Theoretical Study of the Aliphatic-Chain Length's Electronic Effect on

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Theoretical study of the aliphatic-chain-length electronic effect on the corrosion inhibition activity of methylimidazole-based ionic liquids Carolina Zuriaga-Monroy, Raul Oviedo-Roa, Luisa Montiel, Araceli Vega-Paz, J Marin-Cruz, and José-Manuel Martínez-Magadán Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b03884 • Publication Date (Web): 03 Mar 2016 Downloaded from http://pubs.acs.org on March 10, 2016

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Industrial & Engineering Chemistry Research

Theoretical study of the aliphatic-chain length´s electronic effect on the corrosion inhibition activity of methylimidazole-based ionic liquids Carolina Zuriaga-Monroy, Raúl Oviedo-Roa, Luisa E. Montiel, Araceli Vega-Paz, Jesús Marín-Cruz, José-Manuel Martínez-Magadán* Instituto Mexicano del Petróleo, Lázaro Cárdenas Norte 152, San Bartolo Atepehuacan 07730, México, D.F., México

KEYWORDS. Corrosion inhibitor, ionic liquids, Density functional theory, Fukui function, adsorption energy.

ABSTRACT: Density-Functional-Theory based studies about the inhibition of the corrosion affecting the cathode, hematite surface by coverage with methylimidazole-based ionic liquid, IL, were performed. Inhibition performance is tuned through the length of aliphatic chains C attached to the imidazolium aromatic ring, where = 1, … , 20. Frontier molecular orbitals and energy gaps for single ILs and pristine (1 1 2) hematite surface, the energy difference between ILs and hematite-surface, as well as Fukui indices for the ILs and adsorption energies and charge transfers for ILs/hematite surface systems were calculated. Results show that adsorption activity is due to the donation/back-donation bonding among the imidazolium aromatic ring of the ILs and the exposed iron atoms of the hematite surface. Dispersive long-range 1 ACS Paragon Plus Environment


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interactions from the ILs alkyl tails allow a closer bonding of the corrosion inhibitor molecules to the hematite surface, the charge transfer between the IL and the hematite is in C . The optimal alkyl chain size is 18 and this is in fully agreement with the reported experimental alkyl chain size that produces high inhibitory properties of related vinylimidazolium ILs. 1. INTRODUCTION

Despite the great advances in science, corrosion represents a major industrial setback, which causes the detriment of materials and considerable economic losses. This phenomenon occurs when exists a basic corrosion cell with an anode and a cathode connected by a metallic path in contact with an electrolyte[1, 2] and is important in the oil industry, namely in pipelines, vacuum vessels and hydrodesulfuration plants[3-7]. Internal corrosion in pipelines is influenced mainly by CO2, H2S, water, flow velocity and surface condition of the steel[2, 8]. In order to reduce the corrosion problem, the application of corrosion inhibitors is envisaged as an effective and economical solution

[3, 9-13]

. The objective of most protective systems is to

reduce the rate of corrosion to a value that will allow the material to attain its normal or desired lifetime[2, 14]

. A corrosion inhibitor is defined as any chemical substance, which when added in small amounts to an

aggressive system, significantly diminishes the corrosion rate

[3, 4]

. It may restrict the rate of the anodic or

cathodic process by simply blocking active sites on the metal surface[2]. Most organic corrosion inhibitors act by adsorption on the metal surface [10, 12, 15-19], covering the cathode or the anode, preventing further corrosion. Different studies about imidazole derivatives show the importance of the alkyl chain length in the corrosion inhibitors efficiency [4, 5, 10, 15, 16, 18-22], i.e., the hydrophobic chain serves as a barrier versus water and corrosive products[15,

16]

, also it induces a positive value of the

logarithm of the octanol-water partition coefficient[4, 22], and exists a correlation with an optimum corrosion inhibition efficiency at log ≈ 5 which is an important characteristic because ILs operate in systems

2 ACS Paragon Plus Environment

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involving mixtures of oil and water[15]. It is worthy to mention that it was found a significant corrosion inhibition activity in the neutral imidazoline when there are 18 carbon atoms in the chain [5, 21]. The oil field pipeline applications involve brines saturated with carbon dioxide, leading to a pH 4-6. At anodic areas iron dissolves by Fe → Fe + 2e (1) In dearated solutions the cathodic reaction is given by 2H + 2e ↔ H (2) The cathodic reaction is accelerated by dissolved oxygen in accord with the depolarization reaction[15] + 4 + 4

↔ 2

(3) And Talbot[23] propoused: 2Fe + 3H O → Fe O# + 6H + 2e (4) Ionic liquids (ILs) are salts with a cation and an anion

[11, 12, 24, 25]

, the cations of ILs are often large and

therefore the alkyl chain would cover a wide part of the surface[26]. Imidazole–based ILs are good corrosion inhibitors and are used to inhibit the corrosion of steel in acid media, especially since they act as mixedtype inhibitors [11, 12, 17, 26, 27].



