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Formation and Structure of Inhibitive Molecular Film of Oxadiazole on Iron Surface Qi Zheng, Jinyang Jiang, Dongshuai Hou, Shengping Wu, Fengjuan Wang, Yiru Yan, and Wei Sun J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06378 • Publication Date (Web): 10 Sep 2017 Downloaded from http://pubs.acs.org on September 11, 2017

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The Journal of Physical Chemistry

Formation and Structure of Inhibitive Molecular Film of Oxadiazole on Iron Surface Qi Zheng a,b, Jinyang Jiang a,b*, Dongshuai Hou c*, Shengping Wu a,b, Fengjuan Wang a,b

, Yiru Yan a,b, Wei Sun a,b

a

School of Materials Science and Engineering, Southeast University, Nanjing 211189,

China b

c

Jiangsu Key Laboratory of Construction Materials, Nanjing 211189, China Department of Civil Engineering, Qingdao Technological University, Qingdao

266033, China *

Corresponding Author: Jinyang Jiang; Dongshuai Hou

E-mail address: [email protected], [email protected].

ACS Paragon Plus Environment


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Abstract The interaction between organic molecules and metal surface has been intensely discussed these days. In this work, the formation and atomic structure of inhibitive molecular film are revealed in the combination of molecular dynamics simulation and quantum

chemical

calculations.

Adsorption

behavior

of

2,5-bis(4-aminophenyl)-1,3,4-oxadiazole (PAOX) is systematically investigated either in different forms or in different environments. The results indicates that PAOX is a superior corrosion inhibitor, compatible with various environments, for the film effect of protective film formation as well as the solidification effect of aggressive ions binding. Heterocyclic atoms like nitrogen and oxygen are demonstrated to be the reactive sites supported by Fukui function. Additionally, it shows that the organometallic bond of monomer complex is partly covalent and ionic while N18 in PAOX shares the dominative position in bonding behavior. Notably, weak interactions attributed from water molecules in an inhibitor-water system are achieved with the aid of averaged reduced density gradient (aRDG). All these findings provide a new idea for the interpretation of inhibition mechanism in a more realistic condition.


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1. Introduction Corrosion plays an overwhelmingly important role in diverse fields of industry and, consequently, economy.1 It is commonly acknowledged that steel corrosion has a deleterious effect on structure reliability, which leads to hazardous problems in terms of strength safety, mechanical operations and performance durability. On the other hand, acid solutions like hydrochloride (HCl) are widely used for pickling of mild steel, cleaning, descaling, etc. In order to moderate the extra high dissolution rate of metal, one of the protective methods relies on kinds of corrosion inhibitors, which could effectively eliminate corrosion.2,3 Consensus has been reached that heteroatoms (i.e. N, O, S, etc.), polar functional groups (i.e. –OH, -NH2, -SH, etc.), π electrons, and aromatic rings, could greatly enhance the corrosion inhibition efficiency.4–6

Figure 1 Molecular structures of two inhibitors, (A) PAOX and (b) PNOX. Various nitrogenous compounds have been explored as inhibitors, especially some oxadiazole derivatives.7–9 The influence of 2,5-bis(4-aminophenyl)-1,3,4-oxadiazole (PAOX) and 2,5-bis(4-nitrophenyl)-1,3,4-oxadiazole (PNOX) was systematically investigated by Lagrenée,10 shown in Figure 1. Interestingly, PAOX works as a superior organic corrosion inhibitor (with nearly 98% inhibition efficiency in 1 M HCl), while PNOX accelerates the corrosion behavior. These results indicated PNOX has a catalytic effect, both on the hydrogen reduction rate and steel dissolution.10 On the concept of green chemistry, a synthesis protocol was developed,11 avoiding the



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generation of by-product (PNOX) demonstrated in Figure 2. Neverthless, much of these research has mainly focused on inhibition efficiency in the dimension of electrochemistry (i.e. polarization, impedance and weight loss measurements) while the mechanism has been rarely discussed. Recent research on inhibition mechanism has been limited to quantum chemical calculations.12– 14

However, there seems no obvious correlation between their established inhibition

efficiency and computed electronic parameters.15,16 Afterwards, molecular dynamics simulations are excessively simplified in slab models, only considering a vacuum or water layer, which could exist huge discrepancy in actual situations.17–19 In consequence, how to combine the two parts, both quantum chemical calculation and molecular simulation, to reveal the anti-corrosion nature of inhibitor molecules, is thereby an urgent need. All these approaches, from a theoretical perspective, could provide a deeper understanding to the inhibition mechanism, and then give some insights into the design of corrosion inhibition, from an atomic scale.

