possess a large number of functional groups that are potential adsorption centres (-NH₂ group, -SO₂-NH- group, O and/or N heteroatoms and aromatic rings) -, sulfonates, thiols, and thioaldehydes; O-containing compounds that can include benzoates, aldehydes, indanone derivatives; and finally, P-containing compounds as phosphonate derivatives and heteroatom-containing compounds such as azoles. The studies reveal that the inhibition of corrosion processes is mainly attributed to the formation of donor-acceptor complexes ^[4] ^[5] ^[11] ^[12] ^[14] ^[18].

According to observations performed in presence of compounds with heteroatoms in their structure, the corrosion inhibition efficiency follows this tendency: O < N < S < P. This behaviour is also associated with the electronegative character of the involved atoms ^[4] ^[19]. There is a growing interest in defining the best molecular characteristics of a corrosion inhibitor in addition to the effects associated with the presence of heteroatoms, while also taking factors such as cost, toxicity, availability and environmental friendliness into account ^[20].

The following sections contain a review of some of the molecules studied as corrosion inhibitors in different environments. In the cases where the number of compounds evaluated by the authors was larger than four, only the best two and the worst two corrosion inhibitors are included, there is also mentioned the total number of corrosion inhibitors (N_CI) employed in every analysis. For almost all of the studies reviewed in this paper, the corrosion inhibition efficiencies tabulated correspond to the values obtained at the highest inhibitor concentration. It is worth noting that the most efficient corrosion inhibitors tended to be complex molecules with more than one heteroatom in their structure; however, for the purpose of this review, corrosion inhibitors have been classified according to the heteroatom considered of higher interest by the referenced researchers.

The following sections summarize the analysis conditions employed by different researchers and the corrosion inhibition efficiencies obtained by the different techniques; weight loss (Ef_WL), potentiodynamic polarization (Ef_PP), and electrochemical impedance spectroscopy (Ef_EIS), at those conditions. Cases where the theoretical analysis (TA) was applied (A) or not (NA) are mentioned. There is an important number of experimental conditions (Exp.C.) that affect the corrosion inhibition efficiency, among these factors we find: the metallic surface (Met) and the exposure time (t) of this in inhibited and uninhibited solutions, temperature (T), aggressive media and its concentration (Media), as well as the corrosion inhibitor concentration (Co), nature of the anion in the corrosive medium, type of metal, and pH ^[21] ^[22]. The immersion time (a) can affect the natural oxide film of some metallic surfaces, (b) can be responsible for increasing the thickness of the layer formed by corrosion products, which can reduce the corrosion rate, (c) may favour or not the increase of corrosion inhibitor adsorption leading to the formation of uniform and stable films of corrosion inhibitors.

3. N-Containing Corrosion Inhibitors

An important number of molecules evaluated as corrosion inhibitors in acidic media contain N-atoms and the structural properties that are characteristic of high-performance corrosion inhibitors. Table 1 shows some examples of the N-containing corrosion inhibitors evaluated by different researchers.

Table 1. N-containing corrosion inhibitors

Example	Corrosion Inhibitor	Ef_WL/Ef_PP/Ef_EIS	Ref
	(4-Chloro-benzylidene-pyridine-2-yl-amine)	99.5/99.6/99.6	^[23]
Exp. C. N_CI: 3, Met: mild steel, Media: HCl 1.0 M, Co: 2×10⁻⁴–1×10⁻²M, t: 24 h (WL), T: 25 °C, TA: A
	2,5-bis(2-hydroxyphenyl)-1,3,4-oxadiazole	98.2/94.7/99.1	^[624]
Exp. C. N_CI: 2, Met: mild steel, Media: HCl 1.0 M, 0.5 M H₂SO₄, Co: 20–80 mg•L⁻¹, t: 24 h (WL), 20 h (EIS), T: 30 °C, TA: NA
	Tributylamine	97.8/-/-	^[725]
Exp. C. N_CI: 23, Met: 13% Cr steel, Media: HCl (15%w/v), Co: 2%w/v inhibitor and 0.6% w/v formaldehyde (used to minimize hydrogen penetration), t: 3 h, T.: 60 °C, TA: A
	1,2-bisbenzylbenzimidazole	96	^[823]
Exp. C. N_CI: 11, Met: iron, Media: HCl 1.0 M. The analysis technique and the rest of the experimental conditions are not specified. TA: A
	3,4-Dichloro-acetophenone-O-1′-(1′.3′.4′-triazolyl)-metheneoxime (DATM)	92.8/98.7/98.7	^[919]
Exp. C. N_CI: 3, Met: mild steel, Media: HCl 1.0 M, Co:1×10⁻⁵–1×10⁻³M, t: 3 h (WL), 30 min (PP), T: 25 °C, TA: A
	* 2,6-bis-(2-benzimidazolyl) pyridine	-/94–96/97.0	^[105]
Exp. C. N_CI: 4, Met: mild steel, Media: HCl 1.0 M, Co: 0.1–1.0 mM, t: 1–96 h (WL), 45 min (PP), T.: 30 °C, TA: NA
	1-(4-Methyloxyphenylimino)-1-(phenylhydrazono)-propan-2-one	-/95.9/96.2	^[1124]
Exp. C. N_CI: 5, Met: mild steel, Media: HCl 1.0 M, Co: 5×10⁻⁶–7.5×10⁻⁵M, t: 30 min, T: 25 °C, TA: NA
	1-Butyl-2-propylene-2-imidazoline	95.1/-/-	^[1218]
Exp. C. N_CI: 34, Met: stainless steel, Media: HCl 5%, Co: ≈0.1 M, t: 48 h, T: T_R(room temperature), TA: A
	Aniline, N-(p-methoxybenzylidene)	-/94.0/-	^[1326]
Exp. C. N_CI: 4, Met: aluminium, Media: HCl 2.0 N, Co: 10⁻⁵–10⁻²M, t:-, T: 30 °C, TA: NA
	Cyclohexanone oxime	93.9/98.4/95.2	^[1427]
Exp. C. N_CI: 3, Met: aluminium, Media: HCl 1.0 M, Co: 0.2–2.0 mM, t: 2 h, T: 20–50 °C, TA: NA
	6-Bromo-1H-benzimidazole	-/-/89.4	^[1528]
Exp. C. N_CI: 15, Met: carbon steel, Media: HCl 1.0 M, Co:0.1–10 mM, t: 30 min, T: T_R, TA: A
	2-Mercaptobenzimidazole	-/88.7/90.4	^[215]
Exp. C. N_CI: 3, Met: mild steel, Media: HCl 1.0 M, Co: 50–250 ppm, t: 30 min, T: 25 °C, TA: NA
	2-Chloromethylbenzimidazole	-/-/69.7	^[1629]
Exp. C. N_CI: 6, Met: carbon steel, Media: HCl 1.0 M, Co: 1×10⁻³ M, t: -, T: T_R, TA: A
	2,4-Dimercaptopyrimidine	43.0/-/-	^[3] ^[17] ^[30] ^[31]
Exp. C. N_CI: 14, Met: Aramco iron, Media: HCl 2.0 M, Co: 1×10⁻³ M, t: 1 h, T: 40 °C, TA: A
Simbology: TA: theoretical analysis, A: applied, NA: not applied, Exp. C.: experimental conditions; N_CI: number of corrosion inhibitors, Co: inhibitor concentration, t: exposure time, T: temperature, Ef_WL/Ef_PP/Ef_EIS: corrosion inhibition efficiencies obtained by weight loss (WL), potentiodynamic polarization (PP), and electrochemical impedance spectroscopy (EIS), respectively.

