Organic Phosphorus Compounds as Inhibitors of Corrosion of Carbon Steel in Circulating Cooling Water : Weight Loss Method and Thermodynamic and Quantum Chemical Studies

Circulating cooling water plays an important role in industrial water use. In this study, the corrosion inhibition effects of PBTCA, HEDP, and ATMP organic phosphorus inhibitors were investigated using the weight loss method by varying the dosage of inhibitors, ClO2 concentrations, and pH values on carbon steel in recirculating cooling water with a low concentration of ClO2 solution. -e results showed that the three corrosion inhibitors had a satisfactory corrosion inhibition effect and that corrosion inhibition efficiency is positively correlated with the concentration of organic phosphorus inhibitors and pH. -e average corrosion inhibition efficiency of the three inhibitors was about 80% at the concentration of inhibitors � 35mg/L, pH � 9.0, and the concentration of ClO2 � 7.0mg/L, of which the single-phosphorus molecular corrosion inhibitor proved to be the best inhibitor. When the ClO2 concentration was 7mg/L, the corrosion inhibition efficiencies of the three corrosion inhibitors were relatively stable. Using the density functional theory (DFT) algorithm in the Gaussian 09 program, the optimization calculation was completed by the B3LYP/6-31G (d, p) method at the microlevel. -e molecular structures of the three organic phosphorus inhibitors and the number of phosphorus-containing atoms were compared to the sustained-release properties. Organic phosphorus inhibitors, as an electronic buffer, not only provided electrons but also received electrons. -ey formed a complex with iron and zinc ions in water in order to attach to the surface of the carbon steel and to alleviate corrosion. In addition, the adsorption with a metal surface followed the Langmuir adsorption isotherm.


Introduction
Circulating cooling water accounts for 60-90% of total industrial water use [1][2][3].Because of continuous recycling, the water quality of circulating cooling water becomes more concentrated leading to corrosion, fouling, and microbial breeding [4][5][6], which results in lower heat transfer efficiency of heat exchangers, corrosion and perforation of metal pipelines, and safety issues [7,8].
Since the 1930s, the use of organic phosphorus inhibitors in circulating cooling water has alleviated the corrosion of carbon steel [9,10].To inhibit microbial breeding in circulating cooling water, oxidizing or nonoxidizing fungicides are added to the water [9,11,12].e combined use of the corrosion inhibitor and the bactericide has relieved the impact of the challenges mentioned above and has promoted the development of the industrial economy.Organic phosphorus inhibitors, and also in combination with ClO 2 , have good corrosion inhibition properties, but there are only a few articles about their corrosion inhibition mechanism with carbon steel [13,14].A large number of studies have shown that the efficiency of corrosion inhibitors is closely related to their structures [15][16][17].e quantum chemical method can be used to calculate the molecular structure parameters and to explore the mechanism of corrosion inhibition at the microlevel [18,19].Kumar et al. [20] used the AM1 semiempirical quantum chemical method to study the corrosion inhibition mechanism of synthetic organic matter for N80 carbon steel and found that the adsorption of inhibitors followed the Langmuir adsorption isotherm.Gece and Bilgi [21] used the B3LYP/6-311 ++ G (d, p) method to study the mechanism of a nitrogen corrosion inhibitor in acidic media and concluded that the nitrogen atom belongs to the active centre and has good corrosion inhibition performance.Shi et al. [22] studied the adsorption behaviour of four pyrazine inhibitors on a copper surface using the density functional theory and the difference in charge density and distribution analysis.e vertical adsorption of the corrosion inhibitor molecules on the metal surface was by chemical adsorption where the coordination bond was formed.By analyzing the frontier orbitals, it was verified that the active site of the inhibitor was the N atom on the pyrazine ring.
Hitherto, good results have been obtained in the research of nitrogen corrosion inhibitors, but few reports have described the mechanism of action between phosphorus corrosion inhibitors and metal surfaces.In this paper, three kinds of organic phosphorus corrosion inhibitors: 2-phosphate group-1,2,4-tricarboxylate butane (PBTCA), hydroxyethylidene disphosphonic acid (HEDP), and aminotrimethylene phosphonic acid (ATMP), were studied.e corrosion inhibition performance of the organophosphorus corrosion inhibitors in combination with ClO 2 on the carbon steel was analyzed experimentally.e charge distribution, frontier orbit, and adsorption model of stable molecules were investigated using ChemBioOffice 2014, Gaussian 09, and Origin 2017 software to explore the corrosion inhibition mechanism of the organic phosphorus inhibitor on the metal surface and provide theoretical support for its application in circulating cooling water.

