The inhibiting effect of molybdate, chromate, and tungstate salts on the corrosion of steel used in sanitation plants was investigated by potentiodynamic polarization, electrochemical impedance spectroscopy (EIS), and electrochemical frequency modulation (EFM) techniques. The sulfide polluted salt water was simulated by a 3.5 % NaCl and 16 ppm Na2S solution. The results revealed that these inorganic anions are very good inhibitors. Potentiodynamic polarization curves indicated an anodic-type inhibition. The increased concentration of inorganic compounds increases the inhibition; at 250 ppm concentration the inhibition efficiency reached to 95 %, 91.6 %, and 87.5 % for MoO42-, CrO42-, and WO42-, respectively. The adsorption of the inhibitors on the metal surface basically obeys the Langmuir adsorption isotherm equation. Results of EIS measurements suggested that the dissolution of the steel occurs under activation control, and a passive film is probably formed on the metal surface. The electrochemical kinetic parameters calculated from EFM spectra confirm the polarization data.
The use of inhibitors is one of the most practical method for protection against corrosion. Inhibitors are often easy to apply and offer the advantage of in-situ application without causing any significant disruption to the process. However, there are several considerations when choosing an inhibitor: (i) cost of the inhibitor can be sometimes very high when the reagent involved is expensive or when the amount needed is huge, (ii) toxicity of the inhibitor can cause jeopardizing effects on human beings, and other living species, (iii) availability of the inhibitor will determine the selection of it and if the availability is low, the inhibitor becomes often expensive, and (iv) the inhibitor should be environmental friendly. The cost of the inorganic inhibitors is low, but most of them are toxic such as chromate, molybdate, nitrite, arsenate compounds. Molybdate and tungstate salts were reported as corrosion inhibitors since 1939 [1, 2]. Robertson  first studied the mechanism of the inhibitive effect of molybdate and tungstate on the corrosion of carbon steel in neutral solution. Pryor and Cohen  extended Robertson’s work to study the inhibitive mechanism of molybdate. Because molybdate compounds may be less poisonous or non-poisonous , molybdate-based treatment for open recirculating cooling systems has become popular since the early 1980s as an alternative to the toxic and ecologically unacceptable chromate-based inhibitors [6,7]. Obviously, most molybdate-based inhibitors were used in neutral or quasi-neutral media [8, 9] and the effect of inhibition was significant when the concentration of molybdate was very high (thousands of mg/L) . The corrosion inhibition of tungstate was more explored, but most of the studies were in neutral or quasi-neutral solutions, too . The mechanism of inhibitive action of MoO42- has received the attention of researchers  who take into consideration the interaction of the MoO42- anions with the charged metal surface.
The aim of the present work is to investigate the effect of some inorganic anions, as corrosion inhibitors for the steel, namely molybdate, chromate, and tungstate. The experiments were performed in a 3.5 % NaCl and 16 ppm Na2S solution which simulate sulfide polluted salt water.
2.1. Material composition of the sample
The steel material used is steel which was provided from a bridge in a Talkha sanitation plant, Egypt. The samples have the following chemical composition (wt %): 0.20% C, 0.005% Si, 0.248% Mn, 1.832% Zn, and the remainder is iron.
2.2. Aggressive solutions
The aggressive solution of 3.5% NaCl and 16 ppm Na2S was prepared by dissolving the required amount of salts in bidistilled water. All chemicals were analytical-grade reagents. The experiments were carried out under non-stirred and naturally aerated conditions.
Na2MoO4.2H2O, Na2CrO4.2H2O, and Na2WO4.2H2O high-grade reagents were used as inhibitors. The corresponding solutions having 50-250 ppm inhibitor were prepared by dissolving 5-25 mg of each salt in 100 mL of double distilled water.
