Adsorption Behavior of Organic Corrosion Inhibitors on ...€¦ · Sumit Sharma,* Xueying Ko,* Yathish Kurapati,* Himanshu Singh,* and Srdjan Neši´c‡,* Some recent efforts toward

Adsorption Behavior of Organic CorrosionInhibitors on Metal Surfaces—Some New

Insights from Molecular Simulations

Sumit Sharma,* Xueying Ko,* Yathish Kurapati,* Himanshu Singh,* and Srdjan Nešic‡,*

Some recent efforts toward studying adsorption, aggregation, and self-assembly of corrosion inhibitor molecules near metal/waterinterfaces via classical molecular simulations are reported. Two different approaches have been used. In the first approach, a coarse-grainedmodel of corrosion inhibitor molecules is studied, and the following key findings are found: (a) hydrophobic interactions between the alkyltails of corrosion inhibitor molecules are important for the formation of adsorbed self-assembled layers on the metal surface, (b) themorphology of the adsorbed layers are strongly influenced bymolecular geometry, and (c) the relative strength of interactions between polarhead andmetal and between alkyl tail andmetal are important determinants of adsorbed conformations. In the second approach, fully atomisticsimulations are performed for a bulk aqueous phase and near metal/water interfaces of two kinds of model inhibitor molecules—imidazolinium-type and quaternary ammonium-type surfactants. From these simulations, the following are concluded: (a) these inhibitormolecules aggregate in the bulk phase as spherical micelles, (b) the unaggregated inhibitor molecules have a strong tendency to adsorb ontometal surfaces while inhibitor micelles show only a weak tendency to adsorb, and experience a long-range repulsion from the surface. Finally,it is discussed how the coarse-grained and fully atomistic simulations present a unified molecular picture of adsorption and self-assembly ofcorrosion inhibitor molecules on metal surface.

KEY WORDS: adsorption, corrosion inhibitor, micellization, molecular simulation, self-assembly

INTRODUCTION

Corrosion inhibitors are generally defined as chemical sub-stances that are added to the corrosive environment in very smallquantities (typically in the ppm range) in order to mitigatecorrosion. When it comes to internal corrosion of pipelines in theoil and gas industry, corrosion inhibitors are usually injectedinto the flow stream as a mixture of chemicals containing sur-factant molecules.1 The so-called “active component” in thismixture is most commonly an organic surfactant compound(s)with an amphiphilic molecular structure, consisting of a polarhead group and nonpolar hydrophobic tail. The polar head isoften based on nitrogen-containing groups, such as amines,amides, quaternary ammonium, or imidazoline-based salts as wellas other functional groups containing oxygen, phosphorus,and/or sulfur atoms. The length of a hydrocarbon tail which isattached to a polar group typically varies between 12 and 18carbon atoms. The function of the polar head-groups is toprovide a bonding between inhibitor molecules and the steelsurface. Hydrophobic tails which are “facing” the solution arethought to be important in establishment of self-assembledlayer(s) of corrosion inhibitors on the metal surface2 and key tothe protection they offer.

While corrosion inhibitors have been used in the oil andgas industry for many decades, the mechanisms by which thesemolecules are effective in retarding corrosion are still poorlyunderstood. As a result, unforeseen corrosion-related failures of

inhibited oil and gas pipelines remain a major concern for theindustry.

One can imagine that the effectiveness of corrosioninhibition depends on the adsorption characteristics of thesemolecules. Over the years, there were many experimentalstudies of adsorption behavior of corrosion inhibitors,deploying advanced techniques such as electrochemicalimpedance spectroscopy (EIS),3-5 atomic force microscopy(AFM),6-7 laser scattering,8 quartz crystal microbalance(QCM),7,9 sum frequency generation microscopy (SFG),10 etc.It has generally been established that corrosion inhibitormolecules adsorb onto metal surfaces in organized self-assembled layers.

In parallel with the experimental studies, some computa-tional investigations have been undertaken. There are quantum-mechanical studies based on density functional theory (DFT),wherein the focus is to determine binding energies of differentpolar groups on metal surfaces.11-13 DFT calculations deter-mine the equilibrium electronic structure, and no informationon atomic motion at finite temperatures is obtained. For thispurpose, classical molecular dynamics (MD) simulations are useful,wherein atomic motion can be simulated at finite temperatures.Classical MD simulations, so far, have mainly focused on studyingequilibrium conformations of a single corrosion inhibitor mol-ecule adsorbed onto metal surfaces.14-15

The results from experimental studies of inhibitor ad-sorption inevitably produce information that is spatially and

Submitted for publication: July 17, 2018. Revised and accepted: October 2, 2018.Preprint available online: October 2, 2018, https://doi.org/10.5006/2976.

‡ Corresponding author. E-mail: [email protected].* Institute for Corrosion and Multiphase Technology, Ohio University, Athens OH 45701.

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temporally averaged, with maximum resolution of the order ofnanometer and microsecond, respectively. These length- andtime-scales are much larger than those associated with be-havior of individual inhibitor molecules and are more pertinent tobehavior of large groups of molecules, adsorbed on the metalsurface in the form of self-assembled layers. From experimentalresults, molecular-level behavior is indirectly deduced. In orderto connect molecular behavior to experimental observations, thefocus was shifted in this study from simulations of adsorptionof individual molecules to classical MD simulations of a largenumber of molecules to examine their aggregation, adsorp-tion, and self-assembly at the metal surface. The underlying freeenergy landscape of these systems was analyzed using ad-vanced simulation methodologies and is described below. Uniqueinsights obtained from classical MD simulations, which cannotbe obtained either by experimental investigations or by DFTsimulations, are highlighted.

MOLECULAR DYNAMICS SIMULATIONSRESULTS AND DISCUSSION

The work described below is probing molecular-leveldetails of adsorption of corrosion inhibitors on metal surfacesby using classical MD simulations. Before embarking on thediscussion of the results, a brief overview of basic MD simulationconcepts and terminology will be useful.

The dictionary meaning of simulation is “an imitativerepresentation of the functioning of a system or process.” Asthe name suggests, in MD simulations, dynamics/motion ofmolecules in the system is simulated. The term “classical” impliesthat in MD simulations, atomic and molecular motions aredescribed by classical Newtonian mechanics (and not by quan-tum mechanics).16 Often the term “classical” is dropped fromthe name. MD simulations can be performed at different reso-lutions. If each atom in the system is explicitly representedthen these are termed as atomistic MD simulations. If manyatoms are grouped together into a representative united atomor a “bead,” then a molecule may be represented by a collectionof beads or just one bead. Such simulations are termedcoarse-grained (CG) MD simulations.

The term “molecular simulations” is used to collectivelyrefer to all kinds of MD (as well as Monte Carlo) simulations. In anatomistic MD simulation, the simulated system is specified as acollection of atoms in a volume. Atoms interact with each otherthrough a variety of conservative forces, such as: van derWaals, Coulomb, bond forces, etc. Each type of conservativeforce is associated with their potential energy. Fundamentally,all of these forces are electrostatic in nature, but they havedifferent magnitudes and distance-dependence. Hence, thedistance-dependence of potential energies of these forces aredescribed by mathematical functions. These mathematicalfunctions are termed potential for short and are collectivelycalled a force field. Hence, for any configuration of atoms, theforce acting on every atom can be calculated from the forcefield. In a CG system, the force field represents distance-dependence of potential energies between different beadsin the system, rather than between each atom.

In a MD simulation, starting from an initial configuration ofa number of atoms/beads in a given volume, the position andvelocity of each atom/bead is determined at different times byperforming a time-integration of Newtonian equations of motion.As the magnitude of forces between atoms/beads is distance-dependent, the simulated system is evolved by calculating forcesbetween atoms/beads after every small time-step.

The required order of magnitude of the time-step in at-omistic MD simulations is 10−15 s (femtosecond).16 Hence, anatomistic MD simulation spanning 1 ns will require about a millionevaluations of forces for every atom in the system. Because of thecomputational complexities involved, atomistic MD simulationsare generally only able to sample time-scales of the order of 1 ns to1,000 ns. In the case of CG MD simulations, the accessible time-scales may be one to three orders of magnitude larger because ofthe reduced number of degrees of freedom.

