Quantum Chemical Studies on the Corrosion Inhibition of Mild Steel by Piperidin-4-One Derivatives in 1 M H 3 PO 4

The corrosion inhibition properties of 2,6-diphenylpiperidin-4-one (DPP) (1A) and 2,6-diphenyldihydro-2H-thiopyran-4(3H)-one (DPDT) (1B) for mild steel in 1 M phosphoric acid were studied using weight loss, potentiodynamic polarization and electrochemical impedance spectroscopic techniques. The effect of temperature on the corrosion behavior of mild steel has been examined in the temperature range 303 328 K. The inhibition efficiency increases with increasing inhibitor concentration but decreases with increasing temperature. Potentiodynamic polarization studies indicated the mixed nature of inhibitors. The adsorption of the inhibitors on mild steel surface obeyed the Langmuir adsorption isotherms. The density functional theory (DFT) at the B3LYP/631G (d) basis set level was performed on 1A and 1B to investigate the correlation between molecular structure and the corresponding inhibition efficiency (%). The quantum chemical parameters such as EHOMO, ELUMO, the energy gap (E), hardness (η), softness (S), dipole moment (μ), electron affinity (A), ionization potential (I), the absolute electronegativity (χ), the fraction of electron transferred (N), electrophilicity index (ω), the back-donation (EBack-donation) and Mulliken population analysis have been calculated.


Introduction
The protection of metal surface against corrosion is an important industrial and scientific topic.Several ap-proaches have been suggested and implemented to protect metals from the effect of corrosion.Among these approaches the use of corrosion inhibitors is the most common.Corrosion inhibitors are substance that when adsorbed onto the metal-solution interface (through either physisorption or chemisorption) blocks the corrosive material (solution) from coming into contact with metal.A number of heterocyclic compounds containing nitrogen, oxygen and sulphur either in the aromatic or in long chain carbon system have been reported to be effective inhibitors [1].Recently, there has been increasing use of the density functional theory (DFT) methods as a theoretical tool in elucidating the mechanism of corrosion inhibition of heterocyclic organic compounds by several researchers [2]- [5].Quantum chemical methods have already proven to be very useful in determination of the molecular structure as well as elucidating the electronic structure and reactivity.

Experimental Methods
The mild steel sheet (C = 0.2%, Mn = 1.0%,P = 0.25%, S = 0.025% and Rest = Fe) was mechanically press-cut into specimens of dimension 2.5 cm × 1 cm × 0.05 cm and used for the weight loss measurements.For electrochemical methods, the working electrode is made of mild steel rod of same composition inserted in a Teflon tube with an exposed area of 0.1257 cm 2 .The specimens were polished with 320, 400 and 600 grit of emery sheets, washed with distilled water, degreased in acetone and dried in room temperature.The inhibitors used for the study were synthesized by the reported procedure [6].

Weight Loss Method
Gravimetric measurements were performed on mild steel coupons with the above mentioned dimensions in 1 M H 3 PO 4 solution with and without of inhibitors.Every sample was weighted by an electronic balance, and then placed in the acid solution (100 mL).The duration of the immersion was 2 hr at the temperature range from 303 to 328 K.After immersion, the surface of the specimens was cleaned by distilled water, dried and weighed in order to calculate the corrosion rate (CR) and inhibition efficiencies (%).For each experiment, a freshly prepared solution was used and the solution temperature was thermostatically controlled at a desired value.

Electrochemical Studies
Electrochemical measurements were carried out by using an electrochemical work station, ivium instrument.A three electrode compartment cell was used for the electrochemical measurements.A saturated calomel electrode (SCE) and a platinum electrode were used as the reference and the counter electrode, respectively.The potentiodynamic current potential curves were recorded by polarizing the specimen to −250 mV cathodically and +250 mV anodically with respect to OCP at a scan rate of 1 mV•s −1 .Electrode potentials were measured with respect to SCE.The polarization studies were done immediately after the EIS studies on the same electrode without any further surface treatment.The AC impedance was performed in the frequency range from 20 kHz to 200 Hz with a single amplitude of 10 mV.