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The IL 1-butyl-3-methylimidazolium Br ⁄Cl acts as mixed-type inhibitor by a charge transfer chemical mechanism[12]. Another IL with imidazolium having two 18 hydrocarbon tails has good efficiency and a high surface coverage the metal surface[27]. Alkylimidazolium ILs with 4, 6 and 8 carbons in the chain inhibit corrosion and the best is the one with the largest chain length[17, 28]. In turn, it was observed in a series of vinylimidazolium ILs with 4, 8, 12, 18 and 22 carbons length that the one with 18 carbon atoms is the optimum inhibitor,

[29]

. All of the experimental studies mentioned previously were made in an acidic

environmental. Experimental and quantum chemical studies about imidazolium ILs showed that the inhibition efficiency is affected by the length of the alkyl chain [18, 19]. Normally, in the engineering metals and alloys are covered with a comprising thin defective oxide barrier layer (1-3 nm thick). The hematite can form on the surface as a metastable phase. Thus adsorption of the inhibitor takes place, not on a bare metal surface, but it occurs on an oxide surface. This fact has been little appreciated in previous inhibitors studies, where the emphasis has been on describing the adsorption of the inhibitor on a bare metal[30]. Also the Pourbaix Diagram for iron indicates that it is possible to form Fe O# at pH between 4 and 14[8, 30] thereby, some of the corrosion products of iron are composed of hematite α − Fe O# , nonstoichiometric magnetite Fe# O* and lepidocrocite γ − FeOOH. As iron cools from 1000 to 250 °C it oxidizes to form an outmost oxide layer of hematite, Figure 1. In agreement with Pourbaix it is possible assumes passivation with an heterogeneous film of Fe O# alone or by Fe O# ∙ -# * . In dependence of the ions present in the water fraction, the pH of oil/water mixtures are in range to 4.5 to 8.0; however under operation conditions in pipelines pH values are 7.0 to 8.2 suggesting α − Fe O# as the dominant oxide on the Fe surface

[15]

.

Also the analysis of X-ray photoelectron spectroscopy (XPS) of the iron, showed the spectra typical of Fe O#

[20]

and the Mössbauer spectra of steel suggested the formation of hematite[31]. According with the


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results we assume that manufacturing and laying a pipeline made of mild steel leads to a hematite film on the Fe surface and so the α − Fe O# is the surface modeled in our study, which is part of the whole system.

Figure 1 Sketch of corroding Fe surface. Quantum chemical calculations can spread light on experimental investigations or even predict some experimentally unknown properties[32]. Also, they are very useful in determining the molecular and electronic structures as well as in elucidating the chemical reactivity[33]. Herein, they were performed to study the adsorption behavior of some ILs on the .1 1 2/ 0 − Fe O# surface. This approximation might help to understand the aliphatic-chain-length influence on the corrosion inhibition effect of the ILs. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), together called frontier orbitals, are of great interest since the HOMO energy 123454 6 is associated with the electron donating ability of a molecule and the LUMO energy 127854 6 with the ability to accept electrons [30, 34-36]. Theoretical studies about adsorption and corrosion inhibition showed the frontier orbitals do not overlap between them, so there is a good donation and back-donation process between the inhibitor and the metal surface[37]. Another study correlates a high adsorption energy 1∆26 with the smallest LUMOHOMO energy gap[38]. Global electronic indices, such as the energy gap, are used to understand the chemical reactivity of the molecules toward the metallic surface, since as the energy gap decreases, the inhibition efficiency of the molecule increases

[13, 37, 38]

, whereas the local indices, such as Fukui indices, have been employed to

predict the reaction selectivity of atoms at the inhibitors molecules[39, 40]. In the present work, global and local reactivity indices, such as the above mentioned ones, were calculated. We are interested in exploring, through atomistic molecular modeling, the effect on corrosion inhibition by 5 ACS Paragon Plus Environment


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changes in the hydrocarbon chain length from 1 to 20 carbon atoms in ILs used as corrosion inhibitor. In particular, the work aim is to explain the chain length that produces the best corrosion inhibitor and to understand in terms of the electronic properties the IL reactivity as a function of the chain length and the molecular mechanism of corrosion, taking moreover into account the logarithm of the partition coefficient octanol/water (log 4: ). 2. Models and Methodology As mentioned above, we have chosen a hematite surface as the model for the pipeline surface, because our hypothesis is that the ILs interact with α − Fe O# , this is supported by the work of McMahon[20], Ramachandran[15] and Obot[30], in the other hand there are not quantum mechanics results about the corrosion inhibitors on the iron oxide. The most common form of corrosion in the oil industry occurs when steel comes in contact with an aqueous environment. When metal is exposed to a corrosive solution (the electrolyte), the metal atoms at the anode site lose electrons, and these electrons are then absorbed by other metal atoms at the cathode site[2]. Oxidation occurs by the closed circuit constituted through the Fe0 anodic region, the α − Fe O# cathodic and the electrolyte Figure 2, our hypothesis is that the cation as it has positive charge covers the cathode which has negative charge, protecting it and stops the electron flow from anode to cathode, so it is done the passivation.

