How the Inhibition Performance Is Affected by Inhibitor Concentration

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How the Inhibition Performance Is Affected by Inhibitor Concentration: A Perspective from Microscopic Adsorption Behavior Xiao Wang,†,‡ Liang Liu,†,‡ Pan Wang,†,‡ Wen Li,†,‡ Jun Zhang,*,†,‡ and Youguo Yan*,†,‡ †

College of Science, China University of Petroleum, 266580 Qingdao, Shandong People’s Republic of China Key Laboratory of New Energy Physics & Materials Science in Universities of Shandong, China University of Petroleum, 266580 Qingdao, Shandong People’s Republic of China

‡

ABSTRACT: In this work, molecular dynamics simulations were employed to investigate the influence of inhibitor concentration on inhibition performance. The adsorption configuration, adsorption process, and inhibition performance were studied. We found that an ordered self-assembled inhibitor film can form on a metal surface, which plays a key role in corrosion inhibition. When the concentration reaches a critical value, inhibitor molecules organize into a micelle in aqueous solution. Further increasing the concentration did not change the inhibitor film on the metal surface, so that the inhibition efficiency remained at a constant level. Our analyses demonstrate that the number of water molecules displaced by inhibitor molecules, the diffusion of water molecules in the inhibitor film, and the stability of the inhibitor film play key roles in the process of corrosion inhibition. This work provides a thorough molecular-level understanding of inhibition behavior and the role of inhibitor concentration.

1. INTRODUCTION Corrosion results in huge economic losses and many potential safety questions and is thus an important issue in many applications, such as vacuum vessels, oil extraction and processing, hydrodesulfuration plants, and catalytic reactors.1−10 Consequently, corrosion inhibition is of great importance. In corrosion inhibition, organic corrosion inhibitors are generally employed to reduce corrosion.6,11−18 Among corrosion inhibitors, adsorptive inhibitors that take effect by adsorbing onto a metal surface to form protective films are widely used. In the past several decades, the inhibition performances of organic corrosion inhibitors have been investigated sufficiently, and numerous experiments14,16,19−22 have shown that inhibition efficiency is largely dependent on inhibitor concentration. These experimental results illustrate that inhibition efficiency first improves significantly with increasing inhibitor concentration. When the concentration reaches a critical value, the inhibition efficiency remains the same even with further increases in inhibitor concentration. Why does the inhibition efficiency not improve monotonically with increasing inhibitor concentration? Studies of surfactants provide some insight into the answer to this question. It is well-known that surfactant molecules are adsorbed at the oil−water interface to modulate interfacial tension, which decreases as the surfactant concentration is increased within a certain range. However, once the surfactant concentration exceeds the critical micelle concentration (CMC), the excess surfactant molecules form micelles in solution instead of being adsorbed at the oil−water interface. As a result, the interfacial tension does not decrease further. These studies demonstrate that interfacial tension is largely dependent on the adsorption behavior of surfactants at the oil− wate interface. On the basis of surfactant performance, it can be inferred that inhibition performance at different concentrations might be related to the adsorption behavior of an inhibitor on a © 2014 American Chemical Society

metal surface. Hence, motivated by an interest in exploring the mechanism of the effect of inhibitor concentration on inhibition efficiency, we investigated in this work the adsorption behavior of an inhibitor at different concentrations. The adsorption behaviors of inhibitors have been studied by many experimental methods, such as electrochemical impedance spectroscopy (EIS),4,13,23−25 X-ray photoelectron spectroscopy (XPS),26 and Fourier transform infrared (FTIR) spectroscopy.27 In such experiments, the morphologies of the metal surface and the inhibitor film adsorbed on the metal surface are analyzed, and then, the adsorption mechanism of the inhibitor is inferred. Although abundant valuable research has been conducted to investigate the adsorption behavior of inhibitors by experimental methods, it is difficult to observe the dynamic adsorption process and microscopic adsorption configuration experimentally and then determine how the inhibition mechanism is controlled by concentration. In the past two decades, molecular dynamics simulations28−32 have been widely used to explore the adsorption behaviors of organic molecules, as such simulations can provide detailed information about dynamic, energetic, and structural properties at the molecular level. For example, Tummala et al.33 studied the adsorption behavior of surfactants on a silica surface and observed the aggregate morphologies of the surfactants. Tosaka et al.34 carried out molecular dynamics simulations to investigate the adsorption mechanism of a protein on a silica surface at various pH values. These studies illustrate that molecular dynamics simulations are an efficient tool for investigating adsorption processes on solid surfaces. Received: Revised: Accepted: Published: 16785