From the positions and trajectories of atoms/beads thusobtained, thermodynamic properties of the simulated system areevaluated by applying the basic concepts of statistical me-chanics. Statistical mechanics is a branch of physics that describesthe relationship between molecular-level properties and mac-roscopic thermodynamic properties. The basic tenet of statisticalmechanics is that statistical properties of molecular configura-tions correspond to thermodynamic properties. For example,average translational kinetic energy is related to thermodynamictemperature, average total energy of molecules corresponds tothermodynamic energy, total number of possible molecularconfigurations is related to thermodynamic entropy, etc.

Molecular simulations have emerged as a powerful tool tostudy physical properties of systems. The focus here was onapplying MD simulation techniques to understand theadsorption and aggregation behavior of corrosion inhibitormolecules on the metal surface. In the text below, thesimulation strategies and major findings are described.

2.1 | Coarse-Grained Molecular Dynamics Simulationsof Corrosion Inhibitor Adsorption

Generally, collective behavior of large swarms of mole-cules require long time- and length-scales, for example, in phasetransition, during self-assembly and formation of equilibriummorphologies of adsorbed molecules, etc. CG molecular simu-lations are useful for studying these phenomena, as specificchemical details of molecules are not resolved. Rather, potentialfunctions are used to represent overall effective interactionsbetween different segments of the molecules, making the sim-ulated system simpler, and the numerical simulations faster.Hence, one can perform simulations that can cover the requiredtime- and length-scales, in this case those related to formingequilibrium morphologies by corrosion inhibitors adsorbing on ametal surface.

In terms of previous studies using a similar CG approach,Duda, et al., performed a Monte Carlo study of adsorption of CGcorrosion inhibitor molecules in two dimensions to show that thesurface coverage improves with tail-length, mT up to mT = 7 andwith solvophobicity of corrosion inhibitor molecules.17 Wu, et al.,studied micellization of CG ammonium-based surfactants, andfound that the surfactants form spherical micelles at smalleraggregation numbers (<100) and worm-like micelles at largeraggregation number.18 Edwards, et al., created a hexagonalclose packing of different imidazoline-based inhibitor molecules,represented by a CG model, on a surface and performed MDsimulations to determine available free volume for diffusion ofcorrosive species.8 These studies have aided in the under-standing of how corrosion inhibitor molecules aggregate andadsorb on surfaces to inhibit corrosion. A caveat of CG is thatsome degrees of freedom are lost (such as the rotational motion ofan alkyl tail around dihedral angles) and, therefore, there is someloss of entropic terms. Therefore, an effective CG methodologyshould be such that the important degrees of freedom areretained while relatively less relevant ones are restricted.

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Apart from verifying theoretical hypotheses, MD simu-lations can be used as a predictive tool for inhibitor performance.In the present study, systematic investigations of how lateralhydrophobic interactions, the interactions betweenmetal surfaceand inhibitor molecules, and inhibitor geometry affect theadsorption, self-assembly, and aggregation behavior of thesemolecules are performed by studying a phenomenologicalbead-spring model of these molecules.19

2.1.1 | Simulation Setup and System DetailsIn the CG approach, the corrosion inhibitor molecule is

understood to be comprised of two basic parts: a polar groupthat has a strong affinity to bind to the metal surface, and ahydrophobic group that has the ability to form some kind of a“hydrophobic barrier” when organized in self-assembled layerat the metal/water interface. The basic approach behind thedesign of the present CG model of corrosion inhibitor mole-cules is to incorporate these two features into the model andexamine the adsorption and self-assembly behavior.

2.1.1.1 | Potential Functions in the CoarseGrained Model

In the CG description of an amphiphilic corrosion inhibitormolecule, one terminal bead represents the polar head group ofthe molecule and the remaining beads represent the hydro-phobic alkyl tail segments (Figure 1[a]).19 A number of suchcorrosion inhibitor molecules are randomly placed in a simu-lation volume (also called a simulation box), as shown in Figure 1(b).This configuration serves as an initial condition for the MDsimulations.

Bond interactions between neighboring beads in an inhib-itor molecule keep them together and are modeled via a quadraticfunction, also termed harmonic bond potential, given by:

Ub = kbðb − b0Þ2 (1)

where kb is the bond coefficient which determines the stiffnessof the bond potential, b is any instantaneous value of the bondlength, and b0 is the equilibrium value of the bond length betweenthe neighboring beads. Alongwith the bond potential, a harmonicangle potential centered at θ0 is also applied. The functional formof this potential is given by:

Uθ =kθðθ − θ0Þ2 (2)

where kθ is the angle coefficient of the potential, θ is the instan-taneous value of the angle, and θ0 is the equilibrium value of theangle between any three neighboring beads. The angle potentialensures that the angle between three neighboring beads in amolecule is maintained close to θ0 (often equal to 180° for a lineargeometry).

Water molecules are not explicitly included in the CGsimulation system, but their effect on the interactions betweeninhibitor molecules and on the dynamics of inhibitor moleculemotion is implicitly included, as described below.

In an aqueous environment, hydrophobic beads manifestan attractive interaction amongst themselves. In the model, thisattractive interaction between hydrophobic tail beads of dif-ferent inhibitor molecules is represented by a Lennard-Jones (LJ)interaction potential, given by:

ULJðrÞ=4ε��

σ

r

�12

−

�σ

r

�6�

(3)

where ε is termed as the LJ potential well-depth. It signifies how“deep” the minimum of the LJ potential is (Figure 2); a large valueof ε implies a more attractive LJ potential; σ is a measure of size ofthe beads, and r is the distance between the beads. The forcebetween the beads is given by negative gradient of the potentialenergy, that is, ~F= − ∇U. This implies that for a LJ potential,

~F=24ε

�2

�σ

r

�12

−

�σ

r

�6�

~r

r2(4)

(a) (b)

Hydrophobicbeads

Polar bead

FIGURE 1. (a) A schematic of the CG corrosion inhibitor molecule usedin the present study. The blue terminal bead represents the polar headgroup and the cyan beads represent the alkyl tail segments. (b) Asnapshot of simulation system with the simulation volume and therandomly distributed corrosion inhibitor molecules. The yellow planeat the bottom represents the metal surface.

Lennard-Jones

4

3

2

1

0

–1

0.5 1 1.5

r/σσ

U/ε

2 2.5

WCA9-3

FIGURE 2. Three different potential functions used in the CG model:LJ, WCA, and 9-3 potential plotted (scaled by ε) as a function ofdistance (scaled by σ).

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~F=0 when r = 21/6σ. The LJ potential is attractive at large distances(r > 21/6σ) as for these values of r, ~F is in opposite direction as~r.The LJ potential is repulsive at small distances (r < 21/6σ) when ~F isin the same direction as~r. The form of the LJ potential function isplotted in Figure 2, where the potential energy is scaled by ε and thedistance is scaled by σ.

The interaction between the polar head beads of differentinhibitor molecules, as well as between the polar bead of onemolecule and the hydrophobic beads of another, is repre-sented by a purely repulsive Weeks-Chandler-Andersen (WCA)potential.20 The WCA potential is simply modeled as therepulsive part of the LJ potential, given by:

UWCAðrÞ=ULJðrÞ þ ε for r < 21=6σ (5)

and

UWCAðrÞ=0 for r > 21=6σ

This function is also shown in (Figure 2). The rationalebehind using a purely repulsive WCA potential for polar beads isthat in an aqueous environment, polar moieties have similarinteractions with water molecules as with other polar andhydrophobic moieties. As a result, no net attractive interactionbetween different polar groups or between polar and hydro-phobic groups is observed. The strong short-ranged repulsionof LJ and WCA potential represents the “excluded volume”interactions between the different groups.