Figure 2 Circuit constituted by the anode, cathode and the electrolyte. The electron flow occurs from the anode to the cathode. It is known that the most probable exposed hematite surface is the (1 1 2) plane[41]; then, we computationally built a surface whose faces are along this plane by cutting a slab from the bulk crystalline cell included in the database of the Materials Studio (MS) software[42]. Previously to the cutting process, 6 ACS Paragon Plus Environment

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we have assigned spin values to the iron atoms in the hematite primitive cell, according to the spin ordering that leads to the lowest total energy[43-45], which we have confirmed among three different orderings Figure 3.

(a)

(b)

(c)

(d)

Figure 3. Different spin ordering at Fe atoms in the hematite primitive cell. (a) Ball and stick display-style view for atoms and bonds, respectively. (b) + + − −, (c) + − + −, and (d) + − − + spin configurations as seen from the lowest to upper Fe slabs. For an easiest spin-assignation visualization, atoms and bonds are shown in line display style. The (initial) spin sizes 4 (in ħ units) were suggested from the maximum spin the Fe element can have in its electronic configuration, [Ar] ;?@ . Purple and red atom colors stand for iron and oxygen, respectively. We enclosed within a cell with periodic boundary conditions a hematite surface possessing a width of three oxygen slabs and left a 20 A-width vacuum space; this resulted in an unit cell with dimensions of a = 5.43, b = 5.04 and c = 22.26 A. Moreover, in order to calculate the adsorption energy of the ILs on the hematite surface, we have built a simulation cell (SC) whose dimensions were CDE = 32.61, FDE = 30.23, and GDE = 22.26 A, obtained as a 6×6×1 supercell from the hematite-surface-containing unit cell, whereas the ILs models were computer drawn based on methylimidazole, Figure 4. These SC dimensions were sufficient to fully allocate the IL with the maximum length chain. IL ACS Paragon Plus Environment

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Hematite Surface

Figure 4. Atomistic structures of the chemical models for the hematite surface and ionic liquids. Cations of latter consists of an alkyl chain linked to the imidazolium ring, and the anion is the bromide ion. Additionally to atom colors denoted in Figure 3, the white, gray, blue and pink atom colors stand for hydrogen, carbon, nitrogen and bromine, respectively. The geometry of the clean hematite slab, single ILs molecules inside in-vacuum SC and ILs molecules interacting with hematite slab were fully optimized, keeping fixed the SC dimensions, through DensityFunctional-Theory (DFT) energy minimizations by using the MS DMol3 code functional

[48]

[46, 47]

. LDA/VWN

, the DN basis set and the OBS method for DFT dispersion corrections[49] were employed.

Detailed electronic structure for each fully isolated IL, was calculated by using the GGA/PBE functional[50], the DNP basis set and the TS method for DFT dispersion corrections[49]. For in-SC calculations, the run parameters were set at coarse accuracy, i.e., the systems were relaxed until either two of the energy, force and displacements differences between consecutive optimization steps were below 1 H 10* Ha, 0.02 Ha⁄A, and 0.05 A, respectively, whereas in the second calculations, fine-accuracy run parameters were used, i.e., the energy-, force-, and displacement-difference thresholds were 1 H 10J Ha , 0.002 Ha⁄A and 0.05 A, respectively. The isosurface of the frontier molecular orbitals were set at the isovalue of 0.03 (in arbitrary units).


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We have used the Conductor-like Screening Model for Real Solvents (COSMO-RS) quantum chemical theory[51,

52]

to compute the natural logarithm of the octanol-water partition coefficient by means of a

statistical thermodynamics treatment of interacting surface charges of the single molecules. First, by using the TURBOMOLE software[53] through TMoleX interface, Version 3.1 (2011), a DFT-based geometry optimization of each molecule is performed under the COSMO continuum solvation model[54], that is, as if embedded in a dielectric medium via a molecular surface or cavity that is constructed around the molecule. Each segment of this surface is characterized by a screening charge density (SCD), which takes into account the electrostatic screening of the molecule by its surrounding and the back-polarization of the molecule. Afterward, by using the COSMOthermX software, Version C30_1301[55], a liquid mixture is considered under the COSMO-RS model, that is, as an ensemble of closely packed ideally screened molecules in which an electrostatic interaction arises from the contact of the different SCDs calculated by TURBOMOLE using a dielectric constant of infinite value. Finally, the calculation of the octanol-water partition coefficient is toggled in the COSMOthermX run. The energy band gap, 2KLM , is defined as: 2KLM ≡ 27854 − 23454 (5) a large gap indicates low chemical reactivity and a small gap indicates high chemical reactivity[30, 56-58]. The Fukui indices allow identifying those specific atoms at the IL molecules that could favor the linkage on the hematite surface since they are a measure of the capacity to exchange electrons. The Fukui index OP for an atom Q measures changes in the atomic-centered charge when the molecule gains electrons and, hence, corresponds to reactivity with respect to a nucleophilic attack. Conversely, OP corresponds to



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reactivity with respect to an electrophilic attack (i.e., when there is a loss of electrons). Fukui indices are defined as: OP = RP 1S6 − RP 1S − 16

(6)