July 13, 2014 September 18, 2014 October 2, 2014 October 2, 2014 dx.doi.org/10.1021/ie502790c | Ind. Eng. Chem. Res. 2014, 53, 16785−16792

Industrial & Engineering Chemistry Research

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dimensions of the metal surface. Meanwhile, counterions (Na+ and Cl−) were added to achieve charge neutrality in the system. Next, the initial model was constructed by adding the solution layer to the metal surface (see Figure 1c). To study the effect of inhibitor concentration on the adsorption behavior of the inhibitor on the metal surface, five models with different inhibitor concentrations were investigated; specifically, the number N of inhibitor molecules in the system was set as 5, 10, 15, 20, or 30. The condensed-phase-optimized molecular potentials for atomistic simulation studies (COMPASS force field)41 were employed in all simulations. The canonical ensemble (NVT) was applied at 298 K for each system using the velocity Verlet algorithm, and the integration step was set as 1 fs. The temperature was controlled by an Andersen thermostat.42 van der Waals interactions were calculated by an atom-based method with a cutoff distance of 10 Å. Electrostatic interactions were calculated by the Ewald method, which is rather costly but accurate for long-range interactions. During each simulation, the metal surface was constrained as the vibrations of the surface atoms are so small that they can be neglected at room temperature. At the top of every model, a vacuum slab with a thickness of 60 Å was added to avoid interactions between solvent molecules and periodic images of metal molecules due to the boundary conditions. Finally, each system was simulated for 2000 ps to reach equilibrium state, and the last 500 ps of each trajectory was used for analysis.

In this work, our aim was to observe the adsorption behavior of an inhibitor on a metal surface at different concentrations by means of molecular dynamics simulations and to shed light on the mechanism of the effect of the inhibitor concentration on the inhibition efficiency. First, the equilibrium adsorption configurations of inhibitor molecules at different concentrations were investigated. Second, the inhibitor adsorption process was studied to rationalize the driving force controlling conformational changes of the inhibitor at different concentrations. Finally, the influence of the adsorption configuration on the inhibition performance at different concentrations was examined in detail. Our simulation results reveal that inhibition efficiency at various concentrations can be ascribed to different adsorption configurations of inhibitor films.

2. MOLECULAR DYNAMICS SIMULATION DETAILS Molecular dynamics (MD) simulations were carried out with the Discover and Amorphous Cell modules of Materials Studio (Accelrys Inc.). In this work, the model was composed of a metal surface and a layer of inhibitor solution. 2.1. Metal Surface. Inhibitors are often applied in acidic media that contain a variety of anions (e.g., Cl−, SO42−), and some acidic anions are adsorbed on the metal surface, giving the metal surface a negative charge.2,26,35−37 Therefore, the metal surface constructed in this work contained iron atoms and chloride atoms. First, an iron lattice was derived from the structural database of Materials Studio, with characteristic lattice parameters of a = b = c = 2.8664 Å and α = β = γ = 90°. Then, the Fe system was cleaved along the (001) plane, and a sample of nine layers of Fe atoms with a thickness of approximately 10.3 Å was considered in the simulation system. The metal surface was built with dimensions of x = 22.93 Å and y = 22.93 Å. After the iron surface had been built, 16 charged acidic anions (e.g., Cl−) were added to it. The constructed metal surface is presented in Figure 1a.