Ashassi-Sorkhabi et al. ^[2326], studied the effect of three Schiff base compounds as corrosion inhibitors in mild steel exposed to acidic media (HCl 1.0 M). The structure of the Schiff bases, with the presence of a benzene ring and -C=N group, is associated with the formation of an important p bond, which can be considered a good characteristic in a corrosion inhibitor. The p electrons of Schiff base compounds interact with unoccupied orbitals of iron, and also the p* orbital can accept electrons coming from the d orbitals of iron, resulting in the formation of feedback bonds, giving place to adsorption centres. Researchers observed that the inhibition efficiency depended on the type of functional groups attached to the benzene ring and demonstrated that the presence of electron-donating groups (methyl group and chloride) increased the effect of the corrosion inhibitor benzylidene-pyridine-2-yl-amine, and this happened as a result of the increase in the electron density on the nitrogen atom of the C=N group. Gomma et al. ^[2427] performed the analysis of Schiff bases as corrosion inhibitors for aluminium (commercial-grade) in hydrochloric acid solution. Although aluminium possesses a passive oxide film that protects it in various environments, this film is amphoteric and can be dissolved when exposed to acidic media (pH lower than 5) or alkaline media (pH higher than 9) ^[2528]. The corrosion inhibitors evaluated by Gomma et al. ^[2427] caused a displacement of the corrosion potential in the negative direction, which means that the inhibitors employed are cathodic. It was observed that the inhibition efficiency increased as temperature rose, which makes these inhibitors an interesting option to delay the corrosion at elevated temperature conditions. Such behaviour is associated to a diffusion process, in which at a higher temperature the amount of inhibitor that reaches the metallic surface is greater than under lower temperature conditions. Higher temperatures are associated with higher activation energy available for adsorption processes, higher diffusion rate of inhibitor molecules and changes in the inhibitor molecule, causing increases in the electron density in the vicinity of the adsorption centres which, in turn, increases the efficiency ^[2629].

Table 2. S-containing corrosion inhibitors

Example	Corrosion Inhibitor	Ef_WL/Ef_PP/Ef_EIS	Ref
	1-Phenyl thiosemicarbazide	-/100.0/-	^[18]
Exp. C. N_CI: 10, Met: mild steel, Media: H₂SO₄, Co: 1 mMdm⁻³, t: -, T: 30 °C. TA: A
	Phenylthiourea (PTU)	-/-/97.2	^[19]
Exp. C. N_CI: 3, Met: mild steel, Media: H₂SO₄ 0.1 M, Co: 1–10 mM, t:1 h, T: T_R, TA: NA
	2-Mercaptobenzothiazole	-/97/-	^[20]
Exp. C. N_CI: 1, Met: Steel (API 5L X52), Media: H₂SO₄ 1.0 M, Co: 10^−4-–10⁻³ M, t: 30 min, T: 25 °C, TA: A
	4-Hydroxybenzaldehyde thiosemicarbazone	-/97.0/90.0	^[21]
Exp. C. N_CI: 6, Met: carbon steel, Media: HCl 1.0 M, Co: 10⁻⁴–10⁻²M, t: 30 min, T: 25 °C, TA: NA
	2-Mercapto-1-methylimidazole	90.4 /95.5/-	^[22]
Exp. C. N_CI: 1, Met: carbon steel, Media: HClO₄ 1.0 M, Co: 7.510⁻⁵–2.5 10⁻³ M, t:1 h, T: 30 °C, TA: NA
Simbology: TA: theoretical analysis, A: applied, NA: not applied, Exp. C.: experimental conditions; N_CI: number of corrosion inhibitors, Co: inhibitor concentration, t: exposure time, T: temperature, Ef_WL/Ef_PP/Ef_EIS: corrosion inhibition efficiencies obtained by weight loss (WL), potentiodynamic polarization (PP), and electrochemical impedance spectroscopy (EIS), respectively.