2.4. Electrochemical measurements
For electrochemical measurements, the steel cylindrical rods were welded with Cu wire for electrical connection and mounted into glass tubes of appropriate diameter using Araldite to offer an active surface of 1 cm2 geometric area exposed to the test solution. Prior to each experiment, the surface was first abraded with emery paper up 1200 grit size, washed with bi-distilled water, degreased with absolute ethanol and then dried. A conventional electrochemical cell of capacity 100 mL was used; it contains three compartments for working electrode, a platinum foil as counter electrode and saturated calomel electrode (SCE) as reference electrode. The measurements were carried out in 3.5% NaCl with 16 ppm Na2S solution in the presence of various concentrations of the investigated compounds, as environmentally-friendly corrosion inhibitors. For each run, a freshly prepared solution as well as a cleaned set of electrodes were used. Each run was carried out in aerated stagnant solutions at the required temperature (25±1oC), using a water thermostat.
The potentiodynamic polarization curves were recorded at a scan rate of 1 mVs-1 starting from -1.7 V up to -0.1 V (SCE). Before polarization, the open circuit potential of the working electrode was measured as a function of time during 30 min, the time necessary to reach a quasi-stationary value. Impedance measurements were carried out using AC signals of amplitude 5 mV peak to peak at the open-circuit potential in the frequency range 100 kHz and 0.2 Hz. In electrochemical frequency modulation (EFM) measurements two sine excitation waves (2 and 5 Hz frequencies) were applied to the cell simultaneously; in the intermodulation spectra the current response contained supplementary harmonic components. The causality factors (CF-2 and CF-3) were used to validate the data.
All electrochemical measurements were performed using a potentiostat/galvanostat/ZRA analyzer Gamry PCI300/4) (version 3.20). A personal computer with DC105 software for potentiodynamic polarization, EIS300 software for EIS, and EFM140 software for EFM measurements, respectively, as well as Echem Analyst 5.21 were used for data fitting and calculating.
3. Results and Discussion
3.1. Potentiodynamic polarization measurements
Figures 1-3 show the potentiodynamic polarization curves of steel in sulfide polluted salt water without and with different concentrations of inorganic anions at 25oC. The obtained electrochemical parameters: cathodic and anodic Tafel slopes (βc and βa), corrosion potential (Ecorr), corrosion current density (icorr) and corrosion rate (C.R.) are listed in Tables 1-3. The degree of surface coverage, θ, and the inhibition efficiency, IE (%), were calculated by equation (1):
Equation 1: IE = θ×100 = [1 – (icorr(inh)/icorr(free)]×100
where icorr(free) and icorr(inh) are the corrosion current densities by working with uninhibiting and inhibiting solutions, respectively. Addition of inorganic anions reduces the steel corrosion, meaning that the desorption rate of the inhibitor is lower than its adsorption rate . So, it could be concluded that these anions act as anodic inhibitors (βc< βa) for steel in 3.5 % NaCl + Na2S medium by adsorption on the anodic sites of the steel. This kind of inhibitory action was found in different researches [13, 14]. The obtained results of inhibition efficiency listed in Tables 1-3 show that molybdate, chromate, and tungstate are efficient inhibitors in 3.5 % NaCl + Na2S medium. Due to the oxidizing power of molybdate, tungstate and chromate, where the latter is the most oxidizing one, they have the ability for oxidizing ferrous ions, even in acid solution . In addition, molybdate, chromate and tungstate form insoluble complex with the oxidized metal ion (Fe2+). Qualitative evidence indicates that the effects are closely associated with adsorption of the inhibitor ions at the metal interface and this determines inhibitor efficiency rather than homogeneous chemical properties, such as oxidation ability. The singly charged Cl– ions, having a low sphere of hydration, move into the metal / electrolyte interface displacing the inhibitor ions and, in the case of steel, the formed soluble complex accelerates the corrosion; the effect may be counteracted by raising the inhibitor concentration. The adsorption characteristics depend on the competing factors of ion-dipole interaction in the water phase and the solubility of the complex formed by the metal ions at the surface, as well as the chemical nature of inhibitor ions. The solubility constants for compounds of the type FeWO4 and FeMoO4 are unknown, but in general all molybdates and tungstates are classed as insoluble compounds. According to the results, the inhibition efficiency of the studied anions can be arranged in the following order:
Na2MoO4 > Na2CrO4 > Na2WO4.