3. RESULTS AND DISCUSSION 3.1. Adsorption Configurations at Different Concentrations. In this section, the equilibrium adsorption configurations of inhibitor molecules at five different concentrations, as shown in Figure 2, are discussed to reveal the influence of concentration on adsorption behavior. In Figure 2, it can be observed that, at the lowest concentration (N = 5), all of the inhibitor molecules adsorbed onto the metal surface and the metal surface was just partially covered by inhibitor molecules. When the inhibitor concentration was increased (N = 10, 15), more inhibitor molecules adsorbed onto the metal surface and formed an orderly inhibitor film. With further increases in the inhibitor concentration (N = 20, 30), it is interesting to note that the adsorption configuration became distinctly different from that at low concentration. At higher concentration (N = 20), most of the inhibitor molecules adsorbed onto the metal surface to form a self-assembled film, and the rest of the inhibitor molecules randomly dispersed in the aqueous solution. With a further increase in concentration (N = 30), it can be seen that a homologous self-assembled film formed on the metal surface, similar to that at the concentration of N = 20, and then the residual inhibitor molecules aggregated into micelles in solution. Furthermore, the density distribution profiles along the z axis were calculated to analyze the detailed adsorption behavior of inhibitor molecules at different concentrations. The z axis is normal to the metal surface, which was set as the zero point. Panels a and b of Figure 3 show the density distribution profiles of the nitrogen atom in the −NH3+ group and the carbon atom in the alkyl chain, respectively. From Figure 3, some detailed structural information can be obtained. First, the nitrogen atoms mainly distributed in the range of 2.0−4.5 Å, close to the metal surface, whereas the carbon atoms mainly distributed in the range of 4.5−20.0 Å, far from the surface. These results

Figure 1. Simulation model of the inhibitor system on a metal surface: (a) metal surface, (b) inhibitor molecule, (c) inhibitor solution.

2.2. Inhibitor Solution. In this work, thiadiazole38−40 was selected as the inhibitor. According to its pKa value, which can be used to predict the degree of dissociation in acidic solution, the −NH2 group of thiadiazole is protonated in acidic environments, and the structure of protonated thiadiazole was constructed in this work as shown in Figure 1b. After that, an aqueous solution layer containing 1080 water molecules and randomly distributed inhibitor molecules was constructed. The layer X and Y dimensions were the same as the corresponding 16786

dx.doi.org/10.1021/ie502790c | Ind. Eng. Chem. Res. 2014, 53, 16785−16792


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Figure 2. Final snapshots of inhibitor molecules on a metal surface at five different concentrations. Atoms are colored as follows: C, gray; N, blue; S, yellow; Fe, purple; Cl, green; and H, white.

Furthermore, when the number of inhibitor molecules increased from 5 to 15, the density of nitrogen atoms increased (Figure 3a inset), and the average thickness of the hydrophobic film composed of alkyl chains (Figure 3b) increased as well. With a further increase in the number of inhibitor molecules (N = 20), a peak appeared at around 40 Å, which indicates that some inhibitors were distributed in the solution. Further, the average occupied surface area of adsorbed inhibitor molecules was used to characterize the compactness of the self-assembled inhibitor films. When the number of inhibitor molecules was 5, 10, 15, 20, and 30, the average occupied surface area of a single adsorbed inhibitor molecule on the metal surface was 1.05, 0.53, 0.38, 0.33, and 0.33 nm2, respectively. From these calculated results, it can be seen that, at low concentrations, the adsorbed inhibitor film became denser as the inhibitor concentration increased. However, once the concentration reached a critical value (N = 20), the compactness of the self-assembled film remained constant. From the above analysis of adsorption configuration, it can be concluded that, with increasing inhibitor concentration, more inhibitor molecules adsorbed onto the metal surface and formed a self-assembled film to protect the metal surface. When the inhibitor concentration reached a critical value, a dense inhibitor film formed, and further added inhibitor molecules made little contribution to the thickness or compactness of the inhibitor film, instead gathering together to form micelles in solution. Regarding the inhibitor film, it can be seen that the headgroup of the inhibitor molecule with nitrogen adsored onto the metal surface and the alkyl chains extended into the solution. When the inhibitor film formed, the film of hydrophobic alkyl chains effectively isolated the metal surface from the corrosive medium, and corrosion was suppressed. Therefore, the thickness and compactness of the inhibitor film determine the inhibition efficiency. Based on the above discussions, at low concentrations (N = 5, 10, 15, and 20), because of the increasing thickness and density of the inhibitor film, the inhibition efficiency improves continuously with increasing concentration. However, if the

Figure 3. Density profiles of the inhibitor on a metal surface at different concentrations: (a) N atom of −NH3+, (b) C atom of the hydrophobic tail chain.

