Abstract

The behavior of two antidiabetic drugs namely N-[(butylamino) carbonyl]-4-methylbenzenesulfonamide or tolbutamide and N-(hexahydrocyclopentapyrrol-2(1H)-ylcarbamoyl)-4-methylbenzenesulfonamide or gliclazide was theoretically evaluated by the Density Functional Theory (DFT) and the Quantitative Structure Property Relationship (QSPR) methods. Theoretical calculations showed a clear correlation between the descriptor parameters and the inhibition efficicencies. It also permitted to identify the reactivity sites. The results reveal that the molecules studied are good inhibitors of aluminium corrosion in 1M hydrochloric acid. Finally, the Quantitative Structure Property Relationship allowed to find the appropriate set of parameters establishing the relationship between the inhibition efficiency and the molecular descriptors.

1. Introduction

In recent years, corrosion inhibitors have become an effective means of reducing metal corrosion in several sectors ^{1, 2}. Among these metals, we have the aluminum whose lightness is a major asset for the transport equipment and leisure industries. Aluminium is a very active metal ³ which is used in many fields because of its remarkable properties such as its aesthetic qualities and its good corrosion resistance. In particular, it is used in the aviation, automotive, packaging, construction, mechanical engineering and other industries.

This massive use make that aluminium is not escape to corrosion. Indeed, the use of acid solutions ⁴ in industry during operations such as cleaning, degreasing and pickling of metal structures leads to a corrosive attack on aluminium. Corrosion of aluminium is a fundamental concern in academic and industrial circles and has received considerable attention. This attention has focused on the search for biodegradable, eco-compatible and non-toxic molecules capable of reducing aluminium corrosion in acidic environments ^{5, 6}. These organic or inorganic molecules will be added to acid solutions during the various operations to reduce the dissolution of aluminium. Inorganic molecules are mostly carcinogenic and pollute the environment. The current trend is to use organic therapeutic compounds ^{7, 8, 9, 10} because they are generally less toxic and efficient at low concentrations. The literature ^{11, 12, 13} shows that organic compounds, which inhibit aluminium corrosion, contain heteroatoms (N, S, O, P, Se) and/or π bonds in their molecular structure and that these molecules inhibit corrosion by adsorption on the metal surface. Experimental practice is a useful means of finding corrosion inhibitors because it helps to explain the mechanism of inhibition. However, these experiments are often expensive and time consuming and some are based on trial and error.

This observation has encouraged the use of new techniques based on numerical simulation and molecular modelling methods. It is within this context that several researchers ^{14, 15, 16, 17} have used quantum chemical calculations based on Density Functional Theory (DFT) to explain the molecules physicochemical properties and the corrosion inhibition mechanism. DFT is based on Hohenberg and Kohn's theorem ¹⁸ which shows that the energy of the fundamental state of the molecule is the only functional electron density. This theory will be elucidated later thanks to Kohn and Sham ¹⁹ from a system without interactions between the constituents, it gives access to the global and local parameters of the molecules, which allows to explain the metal/molecule interactions. This theoretical approach will be supported by the use of the QSPR method (Quantitative Structure Property Relationship) which is a method for experimentation ²⁰ because it permits to find a relationship between inhibition efficiency and quantum chemical parameters.

The objective of this work is on the one hand to study the inhibition properties of two antidiabetic drugs; tolbutamide and gliclazide as an aluminium inhibitor corrosion in 1M acid hydrochloric solution and on the other hand to find the best set of parameters that could correlate the experimental and calculated inhibition efficiencies of the molecules studied using the QSPR approach.

2. Materials and methods

Gravimetric method is an experimental method which consists of measuring the loss of mass (∆m) suffered by an aluminium sample of surface S, which has been immersed for a time t = 1h in a solution of hydrochloric acid of concentration 1M, maintained at a constant temperature of 298K. During this experiment we used an analytical balance (precision: ±0.1 mg), a proofer and a thermostat water bath.