Experimental Material.
e composition and content of the standard water used in the experiment are shown in Table 1.

Weight Loss Method.
e effect of different inhibitor concentrations, ClO 2 concentrations, and pH values on the corrosion inhibition efficiency of the corrosion inhibitors on carbon steel in circulating cooling water with a low concentration of ClO 2 and zinc ion solution was studied by using the weight loss method.Determination methods and procedures were referenced to the regulation of corrosion resistance of water treatment agents (GB/t 18175-2014) [23,24].
e corrosion rate V and corrosion inhibition efficiency E were determined using the following equations: where W1 and W2 are the weight of specimens before and after corrosion, respectively; F is the surface area of the specimen exposed to cooling water; K is a constant, whose value is 87.6; t is the specimen immersion corrosion time; c is the metal density; and C 0 and C t are corrosion rates in the absence and presence of the inhibitor, respectively.

Quantum Chemical Calculation.
e molecular structures of organic phosphorus inhibitors PBTCA, HEDP, and ATMP were constructed using ChemBioDraw Ultra 14.0, and the RHF/6-31G method of GAMESS was used to preliminarily optimize the structure.Density functional theory (DFT) helps to study the electronic structure of a multielectron system with high computational accuracy [25], so the DFT algorithm in the Gaussian 09 program was used, without any symmetry restriction being imposed, in the B3LYP/6-31G (d, p) method [26].e quantum chemical parameters and related parameters of each molecule were obtained from the output results by optimizing the three inhibitors.
e stable composition of the three corrosion inhibitors after optimization is shown in Figure 1. e quantum chemical parameters included the highest occupied molecular orbital energy (E HOMO ), the lowest unoccupied molecular orbital energy E LUMO , the energy gap (ΔE), the distribution of the atomic Mulliken charge, and the molecular dipole moment (μ).Other relevant parameters included the ionization potential (I), electronegativity χ, electron affinity (A), hardness (η), and affinity index (ω).
ese parameters were calculated using the following equations [27]: (3) 2 Advances in Materials Science and Engineering carbon steel was studied using the carbon steel test, and the test liquid was a mixture of standard water, ClO 2 , and corrosion inhibitor.e concentration of ClO 2 was 7.0 mg/L, the temperature was (40.0 ± 1.0) °C, the pH was 9.0, and the rotation reaction time was 72 h.e experiment was repeated three times, and the average values are shown in Figure 2. e above figure shows that, with the increasing organic phosphorus concentration, the inhibition rate increased gradually and the average inhibition rate of the three corrosion inhibitors reached above 80%.When the concentration was increased to 35.0 mg/L, the corrosion inhibition rate of ATMP was more than 70%. Figure 2 shows that the corrosion inhibition rate of three corrosion inhibitors is in the order of PBTCA > HEDP > ATMP based on the number of phosphorus atoms in the inhibitor.e results also show that the inhibition performance is related to the number of P atoms, and the single-phosphorus molecule inhibitor exhibits a preferable corrosion inhibition effect.