Table 3. O-containing corrosion inhibitors

Example	Corrosion Inhibitor	Ef_WL/Ef_PP/Ef_EIS	Ref
	2-(4-Methylbenzylidene)-3-oxo-2,3-dihydro-1H-indene-1-carboxylic acid	92.0/93.9/92.6	^[2326]
Exp. C. NCI: 3, Met: mild steel, Media: HCl 1.0 M, Co: 10⁻⁶–10⁻³ M, t: 6 h, T: 30 °C, TA: NA
	1-((4-Chlorophenyl)(2-hydroxynaphtalen-1-yl)(phenyl) methyl)urea (CPHU)	90/92.0/-	^[2427]
Exp. C. NCI: 3, Met: mild steel, Media: H₂SO₄ 0.5 M, Co: 2–10 ppm, t: 24 h (WL) and 30 min (PP), T: 20 °C, TA:A
	1,3-Dibromo-5,5-dimethylhydantoin	-/89.8/91.4	^[2528]
Exp. C. NCI: 6, Met: mild steel, Media: HCl 0.5 M, Co: 10–50 ppm, t: 30 min, T: 30 °C, TA:A
	L-ascorbic acid	69.0/-/-	^[2629]
Exp. C. NCI: 1, Met: mild steel, Media: H₂SO₄ 0.01 M, Co: 10⁻⁷–10⁻³ M, t: -, T: T_R, TA: NA
Simbology: TA: theoretical analysis, A: applied, NA: not applied, Exp. C.: experimental conditions; N_CI: number of corrosion inhibitors, Co: inhibitor concentration, t: exposure time, T: temperature, Ef_WL/Ef_PP/Ef_EIS: corrosion inhibition efficiencies obtained by weight loss (WL), potentiodynamic polarization (PP), and electrochemical impedance spectroscopy (EIS), respectively.

Table 4. Multi-heteroatom containing corrosion inhibitors

Example	Corrosion Inhibitor	Ef_WL/Ef_PP/Ef_EIS	Ref
	(2,3,8,9-Dibenzo-4,7-dioxa-13-thia-11,12-diazabicyclo[8.2.1]trideca-10,12-diene (1-MCTH)	97.7/-/-	^[1]
Exp. C. NCI: 5, Met: mild steel, Media: 1.0 M HCl, Co: 110⁻⁶–110⁻⁴ M, t: 24 h (WL), T: 30 °C, TA: A
	Sulphadimethoxine	93.8/84.0/92.1	^[2723]
Exp. C. NCI: 5, Met: mild steel, Media:1.0 M HCl, Co: 1–510⁻⁵ M, t: 30 min, T: 30–50 °C, TA: A
	5-Benzoyl-4-tolyl-6-phenyl-1,2,3,4-tetrahydro-2-thioxopyrimidine	-/93.0/93.0	^[2824] ^[2930]
Exp. C. NCI: 2, Met: stainless steel, Media:1.0 M HCl, Co:110⁻⁴–5 10⁻³ moldm⁻³, t: 30 min, T: 25 °C. The experimental data were obtained by Caliskan, et al. ^[2824]. TA: A
	L-Cysteine	82.2/-/-
Exp. C. NCI: 4, Met: mild steel, Media:0.1 M HCl, Co: 0.1–0.5 gL⁻¹, t: 24, 168 h, T: 30, 60 °C, TA: A
	(E)-N-methyl-2-(1-phenylethylidene)hydrazinecarbothioamide PHCARB	80.7/-/-	^[3031]
Exp. C. NCI: 4, Met: mild steel, Media:0.1 M HCl, Co: 1–510⁻⁴ M, t: 168 h, T: 30 °C, TA: A
	Methionine	72.7/84.6/85.8
Exp. C. NCI: 16, Met: Armco iron, Media: HCl 1.0 M, Co: 10⁻³ M, et: 6 h (WL), 10 y 30 min (PP), T: 35 °C, TA: A
Simbology: TA: theoretical analysis, A: applied, NA: not applied, Exp. C.: experimental conditions; NCI: number of corrosion inhibitors. Co: inhibitor concentration, t: exposure time, T: temperature, Ef_WL/Ef_PP/Ef_EIS: corrosion inhibition efficiencies obtained by weight loss (WL), potentiodynamic polarization (PP), and electrochemical impedance spectroscopy (EIS), respectively.

Table 5. Examples of descriptors used in the theoretical analysis of corrosion inhibitors.