The corrosion rate of aluminium (W) and the inhibition efficiency (IE) were evaluated from the following relationships:

(1)

(2)

Δm : is the mass loss (g) ; m₁ and m₂ are respectively, the weight (g) before and after immersion in the solution test; t : the immersion time (h) ; Se : the total surface of sample (cm²) ; w₀ and w ; are respectively the corrosion rates of aluminium in the absence and presence of each molecule.

Quantum chemical calculation methods are based primarily on solving the Schrödinger equation for a given system with the determination of the system clean energy and wave functions. There are several methods of resolution among these methods we have the Density Functional Theory (DFT). According to this theory, electronic properties can be described in terms of electron density functions. These calculations, which have been carried out with the Gaussian 09 W ²¹ software, using the B3LYP ²² functional with two basis sets including 6-31G (d) and LanL2DZ consist of two steps:

- A graphic presentation of the geometry using a computer graphics software: Gaussview.

- The application of a theoretical method (DFT); this method is implemented in the commercial software (Gaussian).

This method makes it possible to determine the quantum chemical parameters such as E_HOMO (Highest Occupied Molecular Orbital Energy), E_LUMO (Lowest Unoccupied Molecular Orbital Energy), energy gap (ΔE), dipole moment (µ), electronegativity (χ), hardness (η ), softness (S), electrophylicity index (ω), electron affinity (A), ionization energy (I) and the fraction of electron transferred (ΔN) and reactivity parameters.

The QSPR method has been used to develop mathematical models linking physicochemical properties and biological activities to molecular structure ²³. It allows the prediction of inhibition properties of organic compounds. We will apply the non-linear multivariate model proposed by Lukovits et al. ²⁴ to study the interactions between corrosion inhibitors and metal surfaces in 1M HCl, which is based on the Langmuir adsorption isotherm. This model is represented by the relation:

(3)

Where C_i represents the different inhibitors concentrations. A and B are real constants which will be determined when solving the system of equations.

Using four inhibitors concentrations, which are 50𝜇𝑀, 100𝜇𝑀, 500𝜇𝑀 and 1000 𝜇𝑀. We tested sets of three parameters (x_1, x_2, x₃). In this case, the equation becoming:

(4)

This equation allows us to have a system of four equations with four unknowns A, B, D and E. It is thus a question of finding for the molecule the set of coefficients A, B, D and E that permits to obtain the value of the inhibition efficiency closest to the experimental value. The calculations were carried out using the EXCEL software.

3. Results and Discussion

The Chemical structure and the optimized structure of the studied molecules are given by Figure 1.

The values of the inhibition efficiencies determined using the gravimetric method for five different concentrations of each compound are listed in Table 1.

The mains quantum chemical parameters were calculated using the B3LYP/6-31G(d) and B3LYP/LanL2DZ are listed in Table 2.

The ability of a molecule to inhibit corrosion depends on the value of E_HOMO, as the inhibiting effect of a molecule is generally usually ascribed to adsorption of the molecule on the metal surface. A molecule with a high E_HOMO value has the ability to give electrons to a suitable low energy ²⁵, empty molecular orbital and this facilitates its adsorption on the metal surface. The high E_HOMO values of the molecules studied justify their good inhibition efficiencies, therefore these molecules can adsorb to the aluminum surface thus creating a protective layer that will isolate it from the aggressive environment. GC has the highest E_HOMO value -5.5675eV and -5.9573 eV respectively for B3LYP/6-31G (d) and B3LYP/LanL2DZ) which justifies its greater inhibition efficiency, and this is in agreement with the experimental results.

According to the literature, a molecule with a low value of E_LUMO can easily accept electron from an occupied orbital of a metal ²⁶. In our case, the low E_LUMO values of the studied molecule show that they have a tendency to accept electrons from the aluminium. In the Table 2 E_LUMO values follow the trend: GC < TB. Accordingly, GC accepts more electrons than TB, confirming its greater inhibition efficiency.

Energy gap (ΔE = E_LUMO - E_HOMO) is a suitable indicator for interpreting the reactivity of an inhibitor. Indeed, a molecule with a low value of ΔE is more polarizable and generally has a high chemical reactivity ²⁷. The results obtained in the two different basis (Table 2) show that the molecules studied have a low value of ΔE, which therefore favours the exchange of electrons between these molecules and aluminium, as it is easier to remove an electron from the HOMO to the LUMO orbital. This confirms the high inhibition efficiency values obtained experimentally. GC has the best inhibition efficiency as it has the lowest value of ΔE.