The metal surface in the model is represented by asmooth, two-dimensional surface occupying one face of thesimulation box. The strong affinity between the polar beads ofthe corrosion inhibitor molecules and the surface are modeledby a so-called “9-3” interaction potential given by:

U9−3ðzÞ= εs

�215

�σ

z

�9−

�σ

z

�3�

(6)

where εs is the well-depth parameter, and z is the distancebetween the surface and the bead. Consider a slab of LJatoms extending from z = 0 to z → −∞ and infinite in extent in thex and y directions. If a LJ atom is placed at a distance z > 0from such a surface, then the net interaction potential is evalu-ated by integrating the contributions of all of the LJ atoms thatcomprise the surface. Such an integration leads to the 9-3

potential function with the factor εs =2πεsurfρσ3

surf3 where εsurf and

σsurf are LJ interaction parameters of surface atoms and ρ is thenumber density of atoms in the slab. For a hexagonal closed

packing of LJ atoms with σsurf = 1, the factor 2πρ3 = 2.96. The 9-3

potential is also plotted in Figure 2, scaled with εs. As a result ofinteraction contribution from a semi-infinite slab, the excludedvolume of the 9-3 potential is smaller and the repulsive part is“softer” in comparison to the LJ potential. The 9-3 potentialdecays as r−3, and therefore slower than the LJ potential withdistance. The relative magnitudes of potential well-depth para-meters, ε and εs, can be used to set the strengths of differentbead interactions. In the first set of simulations, the interactionsbetween hydrophobic beads of inhibitor molecules and thesurface are set to zero. The underlying reason for this simplifi-cation is to study a minimalist model of inhibitor moleculeswherein the effect of only two interactions is examined: (1)a strong interaction between the polar beads and the surface,and (2) hydrophobic interactions between the tails. In the sub-sequent set of simulations, the interactions between hydro-phobic beads and metal surface are also modeled using the 9-3potential function.

2.1.1.2 | Reduced Units and Simulation ParametersIn this sub-section, the concept of reduced units, which

are commonly used in MD simulations, especially in CG systems,is briefly discussed. In reduced units, the units of energy, mass,and distance are defined in a manner so as to ease thecomputational expense in simulations.16 For this system, theunit of energy is taken as thermal energy, kBT, which is set equalto one, where kB is Boltzmann constant and T is the temper-ature. The potential well-depth, ε, has units of energy, andtherefore is specified in terms of units of thermal energy. Forexample, ε = 0.5 implies that the potential well-depth is 50% ofthermal energy. One can always convert from reduced units toreal units and vice-versa. At 300 K, thermal energy is∼2.5 KJ/mol,so ε = 0.5 implies energy of 1.25 KJ/mol. Mass of each bead isset equal to one in reduced units, which can be understood as themass of one alkyl monomer. The size of a bead, σ, is set to onein reduced units, which is equal to ∼3 Å (0.3 nm). Hence, a lengthof, say 20 in reduced units is 60 Å (6 nm) in real units. Time inreduced units is calculated as t =σð m

kBTÞ1=2. Hence, time of one in

reduced units corresponds to ∼7 ps in real units.Now that appropriate reduced units have been defined, all

system parameters can be specified in terms of these units. TheLJ potential well-depth parameter for interactions betweenhydrophobic tails, ε is varied from 0.01 to 0.08 in the presentsimulations. For a corrosion inhibitor molecule of 20 beads(1 polar and 19 hydrophobic beads), the ε = 0.05 corresponds to∼1 kBT or 2.5 KJ/mol of interaction energy, which is of thesame order of magnitude as the measured hydrophobic inter-action between species of O (1 nm) in size.21 The 9-3 potentialwell-depth parameter for interactions between a polar bead andthe metal surface is εs = 5. This value corresponds to a bindingenergy of 12.5 KJ/mol, which is similar in magnitude to the valuesdetermined by the DFT calculations of polar groups on metalsurface.13

The simulation box size is taken as 20 × 20 × 40 in the X, Y,and Z axes. The metal surface is at Z = 0, i.e., in the XY plane. On theopposite face of the simulation box, there is a noninteractingsurface, or a reflection boundary, used to keep the number ofinhibitor molecules fixed in the simulation system. The simulationsystem is periodic in the X and Y directions. A corrosion inhibitormolecule is comprised of 20 beads and there are 400 moleculesin the simulation box. The equilibrium bond length is b0 = 0.3, andequilibrium angle between beads in a molecule is θ0 = 180°. Thevalue of the bond coefficient, kb, is set to 100 kBT/σ

2. The value ofthe angle coefficient, kθ, is set to 50 kBT/rad

2. Therefore, the kband kθ are sufficiently stiff such that only small fluctuations in thebonds and the angles between the bonds of the corrosioninhibitor molecule are possible.

As the effect of solvent (water) in this simulation system isimplicitly included, that is without having the actual watermolecules accounted for, a Langevin dynamics simulation isperformed to incorporate the effect of solvent on the dynamicsof inhibitor molecules. In a Langevin dynamics simulation, eachmolecule in the system experiences a random Gaussian force aswell as a viscous drag force.16 These two forces replicate thenumerous interactions between corrosion inhibitor moleculesand water molecules that lead to Brownian motion of theinhibitor molecules.

Hence, the phenomenological CGmodel described aboveincorporates effective interactions between inhibitor moleculesthemselves in an aqueous environment and the inhibitormolecules and the metal surface. All simulations are performedusing Large-Scale Atomic/Molecular Massively Parallel

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Simulator (LAMMPS†) MD simulations package.22 For each datapoint (discussed below), the simulations are performed inparallel on eight processors. Equilibrium is obtained after 2 × 108

to 6 × 108 MD time-steps, which took 3 weeks to 9 weeks toexecute. The error bars in the data are generated from three tofour different equilibrated simulation runs.

2.1.2 | ResultsSimulations done using this CG model have provided

interesting new insights into adsorption behavior of corrosioninhibitors on a metal surface. Some of the highlights arediscussed below.

2.1.2.1 | Hydrophobic Interactions of Inhibitor TailsAre Important in Adsorption

It is often presumed in the corrosion community that themain driver of adsorption of corrosion inhibitor molecules is thestrong affinity between the polar head group and the metalsurface. Therefore, many previous studies have focused oncalculating binding energies of different polar groups on metalsurfaces as a surrogate of adsorption efficiency.12-13 However,some experimental evidence suggests that lateral hydro-phobic interactions between the alkyl tails of surfactant mole-cules play an important role in the adsorption process.23-26

In order to elucidate the role of hydrophobic interactionsin adsorption, a series of simulations was performed here,wherein the affinity between the hydrophobic tails of corro-sion inhibitor molecules toward each other was varied bychanging the well-depth of LJ interactions, ε. A small value ofε corresponds to weak affinity between the tails of corrosioninhibitor molecules, while a large value corresponds to strongaffinity. In this set of simulations, the interaction strength be-tween the polar head group of the inhibitors and the metalsurface was kept constant (εs = 5).

Figure 3 shows equilibrium number of adsorbed corro-sion inhibitor molecules, N, on the surface as a function of ε.It is seen that for small values of ε, i.e., when the affinity ofhydrophobic tails towards each other is low, the adsorbednumber of molecules on the metal surface is small, corre-sponding to low, random adsorption. As ε is increased, a dramaticrise in the N is observed. At the highest adsorbed amount(corresponding to ε ≈ 0.065), a self-assembled monolayer (SAM)of adsorbed molecules is formed. When that optimum ε isexceeded, there is decrease in the number of adsorbed mole-cules as they tend to aggregate more strongly in the solutionand make some sort of micelles. This is clearly illustrated inFigure 3, where the snapshots of the simulation box for threedifferent values of ε show different adsorbed states.

To better understand the spatial distribution of adsorbedinhibitor molecules in the SAM formed on themetal surface, radialdistribution function in the XY plane, RDFxy(r) is calculated. TheRDFxy(r) shows local arrangement of other corrosion inhibitormolecules around any given molecule, by determining theaverage number of other molecules at a distance r in the XY planefrom the center of that molecule. This number is divided by thenumber of molecules one would expect if the adsorbed mole-cules were uniformly distributed around the given molecule.Hence, an RDFxy(r) = 1 indicates that molecules do not have anyspecific spatial arrangement. Figure 4(a) shows RDFxy(r) ofadsorbed molecules for ε = 0.065 and ε = 0.03. For ε = 0.065, theRDFxy(r) shows regular peaks as r increases, indicating that

the adsorbed corrosion inhibitor molecules are arranged in aspecific, well-defined arrangement. For ε = 0.03, RDFxy(r) ≈ 1indicates random arrangement, i.e., low adsorption. Note that theRDFxy(r) is small for very small distances. This is simply aconsequence of excluded volume of the molecules.

