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Materials Chemistry and Physics 134 (2012) 54– 60

Contents lists available at SciVerse ScienceDirect

Materials Chemistry and Physics

jo u r n al hom ep age : www.elsev ier .com/ locate /matchemphys

ynergistic effect of 2-oleyl-1-oleylamidoethyl imidazoline ammoniumethylsulfate and halide ions on the inhibition of mild steel in HCl

ongqing Hua,b, Ailing Guoc, Yufeng Genga, Xiaolin Jiaa, Shuangqing Suna, Jun Zhanga,∗

College of Science, China University of Petroleum, Qingdao, Shandong 266555, ChinaKey Laboratory of New Energy Physics and Materials Science in Universities of Shandong (China University of Petroleum), ChinaDepartment of Jingmen Oil Transportation, Sinopec Pipeline Storage and Transportation Corporation, Jingmen, Hubei 448000, China

r t i c l e i n f o

rticle history:eceived 26 April 2011eceived in revised form7 November 2011ccepted 10 February 2012

a b s t r a c t

The effect of 2-oleyl-1-oleylamidoethyl imidazoline ammonium methylsulfate (ODD) and halide ionson corrosion inhibition of mild steel in HCl solution has been studied by experimental and moleculardynamics simulation methods. Synergistic effects were observed between ODD and the halides, and theinhibition efficiency was found to follow the trend ODD–Cl− < ODD–Br− < ODD–I−. In molecular dynamicssimulation, the analysis of fractional free volume and diffusion coefficient showed that the synergistic

eywords:orrosion inhibitorild steel

olarizationolecular dynamics

effect increased in the order ODD–Cl− < ODD–Br− < ODD–I−. The molecular dynamics simulation analysisagreed with the experimental results.

© 2012 Elsevier B.V. All rights reserved.

canning electron microscopy

. Introduction

Organic inhibitors have been widely applied to inhibit the cor-osion of metals in acidic media. A large number of studies aboutorrosion inhibition mechanism have emerged over the past fewears. Originally, the mechanism of single corrosion inhibitor wastudied by the experimental methods. These methods providedome really useful information in explaining the mechanism of sin-le corrosion inhibitor [1–5]. But they were expensive and timeonsuming. Above all, they were unable to present the mechanismf the corrosion inhibitor from a microscopic level. Afterwards,ith the development of computer technology and theoretical pro-

ess, computer simulation methods had evolved to be an efficientethod to study the complex systems at the microscopic level

6–10], and had made it possible to investigate the mechanism ofingle corrosion inhibitor fundamentally. However, for a single cor-osion inhibitor, the selectivity to the environment was so high thathe scope of application was too narrow.

The multicomponent corrosion inhibitors showed more excel-ent performance, such as lower dosage, high efficiency and broad

cope of application. Thus, the study on the mechanism of the multi-omponent corrosion inhibitors was paid more and more attentiono. Many studies had been performed by the experimental methods.

∗ Corresponding author. Tel.: +86 0532 86983418l; fax: +86 0532 86983418.E-mail address: dynamic zh@163.com (J. Zhang).

254-0584/$ – see front matter © 2012 Elsevier B.V. All rights reserved.oi:10.1016/j.matchemphys.2012.02.019

Hosseini et al. [11] studied the inhibition effects of sodium dode-cylbenzenesulphonate (SDBS) and hexamethylenetetramine (HA)on the corrosion of mild steel in sulphuric acid solution usingweight loss, electrochemical impedance and Tafel polarizationmeasurements. Results showed that SDBS and HA presented asynergistic effect within a certain concentration range. Jeyaprabhaet al. [12] explored the influence of halide ions on the adsorptionof diphenylamine on iron surface in 0.5 M H2SO4 solution usingelectrochemical impedance and polarization methods. It wasfound that the inhibition efficiency of diphenylamine increased inthe presence of halide ions, and the decreasing order of synergisticeffect of halide ions was I− � Br− > Cl−. Tavakoli et al. [13], Pavithraet al. [14] and Gao et al. [15] also investigated the synergistic effectof different additives on the corrosion inhibition of various metalsby the experimental methods. However, the studies about syner-gistic effect of corrosion inhibition mechanism were in a stage ofsummary and inference from the experimental phenomena.

