1. Introduction

Copper is widely used as a material in many fields, especially in industry because of its remarkable physical, mechanical, anticorrosion and biological properties [1]. During its use in acidic environments, this metal undergoes corrosion phenomenon. Indeed, the prediction of the long-term behavior of metallic structures, that means the evaluation of the damage which are likely to undergo over time under corrosion action, represents an important challenge, particularly on the economic and scientific levels. The knowledge of the corrosion rate of the metal in a given environment allows the development of a good strategy to monitor its dissolution in order to fight more efficiently against the degradation of materials by choosing the most appropriate protection method [2-5]. In terms of corrosion protection, it is possible to act on several levels. First on the material itself (judicious choice, adapted forms, constraints according to the applications...). Then on the material surface (coating, painting, any type of surface treatment etc.). Finally, on the environment with which the material is in contact (corrosion inhibitors). Currently, several researches are oriented towards at the use of corrosion inhibitors [2-5]. However, the rigid rules on environmental protection recommend the use of inhibitors that are very little toxic, eco-friendly and biodegradable [11-13]. In the course of this work, we made the choice to use loratadine which is a therapeutic molecule (antihistamine) and which meets well the requirements of the new international guidelines on environmental protection. Moreover, it contains heteroatoms (O and N) and bonds (π) that can offer special active electrons or vacant orbitals capable of accepting or giving electrons [14,15].

In recent years, the development of reliable computing tools coupled with the growth in computing power has enabled the implementation of molecular modeling techniques. That is why several works have used quantum chemical methods to explain the metals corrosion inhibition by organic compounds in acidic media [16-22]. These methods, which are generally based on the density functional theory (DFT), contribute largely to the search for effective inhibitors. These theoretical methods, which are less expensive than experimental methods, allow to clearly explain the metal-inhibitor interactions while contributing to a better understanding of the inhibition properties of the studied molecule. Finally, the application of a Quantitative structure-property relationship (QSPR) predictive model in this study will lead to finding a relationship between inhibition efficiency and quantum chemical parameters [23,24].

The aim of the present work is to study the copper corrosion inhibition in nitric acid medium by 4-(8-chloro-5,6-dihydro-11Hbenzo [5,6] cyclohepta [1,2-b] pyridin-11-ylidene)-1-piperidinecarboxylic acid ethyl ester or loratadine from thermodynamic quantities of adsorption and activation and theoretical descriptor parameters such as the energy of the highest occupied molecular orbital (E_HOMO), the energy of lowest unoccupied molecular orbital (E_LUMO), the energy gap (ΔE) between E_LUMO and E_HOMO, the dipole moment (μ), the ionization energy (I), the electron affinity (A), the electronegativity (χ), the hardness (η), the softness (σ), the electrophylicity index (ω), the fraction of electron transferred (ΔN), total energy (E_T) are determined and analyzed. The local reactivity has been analyzed through Fukui function f_k⁺ or f_k^- and dual descriptor (Δf_k⁺ or Δf_k^- ), since they indicate the reactive regions in the form of nucleophilic and electrophilic behavior of each atom in the molecule.

2. Experimental Details

2.1. Materials and Sample Preparation

The inhibitor tested in this work namely loratadine or 4-(8-chloro-5,6-dihydro-11H-benzo [5,6] cyclohepta [1,2-b] pyridin-11-ylidene)-1-piperidine ethyl carboxylate. Analytical grade loratadine was purchased from Sigma Aldrich chemicals and solutions of the following concentrations: 0.0261mM; 0.156mM; 0.210mM and 0.522mM were prepared. The molecular structure is shown in Figure 1. The copper samples of 99.6% purity were in the form of a rod measuring 10 mm in length and 2 mm in diameter. These samples were successively polished with metallographic emery paper with grain sizes ranging from 150 to 600, rinsed with distilled water, degreased with acetone, rinsed again with distilled water and dried in a proofer from MEMMERT at 80°C for 20 min. This pre-treatment is intended to remove all traces of grease and native oxide before use. Analytical grade 70% nitric acid solution from Merck was used to prepare the corrosive aqueous solution. The solution was prepared by dilution of the commercial nitric acid solution using double distilled water. The blank was a 1M HNO₃ solution.