Quantum-Chemical Calculations Methodology
Among quantum chemical methods for evaluation of corrosion inhibitors, density functional theory (DFT) has shown significant promise [7] and appears to be adequate for pointing out the changes in electronic structure responsible for inhibitory action.In order to explore the theoretical-experimental consistency, quantum chemical calculations were performed with complete geometry optimizations using standard Gaussian-03 software package [8].Geometry optimization was carried out by B3LYP functional at the 6-31G (d) basis set [9] [10].

Weight Loss Method
The inhibiting efficiencies and corrosion rate with different concentrations (0.2 mM to 1 mM) of 1A and 1B on mild steel in 1 M H 3 PO 4 at different temperatures (303, 318, 323 and 328 K) have been evaluated by weight loss measurements.The corresponding plots are given in Figure 1 and Figure 2. The results show that the corrosion rate decreases with increasing concentration of the inhibitor and hence the inhibition efficiency increases.Corrosion rate of mild steel increases with increase in temperature in both inhibited and uninhibited solutions.But  the corrosion rate increases more rapidly with temperature in the absence of inhibitors.

Adsorption Isotherms and Evaluation of Thermodynamic Parameters
In order to obtained isotherm, the degree of surface coverage (θ) for the various concentrations of the inhibitor has been calculated.Various adsorption isotherm mentioned above were tested for both 1A and 1B compounds and among them Langmuir adsorption isotherm fits best for the experimental data of 1A compound.Langmuir isotherm is given by where θ is the degree of surface coverage, C is the molar concentration for the bulk of the solution, K ads is the equilibrium constant of the process of adsorption.The Langmuir plot for 1A Compound fits neatly and the slope value is almost equal to unity (Table 1, Figure 3 and Figure 4).Langmuir plot for 1B compound also fits neatly.But the slope value of the Langmuir plot of 1B compound deviates considerably from unity.This deviation may be explained on the basis of interaction among adsorbed species on the surface of the metal.It has been postulated in the derivation of Langmuir isotherm equation that adsorbed molecules do not interact with one another, but this is not true in the case of large organic molecules having polar atoms or groups which can be adsorbed on the cathodic and anodic sites of the metal surface.Such adsorbed species interact by mutual repulsion or attraction.It is also possible that the inhibitor studied can adsorb on the anodic and cathodic sites resulting in deviation from unit gradient [11].
K ads values obtained from Langmuir plots for 1A and 1B compound are included in Table 1.These results confirm the suggestion that large values of K ads mean better inhibition efficiency of the inhibitors, 1A and 1B.They are physically adsorbed on the metal surface, and that the strength of the adsorption decreases with tem-perature.
In Arrhenius equation, the activation energy E a was calculated from the slope obtained by plotting log corrosion rate vs 1000/T (Table 2).From the table E a in the presence of the both inhibitors are higher than those in the uninhibited acid solution.These results indicate physical adsorption.
From the transition equation plot of log W/T against 1/T for mild steel in 1 M H 3 PO 4 solution the absence and presence of different concentration of 1A and 1B gave a straight line with slope equal to ΔH 0 ads /2.303R and intercept is log R/Nh + ΔS 0 ads /2.303R.The positive values of ΔH 0 ads and ΔS 0 ads obtained from the slope and intercept are included in Table 2.The positive value of ΔH 0 ads shows the endothermic nature of steel dissolution process.The positive value of ΔS 0 ads is higher for inhibited solution than that of uninhibited solution.This suggested that randomness occurred on going reactants to the activated complex.