At present, the theoretical study on the synergistic effect ofmulticomponent corrosion inhibitors was scarce. Yan et al. [16]studied the corrosion inhibition properties of pyridine and I− onthe aluminum surface in phosphoric acid by weight loss and quan-tum chemistry method. It showed that there was a synergisticeffect between pyridine and I−. The quantum chemistry calculation

method showed that the net energy of synergistic inhibition wasthe main reason of synergistic effect. Generally, quantum chem-istry method is only applied to a system containing no more than100 atoms or small molecules. But the corrosion process always

S. Hu et al. / Materials Chemistry and Physics 134 (2012) 54– 60 55

roma[i

i(Olwsu

2

2

2

wtpc

a1KTm

gOotK

2

H5t2a

2

ncmmaP

Table 1Description of different simulated models.

Membrane Number of compositions Lxa = Lya = Lza, Å

X− ODD+ Corrosive particle

ODD–Cl− 30 30H3O+ 1

33.61H2O 1

ODD–Br− 30 30H3O+ 1

33.10H2O 1

ODD–I− 30 30H3O+ 1

31.18H2O 1

Fig. 1. Schematic molecular structure of ODD.

efers to a big system, which includes a large number of moleculesr atoms on the interface between a bulk and metal surface. In fact,olecular dynamics (MD) simulation can be performed to study

complex system, such as a interface and diffusion of particles17], etc. However, there were few publications on the synergisticnhibition mechanism studied by the MD simulation.

In this paper, the inhibition effects of 2-oleyl-1-oleylamidoethylmidazoline ammonium methylsulfate (ODD, Fig. 1), halide ionsCl−, Br− and I−) and their mixture (ODD–Cl−, ODD–Br−, andDD–I−) on A3 steel in 0.5 M HCl solution are studied by the weight

oss method and potentiodynamic polarization test. Furthermore,e investigate the synergistic mechanism by molecular dynamics

imulation to explain the synergistic mechanism from the molec-lar level.

. Experimental and computational methods

.1. Experimental method

.1.1. MaterialsExperiments were carried out using A3 steel as the specimen

ith the composition (in wt.%) C 0.17%, Si 0.20%, S 0.03%, P 0.01% andhe remainder being iron. The specimens were ground on SiC water-roof abrasive paper up to 2000 mesh grit, and then ultrasonicallyleaned in the analytical reagent alcohol and dried in air.

Experiments were undertaken in 0.5 M HCl solution in thebsence and presence of different concentrations of ODD (0.1, 0.5,.0, 2.0 and 3.0 g l−1, respectively), KX (1.0 g l−1 for KCl, KBr andI, respectively) and ODD–KX mixtures (both 1.0 g l−1) at 50 ◦C.he temperature was maintained by placing a container in a ther-ostated water bath.The aggressive solution of 0.5 M HCl was prepared using AR

rade chemicals and distilled water. The active constituent ofDD was 80%, and the concentration of inhibitor solutions werebtained by dissolving it in 0.5 M HCl. The mixed inhibitor solu-ions (ODD–KX) were prepared by adding specified amount of ARX to ODD–HCl solution.

.1.2. Weight loss methodIn the weight loss experiment, twelve beakers containing 0.5 M

Cl solution were placed in the thermostated bath maintained at0 ± 0.1 ◦C. A3 mild steel specimens in triplicate were suspended inhe beakers. All the aggressive acid solutions were open to air. After4 h, the specimens were taken out, washed, dried and weighedccurately.

.1.3. Potentiodynamic polarization methodPolarization curve was measured by potentiodynamic tech-

ique. A cell was filled with 250 ml of the test solution and aonventional three-electrode cell was used for electrochemical

easurements. A platinum was used as the auxiliary electrode, aercurous sulfate electrode was used as the reference electrode,

nd A3 steel sheet with 1.00 cm2 was used as the working electrode.rior to each electrochemical measurement, the working electrode

a Lx, Ly and Lz represent the length, width and height of the model constructed,respectively.

was immersed in HCl solution for 1 h to establish a steady opencircuit potential (OCP). All potentials are reported versus that ofthe mercurous sulfate electrode. The potentiodynamic polarizationcurves were carried out in the potential range of −250 to 1200 mV(vs. Hg/Hg2SO4) at a sweep rate of 0.166 mV s−1. The corrosionpotential (Ecorr) and corrosion current density (Icorr) were extractedusing the Tafel extrapolation method by means of a PrincetonApplied Research 352 SoftCorrTM III corrosion measurement sys-tem connected to a computer.