In order to further understand this adsorption behavior,the orientation factor of the adsorbed molecules and themolecules in the bulk phase have been calculated. The ori-entation factor, S, is defined as the largest eigenvalue of thetensor, Q, given by the following equation:27

Qαβ =1.5N

XNi = 1

jniα × niβj −12δαβ (7)

where niα and niβ are the α and β components of the end-to-endunit vector of molecule i, respectively. N is the total number ofmolecules, and δαβ is the Kronecker delta function defined equalto 1 when α = β and 0 otherwise. The value of S = 1 arises whenall of the molecules are perfectly aligned parallel to each other,and S = 0.5 for a completely random orientation of molecules.

In the Figure 4(b), the S for molecules in the adsorbedlayer and in the bulk phase (that is, in simulations with no surface

0Nu

mb

er o

f A

dso

rbed

Mo

lecu

les

(N)

εε

350

300

250

200

150

100

500.02 0.04 0.06 0.08 0.1

(a)

(b)

(c)

FIGURE 3. The number of adsorbed molecules in equilibrium, N, as afunction of the strength of hydrophobic interactions between inhibitortails, ε. Snapshots of the simulation system at different ε values arealso shown: (a) ε = 0.03: low, random adsorption; (b) ε = 0.065:adsorbed SAM; and (c) ε = 0.08: aggregated states in the bulk andthe adsorbed phases.

† Trade name.

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present) is plotted as a function of ε. For small values ofε (<0.04), S is small, which confirms that the molecules areadsorbed in random orientations. The value of S increasessharply with ε and S reaches close to 1 for the adsorbed phasefor ε ≈ 0.065. This observation shows that for the values ofε ≈ 0.065, the tails of adsorbed molecules are aligned parallel toone another, forming a SAM. In the bulk phase, a significantincrease in S is observed only for values of ε ≥ 0.07; however,at the same time a decrease in the adsorption is observed(Figure 3). For these large values of ε, the molecules startaggregating in the bulk phase as well. Hence, one can con-clude that adsorption decreases when the molecules startaggregating in the bulk as micelles. These results show thatby simply changing the strength of hydrophobic interactionsbetween corrosion inhibitor tails, a significantly differentadsorption behavior is observed.

2.1.3 | Adsorption Morphologies Depend on theGeometry of Corrosion Inhibitor Molecules

An area that has received little attention in the corrosionliterature is the morphology of adsorbed corrosion inhibitors onmetal surfaces. With the rationale being that strong affinitybetween the polar head groups and the metal surface is aprerequisite for good adsorption, often surfactants with bulkyhead groups comprised of aromatic or heterocyclic rings aretested for corrosion inhibition.1 By doing this, the effect ofmolecular geometry on the adsorption behavior is not taken intoconsideration properly. To determine the effect of moleculargeometry, the effect of a large head group on the aggregationand adsorption behavior of inhibitor molecules was studied inthis CG model system.

This was done by changing the size of the polar headbead to make it twice that of the hydrophobic beads, that isσP = 2σ. In this case it was found that the inhibitor moleculesaggregate in the bulk as well as adsorb on the metal surface ascylindrical micelles (Figure 5).19 The shape of micelles could bedetermined by calculating various shape factors, such as acy-lindricity and asphericity. These shape factors are calculatedfrom the principle eigenvalues of the radius of gyration squaredtensor of the micelles.19,28 The acylindricity and asphericity ofmicelles of inhibitor molecules in the bulk and in the adsorbed

layer are shown in Figure 5(a). A perfect sphere will have anasphericity value of 0. Similarly, a perfect cylinder will have theacylindricity value of 0.

Clearly, acylindricity is small in both phases, whileasphericity is high, indicating that the micelles are cylindrical inshape. The molecules aggregate to form micellar structuresthat maximize interactions among themselves, or equivalently,minimize the exposed surface area. It can be imagined that alarger head group will lend asymmetry in the molecular geometry,because of which laminar packing of the molecules will beinefficient in maximizing their interactions. Based on geometricalarguments, optimum micellar shapes can be predicted bycritical packing parameter (CPP).29 CPP is a dimensionlessnumber, given by V/(AL) where V is the volume of the tail, A isthe area of the head group, and L is the tail length. Assuming thetail to be a cylinder of excluded volume, V = πσ2L

4 andA= π

4 ðσPþσ2 Þ2, CPP ≈ 0.44, which corresponds to cylindrical

micelles.29

These results corroborate previous AFM results, whereinit is observed that surfactants can adsorb onto surfaces inmicellar structures similar to those observed in the bulkphase.30-31 One would further assume that the morphology of theadsorbed layer will have an effect on the interfacial properties.Hence, these results suggest that molecular geometry particu-larly that of the head group is an important consideration thatshould be accounted for while designing effective corrosioninhibitor molecules. These initial CG simulations suggest thatinhibitor molecules with bulky head groups probably lead to lesseffective SAM.

2.1.3.1 | Kinetics of Adsorption Is Related to DifferentStages of Self-Assembly of the Surface Layer

The kinetics of adsorption and self-assembly of corrosioninhibitors to form surface layers were investigated next. It is to benoted that while the experimental kinetics studies often takehours or even days to reach a steady state, in molecular simu-lations much smaller time-scales are accessible. In thesimulations one can overcome the diffusional barrier by studyingadsorption at much higher concentrations of corrosion in-hibitor molecules than those used in experiments. In thiscase, the kinetics obtained in the simulations may only be

(a) (b)2.51

0.95

0.9

AdsorbedBulk

0.85

Ori

enta

tio

n F

acto

r (S

)

RD

Fxy

(r)

r /σσ ε

0.8

0.75

0.7

0.65

0.6

2

1.5

r

1

0.5

00 2

ε = 0.03ε = 0.065

4 6 8 10 0 0.02 0.04 0.06 0.08 0.1

FIGURE 4. (a) Radial distribution function in the XY plane, RDFxy(r) of adsorbedmolecules for ε = 0.065 and ε = 0.03. The inset shows a schematicon how RDFxy(r) is calculated. (b) Orientation factor, S, of molecules in the adsorbed state and in the bulk phase as a function of ε. Adapted withpermission from Ko and Sharma.19

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qualitatively compared to the experiments, yet the qualitativeconclusions remain valid.

Figure 6(a) shows adsorption kinetics of corrosion in-hibitor molecules (σP = σ, ε = 0.065, εs = 5). Along with the totalnumber of molecules adsorbed, N, the number of adsorbedmolecules with their polar group pointing towards the surfaceis also plotted. The observed kinetics may be approximatelyconsidered as occurring in three stages. In the first stage,the adsorption kinetics are fast and most molecules adsorbwith their polar group toward the surface. Figure 6(b) showsaverage number of distinct clusters of adsorbed moleculesas a function of N. In the first stage, roughly 1/3 of the equi-librium amount is adsorbed and the adsorbed molecules formdistinct clusters on the surface. In the second stage, the rateof adsorption is slower and some molecules adsorb with theirpolar groups pointing away from the surface. In the second

stage, close to 80% of the equilibrium amount is adsorbed.The number of distinct clusters decreases in this stage,indicating that the clusters grow in size and merge witheach other. By the end of the second stage, all of the clustersmerge together into one, forming an adsorbed layer ofinhibitor molecules. In the final third stage of adsorption, nofurther increase in the adsorbed molecules with their polargroup pointing toward the surface is observed. All of themolecules adsorb with their polar group away from thesurface.

