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

1. Introduction

Circulating cooling water accounts for 60-90% of total industrial water use [1-3]. Because of continuous recycling, the water quality of circulating cooling water becomes more concentrated leading to corrosion, fouling, and microbial breeding [4-6], 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]. The 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 Cl[O.sub.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 [15-17]. The 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. The 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. The corrosion inhibition performance of the organophosphorus corrosion inhibitors in combination with Cl[O.sub.2] on the carbon steel was analyzed experimentally. The 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.

2. Experimental Materials and Research Methods

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

2.2. Weight Loss Method. The effect of different inhibitor concentrations, Cl[O.sub.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 Cl[O.sub.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]. The corrosion rate V and corrosion inhibition efficiency E were determined using the following equations:

V = K [[W.sub.1] - [W.sub.2]]/[F x t x [gamma]], E = [[C.sub.0] - [C.sub.t]]/[C.sub.0] x 100, (1)

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; y is the metal density; and [C.sub.0] and [C.sub.t] are corrosion rates in the absence and presence of the inhibitor, respectively.

2.3. Quantum Chemical Calculation. The 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]. The quantum chemical parameters and related parameters of each molecule were obtained from the output results by optimizing the three inhibitors. The stable composition of the three corrosion inhibitors after optimization is shown in Figure 1. The quantum chemical parameters included the highest occupied molecular orbital energy ([E.sub.HOMO]), the lowest unoccupied molecular orbital energy [E.sub.LUMO], the energy gap ([DELTA]E), the distribution of the atomic Mulliken charge, and the molecular dipole moment ([mu]). Other relevant parameters included the ionization potential (I), electronegativity [chi], electron affinity (A), hardness ([eta]), and affinity index ([omega]). These parameters were calculated using the following equations [27]:

I = -[E.sub.HOMO], A = -[E.sub.LUMO], [chi] = [I + A]/2, [eta] = [I - A]/2, [omega] = [[chi square]/2[eta]. (3)

3. Results and Discussion

3.1. Evaluation of Corrosion Inhibition Performance of Organophosphorus Agents. PBTCA, HEDP, and ATMP are commonly used water treatment agents, and they have excellent corrosion and scale inhibition and a moderate price and are suitable for large-scale use. In this section, we studied the influence of three factors: corrosion inhibitor concentration, Cl[O.sub.2] concentration, and pH value, on the corrosion inhibition efficiency of corrosion of carbon steel.

3.1.1. Effect of Inhibitor Concentration on the Inhibition of Corrosion of Carbon Steel. The effect of the concentration of PBTCA, HEDP, and ATMP on the inhibition of corrosion of carbon steel was studied using the carbon steel test, and the test liquid was a mixture of standard water, Cl[O.sub.2], and corrosion inhibitor. The concentration of Cl[O.sub.2] was 7.0 mg/L, the temperature was (40.0 [+ or -] 1.0)[degrees]C, the pH was 9.0, and the rotation reaction time was 72 h. The experiment was repeated three times, and the average values are shown in Figure 2.

The 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. The 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.

3.1.2. Effect of Cl[O.sub.2] Concentration on Corrosion Inhibition of Carbon Steel. Cl[O.sub.2] is a good fungicide and can be combined with a corrosion inhibitor by the compounding technology. The test solution was a mixture of standard water, Cl[O.sub.2], and corrosion inhibitor. The effect of the Cl[O.sub.2] concentration on the inhibition of corrosion of carbon steel was studied. The corrosion inhibitor concentration was 15.0 mg/L, the temperature was (40.0 [+ or -] 1.0)[degrees]C, the pH was 9.0, and the rotation reaction time was 72 h. The 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 Cl[O.sub.2] had a certain inhibitory effect on the slow-release performance of the three inhibitors, but the compound of an inhibitor and Cl[O.sub.2] still had good corrosion inhibition effect. When the Cl[O.sub.2] concentration was increased, the slow-release performance of HEDP steadily decreased. Generally, the average slow-release performance of HEDP and ATMP was lower than that of PBTCA. The slow-release performance of PBTCA showed fewer fluctuations, and its slow-release performance was more stable with Cl[O.sub.2] concentration changes as compared with the inhibitors HEDP and ATMP (Figure 3(b)). However, with the increase in Cl[O.sub.2] concentration, the inhibition rate of ATMP decreased, and the lowest inhibition rate recorded was only about 30%. Once the concentration of Cl[O.sub.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 Cl[O.sub.2] was PBTCA > HEDP > ATMP.