2.1.4. Scanning electron microscopy (SEM)Immersion corrosion analysis of A3 steel samples in 0.5 M HCl

solution with KX (1.0 g l−1 for KCl, KBr and KI, respectively) andODD–KX mixtures (both 1.0 g l−1) at 50 ◦C were performed usingSEM. Immediately after the corrosion tests, the samples were sub-jected to SEM studies to know the surface conditions. S-4800 –the ice emission scanning electron microscope was used for theexperiments.

2.2. Molecular dynamics simulation

In order to study the synergistic effect between ODD and halideion in the same concentration by mean of the inhibition effect ofODD and halides on corrosive particles, the Amorphous Cell mod-ule and Discover module in commercial software package MaterialsStudio 4.4 developed by Accelrys Inc. were used. The AmorphousCell module allows constructing complex amorphous systems. Thefirst step is to build the amorphous systems. Diffusion model wasused to study the synergistic effect between the ODD and halide ionat the molecular scale. Six diffusion models were built by the Amor-phous Cell module [18–20] at an initial density of 1.0 g cm−3. Thelengths of the model and the compositions of the systems containedin each cell are summarized in Table 1. The initial diffusion mod-els of H3O+ in the three inhibitor membrane ODD–Cl−, ODD–Br−

and ODD–I− are shown in Fig. 2. The diffusion models of H2O weresimilar to those of H3O+, so they are not presented in this paper forsimplicity.

The discover module incorporates a broad spectrum ofmolecular mechanics and dynamics methodologies that havedemonstrated applicability to molecular design. The discovermolecular mechanics module allows optimizing a molecularstructure such that its energy is at a minimum by different method-ologies. The discover molecular dynamics module allows selectinga thermodynamic ensemble and the associated parameters, defin-ing simulation time, temperature and pressure and initiating adynamics calculation [21]. In the configuration optimization, thestructure of each system with 3D periodic boundary conditions wasminimized by a smart minimizer method, which switches from a

steepest-descent method to conjugated gradient method, and thenthe Newton method. Molecular dynamics simulations were carriedout for 200 ps to obtain the equilibrium status of systems under NPT(constant number of molecules, constant pressure, and constant

56 S. Hu et al. / Materials Chemistry and Physics 134 (2012) 54– 60

F b) OD( legend

tb

mawcat

fte(oo

3

3

(iccaf

v

wct

TCcl

ig. 2. Diffusion models of H3O+ in the three inhibitor membranes (a) ODD–Cl−; (red), C (gray), N (blue)). (For interpretation of the references to color in this figure

emperature) ensemble at 323 K. A pressure was 0.1 MPa controlledy means of Berendsen Barostat method [22].

After that, the systems with the calculated densities were sub-itted to a 1000 ps MD run under the NVT ensemble. Van der Waals

nd Coulomb interactions were calculated by atom based methodith a cutoff radius of 15.0 A. The working temperature was 323 K

ontrolled by means of the Andersen thermostat method [23] with collision ratio of 1.0. In the process of MD simulation, the trajec-ories would be saved each 1000 fs for the subsequent analysis.

All the MD simulations were performed under COMPASS [24]orce field, which was parameterized to predict various proper-ies (molecular structures, vibrational frequencies, conformationnergies, etc.) for molecules in isolation and in condensed phasesequations of state, cohesive energy density, etc.). The combinationf parameters for organics and inorganics opens up the possibilityf future study of interfacial and mixed systems.

. Results and discussion

.1. Weight loss

The calculated values of corrosion rate (v), inhibition efficiencyIE) and degree of surface coverage (�) for the A3 steel corrosionn 0.5 M HCl solution in the absence and presence of differentoncentrations of corrosion inhibitor (ODD), halides, and ODD inombination with KX at 50 ◦C from the weight loss measurementre shown in Table 2. The value of corrosion rate was calculatedrom the following equation [25,26]:

= (m1 − m2)S × t

(1)

here, m1 and m2 are the masses of the specimen before and afterorrosion, respectively. S is the total area of the specimen and t ishe corrosion time.

able 2alculated values of corrosion rate, inhibition efficiency (IE) and degree of surfaceoverage (�) for A3 steel in 0.5 M HCl solution for the different system from weightoss measurements.