Effect of ClO 2 Concentration on Corrosion Inhibition of Carbon Steel.
ClO 2 is a good fungicide and can be combined with a corrosion inhibitor by the compounding technology.
e test solution was a mixture of standard water, ClO 2 , and corrosion inhibitor.e effect of the ClO 2 concentration on the inhibition of corrosion of carbon steel was studied.e corrosion inhibitor concentration was 15.0 mg/L, the temperature was (40.0 ± 1.0) °C, the pH was 9.0, and the rotation reaction time was 72 h.e experiment was repeated three times, and the average results are shown in Figure 3.
From Figure 3(a), it can be seen that the addition of ClO 2 had a certain inhibitory effect on the slow-release performance of the three inhibitors, but the compound of an inhibitor and ClO 2 still had good corrosion inhibition effect.When the ClO 2 concentration was increased, the slowrelease performance of HEDP steadily decreased.Generally, the average slow-release performance of HEDP and ATMP was lower than that of PBTCA.e slow-release performance of PBTCA showed fewer fluctuations, and its slow-release performance was more stable with ClO 2 concentration changes as compared with the inhibitors HEDP and ATMP (Figure 3(b)).However, with the increase in ClO 2 concentration, the inhibition rate of ATMP decreased, and the lowest inhibition rate recorded was only about 30%.
Once the concentration of ClO 2 was 7 mg/l, the slow-release performance of PBTCA and HEDP was significantly higher than that of ATMP.Overall, the average corrosion inhibition rate of the three corrosion inhibitors in the presence of ClO 2 was PBTCA > HEDP > ATMP.

Effect of pH on Inhibition of Corrosion of Carbon Steel.
e test solution in this test was a mixture of standard water, ClO 2 , and corrosion inhibitor, and the effect of pH on corrosion inhibition was determined.
e initial concentration of the corrosion inhibitor was 15.0 mg/L, the ClO 2 concentration was 7.0 mg/L, the temperature was (40.0 ± 1.0) °C, and the rotation reaction time was 72 h.e experiment was repeated three times, and the average results are shown in Figure 4.
e inhibition rate of the three organic phosphorus reagents increased with increasing pH, indicating that the protective film was more favourable to the reagent formation in the alkaline environment.
is is likely because the concentration of hydrogen ions in water decreases with the increasing pH, and thus, the depolarization of hydrogen ions in the process of metal corrosion is inhibited at high pH.erefore, the tendency to form a protection film on the surface of carbon steel increases, as well as the corrosion inhibition rate.As shown in Figure 4, the corrosion inhibition rate of the three organic phosphorus reagents can be presented as PBTCA > HEDP > ATMP.
e influence of three factors on the inhibition of corrosion of carbon steel was studied by adding different organic phosphorus inhibitor concentrations, ClO 2 concentrations, and pH.e corrosion inhibition rate of the three organic phosphorus inhibitors was above 80%, and the average corrosion inhibition effect was satisfactory.e order of corrosion inhibition effect was PBTCA > HEDP > ATMP.In addition, with the increase in the number of P atoms, the inhibition effect of the corrosion inhibitor decreased; i.e., the corrosion inhibitor with a single phosphorus could exhibit a more effective corrosion inhibition effect.