3.1.3. Effect of pH on Inhibition of Corrosion of Carbon Steel. The test solution in this test was a mixture of standard water, Cl[O.sub.2], and corrosion inhibitor, and the effect of pH on corrosion inhibition was determined. The initial concentration of the corrosion inhibitor was 15.0 mg/L, the Cl[O.sub.2] concentration was 7.0mg/L, the temperature was (40.0 [+ or -] 1.0)[degrees]C, and the rotation reaction time was 72 h. The experiment was repeated three times, and the average results are shown in Figure 4.

The 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. This 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. Therefore, 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.

The influence of three factors on the inhibition of corrosion of carbon steel was studied by adding different organic phosphorus inhibitor concentrations, Cl[O.sub.2] concentrations, and pH. The corrosion inhibition rate of the three organic phosphorus inhibitors was above 80%, and the average corrosion inhibition effect was satisfactory. The 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.

3.2. 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.sup.2+], and [Zn.sup.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. The HOMO orbitals of the PBTCA were essentially distributed on alkyl chains and carboxyl groups linked to the central carbon atom, while some of them were distributed near the phosphorus-oxygen double bonds belonging to the electron loss region. The LUMO orbitals were distributed near P atoms and positively charged carbon atoms which are an easy-to-accept electron region. The HOMO orbits of HEDP were located near oxygen and carbon atoms, while the LUMO orbits were located near P atoms. The 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. The size of [E.sub.HOMO] represents the ability of molecules to provide electrons, while the size of [E.sub.LUMO] represents the electron-accepting capability, and the energy gap, [DELTA]E, represents the stability of the molecule. The smaller the value of [DELTA]E, the more efficient the inhibitor molecule's corrosion inhibition performance. The 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. This 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. Therefore, the corrosion inhibitor molecules cannot provide electrons to empty orbits of iron atoms. The HOMO energies of all three corrosion inhibitor molecules were lower than the minimum empty orbital energy of [Fe.sup.2+] (-1.9048 eV), which conforms to the orbital symmetric principle. Thus, HOMO energies can provide electrons to empty orbits of [Fe.sup.2+]. The difference between HOMO orbital energy of HEDP and LUMO orbital energy of [Fe.sup.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.sup.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. The 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.sup.2+], electrons are provided to PBTCA and ATMP but not to HEDP. The differences between the LUMO orbital energies of PBTCA and ATMP and the HOMO orbital energy of [Fe.sup.2+] are 9.1877 eV and 8.2258 eV, respectively. All three corrosion inhibitors can provide electrons to [Fe.sup.2+] according to the comparison of the differences in HOMO orbital energy of inhibitors and LUMO orbital energy of [Fe.sup.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.sup.2+] and receive electrons from iron atoms and can form chemical bonds with the corrosion medium in cyclic cooling water, thus avoiding corrosion.

[Zn.sup.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.sup.2+] concentration. Moreover, the composite corrosion inhibitor formed by PBTCA, HEDP, and Cl[O.sub.2] presents good corrosion-relieving performance [15]. Table 3 shows that all three inhibitors can provide electrons to [Zn.sup.2+] according to the orbital symmetric principle although their HOMO energies are lower than the LUMO energy of [Zn.sup.2+]. The difference between the HOMO orbital energy of HEDP and the LUMO orbital energy of [Zn.sup.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.sup.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.sup.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.sup.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. The flow graph of electrons is shown in Figure 6.

The 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. The 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. The 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. Therefore, 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 ([chi]), hardness (n), and affinity index ([omega]). The results are shown in Table 3.