OP = RP 1S + 16 − RP 1S6

(7)

where N is the number of electrons, and RP is the electronic charge in the IL molecule at the atomic site Q, respectively[30, 32, 39, 40, 58]. Atomic charges were calculated in the Mulliken [30, 58-60] approximation. Adsorption energy calculations were performed in order to study the IL ability to form a protective film on the α − Fe O# surface, allowing covering of latter and therefore protecting the Fe anodes avoiding the electron flow. The adsorption energy ∆2 [61, 62] of an IL molecule on the hematite surface was calculated by means of the equation ∆2 = 2T7,UVWXLYZ − 12T7 + 2UVWXLYZ 6

(8)

where 2T7 , 2UVWXLYZ and 2T7,UVWXLYZ are the total quantum energy of the isolated IL, the total quantum energy of the pristine hematite surface and the total quantum energy of the interacting IL-hematite surface system, respectively. However, the optimesed IL undergoes deformation with respect to the isolated IL. Therefore, the adsorption energy (∆2) contains deformation energy .2[\] / of the IL molecules. 2[\] was estimated as the energy difference between the energy of the optimized IL and the energy of the IL structure in each adsorption system. All total quantum energies were obtained at the end of molecular geometry optimizations. Negative values of the adsorption energy indicate that there exists an attraction between corrosion inhibitor molecules and the hematite surface. Generally, high absolute value of the adsorption energy denotes strong attraction between corrosion inhibitor molecule and the hematite, i.e., inhibitor can be adsorbed tightly onto the oxide surface (cathode) ILs strongly interacting with the oxide surface


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stopping the electronic flow from the anode to the cathode[2], i.e., the circuit is opened and then the corrosion decreases. The total electronic charge transfer ∆R from hematite surface towards the adsorbed IL molecule was calculated as: ∆R = ∑P.RP,LX_ZW L`UaWM_bac − RP,dZXaWZ L`UaWM_bac /

(9)

The ocatnol/water partition coefficient of an IL allows us to have insights on the IL transport feasibility through two flows that allow IL to arrive onto the pipeline surface. The octanol/water partition coefficient 1Pfg 6 is defined as: Pfg =

hijklmnokp hijqnmrs

(10) where htju is the concentration of the solute t in the solvents (octanol or water) when both solvents are in contact at equilibrium[63]. Due to the wide range values that 4: can have, usually it is reported its logarithm instead, log 4: . 3. Results and discussion In order to investigate the best aliphatic-chain-length of a IL, Figure 4 as corrosion inhibitor is interesting some reactivity indices as well as the adsorption energy between IL and the iron oxide surface (1 1 2). The energy gaps change in all the cases with the aliphatic-chain-length of the ILs and there is not a tendency,, but reach a minimum at C , Table 1. Since a lower 2KLM implies a higher reactivity index, due to the easier electron transfer from the HOMO to the LUMO, it can be inferred that the IL having 18 carbons at the tail is the molecule that could be the most reactive, and with the highest inhibition efficiency[13, 30, 37, 38], this chain length is in agreement with some experimental results [5, 21]. 11 ACS Paragon Plus Environment


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Table 1. Energy gap 2KLM (in eV) for the ionic liquids. Number of alkyl chain 23454 27854 2KLM carbons 1 -5.440 -1.637 3.803 2 -5.645 -1.721 3.924 3 -5.447 -1.651 3.796 4 -5.442 -1.644 3.798 5 -5.432 -1.654 3.778 6 -5.450 -1.653 3.797 7 -5.436 -1.659 3.777 8 -5.438 -1.644 3.794 9 -5.442 -1.665 3.777 10 -5.415 -1.677 3.791 11 -5.420 -1.664 3.756 12 -5.429 -1.656 3.773 13 -5.446 -1.647 3.799 14 -5.403 -1.446 3.957 15 -5.379 -1.451 3.928 16 -5.400 -1.450 3.950 17 -5.427 -1.660 3.767 18 -5.417 -1.663 3.754 19 -5.444 -1.660 3.784 20 -5.450 -1.655 3.795 In general, HOMO and LUMO of the ILs are mainly located at bromide anion and at imidazole cation, respectively, as shown by Figure 5 herein and Figure S1 in Supporting Information. Conversely, the spatial extension of the frontier orbitals of the ILs, as expected since OP and OP calculations involve an electron occupation of the LUMO and one electron vacancy of the doubly degenerate HOMO, respectively. Number of alkyl chain carbons

HOMO

LUMO


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4

Figure 5. Frontier orbital isosurfaces of an ionic liquid. Blue and yellow isosurface colors denote positive and negative wavefunction phases, respectively. Comparison among the Density of States (DOS) of the C IL molecule, Figure 6.a, and those of the cationic and the anionic separated moieties, Figure 6.b, reveals that IL HOMO is due to the anion Br . In fact, Br 4s and 4p DOS peaks bracketed the cationic valence band formed by the 2s and 2p states from C and N; therefore, the IL DOS is essentially the direct sum of the DOS of the separated ions. However, the narrowness of the isolated neutral-IL HOMO DOS peak, Figure 6.a, shows that the interaction of the bromide ion with the hematite would be mainly electrostatical, but not chemical, due to that the Br valence-shell 4v atomic orbitals are fully closed; so, we have excluded the bromide in subsequent DFT calculations for non-interacting single molecules.

a) IL HOMO

IL LUMO

b)

2s and 2p levels of C and N

Cation HOMO (peak shoulder) Cation LUMO

4s levels of Br

-

4p HOMO levels of Br

Cation LUMO

Figure 6 DOS for (a) the IL having the C18, and (b) for the separated anionic and cationic moieties.