Electrochemical Impedance Studies
The corrosion behaviors of mild steel in 1 M H 3 PO 4 in the presence of 1A and 1B have been investigated by electrostatic impedance method at 30˚C.Nyquist plots were recorded.Impedance parameter curves as charge transfer resistance (R t ) and double layer capacitance (C dl ) are shown in Figure 5 and Figure 6.
The charge transfer resistance value increases with the increase in the inhibitor concentration, indicates that the efficiency of the inhibitor increases with concentration.Addition of inhibitor decreases the value of C dl .Decrease in C dl is attributed to an increase in thickness of the electrical double layer with increase in concentration of the inhibitor.

Potentiodynamic Polarization Studies
Potentiodynamic polarization studies were carried out for the corrosion of mild steel in 1 M H 3 PO 4 with/without inhibitors.The electrochemical parameters E corr (corrosion potential) and I corr (corrosion current density) were obtained by the extrapolation of anodic and cathodic Tafel slopes.Tafel constants b a and b c were obtained from the anodic and cathodic polarization curves, respectively (Figure 7 and Figure 8).
The I corr values of 1 M H 3 PO 4 decreases with the addition of 1A and 1B and indicates the inhibiting nature.Moreover, there is a significant decrease in the value of both anodic and cathodic Tafel slopes with the increase in the inhibitor concentration showing that the addition of inhibitors modifies the mechanism of the hydrogen reduction as well as decreases the rate of anodic dissolution in all the cases.This means that inhibitors act by blocking both anodic and cathodic sites and behaves as mixed-type of acid corrosion inhibitors.