Figure 1. Molecular structure of Loratadine (LTD)

2.2. Masse Loss Technique

The mass (m₀) of each treated sample is determined using a precision balance from KERN, before immersion in 50mL of the corrosive 1M nitric acid solution prepared with or without inhibitor. After one hour of immersion at a constant temperature in a thermostat water bath from MEMMERT, each sample is removed from the solution, rinsed thoroughly with distilled water, dried and then re-weighed (m₁) with the balance to calculate the loss in mass (Δm=m₀-m₁). The different temperatures set during the experiment range from 298K to 323K.

2.3. Theoretical Methods

2.3.1. Quantum Chemical Calculations

In order to explain the most important electronic effects manifested by loratadine in copper corrosion inhibition, we have calculated the quantum chemical parameters. All calculations were performed in gas phase using Gaussian 09 software [25]. By improvement of computational method, density functional theory (DFT) has been widely used due to its accuracy and low computational cost to compute a wide variety of molecular properties and has provided reliable results that are consistent with experimental data [26]. The molecular configuration of the inhibitor was geometrically optimized by this theory (DFT) with the functional B3LYP [27] (Becke’s three-parameter with Lee–Yang–Parr hybrid correlation functional) on 6-31 G (d) basis set.

Figure 2. Optimized Structure of loratadine calculated by B3LYP/6-31G (d)

2.3.2. Quantitative Structure-Property Relationship Approach

QSPR approach is used to find a better relationship between experimental inhibition efficiency and theoretical molecular parameters. Moreover the objective of this method is to provide reliable theoretical tools capable of guiding researchers in the conduct of experiments for the discovery of new eco-friendly corrosion inhibitors [28].

For correlating some sets of parameters with the experimental data, a non-linear model was used [28]. This correlation is given by following expression:

(1)

Where A and B are real constants, determined by solving the system of simultaneous equations obtained from different values of inhibitor concentration C_i. In equation (1), a quantum chemical parameter is represented by x_j.

This approach may be validated by statistical indicators whose expressions are as follows:

The Sum of Square Errors (SSE):

(2)

The Root Mean Square Error (RMSE):

(3)

3. Results and Discussion

3.1. Mass Loss Consideration

The corrosion rates (𝑊), the degree of surface coverage (θ) and the inhibition efficiency IE (%) were calculated using the following expressions.

(4)

(5)

(6)

Where m₀ is the mass of the sample before the test, m₁ is the mass of the sample after corrosion, S is the total area of the sample; t is the corrosion time and W the corrosion rate.

Where W₀, and W, are respectively the corrosion rate of the sample in the blank and in the blank containing loratadine.

Figure 3 gives respectively the evolution of the corrosion rate with concentration and temperature. Examination of Figure 3 shows that the corrosion rate increases with temperature for all concentrations. It can be seen that, regardless of temperature, the corrosion rate decreases as the concentration of the inhibitor increases. In the absence of inhibitor, the corrosion rate is very high, which shows that the addition of loratadine to the corrosive medium delays copper corrosion. In addition, the presence of loratadine promotes the creation of a protective layer that prevents copper from losing enough electrons or undergoing strong dissolution in acid. These results reveal that the studied molecule has a good inhibition performance against copper corrosion in nitric acid solution.

Figure 3. Evolution of the corrosion rate as a function of loratadine concentration for different temperatures

Analysis of the figure 4 reveals that the inhibition efficiency increases with temperature over the entire concentration range. For a given temperature, the inhibition efficiency increases with increasing concentration. All these observations show that loratadine acts as an effective inhibitor of copper corrosion in the concentration range studied. This behaviour could be explained by the formation of a physical barrier that separates copper from the nitric acid solution. Indeed, when the temperature rises, loratadine binds to the copper surface reducing its dissolution. This fixation or adsorption becomes important when the concentration of loratadine increases.

Figure 4. Inhibition efficiency versus concentration for different temperatures

3.2. Adsorption Isotherm and Thermodynamic Adsorption Parameters Study

The adsorption isotherms study involved in the process of metals corrosion inhibition by organic molecules allows to show how these compounds bind to the surface of a metal. Indeed The adsorption of an organic adsorbate onto metal–solution interface can be represented by a substitutional adsorption process between the organic molecules in the aqueous solution phase (Org_(sol)) and the water molecules on the metallic surface (H₂O_(ads)) according to the equation [30]:

(7)

Where Org_(sol) and Org_(ads) are respectively the organic species dissolved in the aqueous solution and adsorbed onto the metallic surface. H₂O_(sol) and H₂O_(ads) are respectively the water molecule in the bulk solution and that adsorbed onto the metallic surface; x is the size ratio representing the number of water molecules replaced by one organic adsorbate.