Quantum Chemical Calculation.
In order to investigate the corrosion inhibition mechanism of organic phosphorus corrosion inhibitors on carbon steel at the microscopic level, we used the density functional theory in quantum chemistry to quantify the molecular structure of organic phosphorus corrosion inhibitors, Fe, Fe 2+ , and Zn 2+ .Figure 1 and Table 2 show the geometric structure models and the optimized Mulliken atomic charge distributions of the three organic phosphorus inhibitors by the B3LYP/6-31G (d, p) method.As can be seen from Table 2, the P atoms were positively charged, indicating that they could accept electrons and form chemical bonds, while both N and O have a high negative charge, indicating that they could also be adsorbed onto the surface of the metal atom by the loss of electron interaction.In addition, all the C atoms in the PBTCA molecule that bonded to the C═O double bond were positively charged, while the other alkyl carbon atoms were all negatively charged; alkyl carbon and oxygen atoms in HEDP were also negatively charged; the alkyl carbon atoms in the ATMP were also negatively charged, and all the H atoms were positively charged.All these data are consistent with the results of the induced effect.
Figure 5 shows the frontier orbital diagram of the three organic phosphorus inhibitor molecules after optimization.
e HOMO orbitals of the PBTCA were essentially distributed on alkyl chains and carboxyl groups linked to the  Advances in Materials Science and Engineering central carbon atom, while some of them were distributed near the phosphorus-oxygen double bonds belonging to the electron loss region.e LUMO orbitals were distributed near P atoms and positively charged carbon atoms which are an easy-to-accept electron region.e HOMO orbits of HEDP were located near oxygen and carbon atoms, while the LUMO orbits were located near P atoms.e HOMO orbitals of ATMP were mainly distributed near the central nitrogen and oxygen atoms, even though the LUMO orbitals were mainly distributed near the P11 atomic group.
Table 3 shows a list of quantum chemical parameters optimized for the three organic phosphorus inhibitors.e  size of E HOMO represents the ability of molecules to provide electrons, while the size of E LUMO represents the electronaccepting capability, and the energy gap, ΔE, represents the stability of the molecule.e smaller the value of ΔE, the more efficient the inhibitor molecule's corrosion inhibition performance.e electron-donating capacity order of the three organic phosphorus inhibitors was HEDP > PBTCA > ATMP, the electron-accepting capacity order was PBTCA > HEDP > ATMP, while the energy gap order was PBTCA < ATMP < HEDP. is reflects the high eletrophilicity of PBTCA and high nucleophilicity of ATMP.According to the three principles of orbital bonding (the orbital symmetric principle, the energy approximation principle, and the maximum overlap principle), the HOMO energies of all three corrosion inhibitors are lower than the minimum orbital energy of iron ions (0.6912 eV), which disagrees with the orbital symmetric principle.
erefore, the corrosion inhibitor molecules cannot provide electrons to empty orbits of iron atoms.e HOMO energies of all three corrosion inhibitor molecules were lower than the minimum empty orbital energy of Fe 2+ (−1.9048 eV), which conforms to the orbital symmetric principle.us, HOMO energies can provide electrons to empty orbits of Fe 2+ .e difference between HOMO orbital energy of HEDP and LUMO orbital energy of Fe 2+ is the highest (6.1013 eV), followed by those of PBTCA (5.5092 eV) and ATMP (4.9903 eV).According to the principle of energy similarity, ATMP shows the strongest bonding capacity with Fe 2+ , followed by PBTCA and HEDP.On the contrary, the LUMO energies of HEDP, PBTCA, and HEDP are all higher than the maximum orbital energy of iron ions (−3.0749 eV).According to the orbital symmetric principle, iron ions cannot provide electrons to HEDP and ATMP, but they can offer electrons to PBTCA.
e difference between LUMO energy of PBTCA and HOMO energy of iron ions is 2.1005 eV.Although the LUMO orbital energy of the three corrosion inhibitors is higher than HOMO orbital energy of Fe 2+ , electrons are provided to PBTCA and ATMP but not to HEDP. e differences between the LUMO orbital energies of PBTCA and ATMP and the HOMO orbital energy of Fe 2+ are 9.1877 eV and 8.2258 eV, respectively.All three corrosion inhibitors can provide electrons to Fe 2+ according to the comparison of the differences in HOMO orbital energy of inhibitors and LUMO orbital energy of Fe 2+ .In conclusion, the PBTCA is superior to the other two inhibitors in terms of slow-release performance, which is similar to previous experimental results.Specifically, PBTCA can provide electrons to Fe 2+ and receive electrons from iron atoms and can form chemical bonds with the corrosion medium in cyclic cooling water, thus avoiding corrosion.
Zn 2+ has been proved to be an effective index of the corrosion effect in cyclic cooling water [28].It is necessary to add corrosion inhibitors to water to inhibit corrosion upon the increase of Zn 2+ concentration.Moreover, the composite corrosion inhibitor formed by PBTCA, HEDP, and ClO 2 presents good corrosion-relieving performance [15].Table 3 shows that all three inhibitors can provide electrons to Zn 2+ according to the orbital symmetric principle although their HOMO energies are lower than the LUMO energy of Zn 2+ .
e difference between the HOMO orbital energy of HEDP and the LUMO orbital energy of Zn 2+ (−2.2177 eV) is 5.7884 eV, which is the highest relative to that of PBTCA (5.1963 eV) and that of ATMP (4.6774 eV).According to the energy similarity principle, the descending order of the three inhibitors with respect to the bonding capacity with Zn 2+ is ATMP > PBTCA > HEDP.With abundant negative loads, oxygen atoms and nitrogen atoms in molecules of all three inhibitors easily contribute surplus electrons (Table 2).As a result, water can receive surplus electrons from the three inhibitors, which is attributed to the small content of Zn 2+ in the water.Consequently, chemical bonds are formed and attached on the iron surface, thus further relieving the corrosion of iron.As electron buffers, all three organic phosphorus inhibitors receive electrons from iron atoms due to the positively charged phosphorus atoms.Since oxygen atoms and nitrogen atoms are rich in negative charges and provide electrons to Zn 2+ in water, a two-layer complex is formed in the cyclic cooling water and attaches on the iron surface to protect carbon steel from corrosion.
e flow graph of electrons is shown in Figure 6.
e dipole moment was caused by the uneven distribution of the atomic charges in the molecule and can, therefore, be used to measure the polarity of the inhibitor molecules.e greater the value of the dipole moment, the stronger the polarities of the molecules and the more likely the electrons are to be lost, clearly indicating the weak electron absorption between the corrosion inhibitor molecules and the metal surface.From Table 3, it can be concluded that the order of dipole moment of the three organic phosphorus molecules was ATMP > HEDP > PBTCA.e corrosion inhibitor ATMP had a better electron-donating capability.Hence, PBTCA had a better electron-receiving capability.Because of the high number of P atoms in ATMP, the steric effect was great, which was not conducive to the formation of the dense membrane.erefore, PBTCA showed better corrosion inhibition performance.
According to Koopmans' theorem, quantum chemical parameters are related to the frontier orbital energy, such as ionization potential (I), electron affinity (A), electronegativity (χ), hardness (η), and affinity index (ω).e results are shown in Table 3.
e electron affinity potential indicates the electronic trend of the molecules, and the higher its value, the easier it is to obtain the electron.e order of electron affinity of the Electronegativity represents the ability of molecules to attract electrons.e electronegativity of the three organic phosphorus molecules was PBTCA > HEDP> ATMP, where PBTCA can easily accept electrons and react with metal atoms.Hardness can reflect stability and reactivity of molecules.e hardness of the three organic phosphorus molecules is in the order HEDP > ATMP > PBTCA.According to the principle of "hard close to hard and soft close to soft," HEDP can easily form stable products with ions.e affinity index also represents the affinity of the molecule, and the greater that value, the easier it is to attract the electrons.e three organic phosphorus corrosion inhibitors' affinity index was ranked as PBTCA > HEDP > ATMP.
is clearly shows that PBTCA could accept the electrons easily, which was the main component of the three organic phosphorus corrosion inhibitors.e analysis of electron affinity, electronegativity, hardness, and electronaffinity index of the three organic phosphorus molecules also shows that PBTCA had a better corrosion inhibition performance and it was more likely to accept the free electrons outside the iron atoms and form coordination bonds.e smaller the number of P atoms contained in the molecule, the lesser its steric effect.As a result, PBTCA formed a dense protective film on the surface of the metal, thus hindering corrosion, which satisfies the requirements of prefilm in circulating cooling water.

