Migration of nitrite corrosion inhibitor in calcium silicate hydrate nanopore: A molecular dynamics simulation study

1 Introduction

The concrete environment has high alkalinity, with a pH between 12 and 13, producing a layer of a self-protecting passivation film on the internal steel reinforcement surface (Page and Treadaway, 1982). As one of the main products of cement hydration, Calcium hydroxide (Ca(OH)₂) can prevent the passivation film of steel from being destroyed (Page, 1975). However, as the concrete carbonizes or the pH value of the internal environment decreases significantly, the passivation film is destroyed, and the corrosion cell is formed on the surface of the steel (Bažant, 1979).

The overview of the entire corrosion process reveals that the Cl⁻ is not consumed in the corrosion process but acts as a catalyst to promote corrosion (Thangavel and Rengaswamy, 1998). As a result, even a small amount of Cl⁻ existing can trigger pitting corrosion. Care et al. (2008) found that the volume of steel reinforcement expanded by 6.5 times after corrosion, which causes cracking and peeling of the concrete, thus significantly reducing the load-bearing capacity and durability of the component.

Corrosion inhibitors, which can effectively prevent the corrosion of steel bars, are widely used in the concrete industry (Ormellese et al., 2011; Aydin and Cizmeciglu, 2015; Diamanti et al., 2017; Sun et al., 2019). The widely used corrosion inhibitors include phosphate (Mandal et al., 2020), chromate (Schiessl et al., 2008; Okeniyi et al., 2014), zinc oxide (Devi and Kannan, 2013), gluconate (Li et al., 2015), amines (Qian and Cusson, 2004), nitrite (Krolikowski and Kuziak, 2011; Mandal et al., 2020), and so on (Soylev and Richardson, 2008). Gonzalez compared the different corrosion inhibitors and found that nitrite corrosion inhibitors have a more significant corrosion inhibiting effect than the others (González et al., 1998). So, a lot of research has been carried out on different kinds of nitrite corrosion inhibitors (Garces et al., 2008; Krolikowski and Kuziak, 2011). Ryu found that adding Ca(NO₂)₂ into reinforced concrete can improve the corrosion resistance, shorten the final setting time and improve the early strength (Ryu et al., 2017a). Garcés investigated the effect of pH and the addition amount of NaNO₂ on the corrosion inhibitor effect and found that the corrosion inhibition effect of NaNO₂ is reduced by about 10% under alkaline conditions (Garces et al., 2011). Ryu put the steel bar into the mixed solution of LiNO₂, Ca(OH)₂ and NaCl and found that LiNO₂ could perform a significant corrosion inhibition function at different concentrations of saline solution (Ryu et al., 2017b). Ann found that the addition of a nitrite corrosion inhibitor increased the threshold for chloride ions causing corrosion from 0.18%–0.33% to 0.22%–1.95% (Reou and Ann, 2008). Studies show that LiNO₂ mixed with concrete can improve the strength and durability of concrete (Hori et al., 1991). Hazehara et al. (2020) found that LiNO₂ can improve the working performance of concrete compared with Ca(NO₂)₂ corrosion inhibitor. Moreover, LiNO₂ can effectively stabilize the internal PH value of concrete. Although the effects of corrosion inhibitors on concrete can be understood through experiments, the transport characteristics of ions of inhibitors in the nano-channels inside concrete from a molecular perspective are still unknown.