In this work we attempted various adsorption isotherms and selected those that better reflect loratadine behavior on copper surface. So we have retained Langmuir, Temkin, El-awady and Freundlich isotherms. The equations that define these isotherms are expressed in Table 1.

Table 1. Equation of studied isotherms

Figures 5, 6, 7 and 8 show the representation of these different isotherms.

Figure 5. Langmuir adsorption isotherm plots of LTD on copper in 1M HNO3

Figure 6. Temkin adsorption isotherm plots of LTD on copper in 1M HNO3

Figure 7. El-Awady adsorption isotherm plots of LTD on copper in 1M HNO3

Figure 8. Freundlich adsorption isotherm plots of LTD on copper in 1M HNO3

All the tested isotherms yield straight lines as shown in Figures 5, 6, 7 and 8. Table 2 gives the different parameters of studied isotherms.

Table 2. Isotherms parameters for various temperatures

By looking the table 2, it is clear that the correlation coefficients of Langmuir isotherm are closer to unity than the other isotherms. Thus, this isotherm better reflects loratadine behavior with respect to copper corrosion in 1M HNO₃. Nevertheless, Temkin and El-Awady models can be applied. For Temkin model [31], the parameter f (where 2.303/f is the slope of straight lines) having a positive value, there would be repulsion forces between the molecules adsorbed on copper. As for El-Awady model [32], the inverse of the slopes (1/y) of the straight lines obtained is greater than unity, this means that a Loratadine molecule occupies more than one site. Langmuir adsorption model requires that the interactions between adsorbed particles are negligible and that each site can adsorb only one particle [33]. In this case, loratadine adsorption on copper is not rigorously done according to Langmuir model; it is done according to the modified Langmuir isotherm or Villamil model [34]. This model represented by the equation:

(8)

The knowledge of the suitable adsorption isotherm allows to determine the thermodynamic adsorption parameters. The change in free energy of adsorption (∆G⁰_ads) is calculated using the following relation [35]:

(9)

Where R is the perfect gas constant, T is absolute temperature and the constant 55.5 is the molar concentration of water. K_ads is the equilibrium constant of the adsorption process. The values of Adsorption equilibrium constant are deduced from the parameters of the modified Langmuir isotherm (intercept of straight lines).

With regard to the other thermodyamic adsorption parameters (adsorption enthalpy ∆H⁰_ads and adsorption entropy ∆S⁰_ads, they are calculated using the following relationship:

(10)

The representation of ∆G⁰_ads as a function of temperature (figure 9) leads to the values of ∆H⁰_ads (intercept of straight lines) and ∆S⁰_ads, (the slope of the straight line). The different thermodynamic adsorption parameters are recorded in table 3.

Figure 9. ∆G0ads versus Temperature

Table 3. Kads and thermodynamic adsorption parameters for LTD

The negative values of ∆G⁰_ads indicate the stability of the adsorbed layer on copper surface and the spontaneity of the adsorption process [36]. These values become more and more negative as the temperature rises, reflecting the strengthening of metal-molecule interactions. This reinforcement of interactions could justify the high values of inhibition efficiency obtained experimentally at high temperature. An increase in the equilibrium constant K_ads is also observed when the temperature rises, reflecting the fact that the rise in temperature easily favours the inhibitor adsorption on copper surface. The prediction of adsorption type displayed by the inhibitor can be made by the magnitude ∆G⁰_ads. In our case the values of ∆G⁰_ads range from -38.46 KJ.mol^-1 to 34.39 KJ.mol^-1, indicating a predominant chemisorption process [37,38]. The positive sign of ∆H⁰_ads symbolize the endothermic character of loratadine adsorption on copper in nitric acid solution [39]. The positive values of ∆S⁰_ads indicate that the disorder increases when loratadine adsorbs on the copper surface due to the desorption of water molecules [40].

In order to correctly justify the adsorption mode of the studied molecule, we have used Adejo–Ekwenchi isotherm [41]. Indeed, this isotherm allows us to know the adsorption mode of an organic compound. This model is based on the following equation. Figure 10 shows the representation of this isotherm

(11)

Figure 10. Adejo–Ekwenchi isotherm plots of LTD on copper in 1M HNO3

The parameters for this isotherm are listed in Table 4

Table 4. Adejo–Ekwenchi isotherm parameters

As reflected in Table 4, parameters b and K_AE increase with temperature, showing that the adsorption of loratadine on copper is dominated by chemisorption [42].