The electron affinity potential indicates the electronic trend of the molecules, and the higher its value, the easier it is to obtain the electron. The order of electron affinity of the three organic phosphorus molecules was PBTCA > HEDP > ATMP. PBTCA molecules can easily obtain electrons. Electronegativity represents the ability of molecules to attract electrons. The 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. The 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. The affinity index also represents the affinity of the molecule, and the greater that value, the easier it is to attract the electrons. The three organic phosphorus corrosion inhibitors' affinity index was ranked as PBTCA > HEDP > ATMP. This clearly shows that PBTCA could accept the electrons easily, which was the main component of the three organic phosphorus corrosion inhibitors. The analysis of electron affinity, electronegativity, hardness, and electron-affinity 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. The 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.

3.3. Study on Corrosion Inhibitor Adsorption Behaviour. The 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 [theta].

By the Langmuir adsorption isotherm, the equation is as follows:

[theta]/[1 - [theta]] = K[C.sub.i] (4)

The formula can be concluded as follows:

C/[theta] = C + 1/K, (5)

where C is the concentration of the inhibitor (mg/L) and K is the adsorption equilibrium constant [29]. The result is shown in Figure 7.

It can be seen from Figure 7 that the regression coefficients of the organic phosphorus inhibitors were [R.sub.PBTCA.sup.2] = 0.9931, -[R.sub.HEDP.sup.2] = 0.9927, and -[R.sub.ATMP.sup.2] = 0.9825, respectively, indicating that the inhibitors were Langmuir adsorbed on the surface of carbon steel. The adsorption equilibrium constants were calculated using intercepts as [K.sub.PBTCA] = 0.0732 L/mg, -[K.sub.HEDP] = 0.0737 L/mg, and [K.sub.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

K = [1/[C.sub.solvent]] exp -[DELTA][G.sup.[theta]]/RT, (6)

where [C.sub.solvent] = 55.5, T stands for thermodynamic temperature (K), and R is the gas constant (8.314 J/mol x K). The higher the absolute value of the standard molar adsorption free energy, the higher the stability of the adsorption layer. [DELTA][G.sup.[theta]] is negative throughout the calculation, which means that the adsorption was spontaneous. When the absolute value of [DELTA][G.sup.[theta]] was below 20kJ/mol, the adsorption of the inhibitor molecules on the metal surface was physical adsorption. At an absolute value of [DELTA][G.sup.[theta]] greater than 40 kJ/mol, the corrosion inhibitor molecule formed a covalent bond with the metal surface, which shows the chemical adsorption [18]. The 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 [mathematical expression not reproducible], [DELTA][G.sub.HEDP.sup.[theta]] = 42.743 kJ/mol, and [DELTA][G.sub.ATMP.sup.[theta]] = 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.

4. 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. The following conclusions can be drawn:

(1) The 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) The adsorption of the organophosphorus inhibitor onto the metal surface followed the Langmuir monolayer adsorption.

(3) The 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.

Data Availability

We state that the dataset(s), code, and other digital research materials supporting the results in the article are available from the corresponding author upon request.

Ethical Approval

Research ethics: we state that we did not receive ethical approval from a local ethics committee to carry out our study. Animal ethics: we state that we did not obtain the necessary licences and approvals from our institutional animal ethics committee before conducting our research.

Conflicts of Interest

The authors declare that they have no conflicts of interest.


We would like to thank Harbin Gas Works for making available the corrosion agents for the study. Furthermore, we wish to thank the Harbin Institute of Technology. Liu Liang is grateful for a funded PhD stipend provided by the Nanqi Ren Studio. The research was supported by the Nanqi Ren Studio, Academy of Environment and Ecology, Harbin Institute of Technology (grant number HSCJ201704).


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Liang Liu, Ting-Ting Cao, Qi-Wei Zhang, and Chong-Wei Cui [ID]

Harbin Institute of Technology, School of Environment, Harbin 150090, China

Correspondence should be addressed to Chong-Wei Cui;

Received 14 August 2018; Revised 28 October 2018; Accepted 7 November 2018; Published 2 December 2018

Academic Editor: Alfredo Juan

Caption: Figure 1: Molecular model diagram of three organophosphorus inhibitors. (a) PBTCA. (b) HEDP. (c) ATMP.