Study on Corrosion Inhibitor Adsorption Behaviour.
e adsorption isotherm of a corrosion inhibitor can describe the adsorption behaviour at a certain temperature.In order to study the adsorption models of three organic phosphorus inhibitors, we assumed that they were adsorbed on a single molecular layer on the surface of carbon steel, such that corrosion rate y was approximated by a metal surface coverage θ.
By the Langmuir adsorption isotherm, the equation is as follows: e formula can be concluded as follows: where C is the concentration of the inhibitor (mg/L) and K is the adsorption equilibrium constant [29].e result is shown in Figure 7.
It can be seen from Figure 7 that the regression coefficients of the organic phosphorus inhibitors were R PBTCA 2 � 0.9931, R HEDP 2 � 0.9927, and R ATMP 2 � 0.9825, respectively, indicating that the inhibitors were Langmuir adsorbed on the surface of carbon steel.
e adsorption equilibrium constants were calculated using intercepts as K PBTCA � 0.0732 L/mg, K HEDP � 0.0737 L/mg, and K ATMP � 0.1164 L/mg.According to the adsorption theory, the relationship between the standard molar adsorption free energy and the adsorption equilibrium constant K is where C solvent � 55.5, T stands for thermodynamic temperature (K), and R is the gas constant (8.314J/mol•K).e higher the absolute value of the standard molar adsorption free energy, the higher the stability of the adsorption layer.ΔG θ is negative throughout the calculation, which means that the adsorption was spontaneous.When the absolute value of ΔG θ was below 20 kJ/mol, the adsorption of the inhibitor molecules on the metal surface was physical adsorption.At an absolute value of ΔG θ greater than 40 kJ/mol, the corrosion inhibitor molecule formed a covalent bond with the metal surface, which shows the chemical adsorption [18].e standard molar adsorption free energy of the three organic phosphorus molecules was obtained by introducing the adsorption equilibrium constant conversion unit into the formula, and the results were ΔG PBTCA θ � 43.414 kJ/mol, ΔG HEDP θ � 42.743 kJ/mol, and ΔG ATMP θ � 43.667 kJ/mol, respectively.All values were greater than 40 kJ/mol, demonstrating that the three organic phosphorus corrosion inhibitors formed coordination bonds with the metal surface by chemical adsorption, which impedes metal corrosion.