3.2. Adsorption isotherms
The extent of corrosion inhibition depends on the surface conditions and the mode of adsorption of the inhibitors . One may made the assumption that the corrosion of the covered parts of the surface is equal to zero and that corrosion takes place only on the uncovered parts of the surface.
Lorenz and Mansfeld  classified the modes of inhibition effect of corrosion inhibitors into three categories: (i) the geometric blocking effect of adsorbed inhibitive species on the metal surface, (ii) the effect of blocking the active sites on the metal surface by adsorbed inhibitive species, and (iii) the electrocatalytic effect of either the inhibitor or its reaction products. Adsorption isotherms give information about the interaction of inhibitor anions with steel. In this part of the study, the obtained values of surface coverage θ (see Tables 1-3) were fitted to different adsorption isotherms including Langmuir, Temkin, Frumkin, Flory-Huggins, Friendlich and Henry isotherm. The best fit was obtained by Langmuir isotherm.
The plotting of C/θ against C is given in Figure 4, where straight-line relationships with regression coefficient higher than 0.99 suggest that the adsorption on steel of these studied anions follows perfectly the Langmuir adsorption isotherm:
Equation 2: C/θ = 1/Kads+ C
C is the concentration of inhibitor and Kads is the adsorption equilibrium constant related to the standard free energy of adsorption, ∆G°ads, as following :
Equation 3: Kads = 1/ 55.5 exp (-ΔGºads / RT)
The Langmuir isotherm postulates a monolayer adsorption, hence no interaction between the adsorbate species and the metal surface, and in such circumstances the slope of straight lines should be unity. The deviation of the slope from unity as observed in this study could be interpreted as existence of the interactions between adsorbate species and the metal surface, as well as changes in adsorption heat with increasing surface coverage , factors that were ignored in the derivation of Langmuir isotherm.
Values of the equilibrium constant (Kads) were obtained for the studied anions, Table 4. The results confirm that the adsorption capability of the investigated anions depends on the formation of insoluble complex of these anions precipitated on the metal surface in forms of FeMoO4, FeCrO4 or FeWO4. The increasing in Kads value reflects the increasing adsorption ability.
The standard free energy of adsorption ∆Gºads for each inhibitor was calculated and values were also listed in Table 4. The relatively high negative free energy values may indicate a relatively strong and spontaneous adsorption on the metal surface of the investigated compounds, which explains their high corrosion inhibition efficiency. A value of -40 kJ mol-1 is usually adopted as a threshold value between chemical and physical adsorption . The calculated values of ∆Gºads for the investigated compounds are between -27.9 and -29.5 kJ mol-1, which means that the adsorption of these inhibitors is physically, through electrostatic interaction between these anions and the metal surface. It is also observed that the calculated values of Kads and ΔGoads may be arranged in the following order: Na2MoO4 > Na2CrO4 > Na2WO4. This is in good agreement with the order of %IE of these anions.
3.3. Electrochemical Impedance Spectroscopy (EIS)
The corrosion inhibition processes were also investigated by EIS method at 25oC. Figures 5-7 show the Nyquist plots for corrosion of steel in solution with 3.5% NaCl and 16 ppm Na2S in the absence and presence of different concentrations of investigated compounds. All the impedance spectra were measured at the corresponding open-circuit potentials. It is apparent that Nyquist plots show a single capacitive loop, in both uninhibiting and inhibiting solutions. The data with inhibitor describe a semicircle suggesting that the corrosion process is under charge-transfer control. The depressed semicircle is associated with the roughness of electrode surface and indicates a better quality of the inhibitor anion-containing film. It is obvious that causal relationship exists between adsorption and inhibition. According to Ramachandran , the film formed in the presence of inorganic inhibitors acts as a protective barrier against aggressive ions from the bulk solution. Thus, the corrosion processes in the presence of investigated inhibitors may be also considered under diffusion and charge transfer mixed mechanism.