System (g l−1) Corrosion rate (g m−2 h−1) IE (%) �

Blank 11.530 – –0.1 ODD 0.314 97.195 0.9720.5 ODD 0.309 97.244 0.9721.0 ODD 0.302 97.303 0.9732.0 ODD 0.295 97.365 0.9743.0 ODD 0.295 97.369 0.9741.0 KCl 8.088 27.794 0.2781.0 KBr 7.887 29.583 0.2961.0 KI 1.289 88.492 0.8851.0 ODD + 1.0 KCl 0.289 97.418 0.9741.0 ODD + 1.0 KBr 0.271 97.583 0.9761.0 ODD + 1.0 KI 0.247 97.794 0.978

D–Br−; (c) ODD–I− (Atoms (color): Cl (green), Br (yellow), I (brown), H (white), O, the reader is referred to the web version of the article.)

The inhibition efficiency was obtained by the following equation[27,28]:

IE = v0 − vv0

× 100% (2)

The degree of surface coverage, �, is given by the equation [29]:(3)� = v0−v

v0where, v0 and v are the corrosion rates of the spec-

imens in 0.5 M HCl solution without and with the addition of thecorrosion inhibitor, respectively.

The corrosion rate in the presence of ODD(0.295–0.314 g m−2 h−1) fell significantly below that in theabsence of ODD (11.530 g m−2 h−1). The degree of surface coverageand the inhibition efficiency increased with the increasing corro-sion inhibitor concentration up to 3.0 g l−1. It was attributed to theadsorption of the corrosion inhibitor onto the iron surface whichformed a compact membrane to keep away from the corrosivemedium.

In the presence of halides only, the corrosion rates were inthe range of 1.289 g m−2 h−1 to 8.088 g m−2 h−1. So, the halidesalso decreased the corrosion rate comparing with the blank(11.530 g m−2 h−1). Furthermore, the inhibition efficiency anddegree of surface coverage were found to be in the orderCl− < Br− < I−. This conclusion agreed with the findings of previ-ous reports [12,26,29], which indicated that the radii (Cl− < Br− < I−)and electronegativity (Cl− > Br− > I−) of the halide ions could havean important role on the adsorption.

Comparing with the above two situations, further reduction inthe corrosion rate (0.247–0.289 g m−2 h−1) was observed in thepresence of ODD and KX. The inhibition efficiencies and degreeof surface coverage were larger than those of single ODD and KX,respectively. It revealed that there was a synergistic effect betweenODD and KX. The synergistic effect may result from the follow-ing two points. First, ODD was present in the form of cation inthe acid solution and the halide ions facilitated the adsorptionof ODD on the metal surface by the electrostatic forces. Second,part of the halide ions which transferred into the interspace ofthe inhibitor membrane, increased the compactness of the mem-brane and the degree of surface coverage. Moreover, the inhibitionefficiency and degree of surface coverage increased in the orderODD–Cl− < ODD–Br− < ODD–I−. It was attributed to the increasingradius from Cl− to I−, which resulted in the increasing compactnessof the inhibitor membrane from ODD–Cl− to ODD–I−.

3.2. Potentiodynamic polarization

3.2.1. Corrosion inhibition by ODDThe potentiodynamic polarization curves of A3 steel in 0.5 M

HCl solution in the absence and presence of different concentra-

tions of ODD are shown in Fig. 3. The values of the electrochemicalparameters obtained from the curves are depicted in Table 3, i.e.,corrosion potential (Ecorr), corrosion current density (Icorr), cathodicand anodic Tafel slopes (ˇc and ˇa), and inhibition efficiency for the

S. Hu et al. / Materials Chemistry and Physics 134 (2012) 54– 60 57

Table 3Electrochemical parameters for the corrosion of A3 steel in 0.5 M HCl solution in the absence and presence of different concentrations of ODD.

ODD conc. (g l−1) Ecorr vs. Hg/Hg2SO4 (mV) icorr (�A cm−2) ˇc (mV dec−1) ˇa (mV dec−1) IE (%)

Blank −519.2 725.8 −211.7 127.4 –0.1 −486.9 72.4 −675.5 105.1 90.00.5 −486.9 72.2 −487.6 98.8 90.01.0 −475.0 62.8 −433.0 98.5 91.42.0 −475.2 46.9 −350.1 87.1 93.53.0 −474.8 32.9 −323.7 83.5 95.5

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KX, and the synergistic effect increased in the order ODD–Cl−<ODD–Br− < ODD–I−.

The halide ions adsorbed on the metal surface facilitated theadsorption of corrosion inhibitor by means of the electrostatic

ig. 3. Potentiodynamic polarization curves for A3 steel in 0.5 M HCl in the absencend presence of different concentrations of ODD.

ifferent concentrations of ODD. The inhibition efficiency in eachase is calculated according to Eq. (4) [30].