Figure 2 Synthesis flowchart of PAOX and PNOX. In this work we investigated the adsorption and binding behavior of PAOX on iron surface and theoretically analyzed the atomic structure of inhibitive film via


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modelling approaches, both molecular dynamics simulation and quantum chemical calculations. We showed that PAOX could work as a highly efficient inhibitor for its outstanding anti-corrosion performance in various environments, such as in water and hydrochloride solutions. The adsorption behavior of PAOX, mainly physisorption, was manifested in the aspect of interaction energy. Additionally, Fukui function was employed for reactive sites prediction, and thus some organometallic inhibitive film structures were postulated in the atomic scale. Furthermore, N18 was suggested to be the most dominative position in bonding, confirmed by atom in molecule (AIM) theory. Worthnotingly, we performed weak interaction analysis on an inhibitor-water system and found that vdW effect plays the indispensable role. Additionlly, vdW effect was proved to be susceptible to thermal fluctuation. To sum up, this article has systematically demonstrated the formation behavior of inhibitive film, adsorption and bonding behavior of PAOX on iron surface.

2. Computational methodology 2.1 Slab models Adsorption behavior of PAOX was achieved with the aid of LAMMPS software package. Detail, models with iron (1 1 0) surface was established in a three dimensional box, with a 30Å vacuum slab. Notably, the arrangement of PAOX molecule was nearly randomly distributed near iron surface. Amorphous packing of different molecules was conducted in Monte Carlo method. Exactly, the construction then created a disordered and homogenous structure, corresponding to the realistic models. Verlet algorithm was applied to integrate the trajectories, using a time step of



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0.25 fs. Additionally, canonical (NVT) ensemble combined with Nosé-Hoover thermostat algorithm was chosen at room conditions (298K, 1atm). The simulation continued to 3000 ps to obtain some dynamic parameters, such as mean squared distance (MSD) and radical distribution function (RDF). The trajectories were visualized and plotted using VMD software, version 1.9.2.20

2.2 Force field COMPASS,21 applicable to various chemical systems, was employed to reveal the interaction between organic inhibitors and iron surfaces, in this work. As a general all-atom force field, it has been widely used in model construction and molecular dynamics simulations.

2.3 Averaged non-covalent interaction (aNCI) calculations Averaged non-covalent interaction (aNCI),22 a novel characterization for magnitude of interactions and fluctuations, was firstly introduced, to an inhibitor-water system, for non-covalent interactions extraction and visualization. aNCI was carried out by molecular dynamics in canonical (NVT) ensemble, which somewhat has freezing effect and help further weak interaction analysis.

2.4 Quantum chemical calculations GAMESS, as a highly efficient platform for quantum chemical calculation, was employed for structure optimizations. Basically, B3LYP/6-311G (d, p) was utilized for functional and basis set. Fukui function as well as electron localization function (ELF) of Fe-PAOX complexes was manifested via Multiwfn, version 3.3.8.23

3. Results and discussion


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The operation mechanism of organic corrosion inhibitor remains to be a great challenge. However, it is well acknowledged that high inhibition efficiency greatly depends on the interaction between inhibitor molecules and iron surfaces, which results in the formation of a protective film. However, neither the film formation mechanism nor the atomic structure stability is resolved.

3.1 Adsorption behavior analysis In this subsection, several slab models were established with PAOX molecule in different forms (individually and in monolayer) and in different environments (vacuum, water and hydrochloride acid solution).

Figure 3 Adsorption models for PAOX, (a) individual molecule and (b) monolayer adsorption. Firstly, the adsorption modes of PAOX on iron surface were studied, both individually and in monolayer form. As can be seen from Figure 3, interaction between PAOX and iron surface could be extremely strong that a protective film is formed on the substrate. It could be noticed that PAOX molecules are ideally plane and have a high coverage on iron surface after optimization, which corresponds to classical theory of inhibition mechanism.24,25 Notably, the inhibitive molecular film