Because of the limitations of experimental methods, the molecular dynamics simulations method is used to study the transport behavior of nitrite in nano-channels. MD simulation has been successfully applied to study ion transport behavior in concrete nano-channels channels. Such as, Hou used the method of molecular dynamics simulation to study the transport behavior of chloride ions in concrete microscopic channels. The study found that chloride ions and calcium ions in the channels would form Ca-Cl ion clusters, thus reducing the transport rate of chloride ions. (Hou and Li, 2014). Similarly, the transport and adsorption properties of Na ions in silicate and aluminosilicate nano-channels are investigated. Na ions can be adsorbed on silicate chains by ionic bonds and form ion clusters with water molecules to block the transport of solution (Hou et al., 2018a). The transport characteristics and principles of salt solution in nano-channels with different pore sizes are also revealed (Yang et al., 2019). The penetration of solutions through different mineral and gel channels is being investigated (Hou et al., 2018b). Yu investigated the effect of graphene oxide epoxy (GO-EP) coating on the transport performance of sodium chloride solution in the micro-porous channels and found that the coating could slow down the transport rate in the pores by forming chemical bonds with Na⁺ and Cl⁻ (Yu et al., 2019). In addition, the microscopic mechanisms of the mechanical properties of polymer-reinforced cementitious materials (Chen et al., 2020) and the interfacial bonding between cementitious and reinforced materials (Wang et al., 2020a; Wang et al., 2020b; Wang et al., 2020c) have also been thoroughly studied based on the MD simulation.

Nitrite will pass through the pores of the concrete itself to reach the surface of the reinforcement, forming a dense film of oxides on the surface of the reinforcement to act as a passivation, thereby improving the durability of the reinforced concrete structure. At present, the effects of different types of nitrite on the properties of reinforced concrete have been tested and verified, and there are very few microscopic studies and mechanism studies on the transport characteristics of nitrite, mainly because it is difficult to study with the help of experimental means at the microscopic scale, and molecular dynamics research can make up for this deficiency. The study of micro-view can more thoroughly elucidate the transport mechanism of nitrite in the internal pores of concrete, thus providing guidance for macroscopic research.

Herein, the transport behavior of lithium nitrite, sodium nitrite, and calcium nitrite in the pores of calcium silicate gels are investigated based on MD simulation. The local structure and dynamic behavior of ions in hydrated calcium silicate (CSH) channels are analyzed to reveal the causes that drive and hinder ion transport and explain the different transport behavior of various nitrite solutions. Expectantly, this work can provide fundamental theoretical support for a comprehensive understanding of the transport behavior of other nitrites corrosion inhibitors in the CSH channels and assist in selecting the optimal corrosion inhibitor for the design of highly durable concrete.

2 Simulation methods

2.1 Model construction

In order to investigate the effects of different cations on the transport behavior of nitrite in CSH gel channel, and to reveal their microscopic mechanisms, three kinds of nitrites, NaNO₂, Ca(NO₂)₂, and LiNO₂ are studied. The transport atom model consists of a vacuum layer, CSH channel and a nitrite solution. Since tobermorite 11 Å has a similar multi-layered structure and the same chemical composition to calcium silicate hydrate (Nonat et al., 1998; Nonat, 2004), it has been used as a substitute for calcium silicate hydrate to study the transport behavior of salt solutions (Zhang et al., 2017). Figure 1 shows the initial model of tobermorite 11 Å with the three-dimensional dimensions of 22.32 Å × 22.17 Å×22.77 Å.

FIGURE 1

FIGURE 1. The tobermorite 11 Å origin cell. The green, yellow red, white spheres represent the calcium, silicon and hydrogen, respectively.

Tobermorite is expanded 7 and 2 times along the Y and Z directions, respectively. And then, a calcium silica layer is removed along the Y direction, and the substrates on both sides are shifted outward to form a channel of width 3 nm. Some of the calcium on the surface of the channel is removed, and some of the non-bridged oxygen on the surface is protonated to ensure the charge balance of the channel. A vacuum layer about 7 nm above the CSH substrate is constructed to avoid the influence of periodic boundaries. Three types of nitrite solutions with three-dimensional dimensions of 22.3 Å × 130 Å × 68 Å and a concentration of 1 mol/L are added under CSH substrate, respectively. The final transport model is shown in Figure 2.

FIGURE 2

FIGURE 2. The transport model. (The light blue membrane represents the water molecule. The pink and blue balls represent the cation and the NO₂⁻, respectively).