E = I0corr − Icorr

I0corr

× 100% (4)

here I0corr and Icorr are the corrosion current density values in the

bsence and presence of ODD, respectively.In Table 3, the current density decreased and the inhibition effi-

iencies increased with the increasing concentrations of ODD. Thencrease in the concentration of ODD shifted Ecorr to the positivealues. Moreover, there was a remarkable change in the values ofathodic Tafel slopes (ˇc) and no pronounced change in the val-es of anodic Tafel slopes (ˇa). It revealed that the addition ofDD affected the mechanism involved in the cathodic process. So,

he results indicated that ODD acted predominantly as cathodicnhibitor [31].

.2.2. Effect of KX additivesThe polarization curves for A3 steel in 0.5 M HCl solution in the

bsence and presence of KX (X = Cl−, Br−, and I−) at 50 ◦C werehown in Fig. 4. The polarization parameters deduced from the

urves are listed in Table 4. The addition of the halide ions shiftedcorr positively and reduced the current density compared with thelank. It was attributed to the adsorption of the halide ions on theurface of the metal. Moreover, the inhibition efficiency increased

able 4olarization parameters for A3 steel in 0.5 M HCl solution with 1.0 g l−1 KX and.0 g l−1 ODD + 1.0 g l−1 KX.

System Ecorr vs. Hg/Hg2SO4 (mV) icorr (�A cm−2) IE (%)

Blank −519.2 725.8 –KCl −493.0 590.6 18.6KBr −501.2 481.2 33.7KI −476.4 124.3 82.9ODD + KCl −479.0 58.6 91.9ODD + KBr −500.7 57.5 92.1ODD + KI −489.4 44.2 93.9

Fig. 4. Polarization curves for A3 steel in 0.5 M HCl solution in the absence andpresence of KX at 50 ◦C.

in the order Cl− < Br− < I−. This was consistent with the previousobservation [32]. The larger the ion radius was, the more easily thehalide ion lost the electron and coordinated with the iron.

The polarization curves for A3 steel in 0.5 M HCl solutionwith the different halide ions in the presence of 1.0 g l−1 ODDwere shown in Fig. 5. The polarization parameters deducedfrom the curves are listed in Table 4. When only KX wereadded in the solution, the corrosion was not inhibited effectively.When both ODD and KX were present, the lower corrosion cur-rent density were observed (ODD + Cl−: 58.6 �A cm−2; ODD + Br−:57.5 �A cm−2; ODD + I−: 44.2 �A cm−2, respectively). In Table 3,when only 1.0 g l−1 ODD was added in the solution, the cor-rosion current density were relatively high (62.8 �A cm−2). Itindicated that the synergistic effect appeared between ODD and

Fig. 5. Effect of different halide ions on the polarization curves of A3 steel in 0.5 MHCl in the presence of ODD.

58 S. Hu et al. / Materials Chemistry and Physics 134 (2012) 54– 60

F ion in6

iiotrr

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OgostfiimbwaO

ig. 6. SEM image of surface of mild steel after immersion for 24 h in 0.5 M HCl solut00× (a) KCl; (b) KBr; (c) KI; (a′) ODD–Cl−; (b′) ODD–Br−; (c′) ODD–I− .

nteraction which led to the high inhibition efficiency. The increas-ng ionic radius from Cl− to I− suggested that the compactnessf the inhibitor membrane and the synergistic effect increased inhe order ODD–Cl− < ODD–Br− < ODD–I−. The phenomena had beeneported in the literatures [12,26,29] and accorded well with theesults of weight loss method.

.2.3. Scanning electron microscopyIn order to evaluate the efficacy of KX (X = Cl−, Br−, and I−) and

DD–X, a superficial analysis was carried out. The SEM micro-raphs of the mild steel in 0.5 M HCl solution in the presencef 1.0 g l−1 KX (X = Cl−, Br−, and I−) and ODD–X at 50 ◦C werehown in Fig. 6. There is pitting corrosion on the surface of allhe specimens. It is attributed to the halide ions, which were con-rmed by Yazdanfar et al. [33]. Very minimum corrosion occurs

n the presence of ODD–X and the smoothness of the speci-ens increased in the order ODD–Cl− < ODD–Br− < ODD–I−. It can

e concluded from Fig. 6 that corrosion was inhibited stronglyhen the mixture of ODD and halide ions were present in the

cid medium and hence synergistic effect increased in the orderDD–Cl− < ODD–Br− < ODD–I−.