Quantum Descriptor	Symbol	Description	Reference
Energy of the highest occupied molecular orbital	E_HOMO	Associated with the electron-donating ability of a molecule.	^[5]
Energy of the lowest unoccupied molecular orbital	E_LUMO	Indicates the ability of the molecule to accept electrons.	^[22]
Ionization potential	IP	It is a descriptor of the chemical reactivity of atoms and molecules. IP is the minimum energy required to remove an electron from an atom.	^[2930]
Electron affinity	A	It is a property that determines how susceptible a molecule is towards the attack of a nucleophile.	^[3132]
Dipole moment	_μD	The dipole moment is considered a measure of the stability of the formed complex on a metal surface. It is an indicator of the asymmetry in the molecular charge distribution. It is related to the hydrophobic character of the molecules.	^[2427] ^[3233] ^[3334]
Energy gap	ΔE	ΔE= E_{HOMO −}E_LUMO It has been mentioned that the successful adsorption and proper efficiency of an inhibitor have been characterized by a high E_HOMO, a low E_LUMO_,and a small energy gap. The lower the ΔE is, the higher the stability of the metal-inhibitor interaction.	^[10] ^[3233] ^[3435]
Fraction of electron transferred	ΔN	If ΔN > 3.6, the inhibition efficiency increases	^[10]
Global hardness	η	It is a parameter associated with the resistance of an atom to transfer its charge.	^[10]
Softness	σ	The σ shows the reactivity of the inhibitor molecules in terms of charge transfer.	^[10]
Electronegativity	χ	The electronegativity measures the power of a group of atoms to attract electrons towards itself.	^[10]
Electrophilicity index	ω	It is a reactivity descriptor that allows the quantitative classification of the global electrophilic nature of a molecule. This descriptor has been proposed as a measure of energy lowering due to maximal electron flow between donor and acceptor.	^[9]
Electrodonating power	ω^-	A descriptor associated with the ability of a species to donate electrons.	^[3536]
Electroaccepting power	ω⁺	A descriptor associated with the ability of a species to accept electrons.	^[3536]
Dipole polarizability	α	α is a measure of the mean polarizability. Higher values of α enable a strong adsorption process.	^[9]
Fukui functions	f_k⁺, f_k ^-	These functions indicate the part of the molecule where nucleophilic, electrophilic, and radical attack is most likely to occur.	^[3132]
Partition coefficient	Log P	Log P is a hydrophobic parameter of a molecule.	^[3637]

Table 6. Examples of mathematical models generated for corrosion analysis.