2.2 Simulation detail

The hydrated calcium silicate channel is described by the ClayFF force field (Cygan et al., 2004). This force field can accurately describe the interaction of water and salt solutions with cementitious materials or mineral surfaces (Li et al., 2017; Hou et al., 2018b). The Consistent Valence Force Field (CVFF) is utilized to simulation the NO²⁻, and the geometric rule is selected to unite ClayFF and CVFF force field. This combination to simulate organic additives reinforced cement composites has also been proven to be accurate and feasible (Dauber‐Osguthorpe et al., 1988).

Lammps, a large-scale atomic-molecular simulator, is mainly used for molecular dynamics calculation and simulation work. The entire simulation is divided into two stages based on Lammps software: the pre-equilibrium and transport stages (Plimpton et al., 2007). During the pre-equilibrium stages, the temperature and the time step are set as 300 K and 1 fs, the nitrite solution and the channel are run under the NVT ensemble for 0.5 ns. In order to prevent the solution from entering the CSH channel in the pre-equilibrium stage, a layer of water molecules at the entrance of the CSH channel is fixed. When the whole system reaches equilibrium, the fixed water molecules are completely relaxing, and the nitrite solution is gradually transported into the pore channel by capillary force. The ensemble and the time step remain unchanged during the first stage. The whole transport stage lasts for 3 ns and is saved every 1 ps for data analysis.

3 Results and discussion

3.1 Water and ions transport in the CSH nanopores

The transport process in the CSH nanopore for three kinds of nitrite solutions is presented in Figure 3. Water molecules and ions gradually transport through the CSH gel poles from 0 ps to 2000 ps. During the transport process, the Frontier of the solution exhibits a concave shape. This phenomenon accords with the characteristics of capillary absorption and proves the hydrophilicity of CSH gel. By comparing the screenshots of three solution systems, it can be seen that LiNO₂ solution has a slightly more considerable adsorption speed than that of Ca(NO₂)₂ solution and NaNO₂ solution. Therefore, LiNO₂ as a nitrite inhibitor for concrete is widely used due to its rapid transmission speed in the concrete gel nanopore, and it can quickly reach the surface of the steel bar and play an excellent anti-rust role.

FIGURE 3

FIGURE 3. Snapshots of the water and ions transport process at 0 ps, 500 ps, 1,000 ps, 1,500 ps, and 2000 ps for (A) NaNO₂ solution, (B) Ca(NO₂)₂ solution, and (C) LiNO₂ solution. (Purple, green, pink and blue balls represent sodium ion, calcium ion, lithium ion and nitrate ion respectively. Besides, The green balls in (A) and (B) channel solutions are Ca ions dissolved from the CSH substrate).

In order to quantitatively study the transport process of these nitrite solutions, the movement tracks of the concave surface are monitored, as shown in Figure 4. The depth of penetration versus time relationship curves of water and ions in the CSH nanopores shows a parabolic relation with time, which in line with the traditional capillary adsorption theory of the Lucas-Washburn equation (Ababneh et al., 2013). In the beginning, the ionic penetration curves show a zero-point platform, as shown in Figures 4A,B,C, indicating that no ions are penetrating the gel pore. In addition, there is an overlap of the penetration curves of NO₂⁻ and cation ions, meaning that the transport of the anions and cations is almost synchronous. There are some similarities between water molecules and ions in transportation, but the migration Frontier of ions always lags behind water molecules, which indicates that ions are dragged upward for transport by water molecules. Meanwhile, the zero-point platform of the LiNO₂ is shorter than the other two, and the penetration depth of the NO₂⁻ in LiNO₂ is about 115 Å at 3000 ps, which is similar to Ca(NO₂)₂ but more quickly than NaNO₂. They demonstrate that the NO₂⁻ in LiNO₂ can enter into nanopore more quickly and has a faster transmission speed.

FIGURE 4

FIGURE 4. Depth of penetration versus time relationship curves: (A) NaNO₂ solution, (B) Ca(NO₂)₂ solution and (C) LiNO₂ solution.