the presence of 1.0 g l−1 KX (X = Cl− , Br− , and I−) and ODD–X at 50 ◦C. Magnification

3.3. Molecular dynamics simulation

3.3.1. Fractional free volume (FFV)The free volume of the membrane referred to the volume of

enough large cavities, in which the probe particle could diffusefreely. However, it did not contain those small cavities which wereinaccessible for the probe particle [19,34]. That was because thesmall cavities did not make considerable contribution to trans-port property of the membrane [35]. The FFV was defined by thefollowing equation:

FFV = Vf

Vf + V0× 100% (5)

where Vf is the free volume, and V0 is the volume occupied by thecorrosion inhibitor in the membrane. To obtain the correspondingFFV in each inhibitor membrane, H3O+ and H2O were selected asprobe particles in the system. The free volume distributions of thethree inhibitor membranes probed by H2O are shown in Fig. 7. The

free volume distributions of the three inhibitor membranes probedby H3O+ were similar to those probed by H2O, so they were notpresented in this paper for simplicity. The FFV values of the threeinhibitor membranes are listed in Table 5.

S. Hu et al. / Materials Chemistry and Physics 134 (2012) 54– 60 59

Fig. 7. Free volume distribution of the three inhibitor membranes probed by H2O (a) ODD–Cl−; (b) ODD–Br−; (c) ODD–I− .

Fig. 8. MSD plots of H3O+ and H2O in the three inhibitor membrane

Table 5FFV values of the three inhibitor membranes ODD–Cl− , ODD–Br− and ODD–I−

probed by H3O+ and H2O.

Probe particle FFV (%)

ODD–Cl− ODD–Br− ODD–I−

H3O+ 12.756 8.650 8.319

tFtswIbirtmti

aHH

3

bb

M

membrane, the diffusion coefficient was calculated.In the three inhibitor membranes, the diffusion coeffi-

cients of both corrosive particles exhibited the same trend:

Table 6Diffusion coefficients of H3O+ and H2O in the water and three inhibitor membranes.

Membrane Diffusion coefficient (×10−9 m2 s−1)

H3O+ H2O

Water 0.8310a 2.3920b

ODD–Cl− 0.0095 0.0047ODD–Br− 0.0042 0.0028ODD–I− 0.0008 0.0021

H2O 11.860 7.835 7.501

For the same corrosive particle, the FFV values in thehree inhibitor membranes were all in decreasing order:FV(ODD–Cl−) > FFV(ODD–Br−) > FFV(ODD–I−). It was indicatedhat the number of cavities which were accessible for the corro-ive particle decreased in the order ODD–Cl− > ODD–Br− > ODD–I−,hich was attributed to the increasing ionic radius from Cl− to I−.

n addition, a small FFV contributed to the increased interactionsetween the corrosion inhibitor and the halide ions. The increased

nteractions tightened the packing of the inhibitor membranes andeduced the free volume in the membrane matrix [36]. Therefore,hey had a ability to protect the iron surface against the corrosive

edium. The inhibition efficiency of the inhibitor membrane andhe synergistic effect between ODD and three halide ions increasedn the following order: ODD–Cl− < ODD–Br− < ODD–I−.

In the same corrosion inhibitor membrane, the FFV values werell in the order: FFV(H3O+) > FFV(H2O). It was because the radius of3O+ was smaller than that of H2O [37]. So, the accessible cavity of3O+ was larger than that of H2O.

.3.2. Diffusion coefficient of corrosive particleThe diffusion coefficient of the corrosive particle in the mem-

rane can be calculated from the mean square displacement (MSD)y the Einstein diffusion equation [38,39].

SD =⟨

[Ri(t) − Ri(0)]2⟩ (6)

s ODD–Cl− , ODD–Br− and ODD–I− at 323 K: (a) H3O+; (b) H2O.

D = 16Na

limt→∞

d

dt

Na∑

i=1

⟨[Ri(t) − Ri(0)]2⟩ (7)

where t is time, Ri(t) is the position vector of a molecule at time t, Nis the amount of diffusing molecules. The limiting slope of MSD asa function of time can be used to evaluate the diffusion coefficientof a molecule undergoing random Brownian motion in the threedimensions.