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formed on iron surface also exhibits some specific features, indicated by Figure 3b. It could be found that the morphology of protective film is quite structured and regular. More in detail, electrostatic effect plays a dominated role in film formation. Furthermore, orientation of PAOX molecules on the substrate specifically ascribes to self-assembly behavior of organic molecules while the film skeleton is connected via hydrogen bonds, N…H bonds in particular. All these evidence implies the inhibitor molecule, PAOX, could be highly efficient for anti-corrosion, which is consistent with the experimental findings with 97.8% efficiency obtained by Lagrenée.10

Figure 4 Slab model of PAOX in water solution, (a) molecular configuration of the setup and (b) after 3000 ps’ running. Generally, corrosion inhibitors usually work in a multiunit environment and thus it is essential to take water molecules into account. Instead of the vacuum states


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shown in Figure 3, the effect of water solution is considered and it is demonstrated in Figure 4. Interestingly, PAOX exhibits the hydrophobic feature that PAOX, rather than water molecules, is much more prone to adsorb on iron surface. In other words, anti-corrosion capacity of PAOX still works in the presence of water solution, which means water molecules can only make little disturbance on PAOX. To be considerable, this phenomenon could quite reveal some things. Firstly, PAOX molecule is inclined to adsorb on iron surface for the conjugation effect attributed from benzene ring. Meanwhile, the role of heterocyclic atoms like nitrogen and oxygen could not be neglected as they may bond chemically with some adatoms to form organometallic complexes. All these evidence manifests that atomic structure of inhibitor molecule has a significant impact on efficiency and accordingly affects the inhibition mechanism, which enlightens us to design corrosion inhibitors from an atomic scale. Unfortunately, these interpretations above are mainly based on phenomena illustrations, which seem arbitrary. Thus, interaction energy is calculated for quantitative analysis, defined in eq 1.

= − +

(1)

Here, is the energy of the whole system, is the energy of free inhibitor molecule while is the energy of iron surface (in this case, it is a constant conveniently set to zero since all the surface atoms are kept fixed). On the basis of interaction energy, PAOX molecule proves to be firmly contact with iron surface. Although discrepancy may exist because these energy was calculated by molecular dynamics simulation, it could still be heterogeneous



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compared between PAOX and water molecules. As listed in Table 1, the magnitude difference is huge, implying the anti-corrosion effect PAOX takes. Table 1 Interaction energy of PAOX on iron (1 1 0) surface, as determined by comparative simulation techniques.

(EFe- inhibitor)a /KJ·mol-1

a

PAOX

-351.715

Water

-10.930

Adsorption energy of the isolated molecule on iron surface. In earlier papers, PAOX has been reported as a promising inhibitor in

hydrochloric acid solution, with a superior inhibition efficiency, 97.8%. In consequence, a more realistic slab model is constructed, describing how PAOX works in HCl solution, which is illustrated in Figure 5. In detail, the PAOX to HCl ratio is 1:4, which is artificially amplified in order to reveal the anti-corrosion effect of PAOX, intuitively.


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Figure 5 Slab models of PAOX, (a) in HCl solution and (b) pure HCl solution. After 3000 ps’ NVT running, the energy was principally converged. According to Figure 6, the inhibition mechanism could be summarized into two categories. In the first place, the adsorption behavior of PAOX on iron surface could not be ignored, manifested in Figure 6a,b. There is no denying that the molecular structure as well as reactive sites on PAOX molecule are crucial for the formation of protective film and thus a barrier is formed to defend aggressive ions like hydronium and chloride ions. Additionally, it could be found that PAOX can play the role of aggressive ion solidification,26 indicated by Figure 6c,d. Evidence shows that some clusters are formed and some aggressive ions are wrapped in the middle, thus resulting in an abrupt decrease in ion activity. Interestingly, the binding effect of chloride ions seems much stronger, rather than hydronium. Namely, PAOX is more targeted to chloride,



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which intimates it may adapt to a variety of solutions in the presence of chloride ions. These phenomena could attribute to some quantum chemical properties of ions and inhibitor molecules. In this case, the heterocyclic atoms in PAOX exhibit the positive characteristics under the effect of protonation while chloride ions possess negative charges, which results in intensive electrostatic interactions and hydrogen bond formation, behaving as a cage structure for chloride binding and activity restraining. Meanwhile, the interaction between electron deficiency of benzene rings and lone pair electrons in chloride also plays an indispensable role. On the contrary, the binding effect of hydronium seems relatively weak owing to possessed positive charges, only leading to hydrogen bonds, such as N…H and O…H bonds.