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Fukui indices graphs of the ILs, Figure 7 show that for all ILs the active site having the greatest OP is the atom C6, which is situated in the imidazole ring, whereas that for greatest OP is the bromide ion which is in agreement with the spatial extension of the frontier orbitals Figure 5. The Fukui indices for some cations, Figure 8 show that when the alkyl chain grows from one carbon until just below 18 carbon atoms, both nucleophilic and electrophilic attacks occur on the imidazole ring. The Fukui index OP has maximum values especially on the atom C5 in all the cations, as it occurs at the same atom for the ILs (atom C6 in Figure 7). Conversely, while alkyl-chain is below 18 carbon atoms, there is a major electrophilic reactivity on the carbon atoms of the aromatic ring, mainly at carbon atoms C2 and C3, revealed by the Fukui index OP .


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Figure 7 Fukui indices at each atom in some ILs. The Fukui indices for the rest of the ILs appear in the Supporting Information, Figure S2. The position of nodes in the frontier molecular orbitals, and hence the spatial extensions around adjacent atoms sharing a continuum fragment of these molecular orbitals, can support the identification of the atoms having the highest Fukui-indices values since shortest molecular-orbital fragments confine electrons more intensively. For short-alkyl-chain cations, the frontier orbitals must be located mainly along the imidizazolium ring, Figure 8, whose LUMO energy lies at the bottom of the antibonding π band formed by the C and N vw orbital, Figure 6 b, i.e., the maximum value of OP occurs at the single site isolated by the 15 ACS Paragon Plus Environment


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antibonding character, Figure 9 owing to the topology symmetry of the imidazolium ring; this site is the bridge carbon connecting nitrogen atoms. Conversely, HOMO energy lies at the top of the bonding π band and the shortest molecular orbital fragment, delimited by their two nodes, locates at carbons C2 and C3, Figure 9, explaining the positions of the highest OP values. As the alkyl chain increases, the electrophilic attack progressively diminishes at the imidazolium ring but increases at the alkyl-chain region, Figure 8, so that when the alkyl chain reaches 18 carbons the electrophilic attack predominates on the alkyl-chain region. On the contrary, the nucleophilic attack is always located at the imidazole ring. These behavior dependences of Fukui indices on the alkyl-chain length are comprehensible from the DOS of the cations since energy levels from the alkyl tail split with the chain length, leading to the surpassing of the aromatic π- by the tail sp3-valence band (in fact, the peak shoulder at the HOMO position in cation of IL Figure 6, is the emerging top of the latter valence band), whereas the aromatic π conduction band keeps containing the first unoccupied states (which are the double peak at cation LUMO Figure 6 b).


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Figure 8 Fukui indices at each atom for some cations. The Fukui indices for the rest of the cations appear in the Supporting Information, Figure S3.

C5

C2

C3

Figure 9 Scheme of the π molecular orbitals (MOs) built by the vw states around the aromatic ring of the ILs cations, based on the MOs stationary wave nature. Positive and negative signs denote the π MOs 17 ACS Paragon Plus Environment


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phases. Since there are 6 electrons to be accommodated within 5 π MOs, the three π lowest-energies MOs are fully filled (states labeled 1 to 3), which are bonding because they have less nodes than half number of ring bonds and hence the cations became stable. Remaining 4 and 5 unoccupied MOs are antibonding (they have more nodes than half number of ring bonds). Nodes are indicated by cross symbol, X. The visualization of the DFT-calculated frontier orbitals for some cations clarifies the locations of the electrophilic and nucleophilic attacks, Figure 10. The topologies of these orbitals for short-tail cations are in nice agreement with those sketched at Figure 9. Additionally, as the alkyl chain length increases, the number of nodes along the alkyl chain that a molecular orbital can have grows, and consequently also the electron energies; thus, it is expected that eventually the cation HOMO is made up of the bonding 2p carbon orbitals from the alkyl chain. The DFT results show that both HOMO and LUMO are mainly located on the imidazole ring for cations having alkyl chains from C to Cx , but at C the HOMO starts to move towards the chain, elucidating so the results of the Fukui index OP about the progressive shifting of the electrophilic attack region, Figure 8. A total shift of the HOMO region onto the alkyl chain, and therefore the full separation from the LUMO region, is observed when carbon tail is C ; i.e., electronacceptor and donator regions are detached from each other and therefore the hydrophobic tail and the hydrophilic head become functionalized for electrophilic and nucleophilic attack, respectively.