indicate that the headgroups of the inhibitor molecules adsorbed closely onto the metal surface, whereas the hydrocarbon chains inserted into the solution, and these inhibitor molecules formed an orderly structure on the metal surface. 16787



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concentration of inhibitor is increased to a high level (N = 20, 30), the inhibition efficiency cannot further improve. This inferred rule of changing inhibition efficiency is in good agreement with reported experimental results.43 3.2. Adsorption Process at Different Concentrations. Based on the above adsorption configuration analysis, it can be concluded that there are two types of adsorption behavior of inhibitor molecules at low and high concentrations. Therefore, the inhibitor adsorption process at two concentrations (N = 10, 30) was investigated to rationalize the driving force controlling the adsorption behavior, as shown in Figure 4.

Figure 4. Snapshots of the inhibitor on a metal surface at low (N = 10) and high (N = 30) concentrations for different simulation times.

Figure 5. Density profiles of N atoms in −NH3+ of the inhibitor on a metal surface at (a) low (N = 10) and (b) high (N = 30) concentrations for different simulation times.

At low inhibitor concentration (N = 10), the inhibitor molecules initially distributed randomly in solution. Because of the strong electrostatic attraction between the charged substrate and the protonated inhibitor molecules,44 some nearby inhibitor molecules adsorbed onto the metal surface in a short time (100 ps). The same information can also be obtained from the density profiles of the nitrogen atoms of −NH2 groups (Figure 5a). In Figure 5a, it can be seen that an obvious peak formed at 2.13 Å within the first 100 ps, which indicates that the headgroups of the inhibitor molecules adsorbed onto the metal surface and formed an inhibitor film in the initial stages of the simulation. As the simulation proceeded from 100 to 2000 ps, two main groups of inhibitor molecules can be observed, namely, adsorbed inhibitor molecules on the metal surface and free inhibitor molecules in solution. The inhibitor molecules in solution adjusted their molecular configurations to make the headgroups turn toward the metal surface and the alkyl chains extend into the solution, which might be due to the strong electrostatic attraction between the charged metal surface and the protonated headgroups of the inhibitor molecules. Then, the inhibitor molecules migrated into the initial adsorbed inhibitor film to form a dense inhibitor film. From these evolving snapshots, it can be seen that these inhibitor molecules initially had a random spatial configuration and the tilt angle between the alkyl chain and the metal surface was distributed in a wide range, which means that the inhibitor film was disordered and

loose. As the simulation proceeded , these alkyl chains gradually modulated their tilt angle to become approximately perpendicular to the metal surface, and this phenomenon can be ascribed to the effect of steric hindrance among the alkyl chains of these inhibitor molecules. Because of this approximate vertical adsorption pattern, the occupied area per inhibitor molecule decreased, and more inhibitor molecules in solution were able to adsorb onto the unoccupied metal surface to form a dense film. Correspondingly, the intensity of the first sharp peaks in the density profile increased from an initial value of 0.46 g/cm3 to a final value of 0.78 g/cm3 (Figure 5a). Therefore, at low concentration, the formation of the inhibitor film can be described as follows: Under strong electrostatic attraction, some inhibitor molecules near the metal surface are adsorbed onto the metal surface in a short time, and then they modify their configuration to be approximately perpendicular to the metal surface with a small occupied area. Those inhibitor molecules far from the metal surface initially modify their configurations so that their headgroups are toward the surface and their alkyl chains extend into solution, and then they migrate to the metal surface and form a dense and ordered inhibitor film. At high concentration (N = 30), there are some distinct differences in the adsorption process. At the beginning of the process, all of the inhibitor molecules are similarly distributed randomly in the aqueous solution. As the simulation proceeds, some inhibitor molecules adsorb onto the metal surface with 16788