Figure 6 Two kinds of inhibition mechanism raised in molecular dynamics simulation.


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When it comes to some quantitative parameters, mean squared distance (MSD) can be introduced to estimate the mobility of responding atoms or molecules, defined in eq 2. t = 〈| − 0| 〉

(2)

Here, is the position of atom i in the moment of t.

Figure 7 Mean squared distance (MSD) of different ions, (a) in pure HCl solution and (b) PAOX in HCl solution. Notably, MSD curve is retrieved from the last 1200 ps, which could reflect the stable state. As shown in Figure 7, MSD evolution exhibits liquid characteristics in an



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approximately linear curve, coincident with the liquid environment. Figure 7a demonstrates the mobility of H3O+, Cl- and H2O in pure HCl solution. Generally, the displacements of H2O are larger than those of Cl- and H3O+, implying the thermal instability of H2O. However, when PAOX is added to HCl solution, there exist tremendous changes that curves of H3O+ and Cl- are completely different in Figure 7b. Here take Cl- as an example, the magnitude of displacements are in a sharp decline, elucidating PAOX has an excellent capacity for chloride binding. All these observations are still corresponding to the inhibition mechanism put forward in the fore-mentioned subsections. Table 2 Self-diffusion coefficients of different ions in respective solutions in 298K. Solution

DH2O

DH3O+

DCl

DInhibitor

(10-9 m2/s)

(10-9 m2/s)

(10-9 m2/s)

(10-9 m2/s)

HCl

4.266±0.0175

2.415±0.0296

3.525±0.0590

N/A

PAOX+HCl

4.229±0.0319

2.066±0.0184

2.394±0.0651

0.171±0.0011

Furthermore, self-diffusion coefficient, D in short, is a paramount index for investigation of thermal stability and activity. This parameter can be derived from MSD curves in diffusive regime, by eq 3. 2 ∙ = 〈| − 0| 〉 !

(3)

Table 2 lists the coefficients calculated by eq 3. Actually, the diffusion coefficient value of water molecules is around 4.266×10-9 m2/s, in close proximity with bulk water (2-4×10-9 m2/s), which highlights the benchmark correctness of slab model in


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this work.27 Compared with those in pure HCl solution, the self-diffusion coefficients are declined dramatically, DCl particularly. On the other hand, hydronium usually leads to hydrogenation corrosion while chloride could induce passivation film damage. Smaller values of coefficients reflect the mitigation effect of corrosion, suggesting PAOX could ease the corrosion process and take a positive role in anti-corrosion.

3.2 Fe-PAOX complex analysis As an organic corrosion inhibitor, interplay between PAOX and iron surface mainly depends on the adsorption and bonding behavior of PAOX, thus resulting in the formation of an inhibitive surface film. In this subsection, Fukui function28 was calculated for reactive sites prediction. Moreover, the atomic structure of inhibitive film was speculated for analysis, which is similar to an organometallic film. Finally, electronic structure and stability of Fe-PAOX complex were discussed via some novel descriptors. It is well recognized that reactive sites of inhibitor molecule, especially for electrophiles, are quite revealing something important. Thus, reactive sites are predicted through the method of modified condensed Fukui functions, listed in Table 3. Table 3 Modified condensed (atomic) Fukui functions for PAOX calculated by using the Hirshfeld population analysis method. Atom C1

"#

"$

0.359 0.203



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N2

0.492 0.414

N3

0.492 0.414

C4

0.659 0.203

O5

0.540 0.139

C6

0.215 0.390

C7

0.215 0.390

C8

0.317 0.220

C9

0.177 0.310

C10

0.347 0.306

C11

0.182 0.342

C12

0.354 0.224

C13

0.317 0.220

C14

0.177 0.310

C15

0.347 0.306

C16

0.182 0.342

C17

0.354 0.224

N18

0.257 0.608

N19

0.257 0.608

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As an important descriptor in conceptual density functional theory, Fukui function has been widely used in reactive sites prediction, defined in eq 4,5. %&$ = '& ( + 1 − '& ( (for nucleophilic attack)

(4)

%&# = '& ( − '& ( − 1 (for electrophilic attack)

(5)