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Figure 10. Frontier orbitals of the cationic moiety of the ionic liquids. Blue and yellow isosurfaces of the HOMO and LUMO denote positive and negative wavefunction phases, respectively. Figure S4 in the Supporting Information shows the frontier orbitals for all cations. It is known that interaction among unsaturated hydrocarbons (such as olefins or aromatic rings) and transition-metal-exposing surfaces involves the so-named donation/back-donation mechanism, i.e., bonding occurs as a donation of hydrocarbon π-electrons into the surface transition metal cations and back-donation from the surface transition metal cations into the hydrocarbon antibonding π* molecular orbital. For IL adsorption on hematite surface, our above results suggest that when the alkyl chain size is increasing, the donation and back-donation degree of ILs due to the aromatic imidazolium ring would be gradually diminished and substituted by the long-range dispersive interactions from the saturated hydrocarbon tail. However, donation/back-donation and dispersive bondings act together and so IL-hematite interaction energy would increase with the tail length. Once alkyl chain sizes are just above C , dispersive interactions would hide donation/back-donation bonding since the top of the IL valence energy band now comes from alkyl states and moves up away from the aromatic states. Also, increment of the energy gap 19 ACS Paragon Plus Environment


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weakens the back-donation step due to the growing difficult to reach the conduction energy band bottom, which is composed of the π* aromatic orbitals. Further insights about IL-hematite interactions can be obtained through comparison of molecular orbitals among ILs and spin-containing hematite slab. The + − − + spin ordering of the bulk hematite primitive cell leads to the lowest total energy, Table 2; thus, we assigned to the model slab of hematite. Table 2. Total energy of spin-containing hematite primitive cells. Spin ordering

Energy (kJ/mole)

−−++

-626,843.960

−+−+

-626,844.169

+−−+

-626,848.215

Energy gap calculations for cations confirm that the IL found with the highest reactivity index shown when the chain size is C since the energy gap reaches a minimum of 5.059 eV, Table 3, indicating an increase in the efficiency of inhibition[13, 37, 38]. It is worthy to mention that the hematite-surface energy gap is very small, 0.024 eV, relative to the energy gaps of the cations, indicating a potentially large reactivity of hematite. Table 3. Energy gaps for the cations, and energy differences between the frontier orbitals of the cations and the hematite surface. Energy units are in eV.


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Number of alkyl chain carbons 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

23454 27854

-6.984 -6.988 -6.984 -7.006 -7.011 -7.016 -7.001 -7.003 -7.005 -6.984 -6.977 -6.950 -6.890 -6.910 -6.848 -6.839 -6.833 -6.810 -6.797 -6.781 (1 1 2) -5.718 hematite surface

-1.644 -1.653 -1.661 -1.675 -1.691 -1.684 -1.691 -1.668 -1.701 -1.707 -1.732 -1.702 -1.686 -1.683 -1.712 -1.714 -1.715 -1.751 -1.711 -1.711 -5.694

2KLM

E7854 1hematite6 E7854 1cation6 − − E3454 1cation6 E3454 1hematite6

5.340 5.335 5.323 5.331 5.320 5.332 5.310 5.335 5.304 5.277 5.245 5.248 5.204 5.227 5.136 5.125 5.118 5.059 5.086 5.070 0.024

1.290 1.294 1.290 1.312 1.317 1.322 1.307 1.309 1.311 1.290 1.283 1.256 1.196 1.216 1.154 1.145 1.139 1.116 1.103 1.087

4.074 4.065 4.057 4.043 4.027 4.034 4.027 4.050 4.017 4.011 3.986 4.016 4.032 4.035 4.006 4.004 4.003 3.967 4.007 4.007

Calculations of the energy difference between the LUMO lying in the hematite and the HOMO lying in the cation,

i.e., E7854 1hematite6 − E3454 1cation6,

as

well

as

its

reciprocal E7854 1cation6 − E3454 1hematite6, give a measure of the interaction feasibility between cations and the hematite surface. The lowest energy differences occur by taking the LUMO at the hematite and the HOMO of the cations, Table 3, i.e., IL cations behave as Lewis bases whereas hematite surface as a Lewis acid, so the electron transfer would start in the cations and would finish on the hematite surface. The 21 ACS Paragon Plus Environment


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smallest energy difference among system-crossed frontier orbitals was found for the maximum chain size studied in this paper, C , which could indicate that longer alkyl tails produce better interaction with the hematite surface, Table 3. Final conformations of IL molecules on iron oxide surface show in general that there exists a strong interaction between the bromide ion and the iron of the surface Figure 11. In accordance with the energy differences between the LUMO of the hematite surface and the HOMO of the cations indicating an increasing IL-hematite interaction, it is observed that when chain size increases, IL alkyl chains are getting closer to hematite surface and, moreover, according with the separation of HOMO and LUMO regions in cations starting from the inhibitor IL-18, the methylene groups at the free end of the alkyl chain closely approach to iron atoms of the hematite surface, Figure 11. Conversely, adsorption energy changes with the chain size, but the maximum occurs for IL-19 inhibitor, Table 4.