3.3. Effect of Temperature and Activation Parameters of the Corrosion Process

The effect of temperature on corrosion and its inhibition process for copper in 1M HNO₃ in absence and presence of different concentrations of loratadine at different temperatures ranging from 298K to 323K was evaluated. The dependence of corrosion rate on the temperature can be regarded as an Arrhenius‐type process, the rate of which is given by [43]:

(12)

Where W is the corrosion rate in the presence of inhibitor, E_a the apparent activation energy, R the universal gas constant, A the frequency factor. The plot of logW versus 1/T for copper in the studied solution is given by the figure 11.

Figure 11. Arrhenius plots for copper in 1M HNO3 without and with LTD

Arrhenius plots permit to deduce the values of the activation energies E_a using the slopes of the linear plots. All the obtained values are listed in table 5.

Table 5. Thermodynamic activation parameters of copper dissolution in 1M HNO3 without and with LTD

The temperature effect was also verified by determining the Changes in activation enthalpy ∆H*_a and activation entropy ∆S*_a using Eyring transition state equation.

(13)

This equation can be expressed as:

(14)

Where h the Planck constant, the Avogadro number

The transition state plots of versus is given in Figure 12.

Figure 12. Arrhenius plots for copper corrosion in 1M HNO3 in absence and presence of different concentrations of LTD

∆H*_a and ∆S*_a were computed respectively from the slopes and intercepts of the straight lines obtained. The obtained values are recorded in Table 5.

The apparent activation energy (E_a) values in presence of loratadine are lower than the value obtained without this molecule (Cinh = 0). These observations reveal that the inhibition of corrosion reactions is influenced by chemisorption [44]. E_a decreases when the concentration of inhibitor increases, favouring the Cu²⁺ ions formation and thus the formation of the Cu-Inh complex leading to the reduction of corrosion phenomenon at high temperature. Indeed, the inhibitor adsorbs on metal surface by chemical bonds which are strong (chemisorption) and resists at high temperature. These observations justify the good performance of the molecule when the temperature increases. The values from ∆H*_a are positive and are increasingly lower in presence of loratadine. This reflects an endothermic dissolution process leading to a slow dissolution of copper in the solution studied [45]. The negative sign of ∆S*_a implies that the disorder decreases from reactant to activated complex [46].

3.4. Quantum Chemistry Consideration

In this study the quantum chemical parameters have been calculated by using the conceptual DFT descriptors which are very important to explain the molecule reactivity. In general, this concept permits to confirm the experimental results. Their values are listed in table 6. So, the relationship between these parameters and inhibition efficiency was investigated.

Table 6. Quantum chemical parameters of loratadine, calculated using B3LYP/6‐31G (d)

The expressions used to determine the parameters listed in Table 6 are defined as follows [47-49]:

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

Where and denote respectively the absolute electronegativity of copper and the inhibitor, and are respectively the global hardness of copper and the inhibitor. In this work Δ𝑁 has been determined using = 4.98 eV [50] and = 0 [51], assuming that for a metallic bulk because they are softer than the neutral metallic atoms.

The higher energy of HOMO (E_HOMO) value, the greater is the tendency of the molecule to offer electrons to unoccupied orbital of the metal; in addition, the lower the energy of LUMO (E_LUMO), the higher is the affinity for accepting electrons from the metal surface [52]. The inhibition potential of a reacting organic compound can be evaluated by the orbital energy difference. Furthermore, the smaller of orbital energy difference between the interacting orbitals, i.e. HOMO and LUMO (∆𝐸 = 𝐸_{𝐿𝑈𝑀𝑂} − 𝐸_{𝐻𝑂𝑀𝑂}) would promote strong metal-molecule interaction [53]. In our case, the high value of E_HOMO (-5.6660eV) and the low values of E_LUMO (-1.6910eV) and ∆E (3.9750eV) of loratadine justify the high inhibition efficiency values obtained experimentally.

Global hardness (η) and softness (σ) are related to inhibition efficiency which also depend on the energy gap. In fact a good inhibitor has a high softness value and a low hardness value [54,55]. Loratadine has a low hardness value (η = 1.988 eV) and a high softness value [σ = 0.5031 (eV)^-1] is expected to have a high inhibition efficiency. These values are in agreement with the experimental results.