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Here, '& ( + 1, '& (, '& ( − 1 are electron densities on the kth atom in systems with (N+1), (N), (N-1) electrons. Moreover, atomic electron densities are approximated to their corresponding Hirshfeld atomic charges. It can be inferred from Table 3 that the most favorable sites for electrophilic attack are located in N2, N3 and O5, with the most positive part of % # function delocalization. On the basis of electron denotation, some heterocyclic atoms, such as N and O, are the most prone for electrophile. Meanwhile, the positive charged regions are mainly centered in N18, N19, which indicates nucleophilic attack. In consequence, emphasis should be placed that good inhibition efficiency attributes from a large number of reactive sites to both nucleophilic and electrophilic attacks. Considering the reactive sites of the PAOX molecule, adsorption and bonding may take place in range of these reactive atoms, resulting in the formation of organometallic complexes. It has been frequently proposed that kinds of Fe-PAOX surface complexes are formed involving Fe-N and Fe-O bonds, as heterocyclic atoms like N and O are the most reactive sites verified by XPS.29–31 Unfortunately, the actual structure and its bonding behavior to the iron surface are still open issues. For this reason, several simple models of organometallic association of PAOX molecules are further considered below, exhibited in Figure 8 and Figure 9.



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Figure 8 Fe-PAOX monomer in three bonding modes. Owing to the reactive sites predictions, some isolated complexes with one individual inhibitor molecule are discussed. As shown in Figure 8, deprotonated PAOX molecule could be linked to iron ions to form a simple Fe-PAOX monomer, in three bonding modes based on Fukui function calculations. Taking the symmetry of PAOX molecules into account, sites centered at N18, N2 and O5 is deeply explored and complete details of this case is provided in the following subsection. Organic molecules may form self-assembled organometallic network structures on metal surface.32–35 In Figure 9, the following structures are considered: a PAOX-Fe-PAOX dimer, a periodic *+,-. − /01 linear polymer structure (necklace structure), and a two-dimensional planar-like organometallic network structure, corresponding to Figure 9a,b,c respectively. Interestingly, PAOX molecule possesses unsaturated atoms for bonding with Fe ions, thus this results in intermolecular associations. However, neither steric hindering nor complex stability are studied thoroughly, which means optimizations from both experiments and theories are urgent


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to be resolved. Notably, determination of the exact surface film structure still remains a great challenge. Although some structures postulated in this subsection may not be definitely correct, it could still shed light on further researchers.

Figure 9 Possible structures of organometallic complexes formed between iron adatoms and PAOX molecules. Dimer, periodic linear polymer models and planar-like network structures are shown. In addition to it, the molecular structure of protective film could also be demonstrated with the aid of radical distribution function (RDF), shown in Figure 10. Two different states of corrosion inhibitor, both in gas and water solution, were studied in this subsection and Fe-PAOX monomer complex is used as a simplification for optimization. Detail, the correlation of Fe-O, Fe-N are exhibited in Figure 10a,b, respectively. There exist peaks in the Fe-O correlation, representing the bonding behavior of Fe-PAOX complex. Moreover, several regularly periodical peaks are observed in the green curves, which indicates multilayer adsorption in gas state owing to intermolecular associations like hydrogen bonds manifested before (N…H between nitrogen and hydrogen) and π-hydrogen bonds for benzene ring could act as a hydrogen bond acceptor.36



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Figure 10 Radical distribution functions (RDF) of Fe-PAOX, (a) Fe-O and (b) Fe-N. On the contrary, curves of RDF are greatly smoothed in the presence of water, which indicates water molecules could weaken the intermolecular interactions between PAOX and iron surfaces. In other words, water molecules intensively disturb the adsorption process and then attribute in the priority in monolayer adsorption instead. Focusing on the first peak in Figure 10a, this peak demonstrates the direct bonding behavior of Fe-O, centered at around 2.15 Å. This value coincides with the bond length of Fe…O (2.0038 Å) optimized in monomer structure. Moreover, the first peak shifts in the right in water solution, implying water molecules have a weakening impact on interface, enlarging the Fe…O bonds, as illustrated in atomic schematic


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graph in Figure 10a.

Figure 11 Electron localization function (ELF) of Fe-PAOX complexes, (a) Fe…N18 and (b) Fe…N2 and (c) Fe…O5. As mentioned above, some possible organometallic structures are proposed in Figure 9. In order to clarify the components of organometallic bonds, electron localization function is applied for interplay interpretation. In this subsection, Fe-PAOX monomer complexes are taken into account according to the bonding classifications in Figure 8, and the results are revealed in Figure 11 and Table 4. Electron localization function (ELF), firstly put forward by Becke,37 is defined in eq 6,7,8. It has been universally employed in a variety of systems, like organic and inorganic molecules, atomic crystals, and for different problems, such as classification of chemical bonding and etc.