Molecules Evaluated	Theoretical Calculation	Mathematical Model	R²	Ref.
Schiff base	AM1 semi-empirical method	\( {\small I{E_{exp}}\left( \% \right) = 2.084{E_{HOMO}} - 3.041{E_{LUMO}} + 115.772 } \)	1.00	^[5]
Schiff base	AM1 semi-empirical method	\( {\small IE_{Theor}=\frac{\left(-604.90E_{HOMO}+5864.86E_{LUMO}+1190.06\mu_D-642.67\right)C}{\left[1+\left(-604.90E_{HOMO}+5864.86E_{LUMO}+1190.06\mu_D-642.67\right)C\right]} } \)	0.98	^[5]
Amines, thioureas, acetylenic alcohols	AM1 methodology was used for most descriptors, PC model provided the volume calculations	\( {\small \begin{matrix}lnK_{ads}=-0.93N-7.64P+6.74C-2.27C_{12}+0.94C_{13}-1.06C_1\\-7.22C_2-2.17E_{HOMO}-1.17DP+7.45V-1.15A_1\\-1.81A_2+7.12NCS-1.869NOH-1.085NCR\\\end{matrix} } \)	0.98	^[7]
		\( {\small lnK_{ads}=1.52M-0.79P+0.53C_{12}+0.80NT-0.66NOH } \)	0.86
		\( {\small \begin{array}{*{20}{c}} {{\rm{ ln}}{{\rm{K}}_{{\rm{ads}}}}{\rm{ = }}}&{ - 2.688 \times {{10}^{ - 2}}{A_1} + 0.115{A_2} + 4.530 \times {{10}^{ - 2}}{A_3} + 8.762 \times {{10}^{ - 2}}NB - 1.305 \times {{10}^{ - 2}}NC}\\ {}&{ + 0.102NCS - 4.518 \times {{10}^{ - 2}}NT - 5.172 \times {{10}^{ - 2}}NOH - 1.099 \times {{10}^{ - 3}}NCR + 4.996 \times {{10}^{ - 2}}NR}\\ {}&{ - 6.338 \times {{10}^{ - 2}}N - 0.114ED + 0.184M + 0.180P - 6.838 \times {{10}^{ - 2}}C + 8.092 \times {{10}^{ - 2}}{C_{12}}}\\ {}&{ - 4.783 \times {{10}^{ - 2}}{C_{13}} - 1.130 \times {{10}^{ - 2}}{C_{14}} - 0.167{C_1} - 0.152{C_2} - 0.122{E_{HOMO}}}\\ {}&{{\rm{ - 7.838}} \times {\rm{1}}{{\rm{0}}^{ - 2}}{{\rm{E}}_{{\rm{LUMO}}}}{\rm{ - 7.004}} \times {\rm{1}}{{\rm{0}}^{ - 3}}\Delta {\rm{E + 0.109}}\mu {\rm{ + 0.141V}}} \end{array} } \)	0.85
Triazole derivatives	Density Functional Theory (DFT), B3LYP/6-31G	\( {\small IE_{Theor}=\frac{\left(18.38E_{HOMO}-7.28E_{LUMO}-0.012V+123.36\right)C}{\left[1+\left(18.38E_{HOMO}-7.28E_{LUMO}-0.012V+123.36\right)C\right]} } \) Derived QSAR equation in gas phase	0.94	^[9]
Triazole derivatives	Density Functional Theory (DFT), B3LYP/6-31G	\( {\small IE_{Theor}=\frac{\left(-2.19E_{HOMO}-1.24E_{LUMO}-0.014V-10.94\right)C}{\left[1+\left(-2.19E_{HOMO}-1.24E_{LUMO}-0.014V-10.94\right)C\right]} } \) Derived QSAR equation in aqueous phase	0.95	^[9]
Imidazole derivatives	Restricted Hartree–Fock level (RHF) using MINDO/3, MNDO, PM3 and AM1 semi-empirical SCF-MO methods.	\( {\small I{E_{exp}}\left( \% \right) = 1174.95 + 214.612{E_{HOMO}} - 16.793{E_{LUMO}} } \) Gas phase (series 1)	0.90	^[8]
		\( {\small I{E_{exp}}\left( \% \right) = 517.7 + 53.8{E_{HOMO}} - 1.97{E_{LUMO}} } \) Aqueous phase (series 1)	0.82
		\( {\small I{E_{exp}}\left( \% \right) = 2420.86 + 295.67{E_{HOMO}} - 30.08{E_{LUMO}} } \) Gas phase (series 2)	0.97
		\( {\small I{E_{exp}}\left( \% \right) = 601.53 + 63.07{E_{HOMO}} - 1.405{E_{LUMO}} } \) Aqueous phase (series 2)	0.99
Imidazole and benzimidazole derivatives	---	\( {\small I{E_{exp}}\left( \% \right) = 38.47 + 20.21n\left( N \right) - 7.98N\left( {O + N{H_2}} \right) + 14.94{\eta ^ + } - 17.93{\eta ^ - } } \)	0.97	^[12]
Indole derivatives	DFT, B3LYP functional and 6-31G(2d,2p) basis	\( {\small R_{ct}=150+\left(-359539E_{HOMO}+1585825E_{LUMO}\right)C } \)	0.97	^[1]
Indole derivatives	DFT, B3LYP functional and 6-31G(2d,2p) basis	\( {\small R_{ct}=150+\left(-402535E_{HOMO}+960146E_{LUMO}\right)C } \)	0.97	^[1]
Imidazole and benzimidazole derivatives	DFT: PBE/6-311++G **	\( {\small {E_{exp}}\left( \% \right) = 5130.95 - 32.03\chi + 533.4b{q^{ISO}} + 0.37V + 1433.78{q_{N1}} } \)	0.92	^[3738]
Imidazole, benzimidazole and pyridine derivatives	DFT: PBE/B3LYP/M06, using the orbital basis 6-31G* and 6-311++G**	\( {\small I{E_{exp}}\left( \% \right) = 92.965 + 0.152V + 35.337{\omega ^ - } + 3.592b{q_{ANS}} } \)	0.75	^[15]
Pyrimidine derivatives	DFT BLYP/DNP	\( {\small I{E_{exp}}\left( \% \right) = - 4.324\mu - 46.527{\rm{\Delta }}E + 376.48{q_{N1}} } \)	0.98	^[17]
Thiosemicarbazides	PM3 and MNDO method.	\( {\small IE_{Theor}=\frac{\left(-6.7E_{HOMO}-5.9E_{LUMO}-3.5\mu-43.7\right)C}{\left[1+\left(-6.7E_{HOMO}-5.9E_{LUMO}-3.5\mu-43.7\right)C\right]}\times100 } \)	0.84
Thiosemicarbazides	PM3 and MNDO method.	\( {\small IE_{Theor}=\frac{\left(227.2+23.5E_{HOMO}-3.8\mu\right)C}{\left[1+\left(227.2+23.5E_{HOMO}-3.8\mu\right)C\right]}\times100 } \)	0.92