3.2 Local structure of water and ions

In the first part, the differences in the transport process of three different nitrite solutions in CSH pores are described. Then, the mechanism of the differences in transport behavior will be revealed by analyzing atomic microstructure, chemical bond types, and coordination numbers. The coordination numbers are listed in Table 1.

TABLE 1

TABLE 1. The average coordination number (CN).

The local structure of atoms in the system can be characterized by radial distribution function (RDF). During the process of solution permeation, it is found that water molecules drive NO₂⁻ ions transport forward. In order to compare the differences of water driving force in different nitrite solutions, the RDF of NO₂⁻-Hw (hydrogen in water) is calculated as shown in Figure 5A. The peaks of NO₂⁻-Hw in three kinds of nitrite solutions are all located at 1.85 Å, indicating that the H-bonds are developed between them shown in Figure 5B. In LiNO₂ solutions, not only the peak of NO₂⁻-Hw is the highest, but also the coordination number of NO₂⁻ ions is the largest, which indicates that the interaction between NO₂⁻ ion and water molecules is the strongest in LiNO₂ solution, thereby LiNO₂ solution transports the fastest among the three kinds of nitrite solution. In addition, the NO₂⁻-Hw coordination number in Ca(NO₂)₂ solution is slightly larger than that of NaNO₂, which explains why Ca(NO₂)₂ solution transports faster than NaNO₂ solution.

FIGURE 5

FIGURE 5. The radial distribution function (RDF) of (A) NO₂⁻-H_w and (B) the H-bonds network of NO₂⁻-H_w. (The blue balls are for the nitrogen. The red-white sticks are for the water molecule).

The adsorption of ions on the pore surface can slow down the transport of NO₂⁻ ions. Therefore, the differences in the adsorption behavior of NO₂⁻ ions on the pore surface in three kinds of nitrite solutions have been studied and analyzed. The RDFs of the Ca_sur-NO₂⁻ (Ca_sur represents the Ca of the channel surface) display the peaks at around 2.45 Å, as shown in Figure 6. When NO₂⁻ ions pass through the pore surface, Ca_sur (Ca on the surface of the pore) will capture the NO₂⁻ ions and form a stable ion pair with them, reducing the transport speed of NO₂⁻ ions obviously. By comparing the peak heights, it is found that the Ca_sur in LiNO₂ solution has the most potent ability to capture NO₂⁻, which could slow down the transport speed of NO₂⁻ most. By comparing the peak heights, it is found that Ca_sur in LiNO₂ solution has the most potent ability to capture NO₂⁻, so LiNO₂ solution should possess the slowest transport speed. However, the average coordinate number between NO₂⁻ and Ca_sur can be ignored than the other coordinate numbers for all systems. Therefore, the adsorption of ions on the pore channel surface hardly has any significant effect on the transport speed of NO₂⁻.

FIGURE 6

FIGURE 6. The RDFs of Ca_sur-NO₂⁻.

In addition to considering the adsorption of NO₂⁻ on pore channels surface, the ions pair of nitrite solution in the pore surface should also be considered. In order to trace the local structure of cations in the pore, the RDFs of cation-NO₂^- and cation-O_w have been obtained and shown in Figures 7A,B. The RDFs of cation-O_w and cation- NO₂⁻ display the prominent peaks, revealing that the cations will form NO₂⁻-cation-water clusters in nitrite solution. Taking Ca(NO₂)₂ solution as an example, the formed clusters will affect the transport speed of nitrite solution shown in Figure 7C. Similarly, the transport behavior of sodium chloride solution in the pores of CSH gel also found the same phenomenon: the formation of clusters of cations and chloride ions in the pores will inhibit the transport behavior of the solution (Zhang et al., 2017).

FIGURE 7

FIGURE 7. The radial distribution function (RDF) of (A) Cation-O_w, (B) Cation-NO₂⁻, (C) the ion clusters of the Ca(NO₂)₂ solution.