Quantum Studies
Quantum chemical calculations are confirmed to understand the inhibition mechanism.According to the Frontier Molecular Orbital theory (FMO), the chemical reactivity is a function of interaction between HOMO and    LUMO levels of the reacting species [12].The E HOMO indicates the ability of the molecule to donate electrons to an appropriated acceptor with empty molecular orbitals and the lower is the value of E LUMO indicates its ability of the molecule to accept electrons [13] [14].The higher is the value of E HOMO of the inhibitor, the greater is its ease of offering electrons to the unoccupied d-orbital of metal surface and the greater is its inhibition efficiency.
The calculated E HOMO and E LUMO values of 1A and 1B are included in Table 3. Analysis of the data shows that 1B has lowest energy E HOMO compared in the 1A.On the other hand, the 1A destabilized the HOMO level by 0.0591 eV to increase its donation to the metal surface and increases its tendency to adsorb on the metal surface and accordingly has high inhibition efficiency.The expectation is in good agreement with the experimental observations.It was found that the variation of the calculated LUMO energies among all investigated inhibitors is rulelessly, and the inhibition efficiency is misrelated with the changes of the E LUMO , Table 3.The optimization geometry structure of the inhibitors 1A and 1B were presented in   creases leading to increase in the inhibition efficiency of the molecule [15].Lower values of the energy difference will render good inhibition efficiency, because the energy to remove an electron from the last occupied orbital will be low [16].A molecule with a low energy gap is more polarizable and is generally associated with the high chemical activity and low kinetic stability and is termed as soft molecule [17].Soft molecule is more reactive than a hard molecule because a hard molecule has a large energy gap.The results as indicated in Table 3 shows that inhibitor 1A has the lowest energy gap (0.19014 eV), and inhibitor 1B has highest energy gap (0.23484 eV), this means that the 1A molecule could have better performance as corrosion inhibitor (Figure 10(a), Figure 10(b)).
The dipole moment (µ) is another important electronic parameter, used for the prediction of the direction of a corrosion inhibition process.The dipole moment gives information on the polarity (hydrophobicity) in a bond of a molecule and therefore the electron distribution in the molecule [12] [18].It is generally agreed that the adsorption of high polar compounds possessing high dipole moment on the metal surface should lead to better inhibition.In our study the dipole moment of the 1A compound is 3.6557 eV and 1B compound is 1.4350 eV.The high value of the dipole moment of the 1A inhibitor shows higher inhibition efficiency.
Ionization potential is a fundamental descriptor of the chemical reactivity of atoms and molecules.It is the amount of energy required to remove an electron from a molecule.The lower the ionization potential the easier it is to remove an electron from a molecule.High Ionization energy indicates high stability and chemical inertness and small Ionization energy indicates high reactivity of the atoms and molecules [19].The ionization energy values of the inhibitors (1A and 1B) are 0.20833 eV & 0.2674 eV.The low ionization energy 0.20833 eV of 1A indicates the high inhibition efficiency.
Chemical hardness (global hardness) and softness parameter are related to the description of the hard and soft acid/base through the acid-base theory [19] [20].It is apparent that the chemical hardness fundamentally signifies the resistance towards the deformation or polarization of the electro cloud of the atoms, ions or molecules under small perturbation of chemical reaction.A hard molecule has the least tendency to react while a soft molecule has high tendency to react.A hard molecule has a large energy gap and soft molecule has a small energy gap.In our present study 1A has low hardness value 0.09507 eV compared with the 1B molecule (0.11742 eV).Normally, the inhibitor with least value of global hardness (hence the highest value of global softness) is expected to have the highest inhibition efficiency.The order of softness is such that 1A > 1B.This trend is also in agreement with experimentally determined inhibition efficiency.
Electrophilicity values gives information on the nucleophilic or elecrophilic nature of the molecule.A high electrophilic value informs that the molecule has a high tendency to act as an electrophile while a low value of electrophilicity informs that the molecule has a high tendency to act as a nucleophile.A good, more reactive, nuceophile is characterized by lower value of µ, ω and conversely a good electrophile is characterized by a high value of µ, ω.From the Table 1 the electrophilicity values is such that 1B > 1A.This trend also agrees with experimental results.
The fraction of electrons transferred (N) is also an indication of the ability of the molecule to donate electrons and therefore to bind on the metal surface.It was calculated and tabulated in Table 3.If ∆N < 3.6, the inhibition efficiency increases by increasing electron-donating ability of these inhibitors to donate electrons to the metal surface.The higher the value of ∆N is, the greater the tendency of a molecule to donate electrons to the electron poor species.In the case of corrosion inhibitors, a higher N implies a greater tendency to interact with the metal surface (i.e., a greater tendency to adsorb on the metal surface).Thus, the highest fraction of electrons transferred (36.2193) is associated with the best inhibitor 1A that has the high inhibition efficiency, while the least fraction of electrons transferred (29.1688) is associated with the inhibitor 1B that has the least inhibition efficiency.
According to the simple charge transfer model for donation and back-donation of charges recently proposed [21], an electronic back-donation process might be occurring governing the interaction between the inhibitor molecule and the metal surface.The concept establishes that if both processes occur, namely charge transfer to the molecule and back-donation from the molecule, the energy change is directly proportional to the hardness of the molecule, as indicated in the following expression.The E Back-donation implies that when η > 0 and E Back-donation < 0 the charge transfer to a molecule, fol- lowed by a back-donation from the molecule, is energetically favored.In this context, it is possible to compare the stabilization among inhibiting molecule, since there will be an interaction with the same metal.It is expected that it will decrease as the hardness increases.The use of Mulliken population analysis to estimate the adsorption centers of inhibitors has been widely reported and it is mostly used for the calculation of the charge distribution over the whole skeleton of the molecule [22]- [27].There is a general consensus by several authors that the more negatively charged heteroatom is the more, it can be adsorbed on the metal surface through donor-acceptor type reaction.The calculated Mulliken charges showed that there is more than one active center.Variation in the inhibition efficiency of the inhibitors depends on the presence of electronegative O, S and N atoms as substituents in their molecular structure.The site of ionic reactivity could be estimated from the net charges on a molecule.
It may be noted that in 1A the ring nitrogen has more electronegative charge [N1 (−0.552812)] than the carbonyl oxygen [O7 (−0.445786)].But 2,6-diphenylpiperdin-4-one exhibits boat conformation with carbonyl group and ring nitrogen para position to each other.So both "N" and "O" atoms acts as anchoring sites and get adsorbed onto the mild steel surface.The more positive nature of carbonyl carbon (C4) is adding support to this point.The phenyl rings which are in equatorial position try to have a weak interaction through the π bonding electrons and hence the charge of both C8 and C14 which are away from mild surface decreases.
The C3 (−0.361604) carbon atom is more negative than the other negative carbon atoms in the 1A molecule, due to electron-donating atoms.The presence of donor and acceptor atoms suggests the existence of both intra and inter-molecular hydrogen bonding in the crystalline phase.
In the case of 1B, sulfur atom has a positive charge, which shows the non-participating nature.1B is expected to exist in chair conformations [28] and hence the participation of both carbonyl oxygen and ring "sulphur" in the adsorption process is ruled out.The positive charge of the sulphur atom shows the non-participation of "S" in adsorption process.Therefore, the inhibition efficiency is only due to carbonyl oxygen and hence inhibition efficiency is less than 1A.Therefore, the inhibition efficiency of 1B is only due to oxygen and is comparatively less than 1A.A weak interaction between π bonding electrons in the phenyl ring and metal surface is proved by the positive nature of C8 and C14.The experimental results obtained prove this observation to be true (Figure 11 and Figure 12).From the above discussions, it is clear that 1A with the two anchoring sites shows more inhibition efficiency than 1B.This observation is in good agreement with the experimental results Table 3.