Thiosemicarbazides/ Thiosemicarbazones	Data obtained from literature	\( {\small IE_{exp}=\frac{e^{-2.5219E_{HOMO}-0.5119\mu_D-18.1761}C}{\left(1+e^{-2.5219E_{HOMO}-0.5119\mu_D-18.1761}C\right)} } \)	0.89	^[18]
Thiosemicarbazides/ Thiosemicarbazones	Data obtained from literature	\( {\small {\rm{I}}{{\rm{E}}_{{\rm{exp}}}}{\rm{ = }}\frac{{{{\rm{e}}^{{\rm{263.12}}\Delta {\rm{E - 17.26}}\Delta {\rm{E2 - 999.22}}}}{\rm{C}}}}{{{\rm{1 + }}{{\rm{e}}^{{\rm{263.12}}\Delta {\rm{E - 17.26}}\Delta {\rm{E2 - 999.22}}}}}} } \)	0.88	^[18]
2-Mercaptobenzothiazole	DFT: B3LYP/6-31+G*	\( {\small I{E_{Theor}} = \frac{{\left( {2.23{E_{HOMO}} - 8.37{E_{LUMO}} + 5.47\Delta E + 1.76\Delta N + 6.47\mu + 119.8V + 2.07} \right)C}}{{\left[ {1 + \left( {2.23{E_{HOMO}} - 8.37{E_{LUMO}} + 5.47\Delta E + 1.76\Delta N + 6.47\mu + 119.8V + 2.07} \right)C} \right]}} \times 100 } \)	0.96	^[20]
Urea derivatives	DFT: B3LYP/6-31G	\( {\small ∆E=-0.0024IEexp-4.3145} \)	0.95	^[2427]
Urea derivatives	DFT: B3LYP/6-31G	\( {\small {E_{HOMO}} = - 0.0107I{E_{\exp }} - 4.88596 } \)	0.93	^[2427]
Hydantoin derivatives	DFT: B3LYP/6-31G+(d,p)	\( {\small IE_{Theor}=129.054-0.181Mwt-6.550∆E-174.884∆N+0.484BE } \)	1.00	^[2528]
Hydantoin derivatives	DFT: B3LYP/6-31G+(d,p)	\( {\small I{E_{Theor}} = \frac{{\left( {9.1 \times {{10}^{13}}Mwt + 4.9 \times {{10}^{14}}\Delta N + 9.7 \times {{10}^{13}}\Delta E + 2.4 \times {{10}^{13}}BE - 5.9 \times {{10}^{13}}} \right)}}{{\left( {1 + 1.8 \times {{10}^{13}}Mwt + 1.8 \times {{10}^{16}}\Delta N + 8.1 \times {{10}^{14}}\Delta E - 1.2 \times {{10}^{13}}BE - 7.2 \times {{10}^{15}}} \right)}} } \)	0.99	^[2528]
Polyether compounds	DFT B3LYP/6-31G(d,p)	\( {\small R_t=5+\left(2.710^7E_{HOMO}-7.610^7E_{LUMO}+3.910^6\mu\right)C } \)	0.81	^[1]
Sulphonamide derivatives	DFT: B3LYP/6-311+G(d,p)	\( {\small I{E_{\exp }}\left( \% \right) = \frac{{\left( {2.47\omega + 8.56 \times {{10}^{ - 2}}{E_{LUMO}} - 5.27 \times {{10}^{ - 2}}\mu + 6.20\eta - 4.11 \times {{10}^{ - 2}}LogP - 21.81} \right) * 5000}}{{\left( {1 + \left( {2.47\omega + 8.56 \times {{10}^{ - 2}}{E_{LUMO}} - 5.27 \times {{10}^{ - 2}}\mu + 6.20\eta - 4.11 \times {{10}^{ - 2}}LogP - 21.81} \right) * 50} \right)}} } \)	1.00	^[2723]
Sulphonamide derivatives	DFT: B3LYP/6-311+G(d,p)	\( {\small I{E_{\exp }}\left( \% \right) = \frac{{\left( { - 1.44\Delta E + 3.48{E_{LUMO}} - 3.50{E_{HOMO}} + 1.07\eta + 1.75{\omega ^ + } - 17.85} \right)5000}}{{\left( {1 + \left( { - 1.44\Delta E + 3.48{E_{LUMO}} - 3.50{E_{HOMO}} + 1.07\eta + 1.75{\omega ^ + } - 17.85} \right)50} \right)}} } \)	0.99	^[2723]
Pyrimidine compounds	B3LYP/6-311++G(d,p)	\( {\small I{E_{Theor}}\left( \% \right) = 9.255 \times {10^1} - 3.213 \times {10^{ - 3}}\frac{\chi }{{{C_1}}} + 3.432 \times {10^{ - 7}}\frac{\mu }{{C_2^2}} - 1.768 \times {10^{ - 10}}\frac{{\Delta E}}{{C_3^3}} - 5.859\frac{{{E_{HOMO}}}}{{C_4^4}} } \) * equation for BTPTT, phase gas	0.98	^[2824]
Pyrimidine compounds	B3LYP/6-311++G(d,p)	\( {\small I{E_{Theor}}\left( \% \right) = 9.326 \times {10^1} + 6.249 \times {10^{ - 4}}\frac{{{E_{HOMO}}}}{{{C_1}}} - 1.093 \times {10^{ - 7}}\frac{{{E_{LUMO}}}}{{C_2^2}} } \)	0.99	^[2824]
Amino acids	PM6, PM3, MNDO and RM1 for semi-empirical studies. DFT. Local selectivity	\( {\small IE_{exp}=125.80E_{HOMO}-121.83E_{LUMO}+1402.96 } \) PM6 Hamiltonian	0.93	^[2930]
		\( {\small I{E_{Theor}} = \frac{{\left( {1.085{E_{HOMO}} + 1.114{E_{LUMO}} + \Delta E + 4.128\mu } \right)C}}{{\left[ {1 + \left( {1.085{E_{HOMO}} + 1.114{E_{LUMO}} + \Delta E + 4.128\mu } \right)C} \right]}} \times 100 } \) AM1 Hamiltonian, gas phase	0.86
		\( {\small I{E_{Theor}} = \frac{{\left( {0.896{E_{HOMO}} + 1.38{E_{LUMO}} + \Delta E + \mu + 1.694{E_{diel}} + 18.38} \right)C}}{{\left[ {1 + \left( {0.896{E_{HOMO}} + 1.38{E_{LUMO}} + \Delta E + \mu + 1.694{E_{diel}} + 18.38} \right)C} \right]}} \times 100 } \) RM1 Hamiltonian, aqueous phase	0.96
Carbozones	AM1, PM6, PM3, MNDO and RM1 Hamiltonians. Correlation MP2, basis STO-3G	\( {\small I{E_{exp}}\left( \% \right) = - 14.686{E_{HOMO}} - 48.966 } \)	0.94	^[3031]
Carbozones		\( {\small I{E_{Theor}} = \frac{{\left( {1.0176{E_{HOMO}} + 0.9743{E_{LUMO}} + 1.0351\Delta E + \cos A + \cos V + 428.6731} \right)C}}{{\left[ {1 + \left( {1.0176{E_{HOMO}} + 0.9743{E_{LUMO}} + 1.0351\Delta E + \cos A + \cos V + 428.6731} \right)C} \right]}} } \)	0.83	^[3031]
Simbology