The absolute electronegativity (χ) is the chemical property that describes the ability of a molecule to attract electron towards itself in a covalent bond [50]. The electronegativity value of loratadine is lower than copper, which confirms the electrons movement from loratadine to copper.

For dipole moment , several authors state that the inhibition efficiency increases with increasing values of this parameter [56,57]. Moreover, survey of the literature reveals that several irregularities appeared in case of correlation of dipole moment with inhibitor efficiency [58,59]. So in general, there is no significant relationship between the dipole moment values and inhibition efficiencies.

The fraction of electrons transferred (ΔN) of a molecule reflects its ability to give electrons. According to Lukovits' study, if ΔN < 3.6 then the efficiency of inhibition increases with the molecule's ability to give electrons to the metal [59]. In our work ΔN < 3.6, which shows that loratadine has a good inhibition performance in electron donation.

The electrophilicity index (ω) measures the propensity of chemical species to accept electrons. A high value of (ω) [49] describes a good electrophile, while a low value of (ω) describes a good nucleophile. In our case, the electrophilicity index of the molecule is high, expressing that loratadine is a good electrophile.

Loratadine has negative value of total energy (E_T < 0) and positive value of hardness (η > 0), which proves that the charge transfer from each molecule to the metal is energetically favorable [60]. So, there is a strong interaction between the molecules and the copper surface.

Local reactivity was analyzed by means of Fukui indices and dual descriptor in order to assess the nucleophilic and electrophilic attack centre.

The Fukui [61,62] functions expressed using the limit difference approximation is given as follows

For nucleophilic attack

(24)

For electrophilic attack)

(25)

Where q_k(N+1), N and q_k(N-1) are the electronic population of atom k in (N+1), N and N-1 electrons systems.

The dual descriptor [63,64] is used to locate nucleophilic and electrophilic sites of attack with all possible precision. It is defined by the following expression

(26)

The nucleophilic attack and electrophilic attack are given respectively by the highest and the lowest value of .

All the local parameters are collected in Table 7.

Table 7. Calculated Mulliken atomic charges, Fukui functions and dual descriptor by DFT B3YLP6-31/ G (d)

It is clear from the analysis in Table 7 that N(22) with the high value of and is the most probable nucleophilic attack site while C(33) with the maximum value of and the lowest value of is most probable electrophilic attack site.

The HOMO-LUMO diagrams are presenting by Figure 13.

Figure 13. HOMO (A) and LUMO (B) orbitals of by B3LYP/6-31G (d)

3.5. Quantitative Structure-Property Relationship (QSPR) Assessment

In order to select a set of relevant quantum chemical parameters capable of finding a relationship between these parameters and experimental inhibition efficiencies, QSPR method was used. For this method, we used inhibition efficiencies at 298K in the same concentration range.

The constants determined for the sets of parameters are recorded in the table 8.

Table 8. Values of coefficients A, B, D, E, R2 and Statistical parameters of the sets

The Theoretical versus experimental efficiencies of LTD for different sets are represented in Figures 14.

Figure 14. Theoretical versus experimental efficiencies of LTD for different sets of parameters

Referring to the data in the table 8, it appears that the set of parameter with the lowest value of RMSE and correlation coefficient R²=0.9709 is the best parameter to describe loratadine behavior of copper corrosion inhibition in 1M HNO₃.

4. Conclusions

Mass loss and theoretical method were used to evaluate the copper corrosion inhibition by loratadine in 1M HNO₃. The main finding of this study are as follows:

• Loratadine acts a good inhibitor for copper corrosion in 1M HNO₃ and its Inhibition efficiency increases with increasing concentration and temperature.

• The adsorption of loratadine on copper surface obeys the modified Langmuir adsorption isotherm or Villamil model and is a spontaneous, exothermic process accompanied by an increase in entropy.

• The adsorption process is dominated by chemisorption.

• Thermodynamic activation parameters indicate an exothermic dissolution process.

• The Fukui functions and the dual descriptor have proved that N(22) and C(33) are respectively the probable sites of nucleophilic and electrophilic attack.

• is the best set of parameters for correlating theoretical and experimental inhibitory efficiencies.

• Calculated theoretical parameters support the experimental results.

ACKNOWLEDGEMENTS

The authors gratefully acknowledged the support of the Environmental Science and Technology Laboratory, Daloa (Côte d’Ivoire).