The Li-O_w (oxygen in water) peak location is much far from the others, and its peak is much lower than the others, shown in Figure 7A, indicating the chemical bond between Li and water is the weakest. Similarly, the chemical bond between Li and NO₂⁻ is weaker than other bonds, as shown in Figure 7B, indicating that Li has the weakest binding ability with water molecules and NO₂⁻. As a result, Li ions cannot form stable clusters to reduce the transport speed compared with Ca and Na ions, which explains why NO₂⁻ in LiNO₂ solution has the fastest transport speed.

In addition to the ionic bonding in the above solution, CSH substrate also affects the transport of rust inhibitor molecules in its nanochannel. Figure 8A shows RDFs of CSH substrate oxygen atom (Os) and CSH cation in inhibitor, the RDFs of cation-O_s display the prominent peaks, revealing that the cations will form O_s-cation clusters in the interface of CSH substrate. Both Na ions and Ca ions have peak values at 2.35 Å, while the peak values of Li ions are far away, indicating that Li ions are not easily adsorbed by CSH substrate. As shown in Figures 8B–D, both Ca and Na ions produce ionic bonding with O_s atoms in the CSH substrate, and NO₂⁻ and water molecules are also attracted by cations to form O_s-cation-water (NO₂⁻) clusters, thus affecting the transport of NO₂⁻.

FIGURE 8

FIGURE 8. (A) The RDF of Cation-O_s, the schematic diagram of (B) Ca-O_s, (C) Na-O_s and (D) Li-O_s.

3.3 Dynamics behavior of ions

In order to further analyze the transport behavior of different nitrite solutions in the CSH channel, the number of NO₂⁻ entering the CSH channel and the evolution of NO₂⁻ concentration distribution in three nitrite solutions has been calculated, as shown in Figure 9. As shown in Figures 9A,B, the number of cations and NO₂⁻ in the three nitrite solutions continuously enters the CSH channel with the transmission of the solution, and the ions in LiNO₂ has the largest transmission number, followed by NaNO₂ and Ca(NO₂)₂. Figures 9C–E show the transport of NO₂⁻ in the channel over time to understand the phenomenon, the red circle represents the depth of ion aggregation, and the yellow circle represents the final depth of ion penetration. The penetration depth of NaNO₂ is less than that of the other two nitrite solutions, and NO₂⁻ ions in NaNO₂ are concentrated in about half of the maximum penetration depth, as shown in Figure 9C, which indicates that only a few NO₂⁻ ions in NaNO₂ can arrive at the top of the concave liquid surface. Compared with NaNO₂, Ca(NO₂)₂ and LiNO₂ have the same higher penetration depth. The main difference between them is that NO₂⁻ in Ca(NO₂)₂ solution is mainly distributed in the lower part of the channel, and NO₂⁻ in LiNO₂ solution is mainly distributed in the upper boundary of the channel, as shown in Figures 9D,E. As a result, even the Ca(NO₂)₂ and the LiNO₂ solution possess the same penetration depths, a greater amount of NO₂⁻ in LiNO₂ solution can be transported more depth. It indicates that LiNO₂ can penetrate the microporous channel of cement and reach the surface of reinforcing steel faster to play a promotional role in anti-corrosion.

FIGURE 9

FIGURE 9. The schematic diagram of the number of ions entering the CSH channel over time (A) cations, (B) NO₂⁻, the evolution of NO₂⁻ concentration distribution of three kinds of nitrite solutions: (C) NaNO₂, (D) Ca(NO₂)₂, (E) LiNO₂. The red circle represents the depth of ion aggregation and the yellow circle represents the final depth of ion penetration.