References

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1. Introduction

2. Corrosion Inhibitors

3. N-Containing Corrosion Inhibitors

Table 1. N-containing corrosion inhibitors

Example

Corrosion Inhibitor

EfWL/EfPP/EfEIS

Ref

(4-Chloro-benzylidene-pyridine-2-yl-amine)

99.5/99.6/99.6

Exp. C. NCI: 3, Met: mild steel, Media: HCl 1.0 M, Co: 2×10−4–1×10−2 M, t: 24 h (WL), T: 25 °C, TA: A

2,5-bis(2-hydroxyphenyl)-1,3,4-oxadiazole

98.2/94.7/99.1

Exp. C. NCI: 2, Met: mild steel, Media: HCl 1.0 M, 0.5 M H2SO4, Co: 20–80 mg•L−1, t: 24 h (WL), 20 h (EIS), T: 30 °C, TA: NA

Tributylamine

97.8/-/-

Exp. C. NCI: 23, Met: 13% Cr steel, Media: HCl (15%w/v), Co: 2%w/v inhibitor and 0.6% w/v formaldehyde (used to minimize hydrogen penetration), t: 3 h, T.: 60 °C, TA: A

1,2-bisbenzylbenzimidazole

96

Exp. C. NCI: 11, Met: iron, Media: HCl 1.0 M. The analysis technique and the rest of the experimental conditions are not specified. TA: A

3,4-Dichloro-acetophenone-O-1′-(1′.3′.4′-triazolyl)-metheneoxime (DATM)

92.8/98.7/98.7

Exp. C. NCI: 3, Met: mild steel, Media: HCl 1.0 M, Co:1×10−5–1×10−3 M, t: 3 h (WL), 30 min (PP), T: 25 °C, TA: A

* 2,6-bis-(2-benzimidazolyl) pyridine

-/94–96/97.0

Exp. C. NCI: 4, Met: mild steel, Media: HCl 1.0 M, Co: 0.1–1.0 mM, t: 1–96 h (WL), 45 min (PP), T.: 30 °C, TA: NA

1-(4-Methyloxyphenylimino)-1-(phenylhydrazono)-propan-2-one

-/95.9/96.2

Exp. C. NCI: 5, Met: mild steel, Media: HCl 1.0 M, Co: 5×10−6–7.5×10−5 M, t: 30 min, T: 25 °C, TA: NA

1-Butyl-2-propylene-2-imidazoline

95.1/-/-

Exp. C. NCI: 34, Met: stainless steel, Media: HCl 5%, Co: ≈0.1 M, t: 48 h, T: TR (room temperature), TA: A

Aniline, N-(p-methoxybenzylidene)

-/94.0/-

Exp. C. NCI: 4, Met: aluminium, Media: HCl 2.0 N, Co: 10−5–10−2 M, t:-, T: 30 °C, TA: NA

Cyclohexanone oxime

93.9/98.4/95.2

Exp. C. NCI: 3, Met: aluminium, Media: HCl 1.0 M, Co: 0.2–2.0 mM, t: 2 h, T: 20–50 °C, TA: NA

6-Bromo-1H-benzimidazole

-/-/89.4

Exp. C. NCI: 15, Met: carbon steel, Media: HCl 1.0 M, Co:0.1–10 mM, t: 30 min, T: TR, TA: A

2-Mercaptobenzimidazole

-/88.7/90.4

Exp. C. NCI: 3, Met: mild steel, Media: HCl 1.0 M, Co: 50–250 ppm, t: 30 min, T: 25 °C, TA: NA

2-Chloromethylbenzimidazole

-/-/69.7

Exp. C. NCI: 6, Met: carbon steel, Media: HCl 1.0 M, Co: 1×10−3 M, t: -, T: TR, TA: A

2,4-Dimercaptopyrimidine

43.0/-/-

Exp. C. NCI: 14, Met: Aramco iron, Media: HCl 2.0 M, Co: 1×10−3 M, t: 1 h, T: 40 °C, TA: A

Table 2. S-containing corrosion inhibitors

Example

Corrosion Inhibitor

EfWL/EfPP/EfEIS

Ref

1-Phenyl thiosemicarbazide

-/100.0/-

Exp. C. NCI: 10, Met: mild steel, Media: H2SO4, Co: 1 mMdm−3, t: -, T: 30 °C. TA: A

Phenylthiourea (PTU)

-/-/97.2

Exp. C. NCI: 3, Met: mild steel, Media: H2SO4 0.1 M, Co: 1–10 mM, t:1 h, T: TR, TA: NA

2-Mercaptobenzothiazole

-/97/-

Exp. C. NCI: 1, Met: Steel (API 5L X52), Media: H2SO4 1.0 M, Co: 10−4-–10−3 M, t: 30 min, T: 25 °C, TA: A

4-Hydroxybenzaldehyde thiosemicarbazone

-/97.0/90.0

Exp. C. NCI: 6, Met: carbon steel, Media: HCl 1.0 M, Co: 10−4–10−2 M, t: 30 min, T: 25 °C, TA: NA

2-Mercapto-1-methylimidazole

90.4 /95.5/-

Exp. C. NCI: 1, Met: carbon steel, Media: HClO4 1.0 M, Co: 7.510−5–2.5 10−3 M, t:1 h, T: 30 °C, TA: NA

Table 3. O-containing corrosion inhibitors

Example

Corrosion Inhibitor

EfWL/EfPP/EfEIS

Ref

2-(4-Methylbenzylidene)-3-oxo-2,3-dihydro-1H-indene-1-carboxylic acid

92.0/93.9/92.6

Exp. C. NCI: 3, Met: mild steel, Media: HCl 1.0 M, Co: 10−6–10−3 M, t: 6 h, T: 30 °C, TA: NA

1-((4-Chlorophenyl)(2-hydroxynaphtalen-1-yl)(phenyl) methyl)urea (CPHU)

90/92.0/-

Ef_WL/Ef_PP/Ef_EIS

Exp. C. N_CI: 3, Met: mild steel, Media: HCl 1.0 M, Co: 2×10⁻⁴–1×10⁻²M, t: 24 h (WL), T: 25 °C, TA: A

Exp. C. N_CI: 2, Met: mild steel, Media: HCl 1.0 M, 0.5 M H₂SO₄, Co: 20–80 mg•L⁻¹, t: 24 h (WL), 20 h (EIS), T: 30 °C, TA: NA