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their headgroups adhered to the metal surface, and an orderly and dense self-assembled film is formed. This dense inhibitor film saturates the adsorption of inhibitor molecules, and there is no remaining space for further adsorption of inhibitor molecules. This can also be validated from the almost unchanged intensity of first peak in Figure 5b. As the simulation proceeds, the inhibitor molecules in solution exhibit two types of behavior. First, the inhibitor molecules near the formed inhibitor film primarily adjust their configurations (with the alkyl chains toward the metal surface and the headgroups extended into solution) and then migrate toward and adsorb onto the existing inhibitor film originating from the nonbonded interactions between inhibitor molecules. These inhibitor molecules are located in the range between 15 and 25 Å, as shown in Figure 5b. Second, the inhibitor molecules far from the formed inhibitor film gather together to form micelles as a result of the hydrophobic interactions of the alkyl chains, which can be identified in Figure 5b in the range between 30 and 50 Å. This phenomenon is universal in the research of surfactants at concentrations above the CMC. Based on the above analysis of the adsorption process, it can be inferred that the adsorption behavior of inhibitors is mainly determined by two types of interactions. One is the electrostatic attraction between inhibitor molecules and the metal surface, and the other is the hydrophobic interactions of the alkyl chains. When the concentration is low, the electrostatic attraction between the inhibitor molecules and the metal surface plays a pivotal role in the adsorption process, resulting in the adsorption of all available inhibitor molecules on the metal surface. With increasing concentration, the metal surface becomes completely occupied by inhibitor molecules, and adsorption become saturated; then, the electrostatic attraction between the metal surface covered by adsorbed inhibitor molecules and the free inhibitor molecules in solution is significantly weakened. Consequently, the hydrophobic interactions of the inhibitor molecules play a dominant role in the subsequent adsorption, resulting in the adsorption of inhibitor molecules onto the existing inhibitor film and the formation of micelles in solution. 3.3. Inhibition Mechanism at Different Concentrations. From the above analyses, it can be concluded that the adsorption configuration largely depends on the inhibitor concentration. In this section, the inhibition mechanism controlled by inhibitor concentration is discussed in terms of three aspects of adsorption behavior. Specifically, we propose that the ability of inhibitor molecules to displace water molecules, the migration ability of water molecules in the inhibitor film, and the stability of the inhibitor film can be used to explain the inhibition mechanism. 3.3.1. Capability of Displacing Water Molecules. In the process of corrosion, the water near a metal surface plays an important role as a transfer medium for corrosive species. Therefore, when inhibitor molecules adsorb onto the metal surface, some water molecules near the metal surface are displaced, and the diffusion of corrosive species is weakened, thus leading to the inhibition of the corrosion process. The more water molecules are displaced, the higher the inhibition efficiency is. Therefore, the capability of inhibitor molecules to displace water molecules is crucial in evaluating the inhibition efficiency. Figure 6 shows the density distribution profiles of water molecules at different concentrations. In Figure 6, there is a distinct peak at around 2.13 Å, and the intensity of this peak is

Figure 6. Density profiles of the oxygen atoms in water molecules at different concentrations.

much higher than that of the bulk solution, which indicates that a layer of interfacial water is adsorbed onto the metal surface as a result of the attraction between the charged metal surface and the polar water molecules. Next to the first strong peak, there is a second peak of water molecules at around 4.78 Å. The existence of the second peak can be ascribed to the relatively strong attraction between the electronegative nitrogen atom of the five-atom ring of the inhibitor molecule and the polar water molecules. In the range between 4.78 and 20 Å, the density of water molecules is lower than that in the bulk solution, which means that water molecules have been displaced by inhibitor molecules. Furthermore, it can also be seen that, with increasing inhibitor concentration, the density of water in this region decreases, which indicates that more water molecules near the metal surface are displaced. As a result, the inhibition efficiency is improved. 3.3.2. Migration Capacity of Water Molecules. In addition to the number of water molecules, the migration of water molecules through the inhibitor film is another pivotal factor determining corrosion behavior. The motion of water molecules in the inhibitor film could promote the formation of transferring channels through which corrosive particles could move to reach the metal surface. As a result, a low migration rate of water molecules would reduce the exchange of corrosive species, and corrosion would be inhibited. According to the above analyses, there are three types of water molecules in the simulation systems: interfacial water molecules strongly bound to the metal surface, water molecules constrained in the inhibitor film, and free water molecules in the bulk solution. Herein, the highest concentration is taken as an example, and the mean square displacement (MSD) curves of these three types of water molecules are proposed to evaluate their migration behaviors, as the changing rule in all five models is the same. A low slope of the curve means that the motion of water is slow, and this phenomenon leads to the difficult exchange of corrosive species and a high inhibition efficiency. Figure 7 shows the MSD profiles of the three types of water molecules. In Figure 7, the slope of MSD curve of interfacial water is much lower than those of the other two layers, which indicates that these water molecules have a weak migration capacity. Thus, these bound interfacial water molecules make little contribution to corrosion because of their weak transfer 16789