According to some authors ^{28, 29} high value of dipole moment (µ) lead to a good inhibition efficiency of an organic molecule. However, many other authors ^{30, 31} state that low dipole moment values favour the adsorption process.

Considering these contradictory views on this indicator, no interpretation related to the behavior of the studied molecules can be made in our work.

The ionization potential (I) and electron affinity (A) of the molecules are calculated according to Koopmans’s theorem ³² using the following equations

(5)

(6)

The two quantum chemical parameters I and A are related respectively to the HOMO and LUMO energies. According to the literature ³³ a molecule with a low ionization energy value is high reactive. The values obtained in the different basis of TB and GC are low compared to values obtained in the literature ^{34, 35}, which justifies their high inhibition efficiency. The lower value of GC confirms its greater inhibition efficiency.

Referring to Koopmans theorem ³², the electronegativity (𝜒) and the global hardness (𝜂) can be written in terms of ionization potential (𝐼) and the chemical affinity (A).

(7)

(8)

Chemical softness S ³⁶ is estimated by the above equation :

(9)

The electronegativity (χ) of a molecule reflects its ability to attract electrons when forming a chemical bond with another element. In general, TB and GC have lower electronegativity values than aluminium (4.28eV), which shows that aluminium attracts more electrons than TB and GC. This implies that the electrons move easily from each molecule to aluminum.

Global softness (S) and global hardness η (eV) are also used to measure the molecular stability and reactivity. A hard molecule has a large energy gap and a soft molecule has a small energy gap ³⁷. It is shown from the calculations that GC has the least value of global hardness (1.6867 eV, 1.6856eV) and the highest value of global softness (0.5929(eV)^-1, 0.5932(eV)^-1)) is expected to have the highest inhibition efficiency. These results are consistent with experimental inhibition efficiencies.

According to Pearson theory ³⁸ the fraction of transferred electrons (ΔN) from the inhibitor molecule to the metallic atom can be expressed by:

(10)

Where χ_Al and η_Al, χ_inh and η_inh denote electronegativity and hardness of aluminium and the inhibitor molecule respectively.

We use the theoretical value of χ_Al = 4.28 𝑒𝑉/𝑚𝑜l ³⁹ and η_Al = 0 ⁴⁰, for the calculation of the number of transferred electrons.

In our case, the values of ΔN are positive in the 6-31G(d) basis set for the inhibitors and only positive for GC in LanL2DZ basis set, which could explain that the molecules provide electrons to the aluminium ⁴¹, these electrons transfers justify the existence of the chemical adsorption. Whereasin LanL2DZ basis ΔN value of TB is negative, this means that TB does not provide electrons to the aluminium, which would rather militate in favour of a physical adsorption process.

The global electrophilicity index (ω), introduced by Parr ⁴², and calculated using the electronic chemical potential and chemical hardness is given by:

(11)

According to the definition, this index measures the ability of a chemical species to accept electrons ⁴². The low value of ω defines the nucleophilic character and the high value defines the electrophilic character. In our study, the compounds studied have low values of ω which reflects their electrophilic character, so the molecules have the possibility to receive electrons from the aluminium orbitals.

The best way to analyze the local selectivity of a corrosion inhibitor is to use the Fukui function and the dual descriptor. The Fukui function ⁴³ is defined as the derivative of the electronic density with respect to the number of electrons:

Nucleophilic attack:

(12)

Electrophilic attack:

(13)

Where is the electron density at a point r in space around the molecule, N corresponds to the number of electrons in the neutral molecule, corresponds to an anion with an electron added to LUMO of the neutral molecule and corresponds to a cation with an electron removed from HOMO of the neutral molecule

In practice, Mulliken charges lead to the condensed Fukui functions ⁴⁴:

Nucleophilic attack:

(14)

Electrophilic attack:

(15)

In order to determine precisely the individual sites of attack having a particular behavior within the molecule the dual descriptor ^{45, 46} is used, expressed by the following relationship:

(16)

The condensed form of the dual descriptor is given by the following relation:

(17)

For the process is driven by a nucleophilic attack, when the process is driven by an electrophilic attack.