Exp. C. N_CI: 23, Met: 13% Cr steel, Media: HCl (15%w/v), Co: 2%w/v inhibitor and 0.6% w/v formaldehyde (used to minimize hydrogen penetration), t: 3 h, T.: 60 °C, TA: A

Exp. C. N_CI: 11, Met: iron, Media: HCl 1.0 M. The analysis technique and the rest of the experimental conditions are not specified. TA: A

Exp. C. N_CI: 3, Met: mild steel, Media: HCl 1.0 M, Co:1×10⁻⁵–1×10⁻³M, t: 3 h (WL), 30 min (PP), T: 25 °C, TA: A

Exp. C. N_CI: 4, Met: mild steel, Media: HCl 1.0 M, Co: 0.1–1.0 mM, t: 1–96 h (WL), 45 min (PP), T.: 30 °C, TA: NA

Exp. C. N_CI: 5, Met: mild steel, Media: HCl 1.0 M, Co: 5×10⁻⁶–7.5×10⁻⁵M, t: 30 min, T: 25 °C, TA: NA

Exp. C. N_CI: 34, Met: stainless steel, Media: HCl 5%, Co: ≈0.1 M, t: 48 h, T: T_R(room temperature), TA: A

Exp. C. N_CI: 4, Met: aluminium, Media: HCl 2.0 N, Co: 10⁻⁵–10⁻²M, t:-, T: 30 °C, TA: NA

Exp. C. N_CI: 3, Met: aluminium, Media: HCl 1.0 M, Co: 0.2–2.0 mM, t: 2 h, T: 20–50 °C, TA: NA

Exp. C. N_CI: 15, Met: carbon steel, Media: HCl 1.0 M, Co:0.1–10 mM, t: 30 min, T: T_R, TA: A

Exp. C. N_CI: 3, Met: mild steel, Media: HCl 1.0 M, Co: 50–250 ppm, t: 30 min, T: 25 °C, TA: NA

Exp. C. N_CI: 6, Met: carbon steel, Media: HCl 1.0 M, Co: 1×10⁻³ M, t: -, T: T_R, TA: A

Exp. C. N_CI: 14, Met: Aramco iron, Media: HCl 2.0 M, Co: 1×10⁻³ M, t: 1 h, T: 40 °C, TA: A

Ef_WL/Ef_PP/Ef_EIS

Exp. C. N_CI: 10, Met: mild steel, Media: H₂SO₄, Co: 1 mMdm⁻³, t: -, T: 30 °C. TA: A

Exp. C. N_CI: 3, Met: mild steel, Media: H₂SO₄ 0.1 M, Co: 1–10 mM, t:1 h, T: T_R, TA: NA

Exp. C. N_CI: 1, Met: Steel (API 5L X52), Media: H₂SO₄ 1.0 M, Co: 10^−4-–10⁻³ M, t: 30 min, T: 25 °C, TA: A

Exp. C. N_CI: 6, Met: carbon steel, Media: HCl 1.0 M, Co: 10⁻⁴–10⁻²M, t: 30 min, T: 25 °C, TA: NA

Exp. C. N_CI: 1, Met: carbon steel, Media: HClO₄ 1.0 M, Co: 7.510⁻⁵–2.5 10⁻³ M, t:1 h, T: 30 °C, TA: NA

Ef_WL/Ef_PP/Ef_EIS

Exp. C. NCI: 3, Met: mild steel, Media: HCl 1.0 M, Co: 10⁻⁶–10⁻³ M, t: 6 h, T: 30 °C, TA: NA

Exp. C. NCI: 3, Met: mild steel, Media: H₂SO₄ 0.5 M, Co: 2–10 ppm, t: 24 h (WL) and 30 min (PP), T: 20 °C, TA:A

Exp. C. NCI: 1, Met: mild steel, Media: H₂SO₄ 0.01 M, Co: 10⁻⁷–10⁻³ M, t: -, T: T_R, TA: NA

Ef_WL/Ef_PP/Ef_EIS

Exp. C. NCI: 5, Met: mild steel, Media: 1.0 M HCl, Co: 110⁻⁶–110⁻⁴ M, t: 24 h (WL), T: 30 °C, TA: A

Exp. C. NCI: 5, Met: mild steel, Media:1.0 M HCl, Co: 1–510⁻⁵ M, t: 30 min, T: 30–50 °C, TA: A

Exp. C. NCI: 2, Met: stainless steel, Media:1.0 M HCl, Co:110⁻⁴–5 10⁻³ moldm⁻³, t: 30 min, T: 25 °C. The experimental data were obtained by Caliskan, et al. ^[2824]. TA: A

Exp. C. NCI: 4, Met: mild steel, Media:0.1 M HCl, Co: 0.1–0.5 gL⁻¹, t: 24, 168 h, T: 30, 60 °C, TA: A

Exp. C. NCI: 4, Met: mild steel, Media:0.1 M HCl, Co: 1–510⁻⁴ M, t: 168 h, T: 30 °C, TA: A

Exp. C. NCI: 16, Met: Armco iron, Media: HCl 1.0 M, Co: 10⁻³ M, et: 6 h (WL), 10 y 30 min (PP), T: 35 °C, TA: A

E_HOMO

E_LUMO

ΔE= E_{HOMO −}E_LUMO

It has been mentioned that the successful adsorption and proper efficiency of an inhibitor have been characterized by a high E_HOMO, a low E_LUMO_,and a small energy gap. The lower the ΔE is, the higher the stability of the metal-inhibitor interaction.