It is to be noted that many previous researchers havestudied adsorption kinetics of surfactant molecules on differentsurfaces using a QCM. They have reported multistage ad-sorption kinetics and have hypothesized the adsorption mech-anism qualitatively similar to what was observed in the presentkinetics study.32-34

350(a) (b)

TotalPolar

14

12

10

8

6

4

2

0

300

250

200

150

100

50

00 10 20 30 40 50 60 70

Nu

mb

er o

f A

dso

rbed

Clu

ster

s

Number of Adsorbed Molecules (N)Time (104 σσ (m/kB T)1/2)

Nu

mb

er o

f A

dso

rbed

Mo

lecu

les

0 50 100 150 200 250 300 350

FIGURE 6. Kinetics of adsorption of molecules. (a) The red line shows adsorption of molecules with their polar group toward the surface; the blueline shows total number of adsorbed molecules. (b) Number of distinct adsorbed clusters of molecules identified as a function of the number ofadsorbed molecules, N.

0.04

1

0.8

(a) (b)Acylindricitybulk

Acylindricitysurf

Asphericitybulk

Asphericitysurf

Sh

ape

Fac

tor

εε

0.6

0.4

0.2

00.06 0.08 0.1 0.12

FIGURE 5. (a) Acylindricity and asphericity shape factors of micelles of inhibitor molecules in the adsorbed and the bulk phase as a function of ε.(b) A snapshot of the simulation system for ε = 0.11. Different micelles are identified by different colors for ease of visualization. Adapted withpermission from Ko and Sharma.19

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2.1.3.2 | Strong Interactions Between Inhibitor Tail andMetal Surface Alter Adsorbed Conformations

In the simulations discussed above, the interactionsbetween alkyl tails and metal surface have been ignored. Therationale was to develop a minimalist model of inhibitormolecules wherein the effects of a strong polar group-metalinteraction and hydrophobic interaction between tails arestudied. In this section, the simulation results are discussedwherein the interactions between alkyl tails and metal atomswere incorporated in the model. With the inclusion of interactionsbetween tail and surface, an inhibitor molecule will have apreference to adsorb in two different configurations: the first onebeing “lying-down” on the surface, and second one being“standing-up” with only the polar group interacting with thesurface. In case of isotropic interactions between species, the“lying-down” configuration will be preferred in the dilute limit asthis will allow the polar bead, as well as the tail, to interact withthe surface. On the other hand, when the adsorbed concentrationof inhibitor molecules increases, the molecules may prefer toattain the “standing-up” configuration as this will allow (a) moremolecules to adsorb with their polar group interacting with thesurface, and (b) hydrophobic interactions between the tails ofstanding-up adsorbed inhibitor molecules. The effect of tail-metal interactions on the adsorption behavior can be understoodby a theoretical model illustrated below.

Consider a linear corrosion inhibitor molecule, which canthought of as a cylinder of cross-sectional area Ac, length l, anddiameter d. Let εs be the interaction between a polar group andthe surface; ε be the hydrophobic interaction between alkylbeads; and εt be the interaction between an alkyl bead and thesurface. The total energy of interaction in the lying-downconfiguration of a molecule is given by:

Elying = εs þ nεt (8)

where n is the number of beads in the alkyl tail. As the adsorptionconcentration increases, the molecules will prefer to stand-upif the adsorption of more molecules in the standing-up config-uration is energetically favorable. The relative magnitude of theenergy associated with the standing-up and lying-down config-urations can be compared by the following ratio:

Estanding

Elying=l d fAc

εsεs þ nεt

(9)

where f is the packing efficiency of molecules in the standing-upconfiguration. For this CG model of corrosion inhibitors: l = 6σ,d = σ, f = 0.62, Ac= πd 2/4, and n = 19. The value of f is calculatedfrom the result that on an average 315molecules adsorb in theSAM configuration on the 20 σ × 20 σ surface (Figure 3). To testthe validity of this theoretical model, molecular simulations ofsystems have been performed with different values of polargroup-surface interaction, εs, and tail-surface interaction, εt,with tail-tail interaction ε fixed at 0.065. ε = 0.065 is chosenbecause a SAM is formed for this value (Figure 3).

Figure 7 summarizes the simulation results. The bluesquare points represent simulations in which a standing-upconfiguration (eventually leading to the formation of SAM) ofmolecules in the adsorbed state is formed. The red circle pointsrepresent simulations in which lying-down configuration ofmolecules is observed. The line represents the theoretical model

when the ratio Estanding

Elying= 1 (Equation [9]). The theoretical model

seems to be quantitatively accurate in delineating the lying-down

and standing-up configurations. The one mismatch at εs = 3and εt = 0.5525 is probably because, for these strong tail-surfaceinteractions, the energy penalty for a molecule to stand-up islarge. As a result, the molecules are kinetically trapped in thelying-down configurations. From Figure 7 and this theoreticalmodel, it is clear that a strong interaction between the polar headand the surface is favorable for the formation of a well-packedSAM of adsorbed molecules.

In the case of standing-up configuration, eventually aSAM of adsorbed molecules is formed. In the case of lying-downconfiguration, multiple layers of adsorption are seen withmolecules stacking on top of each other. Figure 8 shows dis-tribution profiles of equilibrium-adsorbed configurationsobtained for (a) the standing-up case (εs = 2 and εt = 0.3575), and(b) the lying-down case (εs = 2 and εt = 0.4875) as a function ofdistance from the surface, z. A single peak in case (a) showsformation of a SAM, while multiple, periodic peaks in case(b) show stacking up of molecules. The distribution profile isobtained by counting the average number of molecules at adistance z from the surface and dividing it by the average numberone would expect in the case of uniform distribution ofmolecules in the entire simulation box.

In summary, through a simple CG representation ofcorrosion inhibitor molecules, some interesting insights into theadsorption and self-assembly behavior of these molecules areobtained. An important learning is that a strong affinity betweenthe polar group and the metal surface is not sufficient for goodadsorption. The lateral hydrophobic interactions between tailsplay an important role in adsorption. Another interesting resultis that the morphology of the adsorbed surfactant film will likelydepend on the molecular geometry. Furthermore, the kineticsof formation of adsorbed inhibitor film reveal that the initialadsorption is dominated by the interaction between polargroup and the metal surface, but the subsequent adsorptionis driven by lateral hydrophobic interactions. Lastly, stronginteractions between alkyl tail and metal surface may alter theadsorbed conformations.

Lying-downStanding-up

0.6

0.5

0.4

0.3

0.2

0.10 1 2 3

εεs

ε t

4 5 6

FIGURE 7. Summary of simulation results performed with differentvalues of εs and εt. The black line indicates the theoretical condition ofEstanding = Elying as per Equation (9). It is observed that the theoreticalprediction is quite accurate in predicting adsorbed conformations ofthe molecules.

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2.2 | Atomistic Molecular Dynamics Simulationsof Corrosion Inhibitors

While CG models are suitable for studying longer time-scale and larger length-scale adsorption and self-assembly be-havior of larger numbers of inhibitor molecules, atomisticsimulations are more useful for studying smaller number ofmolecules over shorter time- and length-scales, while enablingone to use full chemical detail in the definition of the molecules.The goal here was to use atomistic modeling to determinerelative stability of different states in which inhibitor moleculesmay exist near interfaces and in the bulk aqueous phase, asindicated by the schematic phase diagram shown in Figure 9.

The long-term goal is to investigate and define thecomplete phase diagram shown in Figure 9. Once the relativestability of different phases as well as the transitions betweenthe phases are determined, the dominant mechanisms by whichinhibitor molecules adsorb, self-assemble on surfaces, and

aggregate in the bulk phase will be understood. Clearly, getting tothat level will take a few more years of concentrated effort;however, the most interesting learnings made on this journey sofar are discussed below.

Fully atomistic simulations allow inclusion of chemicaldetails in molecule definition and explicit representation of sol-vent molecules in the system. Specifically, the focus here wason studying model corrosion inhibitor molecules, such asimidazolinium-type and quaternary ammonium-type surfac-tants. Figure 10 shows the exact molecules that were studied sofar: (a) two imidazolinium-type molecules: one with a 17 carbonlong hydrophobic tail (Imid-17) and one with a 10 carbon long tail(Imid-10); and (b) two quaternary ammonium-type molecules:one with a 10 carbon long tail (Quat-10) and one with a 16 carbonlong tail (Quat-16).35 Simulations of these molecules in the bulkaqueous phase and near metal/water interfaces have providedinteresting new insights, discussed below.