It took about 500 ps for the system to reach a stable equilibriumstate. The maximum fluctuations of energy and temperature were0.2% and 1.0%, respectively. The MSD curves of H3O+ and H2O in thethree inhibitor membranes at 323 K are shown in Fig. 8. The anoma-lous diffusion [40,41] took place between 900 ps and 1000 ps. Thusthe effective diffusion coefficients calculated from the MSD slopesover 500–900 ps by means of Eq. (7) are shown in Table 6. Thediffusion coefficients of H3O+ and H2O in the three inhibitor mem-branes sharply decreased comparing with those in water withoutany corrosion inhibitors. It indicated that there was a high abilityfor the three inhibitors to inhibit the diffusion of the two corro-sive particles. In order to study the inhibition effect of the inhibitor

a Taken from [42].b Taken from [37]. In this reference, the experimental value of the diffusion coef-

ficient of water was 2.34 × 10−5 cm2 s−1.

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0 S. Hu et al. / Materials Chemi

(ODD–Cl−) > D(ODD–Br−) > D(ODD–I−). The higher the diffusionoefficient was, the lower the ability to protect the iron surfacegainst the corrosive medium would be, which would cause theower inhibition efficiency. Accordingly, the diffusion coefficient ofhe corrosive particles became inverse proportion with the inhibi-ion efficiency. The synergistic effect between the three halide ionsnd ODD increased in the order: ODD–Cl− < ODD–Br− < ODD–I−.t was in accordance with the experimental result. Further com-arison found that D(H3O+) was higher than D(H2O), which wasttributed to the stronger Coulomb interaction between H3O+ andhe membrane than that between H2O and the membrane.

Based on these results, the FFV of inhibitor membrane and diffu-ion coefficient of corrosive particle appeared capable of evaluatinghe synergistic effect between corrosion inhibitor and the addictiven the corrosion inhibition of mild steel in 0.5 M HCl solution at0 ◦C.

. Conclusions

. ODD was an effective imidazoline inhibitor to A3 steel in HClsolution. The inhibition efficiency increased with the increas-ing concentration of ODD. Moreover, the halides (KCl, KBr andKI) decreased the corrosion rate, and the inhibition efficiencyincreased in the order Cl− < Br− < I−, which indicated that theradii (Cl− < Br− < I−) and electronegativity (Cl− > Br− > I−) playeda significant role in the adsorption process.

. Synergistic effect was observed between ODD and the halides.There were two reasons. One was that the halides facilitatedthe adsorption of ODD on the metal surface by the electrostaticforces. The other was that the halides increased the compactnessof the membrane and the degree of surface coverage. With theincreasing radii of the ions from Cl− to I−, the synergistic effectincreased in the following order ODD–Cl− < ODD–Br− < ODD–I−.The synergistic effect obtained from the weight loss, potentiody-namic polarization and SEM were in reasonably good agreementwith each other.

. The FFV of the three inhibitor membranes and the diffu-sion coefficients of corrosive particles decreased in the orderODD–Cl− > ODD–Br− > ODD–I−. So, the compactness of the mem-branes increased in the order ODD–Cl− to ODD–I−. It wasthe main reason that the synergistic effect increased in theorder ODD–Cl− < ODD–Br− < ODD–I−. Moreover, the moleculardynamics simulation analysis was in accordance with the exper-imental results.

cknowledgments

This work was funded by Corrosion Inhibitor Research Programor Puguang Gas Filed of Sinopec (No. 309003), CNPC Innovationoundation (No. 2011D-5006-0202) and Postgraduate’s Innovationoundation (No. S10-30).

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d Physics 134 (2012) 54– 60

References

[1] I. Ahamad, R. Prasad, M.A. Quraishi, Corros. Sci. 52 (2010) 1472–1481.[2] G.E. Badr, Corros. Sci. 51 (2009) 2529–2536.[3] M.A. Hegazy, M.F. Zaky, Corros. Sci. 52 (2010) 1333–1341.[4] E.E. Oguzie, S.G. Wang, Y. Li, F.H. Wang, J. Phys. Chem. C 113 (2009)

8420–8429.[5] Z.H. Tao, S.T. Zhang, W.H. Li, B.R. Hou, Corros. Sci. 51 (2009) 2588–2595.[6] M.K. Awad, M.R. Mustafa, M.M. Abo Elnga, J. Mol. Struct. (Theochem) 959 (2010)

66–74.[7] B. Gómez, N.V. Likhanova, M.A. Domínguez-Aguilar, O. Olivares, J.M. Hallen,