a) IL-1

b) IL-4

c) IL-5

d) IL-18

e) IL-19

f) IL-20


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Figure 11. Final conformations of (a) IL-1, (b) IL-4, (c) IL-5, (d) IL-18, (e) IL-19 and (f) IL-20 inhibitor molecules adsorbed on the .1 1 2/ hematite surface Table 4. Adsorption energies among some ionic liquids and the metal-oxide surface. System IL-1 IL-4 IL-5 IL-18 IL-19 IL-20

∆2 (kJ/mole) -459.286 -545.397 -559.903 -944.797 -1,062.104 -1,027.636

Calculations of the electronic charge transfer onto ILs from hematite surface reveal that all of the ILs lose electrons since ∆R is always positive, Table 5, and that the maximum charge transfer occurs for the IL-18 inhibitor, confirming again the hiding of the donation/back-donation binding mechanism by the dispersive interactions. At this point it is worthy to mention that, although the increasing adsorption energy is really important to successfully link corrosion inhibitor molecules to hematite surface, for solving the corrosion problem it is necessary to inhibit active anode or cathode sites to open the circuit since at this way the electron flow is avoided, i.e., the main effect that drives the corrosion inhibitor is the charge transfer, so the best inhibitor according to all of the above analysis would be the IL-18 inhibitor, an insight which is reinforced by the maximum ∆R, the fact that IL-18 is the best is in agreement with some experimental results [5, 21].

Table 5. Electronic charge transfer from ILs to the hematite surface. System

IL-1

Charge transfer ∆ (in units of e) 0.766 23

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IL-4 IL-5 IL-18 IL-19 IL-20

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0.897 0.932 1.326 1.307 1.244

Particularly in the IL-18, a detailed look on the charge transfer shows that the bromine donates electrons to the surface since it gives +0.495 e, whereas the carbon bonded to the nitrogen atoms is the site of the imidazole ring that accepts more electrons with a gain of −0.054 e; finally the alkyl chain as a whole donates electrons, especially from the hydrogen being nearest to the hematite surface which gets +0.062 e. All these charge transfers are consistent with the Fukui indices since above it was found that the bromide ion and the alkyl chain have the highest values of OP for the IL and the cation, respectively, and conversely the highest value of OP is found at the C atom that bridges N atoms in aromatic ring, labeled as C6 in IL or C5 in the cation.

LUMO for interacting IL-hematite systems, Figure 12, confirm that bromide ion cedes electrons to the hematite surface since 4p Br states become now partially unoccupied. However, these states also appear within the interacting-systems’s HOMO as having an antibonding mixing with the Fe 3d states of the Fe atom nearest neighbor to bromide, and moreover the resulting Br-Fe bond distance, 2.41 Å, is around 14% greater than the largest Fe-O covalent bond length in bulk hematite crystal. Thus, bromide ion keeps its ionic character when binds to an exposed iron of the hematite surface. It should be noted that for all ILs there are not contributions of the imidazolium aromatic ring to the interacting-systems’s HOMO, but up from the IL-18 inhibitor it is visible a small contribution of the alkyl chain, whose dispersive long-range interactions begin to predominant, leading to higher adsorption energies. System

HOMO

LUMO 24

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Hematite

IL-1

IL-4

IL-5

IL-18

IL-19

IL-20



Figure 12. Frontier orbitals of the hematite surface interacting with IL-1, IL-4, IL-5, IL-18, IL-19 and IL20 inhibitors. Blue and yellow isosurfaces of the HOMO and LUMO denote positive and negative wavefunction phases, respectively.

Calculations of the logarithm of the partition coefficient octanol/water, Figure 13, indicate that as the chain length increases, the character of IL molecules passes from hydrophilic to hydrophobic, and latter character keeps increasing.

8.00

Partition coefficient

6.00 4.00

Log10 POW

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2.00 0.00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -2.00 -4.00 -6.00

Chain length

Figure 13. Logarithm of the octanol/water partition coefficients for the ILs. This fact is convenient for the corrosion inhibition, especially in the oil industry, since the transport of the corrosion inhibitors through oil to reach pipeline surfaces is a great problem. Positive values of the partition-coefficient logarithm means the corrosion inhibitors would be dissolved by hydrophobic molecules, like alkanes and oils, but not by water. For the best corrosion inhibitor suggested from all above analyses, namely the IL-18, the calculated partition coefficient is 5.48, which indicates that there are around .; IL molecules in the octanol phase per each IL molecule in the aqueous phase; this ensures that the transport of the inhibitor to the surface of the oil pipeline is feasible through the oil. The IL-18 partition coefficient is in agreement with the correlation of Ramachandran[15]. 4. Conclusions 26 ACS Paragon Plus Environment