Conclusion
In this paper, three organophosphorus inhibitors, PBTCA, HEDP, and ATMP, were used as the research objects, and the influence factors of corrosion inhibition efficiency and corrosion inhibition mechanism on carbon steel in circulating cooling water were discussed.e following conclusions can be drawn: (1) e weight loss method proved that the average inhibition rate of the three organic phosphorus corrosion inhibitors was more than 80%, the inhibition rate increases with the increasing concentration of inhibitors and decreases with the increase in the number of P atoms, and the corrosion inhibition effect of single-phosphorus inhibitor PBTCA was better.
(2) e adsorption of the organophosphorus inhibitor onto the metal surface followed the Langmuir monolayer adsorption.(3) e DFT algorithm in Gaussian 09 software was used to optimize the inhibitors at the theoretical level by the B3LYP/6-31G (d, p) method.According to molecular layout analysis and frontier orbital theory, the three organophosphorus corrosion inhibitors were used as electron buffers.By receiving the free electron of the outer orbit of the iron atom, the inhibitor and iron atom can form the stable coordination bond and form a protective film on the metal surface to obstruct the metal corrosion.At the same time, the inhibitor can provide electrons to zinc ions present in the water, forming complex compounds and meeting the requirements of the premembrane in circulating cooling water.

Figure 3 :Figure 4 :
Figure 3: (a, b) Corrosion inhibition rate of carbon steels with different concentrations of ClO 2 .

Figure 6 :
Figure 6: Electron-flow diagram of the corrosion inhibition mechanism between the inhibitor and carbon steel.

Figure 7 :
Figure 7: Isotherm fitting of three organic phosphorus inhibitors to Langmuir adsorption.

Table 1 :
e composition and content of the standard water used in the experiment.

Table 2 :
e charge distribution of the Mulliken atom in the three corrosion inhibitors.

Table 3 :
Quantum chemical parameters of the three organic phosphorus inhibitors at the B3LYP/6-31G (d, p) theoretical level.