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E inhibitor/surface =

Etotal − (Einhibitor + Esurface) Ninhibitor

(2)

where Ninhibitor is the number of the inhibitor molecules adsorbed on the surface; Einhibitor/surface is the interaction energy; Einhibitor and Esurface denote the energies of an inhibitor molecule and the metal surface, respectively; and Etotal refers to the total energy of the overall system. In addition, the van der Waals potential EvdW and electrostatic potential Eele were also calculated. These calculated interaction energies are presented in Table 1. Table 1. Interaction Energies between the Inhibitor Molecule and the Metal Surface at Different Inhibitor Concentrations

Figure 7. MSD profiles of water molecules at high concentration (N = 30) for three different layers.

capability. The water molecules constrained in the inhibitor film, unlike the interfacial water molecules, have a certain migration capability. Meanwhile, the diffusion coefficients (D) of the five models present the same changing rule, which is described by the equation D=

1 d lim 6 t →∞ dt

i

Etotal (kcal/mol)

EvdW (kcal/mol)

Eele (kcal/mol)

5 10 15 20 30

−1169.18 −1236.91 −1283.78 −1768.37 −1778.29

−12.9601 −7.3836 −8.6082 −7.1793 −6.5698

−1156.22 −1229.52 −1283.78 −1761.19 −1771.72

As shown in Table 1, all of the interaction energies were found to be negative, which means that the interaction between inhibitor molecules and the metal surface if attractive. A further comparison indicates that the absolute value of the interaction energy increased with increasing concentration. This indicates that the adsorption strength of an inhibitor molecule on the metal surface increased, resulting in more stable adsorption of the inhibitor film. It is well-known that the stability of the adsorbed inhibitor film is crucial for inhibition. The more stable the inhibitor film is, the higher the inhibition efficiency is. Therefore, in terms of adsorption strength, it can be inferred that an inhibitor film at high concentration has a high inhibition efficiency. Furthermore, the transfer coefficient of the inhibitor film was calculated to evaluate the dynamic stability of the inhibitor film. Generally, an inhibitor film that moves quickly on a metal surface has intense thermal motion and can form more cavities and channels, which could allow corrosive particles into the inhibitor film. If the inhibitor film had a large self-diffusion coefficient, these cavities would move, resulting in the migration of the corrosive species incorporated therein and inducing corrosion.47 As a result, the inhibition efficiency would be low. In this work, the transfer coefficients of inhibitor molecules at different inhibitor concentrations were calculated. When the number of inhibitor molecules was 5, 10, 15, 20, and 30 (i.e., as the inhibitor concentration increased), the transfer coefficients were found to be 1.31 × 10−12, 0.97 × 10−12, 0.87 × 10−12, 0.61 × 10−12, and 0.61 × 10−12 m2·s−1, respectively. That is, as the inhibitor concentration increased, the transfer coefficient first decreased and then reached a stable value at high inhibitor concentration (N = 20, 30). Therefore, in terms of the transfer coefficient of the inhibitor film, it can be inferred that the inhibition efficiency is high at high inhibitor concentrations. From all of the above analyses, it can be concluded that the inhibition efficiency increased with increasing concentration and a high inhibition efficiency can be ascribed to three factors: a high capability of inhibitor molecules to displace water

n

∑ ⟨|R i(t ) − R i(0)|2 ⟩

inhibitor concentration (N)