Atomic dynamics behavior is crucial for the transport behavior of the solution. Simultaneously, the time correlation function is a powerful tool to determine the stability of chemical bonds. Therefore, based on atomic dynamics, the time correlation function (TCF) has been used to evaluate the stability of chemical bonds between ion pairs (Hou et al., 2014). The results are calculated by Eq. 1 and shown in Figure 10. Then the mean square displacement (MSD) is used to visually characterize the diffusion of ions in the pores (Hou and Li, 2014).Where δb (t) = b(t)-, b(t) is a binary indicator with a value of one if a chemical bond is formed, otherwise a value of 0 instead, at the same time, the faster the TCF curve decays with time, the weaker the bond connection. The decay orders of the cation-O_w TCF and cation -NO₂^- TCF curves presented the same regular, which are LiNO₂> NaNO₂> Ca(NO₂)₂, indicating that the chemical bonds of Li-O_w and Li-NO₂^- are the most vulnerable, respectively, as shown in Figures 10A,B. Therefore, the effect of ion clusters in LiNO₂ solution on the transport process is the weakest, and the transport speed of NO₂⁻ in LiNO₂ solution is faster than that in the other two solutions. In addition, the difference of TCF curves of NO₂⁻-H_w in three nitrite solutions is almost invisible, which indicates that the stability of NO₂⁻-H_w bond in different nitrite solutions is almost the same, as shown in Figure 10C.

FIGURE 10

FIGURE 10. Time correlated function (TCF) of (A) NO₂⁻-H_w, (B) Casur-NO₂⁻, (C) Cation-O_w.

MSD is a measure of ion diffusion velocity, and its slope is directly proportional to the diffusion coefficient. The MSD of the NO₂⁻ in the three kinds of nitrite solution has been calculated and exhibited in Figure 11. It is clearly shown that the MSD of NO₂⁻ in the LiNO₂ solution is much higher than that of the other two due to the chemical bond between Li-O_w and NO₂⁻ is the weakest, so it cannot effectively limit its diffusion. Therefore, MSD results once again demonstrate that NO₂⁻ in LiNO₂ solution has the highest diffusion coefficient and the fastest transport speed in the CSH channel during the three kinds of nitrite solution.

FIGURE 11

FIGURE 11. MSD of NO₂⁻ in three kinds of nitrite solution.

4 Conclusion

The transport behavior of three kinds of nitrite corrosion inhibitors in cement microporous channels is investigated based on MD simulation, and the differences in transport speed have been demonstrated by the local structure and dynamics behavior. The main conclusions are summarized as follows:

1) The transport process and dynamic analysis indicates that the NO₂⁻ penetration depth of LiNO₂ is similar to that of Ca(NO₂)₂ but much greater than that of NaNO₂. In addition, the NO₂⁻ in LiNO₂ solution is mainly distributed in the upper boundary of the channel, while the NO₂⁻ in Ca(NO₂)₂ solution is mainly distributed in the lower part of the channel. Transport simulations indicate that LiNO₂ can penetrate the microporous channel of cement and reach the surface of reinforcing steel faster.

2) An analysis of the local structure of ions in the pore channel reveals that the NO₂⁻-cation-water and O_s-cation-NO₂⁻ clusters inhibits solution transport speed. Local structure analysis reveals that Li has the weakest ability to bind water molecules, NO₂⁻ and CSH substrate, resulting in Li⁺ ions cannot form stable clusters to reduce the ion transport speed as Ca and Na ions. In addition, the abortion effect of the channel is negligible because of the minimal coordination number of Ca_sur-NO₂⁻. Therefore, NO₂⁻ in LiNO₂ solution has the fastest transport speed (Plimpton et al., 2007; Wang et al., 2020c).

Data availability statement

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession numbers can be found in the article/Supplementary Material.

Author contributions

XH: Methodology, conceptualization, investigation, Data curation, Writing—original draft. HZ: Writing—review, editing, supervision. RT: Investigation, editing. PW: Methodology, supervision.

Funding

Financial support from National Natural science foundation of China under Grant Nos. U1806225, 52108224, 51908308, Natural science foundation of Shandong Province under Grant ZR2019PEE004, Taishan Scholar Foundation of Shandong Province under Grant Nos. ts20190942, China Postdoctoral Science Foundation under Grant 2019M652345.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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