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3/ =

C

6E ⁄! FGH I⁄! + GJ I⁄! K

(8)

>?

+

7

@∇>A @

(7)

? |7

B

C =

(6)

$*4 ⁄45 17

= ∑ 9 |∇; | − =

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>A

Here, 9 is occupation number of orbital i, ; is orbital wavefunction. The larger the electron localization is in a region, the more likely the electron motion is confined within it. In other words, a larger ELF value means electrons are greatly localized, which indicates there exist a covalent bond, a long pair or inner shells of atom involved. As shown in Figure 11, the value of ELF is within the range of [0, 1], which means the red represents higher ELF while the blue means lower values. Similarities of three panels in Figure 11 lie in the electron depletion of organometallic bonds, either Fe…N or Fe…O. However, ELF values in the region of benzene rings depicted in red maps, are extremely large, which means some covalent bonds could form in these regions. Findings manifest that the organometallic bonds are sort of ionic, suggesting PAOX may adsorb on iron surface through electrostatic interactions at the very beginning, and then bonded with iron adatoms via partially ionic bonds and covalent bonds. Meanwhile, some topological parameters at the bond critical points (BCP) were also calculated via atoms in molecule (AIM) theory for quantitative comparisons,38 and the results are listed in Table 4. Table 4 Some topological parameters at the BCPs of the PAOX…Fe contacts a. BCP

ρbcp

▽2ρbcp

Hbcp


ELFbcp

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a

Fe …N18

0.0923

0.363

-0.0178

0.198

Fe …N2

0.0388

0.494

-0.00602

0.0892

Fe …O5

0.0678

0.473

-0.00199

0.0719

The topological parameters above are electron density, the Laplacian of electron

density, Hamiltonian kinetic energy and electron localization, respectively. In general, magnitude of electron density represents the bond strength while Laplacian of electron density can manifest the bond types. Emphasis should be placed that the bond is covalent if ∇ GLM > 0 and OLM < 0. Considering the symbols of some parameters in Table 4, it could be inferred that these organometallic bonds are partially covalent. Furthermore, small values in electron density and ELF demonstrate these bonds are not strong enough, which also means these bonds are metastable. Notably, Fe…N18 has the highest electron density and ELF, reflecting its dominative position in organometallic bonding behavior. To sum up, research efforts in this subsection have been devoted to the determination of organometallic complex through a theoretical approach, in terms of reactive sites prediction, complex postulation and bond component analysis.

3.3 Weak interaction analysis There is no denying that the water molecule plays an indispensable role in a typical inhibition environment. However, little attention has been attracted to resolve the effect of water molecules. Actually, water molecules could greatly disturb the inhibition mechanism and thus influence corrosion inhibition efficiency.24 In this subsection, a new averaged non-covalent interaction index (aNCI) along with a



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thermal fluctuation index (TFI) was provided in an inhibitor-water system, to characterize the magnitude of interactions and fluctuations. In order to analyze non-covalent interactions in thermally fluctuating systems, for instance, trajectories generated form molecular dynamics simulation, a new definition is reinterpreted by Wu, considering averaged reduced density gradient (aRDG or Q̅) and thermal fluctuation index (TFI or f),22 is defined in eq 7,8. SSSSSS = Q

SSSSSSSSSS |∇W | ∙ SSSSSSX⁄V !T 7 U⁄V W

% =

YZW[ \

]^ZW[ \

(7) (8)

Here, G is the electron density from structure i.

Figure 12 Plot of averaged reduced density gradient versus electron density in a PAOX- water system, where λ2 on the axis is the second eigenvalue of density Hessian matrix. As shown in Figure 12, aRDG with respect to electron density is plotted and non-covalent interaction regions can be identified.39 Strikingly, some spikes which are