(1)

where Ri(t) and Ri(0) are the positions of corrosive species i at time t and 0, respectively, and |Ri(t) − Ri(0)|2 is the meansquare displacement (MSD). When the number of inhibitor molecules was 5, 10, 15, 20, and 30, the diffusion coefficient of water molecules in the inhibitor film was 2.8 × 10−11, 2.4 × 10−11, 1.9 × 10−11, 0.067 × 10−11, and 0.056 × 10−11 m2·s−1, respectively. Comparing these data, the diffusion coefficients in the five inhibitor films are much smaller than that in the bulk solution (2.3920 × 10−9 m2· s−1),45 which means that the inhibitor films effectively restrained the migration of water molecules. Accordingly, the presence of the inhibitor film resulted in the inhibition of corrosion. Further comparing the diffusion coefficients in the five inhibitor films, it can be seen that, with increasing inhibitor concentration, the diffusion coefficient decreased, implying an increasing inhibition efficiency. 3.3.3. Stability of the Inhibitor Film. The stability of the inhibitor film is very important in inhibition to maintain effective protection for the metal surface. Here, the adsorption strength and self-diffusion coefficient are proposed to evaluate the stability of the inhibitor film. The results reported above clearly show that the dynamic properties of water have a significant influence on inhibition performance at different concentrations. Similarly, the dynamic properties of the inhibitor film were also analyzed to investigate their effect on inhibition performance. In this section, two important dynamic properties of inhibitor films, namely, the adsorption strength and stability of the inhibitor film, are evaluated to study the influence of concentration on inhibition performance. In this work, the adsorption strength of the inhibitor film was studied in terms of the interaction energy between a single inhibitor molecule and the metal surface. The interaction energy was calculated as46 16790



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(4) Gómez, B.; Likhanova, N. V.; Domínguez Aguilar, M. A.; Olivares, O.; Hallen, J. M.; Martínez-Magadán, J. M. Theoretical Study of a New Group of Corrosion Inhibitors. J. Phys. Chem. A 2005, 109, 8950. (5) Tedim, J.; Poznyak, S. K.; Kuznetsova, A.; Raps, D.; Hack, T.; Zheludkevich, M. L.; Ferreira, M. G. S. Enhancement of Active Corrosion Protection via Combination of Inhibitor-Loaded Nanocontainers. ACS Appl. Mater. Interfaces 2010, 2, 1528. (6) Fazal, M. A.; Haseeb, A. S. M. A.; Masjuki, H. H. Effect of different corrosion inhibitors on the corrosion of cast iron in palm biodiesel. Fuel Process. Technol. 2011, 92, 2154. (7) Gomez, H.; Ram, M. K.; Alvi, F.; Stefanakos, E.; Kumar, A. Novel Synthesis, Characterization, and Corrosion Inhibition Properties of Nanodiamond−Polyaniline Films. J. Phys. Chem. C 2010, 114, 18797. (8) Cao, Z.; Tang, Y.; Cang, H.; Xu, J.; Lu, G.; Jing, W. Novel benzimidazole derivatives as corrosion inhibitors of mild steel in the acidic media. Part II: Theoretical studies. Corros. Sci. 2014, 83, 292. (9) Obot, I. B.; Gasem, Z. M. Theoretical evaluation of corrosion inhibition performance of some pyrazine derivatives. Corros. Sci. 2014, 83, 359. (10) Finšgar, M.; Jackson, J. Application of corrosion inhibitors for steels in acidic media for the oil and gas industry: A review. Corros. Sci. 2014, 86, 17. (11) Tomala, A.; Naveira-Suarez, A.; Pasaribu, R.; Doerr, N.; Werner, W. S. M.; Stoeri, H. Behaviour of Corrosion Inhibitors Under Different Tribological Contact. Tribol. Lett. 2011, 45, 397. (12) Olivares-Xometl, O.; Likhanova, N. V.; Domínguez-Aguilar, M. A.; Arce, E.; Dorantes, H.; Arellanes-Lozada, P. Synthesis and corrosion inhibition of α-amino acids alkylamides for mild steel in acidic environment. Mater. Chem. Phys. 2008, 110, 344. (13) Desimone, M. P.; Grundmeier, G.; Gordillo, G.; Simison, S. N. Amphiphilic amido-amine as an effective corrosion inhibitor for mild steel exposed to CO2 saturated solution: Polarization, EIS and PMIRRAS studies. Electrochim. Acta 2011, 56, 2990. (14) Duda, Y.; Govea-Rueda, R.; Galicia, M.; Beltrán, H. I.; ZamudioRivera, L. S. Corrosion Inhibitors: Design, Performance, and Computer Simulations. J. Phys. Chem. B 2005, 109, 22674. (15) Ramachandran, S.; Tsai, B.-L.; Blanco, M.; Chen, H.; Tang, Y.; Goddard, W. A. Atomistic Simulations of Oleic Imidazolines Bound to Ferric Clusters. J. Phys. Chem. A 1997, 101, 83. (16) Kern, P.; Landolt, D. Adsorption of organic corrosion inhibitors on iron in the active and passive state. A replacement reaction between inhibitor and water studied with the rotating quartz crystal microbalance. Electrochim. Acta 2001, 47, 589. (17) Fu, J.; Li, S.; Wang, Y.; Liu, X.; Lu, L. Computational and electrochemical studies on the inhibition of corrosion of mild steel by L-cysteine and its derivatives. J. Mater. Sci. 2011, 46, 3550. (18) Fu, J.; Zang, H.; Wang, Y.; Li, S.; Chen, T.; Liu, X. Experimental and Theoretical Study on the Inhibition Performances of Quinoxaline and Its Derivatives for the Corrosion of Mild Steel in Hydrochloric Acid. Ind. Eng. Chem. Res. 2012, 51, 6377. (19) de Oliveira Wanderley Neto, A.; Moura, E. F.; Júnior, H. S.; Dantas, T. N. d. C.; Neto, A. A. D.; Gurgel, A. Preparation and application of self-assembled systems containing dodecylammonium bromide and chloride as corrosion inhibitors of carbon-steel. Colloids Surf. A 2012, 398, 76. (20) Finšgar, M.; Lesar, A.; Kokalj, A.; Milošev, I. A comparative electrochemical and quantum chemical calculation study of BTAH and BTAOH as copper corrosion inhibitors in near neutral chloride solution. Electrochim. Acta 2008, 53, 8287. (21) Ahamad, I.; Quraishi, M. A. Bis (benzimidazol-2-yl) disulphide: An efficient water soluble inhibitor for corrosion of mild steel in acid media. Corros. Sci. 2009, 51, 2006. (22) Reyes, Y.; Rodríguez, F. J.; del Río, J. M.; Corea, M.; Vázquez, F. Characterisation of an anticorrosive phosphated surfactant and its use in water-borne coatings. Prog. Org. Coat. 2005, 52, 366. (23) Borisova, D.; Möhwald, H.; Shchukin, D. G. Influence of Embedded Nanocontainers on the Efficiency of Active Anticorrosive