Conclusions
 The inhibitors 1A and 1B shows a high efficiency towards corrosion of mild steel with increase in the concentration of inhibitor.The effect of temperature indicates that the inhibition efficiency decreases with rise in temperature. The activation energy (E a ) is higher for inhibited acids than for uninhibited acids showing the temperature dependence of inhibition efficiency.The negative value of ΔH* and ΔS* indicates exothermic reaction. The negative value of ΔG 0 ads indicates the spontaneous adsorption of the inhibitor.The adsorption of the inhibitor follows Langmuir and El-Awady adsorption isotherm. Potentiodynamic polarization curves indicate that all the inhibitors behave as mixed type inhibitors. 1A has the highest inhibition efficiency because it had the highest HOMO energy and N values and lowest energy gap it was most capable of offering electrons and it could have a better performance as corrosion inhibitor. The parameters hardness (η), softness (S), dipole moment (µ), electron affinity (A), ionization potential (I), the absolute electronegativity (χ), the fraction of electron transferred (N) confirms the inhibition efficiency in order of 1A > 1B.Good correlation between the theoretical and experimental data which confirms the reliability of the quantum chemical methods to study the inhibition of corrosion of metal surface.

Figure 1 .
Figure 1.Plot of inhibition efficiency (%) vs concentration (mM) for the corrosion inhibition of 1A on mild steel in 1 M phosphoric acid (H 3 PO 4 ).

Figure 2 .
Figure 2. Plot of inhibition efficiency (%) vs concentration (mM) for the corrosion inhibition of 1B on mild steel in 1 M phosphoric acid (H 3 PO 4 ).

Figure 5 .
Figure 5. Nyquist diagram for mild steel in 1 M H 3 PO 4 for selected concentrations of 1A.

Figure 6 .
Figure 6.Nyquist diagram for mild steel in 1 M H 3 PO 4 for selected concentrations of 1B.

Figure 7 .
Figure 7. Polarization curves for mild steel in 1 M H 3 PO 4 for selected concentrations of 1A.

Figure 9 .Figure 8 .
Figure 8. Polarization curves for mild steel in 1 M H 3 PO 4 for selected concentrations of 1B.

Figure 9 .
Figure 9.The optimized molecular structure of 1A and 1B using DFT at the B3LYP/6-31G (d) basis set level.
C C C O C C C C C C C C C C
C C S O C C C C C C C C C C

Table 1 .
Some parameters from Langmuir isotherm model for mild steel in 1 M H 3 PO 4 .

Table 2 .
Some Activation parameters of H 3 PO 4 on mild steel.
C C H H H H H H H H H H H H H H H H