Unaggregated Micelles in bulk

Adsorbed micelles

SAM

Metal Surface

FIGURE 9. A schematic showing some possible states of corrosion inhibitor molecules in bulk aqueous phase and near metal/water interfaces.

25(a) (b)

20D

istr

ibu

tio

n P

rofi

le

Dis

trib

uti

on

Pro

file

15

10

5

0

25

20

15

10

5

00 5 10

z/σ z/σ15 20 0 5 10 15 20

FIGURE 8. Distribution profile of center of mass of corrosion inhibitor molecules in the equilibrium configurations as a function of distance fromthe surface, z, for (a) εs = 2 and εt = 0.3575, and (b) εs = 2 and εt = 0.4875. From Figure 7, it is seen that the case (a) corresponds to that ofstanding-up configurations, which leads to formation of a SAM. Therefore, the distribution profile shows a peak and a shoulder. The case(b) corresponds to the lying-down configurations. This eventually leads to multiple layers of adsorbed molecules in the lying-down config-urations. Hence, the distribution profile shows periodic peaks. The insets show illustrations of the final adsorbed configurations in the two cases.

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2.2.1 | Simulation Setup and System DetailsThe imidazolinium-type and quaternary ammonium-type

molecules are protonated at the polar group and therefore carryan overall charge of +1. In order to calculate partial charges onatoms of inhibitor molecules, B3LYP level DFT calculations wereperformed with 6-31G(d,p) orbital basis sets and implicit waterusing Gaussian 09† software.36 From these DFT calculations, itcan be observed that the +1 charge on the polar head group ofimidazolinium-type molecules is delocalized among the twonitrogen atoms and the carbon atom in between them. Thesimulation system includes chloride ions to maintain the overallsystem charge neutrality. Water molecules are explicitlymodeled using the single point charge enhanced (SPC/E) watermodel, which is a rigid, three-atom model. In the SPC/E model,there is a fixed partial charge of −0.8476e on the oxygen atomand +0.4238e on the hydrogen atoms, the H-O-H bond angle is109.47°, and the O-H bond length is 1 Å (0.1 nm).37 The metalsurface is represented by six layers of a close-packed face-centered cubic (111) lattice plane of gold atoms with the latticeconstant of 4.08 Å (0.408 nm). The gold surface is orientedparallel to the XY plane in the simulation box. Adsorption wasstudied on gold surface rather than on iron because the forcefield parameters for gold are available in the interface force field.While this is a drawback if one seeks to understand theadsorption of corrosion inhibitor molecules on steel, the authorsbelieve that the general features of the adsorption behaviorcaptured on a gold surface will be similar to that on an ironsurface. This is because just like iron, gold has strong affinityfor water as well as surfactants and is highly polarizable.Furthermore, previous researchers have studied adsorption ofcorrosion inhibitor molecules on gold surfaces via QCMexperiments and have reported similar adsorption behavior.38

The simulation box is periodic in the X and Y directions, inthe same way as was done above for CG simulations. On the faceopposite to the gold surface, a noninteracting reflecting sur-face is placed to keep the simulation system volume constant.The dimensions of the simulation box is 52 Å by 54 Å by 190 Å(5.2 nm by 5.4 nm by 19 nm). The simulation box is significantlylarger in the Z dimension to ensure that the liquid columnplaced over the gold surface is representative of the bulkaqueous phase. The interactions of gold atoms with otherspecies are modeled using the interface force field.39-40 Theinterface force field is parameterized in the functional form ofLJ potential. The parameterization is done to reproduce the

interfacial tension and bulk density of metals. The interactionsof corrosion inhibitor molecules with other species is modeledusing the general amber force field (GAFF), which is a widelyused force field for surfactants and organic molecules.41 In theGAFF force field, the nonbonded interactions between atomsis represented by LJ and Coulombic potentials. The bond andangle potentials are represented by harmonic functions. Alongwith these, there is potential energy associated with dihedralangles in molecular segments. The force field parameters inGAFF are determined by fitting many experimentally determinedproperties, such as densities, enthalpies of vaporization, bondvibration frequencies, etc.41-42 The interaction parameters ofchloride ions are from the Joung-Cheatham model,43 which isa widely used force field for alkali and halide ions in explicit water.In the Joung-Cheatham model, the interaction potentials ofmonovalent ions are represented by LJ and Coulombic poten-tials. The potential parameters are fitted to hydration freeenergies, lattice energies, and lattice constants.

Total number of water molecules in the simulation systemwas 15,000. All simulations are performed at a temperatureof T = 300 K. The simulations are performed in the canonicalensemble, that is, by keeping the temperature, volume, andtotal number of molecules in the system fixed. In order tomaintain the pressure in the simulation system at saturationpressure, a vapor spaceofwidth∼5Å (∼0.5nm) is created at thetop of the simulation box.35 This methodology is used because aconstant temperature and pressure MD simulation requiresadjustment of the simulation box size, which is not possible in thissystem because of the presence of a lattice of gold atoms.

For comparison purposes, atomistic MD simulations ofcorrosion inhibitor molecules in the bulk aqueous phase werealso performed, that is, in the absence of a solid metal surface.In these simulations, the simulation box was periodic in all threedirections. These atomistic MD simulations were also per-formed at the temperature of T = 300 K. The size of the simulationbox is 50 Å × 50 Å × 50 Å (5 nm × 5 nm × 5 nm). The number ofwater molecules in the simulation box is ∼3,500.

All MD simulations were performed using LAMMPS†.22 Forbulk simulations, constant temperature and pressure MD simu-lations were performed (P = 1 bar [100 kPa]). The atomistic MDsimulations were performed in parallel on 28 processors. For themicelle formation studies (discussed below), 31 ns to 46 nslong MD simulations were performed. Approximately 3 ns ofatomistic MD simulation takes 1 d on 28 processors. For freeenergy calculations using umbrella sampling (discussed below),64 different umbrella sampling windows of 6 ns to 9 ns eachwere generated for each free energy calculation.

2.2.2 | Results2.2.2.1 | Micelle Formation in the Bulk Solution andTheir Characteristics Depend on the Type ofInhibitor Molecule

At concentrations above the critical micelle concentra-tion (CMC), inhibitor molecules are expected to aggregate asmicelles. It was found that both groups of molecules Imid-10/Imid-17 and Quat-10/Quat-16 molecules aggregate into micelleswith a roughly spherical shape. Figure 11 shows snapshots ofthe micelles formed by different compounds with differentnumbers of molecules. In these micelles, the hydrophobic alkyltails of the molecules form the core, while the polar head groupsremain on the periphery, facing the water molecules.

From Figure 11, the Imid micelles appear to be moredensely packed than the Quat micelles. Indeed, the calculated

Imid-10 Quat-10

Imid-17Quat-16

FIGURE 10. The two imidazolinium-type (Imid-10 and Imid-17) and thetwo quaternary ammonium-type (Quat-10 and Quat-16) model corro-sion inhibitor molecules used in the atomistic simulations. Blue beadsrepresent the nitrogen atom, dark gray beads represent carbonatoms, and light gray beads represent hydrogen atoms.

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number density of Imid-10 micelle consisting of 18 moleculesis 0.28 heavy atoms/Å3, whereas that of Quat-10 micelle with 18molecules is 0.26 heavy atoms/Å3. For Imid-17 micelle with 19molecules, the number density is 0.35 heavy atoms/Å3, while thatof Quat-16 with 19 molecules is 0.30 heavy atoms/Å3. Hence,in general, Imid micelles have a higher number density ascompared to the Quat micelles. Furthermore, in the Quatmicelles, the polar head group seems to protrude out of themicelle, which is not seen for Imid micelles. This difference inmicellar structure could be because in Quat molecules, thecharge on the polar head group is localized on the nitrogenatom, while in Imid molecules, the charge is delocalized partiallyon the imidazoline ring, which reduces Coulombic interactionsin case of Imid molecules.

The asphericity of Imid-10 and Imid-17 micelles com-prised of different number of molecules, Nmicelles, is plotted inFigure 12(a). It is observed that except for small sized-micelles(Nmicelles ≤ 5), the asphericity is small, indicating that the micellesare pretty much spherical in shape.