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associated with weak interactions appear in Figure 12. As the color bar in Figure 13 illustrates, points in different regions, with various values, can represent distinct meanings. In this case, the sturdy spike, in the right region, suggests strong and wide van der Waals (vdW) interactions while the other three spikes may be owing to the steric effect of rings, both from benzene and heterocyclic rings. Surprisingly, no spikes representing hydrogen bonds are observed, as it is quite common in a pure water system (Figure S4). This phenomenon may be illuminated that hydrogen bonds in a PAOX-water system are not as stable as in a pure water system. And the N…H bonds between nitrogen and hydrogen could be easily disturbed by thermal fluctuations. Namely, either intermolecular interactions of inhibitors or interplay between PAOX and iron surface are easily influenced by water molecules, mainly attributed from mutual vdW interactions, and thus lead to differences in corrosion inhibition efficiency.24,40

Figure 13 Interactions in a PAOX- water system under 1000 snapshots aNCI analysis in (a-d), and fluctuation index visualization in (e-f)



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Additionally, the isodensity contours are visualized in Figure 13 to intuitively reveal the weak interactions, as a supplement to some descriptors like RDF. The color bar classified the non-covalent interactions into three categories with different colors. Evidence is inferred that vdW interactions are dominated in this system, centering around PAOX molecule. After noise shielding process in Figure 13a, a rich visualization of non-covalent interactions is provided in Figure 13b,c,d. From Figure 13b, with the isovalue of aRDG equals to 0.25, it is apparently observed that intensive steric effect exists in the center of the rings shown in red ellipses, which reflects the spikes in Figure 12. In contrast, the scattered green isosurface exhibits preferential directions as some lamellae are mainly concentrated in the vicinity of the nitrogen atoms, which indicates nitrogen can behave as a reactive site and is much prone for interact with water molecules. In other words, when organometallic bonds like Fe-N is formed, water molecules would exceedingly disturb the stability of Fe-N and inevitably increase the bond length (from 1.9991 Å to 2.3560 Å), owing to the tendency to vdW interactions. This coincides with the findings obtained via RDF functions. Moreover, PAOX molecule is covered with a green isosurface when the isovalue gets bigger. Figure 13c,d reflects the fact that PAOX molecule is much vulnerable to vdW interactions influenced by vicinal water molecules. On the contrary, thermal fluctuation index (TFI) is calculated to examine the stability of weak interactions, mainly focusing on vdW force and steric effect. As shown in Figure 13e,f, the blue regions reflect weak interactions are more stable while the red represent the opposite. Figure 13e,f manifest that steric effect in rings is much


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stable in a blue region. Nevertheless, the vdW regions are totally in red, rendering that this kind of interaction is evidently flexible and unstable, which can be easily distorted by thermal motions.41,42 In brief, the role of water molecule takes in the inhibition mechanism is revealed with the aid of weak interaction analysis. Interactions of PAOX in a water system are dominated by steric effect and unstable vdW force. All these evidence accumulated could provide us a deep understanding to the role of water molecules take in inhibition mechanism.

4. Conclusions In this work, inhibition mechanism of PAOX was systematically investigated by theoretic calculations, both quantum chemistry and molecular dynamics simulations. Conclusions can be made in the following perspectives. In the aspect of interaction energy, PAOX molecule proves to be firmly contact with iron surface, either in an individual molecule or in a monolayer form, implying the anti-corrosion effect PAOX takes. Dynamically, values of diffusion coefficients like H3O+ and Cl- are in an abrupt reduction owing to the inhibition effect PAOX acts. The formation of protective film mainly attributes to superior inhibition efficiency. Meanwhile, the solidification effect of aggressive ions is observed, which promotes the anti-corrosion behavior. Structurally, PAOX molecule is calculated in the theory of Fukui function. Heterocyclic atoms like N and O are prone for reactive sites. Some possible organometallic complexes, such as linear polymer or plane networks, are postulated



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and structurally optimized. Additionally, the components of organometallic bond are revealed to be partially ionic and covalent, which suggests metastable features for adsorption and bonding. Innovatively, interaction between inhibitor and water molecules is characterized with the aid of averaged reduced density gradient (aRDG). vdW interaction seems to be the dominative regime in an inhibitor-water system. Besides, the effect of water disturbance is analyzed by thermal fluctuation index in molecular scale. All these findings could provide a new idea for the interpretation of inhibition mechanism in a more realistic condition.

Acknowledgements The authors greatly acknowledge the support from the National Natural Science Foundation of China (No. 51278098, 51678144), the National Basic Research Program of China “973 Project” (No. 2015CB655100), and the Industry-University Research Cooperative Innovation Fund of Jiangsu Province (No. BY2013091).

Supporting Information Comparisons between PAOX and PNOX; pure water system analyzed by aRDG.

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