Caption: Figure 2: Effect of concentration of the three corrosion inhibitors on the inhibition of corrosion of carbon steel.

Caption: Figure 3: (a, b) Corrosion inhibition rate of carbon steels with different concentrations of Cl[O.sub.2].

Caption: Figure 4: Corrosion inhibition rate of the corrosion inhibitor to carbon steel at different pH.

Caption: Figure 5: Optimized frontier orbitals of organic phosphorus inhibitors. (a) HOMO of PBTCA. (b) LUMO of PBTCA. (c) HOMO of HEDP. (d) LUMO of HEDP. (e) HOMO of ATMP. (f) LUMO of ATMP.

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

Caption: Figure 7: Isotherm fitting of three organic phosphorus inhibitors to Langmuir adsorption.
Table 1: The composition and content of the standard water used in the

Ion                     [Ca.sup.2+]    [Mg.sup.2+]     [Na.sup.+]

Concentration (mg/L)        200             48            305

Ion                     [Zn.sup.2+]     [Cl.sup.-]

Concentration (mg/L)         5             426

Ion                     S[O.sup.2-.sub.4]    HC[O.sup.-.sub.3]

Concentration (mg/L)           192                  122

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

     PBTCA                  HEDP                  ATMP

 Atom     Mulliken     Atom     Mulliken     Atom     Mulliken
           charge                charge                charge

  P1       1.1658       P1       1.1134       C1      -0.2667
  C2      -0.2905       O2      -0.5764       N2      -0.4657
  C3      -0.1777       O3      -0.5953       P3       1.1046
  C4      -0.2663       C4      -0.1195       C4      -0.2575
  C5      -0.2588       O5      -0.6431       C5      -0.2861
  O6      -0.5877       P6       1.1237       O6      -0.6589
  O7      -0.5932       O7      -0.5694       O7      -0.6391
  O8      -0.6405       O8      -0.6027       O8      -0.6129
  C9       0.6524       O9      -0.6360       O9      -0.6436
 O10      -0.5367      O10      -0.5683      O10      -0.6735
 O11      -0.4980      C11      -0.3356      P11       1.1320
 C12       0.6226      H12       0.3999      O12      -0.6159
 O13      -0.5344      H13       0.3958      O13      -0.5825
 O14      -0.5040      H14       0.4016      P14       1.1323
 C15       0.5876      H15       0.4087      O15      -0.6002
 O16      -0.5478      H16       0.3616      O16      -0.5800
 O17      -0.4948      H17       0.1451      H17       0.1858
 H18       0.1462      H18       0.1447      H18       0.1650
 H19       0.1433      H19       0.1517      H19       0.1936
 H20       0.1970                            H20       0.1751
 H21       0.1839                            H21       0.1911
 H22       0.1469                            H22       0.1927
 H23       0.1654                            H23       0.4111
 H24       0.3972                            H24       0.3915
 H25       0.4024                            H25       0.4062
 H26       0.3761                            H26       0.3995
 H27       0.3741                            H27       0.4033
 H28       0.3690                            H28       0.3987

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

Corrosion inhibitor                           Corrosion inhibitor

Quantum chemical parameters        PBTCA         HEDP         ATMP

[E.sub.HOMO] (eV)                 -7.5811      -7.5321      -6.4845
[E.sub.LUMO] (eV)                 -0.3320       0.6857       0.9960
[DELTA]E (eV)                     -7.2491      -8.2178      -7.4805
Dipole moment (debye)              3.7949       5.7964      12.0357
Electron affinity (A)              0.3320      -0.6857      -0.9960
Electronegativity ([chi])          3.9566       3.4232       2.7443
Hardness ([eta])                   3.6246       4.1089       3.7403
Affinity index ([omega])           2.1595       1.4260       1.0068
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Title Annotation:Research Article
Author:Liu, Liang; Cao, Ting-Ting; Zhang, Qi-Wei; Cui, Chong-Wei
Publication:Advances in Materials Science and Engineering
Date:Jan 1, 2018
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