Diffusion coefficient of micelles of different sizes calcu-lated from the simulations are shown in Figure 12(b). In thesesimulations, the concentration of Imid-10/Imid-17 molecules inthe system was kept the same for all micelles, equal to 0.09 M.Diffusion coefficient was calculated by using Einstein’s

relation, which states that <MSD> = 6Dt, where <MSD> stands foraverage mean square displacement, D is the diffusion coef-ficient, and t is the time. As expected, D decreases as themicellesbecome bigger. Imid-10micelles have larger D as compared toImid-17 micelles, owing to their smaller size.

2.2.2.2 | Corrosion Inhibitor Molecules Form Micellesnear the Metal/Water Interface

As a first step towards understanding the behavior ofcorrosion inhibitor molecules and their adsorption on metalsurfaces, a gold surface was introduced at the bottom of thesimulation box as indicated in Figure 13. After reaching equilib-rium, the following observations could be made: (a) mostinhibitor molecules aggregated in the aqueous phase as micellesand did not adsorb on the metal surface; and (b) few inhibitormolecules (4 to 5 out of 64) adsorbed on the metal surface withthe alkyl tails lying flat on the metal surface. The underlyingreasons for these observations will be discussed below.

These results suggest that corrosion inhibitors aggre-gated in micelles have a weak tendency to adsorb on to a metalsurface. On the other hand, unaggregated corrosion inhibitormolecules have a strong tendency to adsorb. To further un-derstand the adsorption behavior, the free energy of

(a) (b)

(d) (e)

(c)

FIGURE 11. Snapshots of (a) an Imid-10 micelle consisting of 18 molecules, (b) an Imid-17 micelle consisting of 19 molecules, (c) a Quat-10micelle consisting of 18 molecules, and (d) and (e) Quat-16 micelles with consisting of 10 and 19 molecules, respectively. Yellow segmentsrepresent the alkyl tails, and red segments represent the polar head group.

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adsorption of corrosion inhibitor molecules in infinite dilution andin the micellar state were calculated.

2.2.2.3 | Unaggregated Corrosion Inhibitor MoleculesShow a Strong Tendency to Adsorb onto theMetal Surface

For both Imid-10 and Imid-17 molecules, the free energyof adsorption in infinite dilution was calculated using a simulationmethodology called “umbrella sampling.”44 Before discussingthe results, a brief introduction to free energy calculations andthe umbrella sampling methodology might be helpful. Recallthat for a closed system, that is, for a systemwith fixed number ofparticles N, volume V, and temperature T, thermodynamicequilibrium is reached when the Helmholtz free energy F isminimized. Therefore, in a canonical ensemble MD simulation(using a system with constant number of molecules in a constantvolume at constant temperature), the equilibrium state will be alocal minimum of the free energy landscape. Suppose one isinterested in studying the transition from one thermodynamicstate A to another state B. This transition can be followed bycalculating the value of some thermodynamic variable, termedas reaction coordinate, which is a measure of the path traversedfrom A to B. For example, adsorption transition of a moleculefrom the bulk aqueous phase onto the metal surface can befollowed by the reaction coordinate defined as the distancebetween the center of mass of the molecule and the metalsurface, ξ. If, for each value of the reaction coordinate ξ, onecalculates F(ξ), then one has determined the free energy profile ofthe system transitioning from state A to state B.

However, there are certain problems associated withdirectly calculating F(ξ). If the states A and B are both localminimum of the free energy landscape, then a straightforwardMD simulation will either equilibrate to the state A or to the stateB, and will only sparsely sample state points in between A andB. Hence, to generate F(ξ) for all ξ, the umbrella samplingmethodology comes in handy. In umbrella sampling, a har-monic bias potential of the form, Ubias = k(ξ − ξo)

2, where ξ is theinstantaneous value of the reaction coordinate and ξo is theset-value, is applied. The bias potential ensures that the simu-lation system samples state points close to ξo. By system-atically changing the value of ξo in a series of MD simulations,

one can sample all values of ξ between the states A and B.From the biased sampling so obtained from umbrella samplingsimulations, one can determine unbiased free energies, F(ξ), byinvoking laws of statistical mechanics. Specifically, a procedureknown as weighted histogram analysis method (WHAM) hasbeen used for un-biasing these simulations. Discussion of WHAMequations is beyond the scope of this paper, but an interestedreader can refer to the cited publication.45

Now getting back to the results: Figure 14 shows freeenergy profiles of adsorption of Imid-10 and Imid-17 moleculeson to the metal surface at infinite dilution.35 Clearly, bothinhibitor molecules demonstrate a strong tendency to adsorbwith no free energy barrier to adsorption. The adsorptionfree energy is found to be ∼30 kBT. Furthermore, the affinity toadsorb for both the molecules is found to be similar. The Imid-17molecule has a larger enthalpy of adsorption on the metalsurface, owing to its longer alkyl tail; however, its adsorptionis also accompanied by a larger entropic loss.35 Hence, thereis an enthalpy-entropy compensation between these twomolecules, which results in similar free energy of adsorption.

The free energy profiles are not smooth. This is becausethe orientational space of the molecules was not exhaustivelysampled. Ideally, one can do so by applying another harmonicbias potential in the orientational space. However, such a cal-culation will require at least an order of magnitude moresimulations. In Figure 14 (inset), a snapshot of an adsorbedconfiguration of Imid-17 molecule is shown. The moleculeadsorbs with the alkyl tail lying flat on the metal surface becausein this configuration the alkyl tail as well as the polar headgroup of themolecule are able to interact favorably with themetalsurface.

2.2.2.4 | Micelles of Corrosion Inhibitor MoleculesHave a Weak Tendency to Adsorb onto theMetal Surface

To study the adsorption behavior of inhibitor micellesformed in the bulk, adsorption free energy profiles of Imid-10 andImid-17 micelles comprised of 18 and 19 molecules, re-spectively, were calculated using umbrella sampling. For thiscalculation, the reaction coordinate, ξ, is chosen as the

Imid-10 Imid-10

Imid-17 Imid-17

1 0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0.8

0.6

0.4

0.2

00 5 10 15 20

Micelle Size (Nmicelle) Micelle Size (Nmicelle)

Asp

her

icit

y

Dif

fusi

on

Co

effi

cien

t ×

10–9

/ (m

2 /s)

(a) (b)

25 30 35 0 5 10 15 20 25 30 35

FIGURE 12. (a) Asphericity, and (b) diffusion coefficient of Imid-10 and Imid-17 micelles comprised of different number of molecules, Nmicelle.

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distance between the center of mass of the micelle and the metalsurface. Figure 15 shows the free energy profiles.35 It isobserved that the inhibitor micelles experience a repulsion fromthe metal surface at distances as large as 50 Å to 60 Å (5 nm to6 nm). The repulsion is long-ranged considering that the radius ofthese micelles is ∼15 Å (∼1.5 nm). This long-ranged repulsionis observed because the micelles are surrounded by a largecorona of counter-ions as well as their solvation shells.35 Thiscorona of the micelle is disturbed as the micelle approaches themetal surface which gives rise to the observed repulsion.

Furthermore, the free energy profiles have a maximum ata ξ of 21 Å (2.1 nm) followed by a local minimum. This maximumin the free energy profile corresponds to the removal ofadsorbed layers of water on the metal surface.35 At the locationof local minimum (∼15 Å [1.5 nm]), the micelles are in contactwith the metal surface.

Figure 16 shows a snapshot of the Imid-17 micelle incontact with the metal. In the simulations, micelles breaking apartupon adsorption were not observed. It is interesting to com-pare these profiles with the ones obtained for the infinite dilutioncase (Figure 14). While the unaggregated molecules show astrong tendency to adsorb on to the metal surface, the micellesexperience a long-range repulsion from the surface. Theseresults explain why in the straightforward MD simulations, it wasfound that most inhibitor molecules in the micellar form do notadsorb, whereas some unaggregated molecules adsorb on thesurface.