J.M. Martínez-Magadán, J. Phys. Chem. A 109 (2005) 8950–8957.[8] G. Gece, Corros. Sci. 50 (2008) 2981–2992.[9] K.F. Khaled, Electrochim. Acta 54 (2009) 4345–4352.10] X.H. Li, S.D. Deng, H. Fu, Corros. Sci. 53 (2010) 302–309.11] M. Hosseini, S.F.L. Mertens, M.R. Arshadi, Corros. Sci. 45 (2003) 1473–1489.12] C. Jeyaprabha, S. Sathiyanarayanan, G. Venkatachari, Electrochim. Acta 51

(2006) 4080–4088.13] H. Tavakoli, T. Shahrabi, M.G. Hosseini, Mater. Chem. Phys. 109 (2008)

281–286.14] M.K. Pavithra, T.V. Venkatesha, K. Vathsala, K.O. Nayana, Corros. Sci. 52 (2010)

3811–3819.15] H. Gao, Q. Li, Y. Dai, F. Luo, H.X. Zhang, Corros. Sci. 52 (2010) 1603–1609.16] X.C. Yan, D.M. Luo, Interface Chemistry, Chemical Industry Press, Beijing, 2005,

p. 278.17] L. Garrido, J. Pozuelo, M. López-González, J.H. Fang, E. Riande, Macromolecules

42 (2009) 6572–6580.18] K.S. Chang, Y.H. Huang, K.R. Lee, K.L. Tung, J. Membr. Sci. 354 (2010)

93–100.19] K.S. Chang, C.C. Tung, K.S. Wang, K.L. Tung, J. Phys. Chem. B 113 (2009)

9821–9830.20] C. Nagel, K. Günther-Schade, D. Fritsch, T. Strunskus, F. Faupel, Macromolecules

35 (2002) 2071–2077.21] K.F. Khaled, M.A. Amin, Corros. Sci. 51 (2009) 1964–1975.22] H.J.C. Berendsen, J.P.M. Postma, W.F. van Gunsteren, A. DiNola, J.R. Haak, J.

Chem. Phys. 81 (1984) 3684–3690.23] H.C. Andersen, J. Chem. Phys. 72 (1980) 2384–2393.24] H. Sun, J. Phys. Chem. B 102 (1998) 7338–7364.25] G.N. Mu, X.M. Li, G.H. Liu, Corros. Sci. 47 (2005) 1932–1952.26] S.A. Umoren, O. Ogbobe, I.O. Igwe, E.E. Ebenso, Corros. Sci. 50 (2008) 1998–

2006.27] A.S. Fouda, H.A. Mostafa, F. El-Taib, G.Y. Elewady, Corros. Sci. 47 (2005)

1988–2004.28] X.M. Li, L.B. Tang, L. Li, G.N. Mu, G.H. Liu, Corros. Sci. 48 (2006) 308–321.29] E.E. Ebenso, Mater. Chem. Phys. 79 (2003) 58–70.30] P.C. Okafor, Y.G. Zheng, Corros. Sci. 51 (2009) 850–859.31] S.S. Abd El Rehim, H.H. Hassan, M.A. Amin, Mater. Chem. Phys. 78 (2003)

337–348.32] Y. Feng, K.S. Siow, W.K. Teo, A.K. Hsieh, Corros. Sci. 41 (1999) 829–852.33] K. Yazdanfar, X. Zhang, P.G. Keech, D.W. Shoesmith, J.C. Wren, Corros. Sci. 52

(2010) 1297–1304.34] J.H. Zhou, R.X. Zhu, J.M. Zhou, M.B. Chen, Polymer 47 (2006) 5206–5212.35] J. Kruse, J. Kanzow, K. Rätzke, F. Faupel, M. Heuchel, J. Frahn, D. Hofmann,

Macromolecules 38 (2005) 9638–9643.36] K.L. Tung, K.T. Lu, J. Membr. Sci. 272 (2006) 37–49.37] H. Yang, Y. Liu, H. Zhang, Z.S. Li, Polymer 47 (2006) 7607–7610.38] R. Babarao, J.W. Jiang, Langmuir 24 (2008) 5474–5484.39] O.E. Haas, J.M. Simon, S. Kjelstrup, J. Phys. Chem. C 113 (2009) 20281–

20289.40] D. Hofmann, L. Fritz, J. Ulbrich, D. Paul, Comput. Theory Polym. Sci. 10 (2000)

41] F. Müller-Plathe, S.C. Rogers, W.F. van Gunsteren, Chem. Phys. Lett. 199 (1992)237–243.

42] L.F. Liu, J.X. Liu, J. Zhang, L. You, L.J. Yu, G.M. Qiao, Chem. J. Chin. Univ. 31 (2010)537–541.