The EIS data were simulated using equivalent electric circuits as shown in Figure 8, where RS represents the solution (electrolyte) ohmic resistance, Cdl – the double layer capacitance and Rct – the charge transfer resistance (polarization resistance).
The capacity of double layer Cdl can be calculated from the following equation:
where fmax is the frequency at which the imaginary component of the impedance is maximal. The parameters obtained from impedance measurements with each inhibitor are given in Tables 5-7. It can see from these Tables that the values of charge transfer resistance increase with inhibitor concentration . In the case of impedance studies, IE (calculated using Rct values) increases with inhibitor concentration, too. Thus, the impedance study confirms the inhibiting character of inorganic anions illustrated above using potentiodynamic polarization method. It is also noted that the Cdl values tend to decrease when the concentration of these anions increases. This decrease in Cdl, which can result from a decrease in local dielectric constant and/or an increase in the thickness of the electrical double layer, suggests that the molecules of inhibitor have an inhibiting function by adsorption at the metal/solution interface .
The increase of Rct values and the decrease of Cdl values with inhibitor concentrations may be due to the gradual replacement of water molecules by the adsorption of the inhibitor molecules on the metal surface, thus decreasing the extent of corrosion process. It can be seen that the inhibition efficiency obtained by EIS method for the investigated anions is in the order:
Na2MoO4 > Na2CrO4 > Na2WO4.
3.4. Electrochemical Frequency Modulation (EFM)
EFM is a non-destructive corrosion measurement technique that can directly give values of corrosion current without prior knowledge of Tafel constants . The intermodulation spectra obtained from EFM measurements are presented in Figures 9-11 as confirmation of steel corrosion in 3.5% NaCl + 16 ppm Na2S solution containing different concentrations of Na2MoO4, Na2CrO4, and Na2WO4 at 25 °C. Each spectrum is a current response as a function of frequency. The two large peaks are the response to the 2 Hz and 5 Hz excitation frequencies. The calculated corrosion kinetic parameters (icorr, βa, βc, CF-2 and CF-3) for 3.5% NaCl + 16 ppm Na2S blank solution and with different concentrations of the investigated inhibitors at 25°C are given in Tables 8-10. From these Tables it is obvious that the corrosion current densities decrease by increasing the concentration of the anions and hence the inhibition efficiency increases. Also it is clear that the causality factors are very close to theoretical values (2 or 3, respectively), which according to EFM theory should guarantee the validity of Tafel slope and corrosion current densities. In addition, the values of causality factors indicate that the measured data are of good quality . The obtained results showed good agreement of inhibition efficiency obtained from the potentiodynamic polarization, EIS and EFM methods. The inhibition efficiency obtained by inorganic compounds may be certainly arranged in the order:
Na2MoO4 > Na2CrO4 > Na2WO4.
Sodium molybdate, chromate, and tungstate are good inorganic inhibitors to prevent steel corrosion in sulfide polluted salt water and may be used in sanitation plants.
Within 50-250 ppm concentration range of inhibitor the inhibition efficiency increases with anion concentration reaching maximal values of 95, 91.6 and 87.5 % for MoO42-, CrO42-, and WO42-, respectively, determined from potentiodynamic polarization curves. The inhibition is due to the adsorption of the inhibitor species and possible formation of complex molecules between Fe2+ and these anions. The adsorption on the metal surface obeys Langmuir adsorption isotherm.
Nyquist plots recorded as impedance spectra at open-circuit potential showed a single capacitive loop, in both uninhibiting and inhibiting solutions. The charge-transfer resistance increases and double layer capacitance decreases with respect to the blank solution when each inhibitor is added. Inhibition efficiencies obtained with EIS and EFM techniques are in good agreement with values obtained from polarization curves measurements.
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