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The corrosion inhibitor performance of ILs was investigated through molecular modeling studies, focusing on the effect of the alkyl chain length of the IL molecule over the adsorption energy and over charge transfer from IL molecule towards hematite surface. Additionally, reactivity analyses of the IL, inferred from the energy gap of the IL and from the energy difference between a frontier molecular orbital lying on the IL cation and another one on the hematite surface, suggest that the best corrosion inhibitor performances are shown by IL possessing bigger alkyl chains. The increase with alkyl size of the adsorption energy over the oxide surface indicated that the corrosion inhibitor can cover more tightly the hematite surface, giving electrons, so the IL neutralize the cathode and the electron flow from anode Fe to cathode is stopped, and this effect is maximum for IL possessing 18 carbons at the alkyl tail. This optimal chain size is in agreement with the experiment results reported at literature [5, 21]. ASSOCIATED CONTENT Supporting Information Figure S-1 illustrates the frontier orbitals of the 20 ionic liquids. Blue and yellow isosurface colors denote positive and negative wavefunction phases respectively. Figure S-2 shows Fukui indices of each atom for the 20 ionic liquids. Figure S-3 explains the Fukui indices of each atom for the 20 cations of the ionic liquids and Figure S-4 demonstrates frontier orbitals of the cationic moiety of the ionic liquids. Blue and yellow isosurfaces of the HOMO and LUMO denote positive and negative wavefunction phases. AUTHOR INFORMATION Corresponding Author * Tel.: +5255 91758426. E-mail: [email protected] ACKNOWLEDGEMENTS



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We gratefully acknowledge support provided by project 144397 of the SENER-CONACYT-Hidrocarburos (IMP-Y.00119) grant. CZM wants to acknowledge the financial support from the Mexican government through Consejo Nacional de Ciencia y Tecnología (Conacyt), and Instituto Mexicano del Petróleo for a Ph.D. scholarship. Authors acknowledge support from La Red de Fisicoquímica Teórica (RedFQT) del Consejo Nacional de Ciencia y Tecnología (Conacyt). REFERENCES (1) Byars, H.G., Corrosion Control in Petroleum Production 2nd Edition ed 1999: NACE International. (2) Popoola L. T., Grema A.S., Latinwo G. K., Gutti B. and Balogun A.S., Corrosion problems during oil and gas production and its mitigation. IJIC. 2013, 1 - 15. (3) Olivares-Xometl O., Likhanova N.V., Domínguez-Aguilar M.A., Hallen J.M., Zamudio L.Z., Arce E., Surface analysis of inhibitor films formed by imidazolines and amides on mild steel in an acidic environment. Appl. Surf. Sci. 2006, 252, 2139-2152. (4) Duda Y., Govea-Rueda R., Galicia M., Beltrán H.I., and. Zamudio-Rivera L.S., Corrosion Inhibitors: Design, Performance, and Computer Simulations. J. Phys. Chem. 2005, 109, 22674 - 22684. (5) Jovancicevic V., Ramachadran S., Prince P., Inhibition of Carbon Dioxide Corrosion of Mild Steel by Imidazolines and Their Precursors. NACE International, 1999, 55, 449 - 455. (6) Döner A., Solmaz R., Özcan M., Kardas G., Experimental and theoretical studies of thiazoles as corrosion inhibitors for mild steel in sulphuric acid solution. Corros. Sci. 2011, 53, 2902-2913. (7) Musa A.Y., Kadhum A.A.H., Mohamad A.B., Takriff M. S., Experimental and theoretical study on the inhibition performance of triazole compounds for mild steel corrosion. Corros. Sci. 2010, 52, 3331-3340. (8) Ossai, C.I., Advances in Asset Management Techniques: An overview of Corrosion Mechanisms and Mitigation Strategies for Oil and Gas Pipelines. ISRN Corrosionn, 2012, 2012, 10. (9) Sheikhshoaie I., Nezamabadipour H., Theoretical study on the structural effect of some organic compounds as corrosion Inhibitors on mild steel in acid media. Bull. Chem. Soc. Ethiop., 2009, 23, 309 313. (10) Feng L, Yang H., Wang F., Experimental and theoretical studies for corrosion inhibition of carbon steel by imidazoline derivative in 5% NaCl saturated Ca(OH)2 solution. Electrochim. Acta. 2011, 58, 427-436 (11) Zhang Q.B., Hua Y.X., Corrosion inhibition of mild steel by alkylimidazolium ionic liquids in hydrochloric acid. Electrochim. Acta. 2009, 54, 1881-1887. (12) Ashassi-Sorkhabi H., Es´haghi M., Corrosion inhibition of mild steel in acidic media by [BMIm]Br Ionic liquid. Mater. Chem. and Phys. 2009, 114, 267 - 271. (13) Zhang J., Qia G., Hu S., Yan Y., Ren Z., Yu L., Theoretical evaluation of corrosion inhibitors performance of imidazoline compounds with different hydrophilic groups. Corros. Sci. 2011, 53, 147 152.. (14) Garverick, L., Corrosion in Petrochemical Industry, ed. ASM International 2011, United States of America. (15) Ramachandran S, Tsai B-L., Blanco M., Huey C., Tang Y., and Goddard W.A., Self-Assembled Monolayer Mechanism for Corrosion Inhibition of Iron by Imidazolines. Langmuir, 1996, 12, 6419 - 6428. (16) Edwards A., Osbone C., Webster S., Klenerman D., Joseph M., Ostovar P and Doyle M, Mechanistic of the corrosion inhibitor oleic imidazoline. Corros. Sci. 1994, 36. 315 - 325. 28 ACS Paragon Plus Environment

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Theoretical Study of the Aliphatic-Chain Length's Electronic Effect on

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