2.2.2.5 | Adsorbed Layer of Corrosion InhibitorsIn the CG molecular simulations, it was shown that the

nature of the adsorbed layer of inhibitor molecules depends onthe ratio Estanding

Elyinggiven by Equation (9). For the fully atomistic

model of corrosion inhibitors, this ratio is calculated usinginteraction parameters of the force field (εs = 7.55 Kcal/mol,εt = 2.21 Kcal/mol) and molecular properties (Ac = 0.14 nm2,l = 1.5 nm [Quat-10] / 2.3 nm [Quat-16], n = 10 [Quat-10] / 16[Quat-16], f = 0.57). This ratio is estimated to be roughly 0.45,which indicates that the adsorbed layer should compriseof inhibitor molecules lying flat on the surface. In orderto study the nature of the adsorbed layer, an initial config-uration was created wherein Quat-10/Quat-16 inhibitormolecules are arranged in a planar arrangement over agold surface (Figure 17[a]). Starting from this initial config-uration, isothermal-isobaric ensemble MD simulations wereperformed at temperature T = 300 K.

After an extremely long simulation of 320 ns, theadsorbed layer of inhibitor molecules was observed undergoinga significant rearrangement wherein the molecules eventu-ally end up adsorbing parallel to the surface (Figure 17[b]).Because of the space constraint, the remaining moleculesdesorb and aggregate in micellar form in the bulk phase. Whilethese results align well with the theoretical model of Equa-tion (9) and CG simulations, they are in contrast with the typicalinterpretations stemming from experimental studies, where itis stated that corrosion inhibitor molecules adsorb with theirpolar groups toward the metal surface and the hydrophobictails pointing toward the solution. A source of discrepancycould be that the strength of interaction between the polar-head group and the metal surface is stronger than what was inthis model (indicating possibly a much stronger physical orchemical interaction). This aspect will be explored further infuture work.

To summarize, through atomistic MD simulations, it isrevealed that unaggregated corrosion inhibitor molecules ex-hibit strong affinity toward adsorption. On the other hand,micelles of corrosion inhibitor molecules have a weaker ten-dency to adsorb and are metastable in the adsorbed state. Adecrease in adsorption with the aggregation of inhibitor mole-cules in the bulk phase is also observed in the CG simulations(Figure 3), but this effect is more pronounced in atomisticsimulations wherein water and counter-ions are explicitlyincluded in the system. At infinite dilution, the inhibitor mole-cules adsorb with their alkyl tails parallel to the metal surfacebecause of affinity of the tail for the metal. In the adsorbed layeras well, the inhibitor molecules are found to adsorb with theiralkyl tails parallel to the metal surface. These results are incontrast with typical interpretations which have corrosioninhibitor molecules arranging themselves in SAM withpolar group towards the metal surface and alkyl tailtowards water.

FIGURE 13. A snapshot of the simulation system with 64 Imid-17molecules in water near a gold lattice, yellow atoms are parts of alkyltails, red atoms are parts of polar head groups, golden color atomsrepresent gold atoms, blue represents chloride ions, and cyan repre-sent water molecules. Adapted with permission from Kurapati andSharma.35

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SUMMARY, CAVEATS, AND FUTURE WORK

Classical molecular simulations complement experi-ments in deciphering the behavior of physical systems byproviding a window to observe the nanoscale. In this paper,

recent efforts in using molecular simulations to understandadsorption, aggregation, and self-assembly of corrosioninhibitor molecules on metal surfaces are discussed. Newinsights have emerged from these simulations, which in somecases, challenge the long-standing presumptions, and in othercases, validate them. Major findings from these coarse-grained simulations are that (a) hydrophobic interactionsplay an important role in the adsorption and self-assemblyprocesses, (b) molecular geometry has a significant effect onthe morphology of the adsorbed layer, and (c) the relativestrength of polar head-metal and alkyl tail-metal interactions areimportant determinants of adsorbed conformations. Theatomistic simulations reveal that the adsorption behavior ofinhibitor molecules is strongly dependent on their aggrega-tion state. While unaggregated molecules have a strong ten-dency to adsorb on to the metal surface, micelles experience

40

35Imid-10

Imid-1730

25

20

15

10

5

00 5 10

ξ ξ (Å)

Fre

e E

ner

gy

(kB

T)

15 20 25

FIGURE 14. Free energy of adsorption profiles for Imid-10 and Imid-17 molecules on a gold lattice at infinite dilution; inset: equilibrium adsorbedconfiguration of the Imid-17 molecule. Adapted with permission from Kurapati and Sharma.35

(a)

(b)ξξ (Å)

ξ (Å)

Fre

e E

ner

gy

(kB

T)

Fre

e E

ner

gy

(kB

T)

40

35

30

25

20

15

10

5

00 10 20

4 kBT

13 kBT

10 kBT 16 kBT

30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

40

35

30

25

20

15

10

5

0

FIGURE 15. Free energy profiles of adsorption of (a) Imid-10 micelle,and (b) Imid-17 micelle comprised of 18 and 19 molecules, respec-tively. Adapted with permission from Kurapati and Sharma.35

FIGURE 16. A snapshot of an Imid-17 micelle adsorbed on the metalsurface. Adapted with permission from Kurapati and Sharma.35

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a long-range repulsion from the surface. This result suggeststhat efficient corrosion inhibition will be observed at corrosioninhibitor concentrations below the critical micelle concentration(CMC) because unaggregated molecules readily adsorb. Onthe other hand, above the CMC, the inhibitor molecules formmicelles which show a weak tendency to adsorb.

These are useful results which will help researchers incorrosion inhibition to develop better strategies to design anddeploy corrosion inhibitors for field applications. That said,it will be appropriate to comment that this has so far only“scratched the surface” and a lot more information can begained from molecular simulations of these systems. Thereis a need to systematically explore how the adsorption andaggregation behavior changes as the chemistry of the moleculesis changed, and how the physical properties of the metal/waterinterfaces are affected as a result. The results of these simula-tions will be on a stronger footing once their predictions arevalidated via synergistic experiments. Furthermore, the sensi-tivity of the results on the models used in these simulationsneeds to be carefully examined. In the CG simulations, the effectof water is incorporated through an effective hydrophobicattraction between alkyl tails and Langevin dynamics, whichmimics random collisions between solute and solvent mole-cules. However, in the absence of explicitly represented watermolecules, many differences in the simulation results mayoccur. The atomistic simulations show that near metal surfaces,the water molecules arrange in two layers. Furthermore, in theatomistic simulations it was observed that the interactions be-tween the solvation shell of inhibitor micelles and the adsorbedlayers of water result in a long-range repulsion between themicelles and the surface. These effects will not be observed inthe case of implicitly-included water.

Finally, it is important to mention some caveats of molec-ular simulations. Certain assumptions and simplifications aremade in designing the simulation systems, which can be a

source of errors in the results. First, the force fields used inmolecular simulations are developed by fitting simulationsresults to some thermodynamic properties determined fromexperiments. Hence, the designed force fields may be good atreproducing some thermodynamic properties but not others.These force fields are assumed to be transferable from onesystem to another, which may not always be the case.Furthermore, polarizability of different species is often ignoredin molecular simulations. Some polarizable force fields have beendeveloped, but their performance are not observed to beoverall better than that of nonpolarizable force fields, and hencethey have not become popular. Classical molecular simulationscannot capture chemical reactions, such as bond forming orbreaking, which may occur in some systems. Because of thecomputational complexity of molecular simulations, the systemsizes are of the order of 10 nm to 100 nm. As a result, theconcentration of solutes in the simulations is often taken to behigher than in experiments.

ACKNOWLEDGMENTS

Acknowledgment is made to the donors of the AmericanChemical Society Petroleum Research Fund (ACS PRF No.56892-DNI6) for support of this research. This work is partiallysupported by the NSF CBET Grant No. 1705817. The authorsthank researchers at the Institute for Corrosion and Multi-phase Technology (ICMT) for useful discussions. Computationalresources for this work were provided by the Ohio Super-computer Center.

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FIGURE 17. (a) A snapshot of initial configuration of simulation system with an adsorbed layer of Quat-10 molecules on the gold surface. Yellowrepresents the alkyl tails, red represents the polar head group, and blue represents chloride. Water molecules are represented by red (oxygen)and white (hydrogen). (b) A snapshot of the simulation system after 320 ns of MD simulation (water molecules not shown for clarity).

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