molecules, a low migration rate of water molecules through the inhibitor film, and a more stable inhibitor film.

4. CONCLUSIONS In this work, molecular dynamics simulations were employed to investigate the microscopic inhibition performance of an inhibitor at different concentrations. From a comparison of the adsorption configurations of inhibitor molecules at different concentrations, it can be concluded that ordered self-assembled inhibitor films can form on metal surfaces, which plays a key role in corrosion inhibition. When the concentration reaches a critical value, the inhibitor molecules organize into micelle in aqueous solution. Further increasing the concentration does not change the inhibitor film on the metal surface; as a result, the inhibition efficiency remains at a constant level. The inhibitor adsorption process was investigated to rationalize the driving force promoting conformational changes of inhibitor molecules. At low concentration, the strong interaction between the surface and the inhibitor induces the adsorption of inhibitor molecules onto the metal surface. With increasing inhibitor concentrations, when the metal surface is completely covered with inhibitor molecules, the interaction between the inhibitor molecules and the metal surface decreases significantly. Then, as a result of the hydrophobic interactions of the inhibitor molecules, some added inhibitor molecules adsorb onto the first-layer inhibitor film, and the others gather to form micelles in solution. Finally, the inhibition mechanism was discussed in terms of aspects of adsorption performance. It was demonstrated that the number of water molecules displaced by inhibitor molecules, the diffusion of water molecules in the inhibitor film, and the stability of the inhibitor film play key roles in the process of corrosion inhibition. Our research provides a thorough molecular-level understanding of inhibition behavior and the role of inhibitor concentration.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel./Fax: 86-053286983366 (J.Z.). *E-mail: [email protected]. Tel./Fax: 86-0532-86983415 (Y.Y.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (51034007, 51302321), the PetroChina Innovation Foundation (2013D-5006-0206), and the Fundamental Research Funds for the Central Universities (14CX02002A, 13CX05019A).

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REFERENCES

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How the Inhibition Performance Is Affected by Inhibitor Concentration

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