All the Fukui functions and dual descriptors are tabulated in Table 3 and Table 4.

The dual descriptor is able to unambiguously specify true sites for nucleophilic and electrophilic attacks; furthermore, the dual descriptor is less affected by the lack of relaxation terms than the Fukui function ⁴⁵.

The atom that has the high value of and represents the most probable site for nucleophilic attacks. While the atom that has the highest value of and the lowest value of represents the most probable site for electrophilic attacks.

Thus, the analysis of the Table 3 indicates that S(15) atom is the most probable site for nucleophilic attacks and O(23) atom is the most probable site for electrophilic attacks for TB.

For GC, S(25) atom is the most likely site for nucleophilic attacks because it has the highest values of and Although O(30) atom has the highest value of it is not the most likely site for electrophilic attacks because it has not the lowest value of In this case, O(31) atom which has the lowest value of is the most likely site for electrophilic attacks.

The most likely center for nucleophilic attacks where the system receives electrons is located in the LUMO electron density region, while the most likely center for electrophilic attacks where the system provides electrons is located in the HOMO electron density region.

The HOMO and LUMO density diagrams are given in Figure 2.

The method consists to correlate some sets of composite indexes (quantum chemical and reactivity parameters) with the experimental corrosion inhibition efficiency of the molecules studied. The chemical structure is represented at the molecular level by some sets of descriptors that can be mathematically related to experimental properties with the QSPR model.

The values of the different coefficients calculated with the EXCEL software for the different sets of parameters are recorded in the Table 5 and Table 6.

The calculated inhibition efficiencies versus the experimental are shown in Figure 3 for TB and Figure 4 for GC.

An examination of Figure 3 and 4 reveals that the correlation coefficients are nearly equal to unity. We are going to analyze some statistical parameters in order to find the set of parameters which best describes the behavior of the molecules.

Three statistical parameters were determined to unambiguously find the best set of parameters. They are expressed as:

The Sum of Square Errors (SSE) :

(18)

The Root Mean Square Error (RMSE) :

(19)

The Mean Percent Deviation (MPD):

(20)

The different values of these statistical indicators of TB and GC are recorded in Table 7.

Analyzing the Table 7, the best set for correlating experimental and theoretical inhibition efficiency for TB and GC is the set of parameters (χ, ∆E, η) because the statistical parameters values SSE, RMSE and MPD of QSPR model are low. This set of parameters will allow to theoretically calculate the inhibition efficiency of each molecule tested, which can guide the experimenter in the practical phase.

Therefore, correlation coefficients alone are not recommended to validate the QSPR model when describing the behavior of a molecule. Statistical parameters need to be combined in order to have a rigorous and complete validation. In this work the set of parameters (∆E, μ, ω) which has the correlation coefficient closest to the unity (0.9932 for TB and 0.9891 for GC) is not the best set for for interpreting the behavior of the inhibitors because the statistical parameters are not the lowest.

4. Conclusion

Within the framework of this work, the following conclusions can be drawn:

1. The two compounds (TB and GC) exhibit a very good performance as inhibitors for aluminium corrosion in 1M HCl

2. GC has the highest inhibition efficiency than TB because it has the highest E_HOMO and lowest energy gap.

3. Theoretical and experimental results are in agreement.

4. The electrophilic and nucleophilic attack sites corresponding to the active atoms responsible for the local reactivity of each inhibitor were identified using Fukui functions and the dual descriptor.

5. (χ, ∆E, η) is the best set of parameters for modeling the inhibition efficiency of TB and GC molecules in the studied solution.

6. QSPR model can be used to forecast the inhibition efficiency of an inhibitor because it allows to find the set of parameters capable of predicting the capacity of an organic compound to be an inhibitor.

Acknowledgements

The authors gratefully acknowledged the support of Environmental Training and Research Unit of Daloa (Côte d’Ivoire).and the Laboratory of physical chemistry of Felix Houphouët Boigny university of Abidjan (Côte d’Ivoire).

References