Quantum chemical calculation studies for interactions of antiwear lubricant additives with metal surfaces

Abstract

Theoretical calculations based on density functional theory (DFT) have been performed to correlate experimentally observed antiwear properties of Schiff base lubricant additives derived from condensation of salicylaldehyde with N-phenylthiosemicarbazide, [(E)-1-(2-hydroxybenzylidene)-4-phenylthiosemicarbazide; H₂STC-Ph], N-p-tolylthiosemicarbazide [(E)-1-(2-hydroxybenzylidene)-4-p-tolylthiosemicarbazide; H₂STC-p-MePh] and N-(4-chlorophenyl)thiosemicarbazide, [(E)-1-(2-hydroxybenzylidene)-4-(4-chlorophenyl)thiosemicarbazide; H₂STC-p-ClPh] with their chemical structure. antiwear properties have been discussed on the basis of the interactions between the additive molecules and the metal surface. In order to compare the antiwear behavior of different additives, various parameters such as frontier molecular orbital energy E_HOMO (Energy of Highest Occupied Molecular Orbital), E_LUMO (Energy of Lowest Unoccupied Molecular Orbital), the energy gap (ΔE), mutual orbitals’ interactions between additive molecules and metal surface (ΔE₁ & ΔE₂), global properties (hardness and softness) and the dipole moment have been calculated and correlated with the respective energies of the metal surface. The quantum chemical calculations (QCC) have shown that the wear-reducing behavior of Schiff bases increases with an increase in E_HOMO, decrease in E_LUMO, decrease in the energy gap between E_LUMO and E_HOMO and increase in the dipole moment of the additives. The results obtained by quantum chemical calculations are in good agreement with the experimental results.

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1. Introduction

Lubricants play an important role in reducing friction and wear between moving surfaces. In the boundary lubrication regime, the formation of a surface chemical reaction film is a determining factor in minimizing the friction and wear. In order to increase the mechanical efficiency of a machine an appropriate additive should be added to a lubricant to reduce surface damage.¹ There has been extensive research for several decades on organic compounds containing hetero-atoms like sulfur,^2,3 phosphorous,^4,5 halogen,^6,7 nitrogen and their metal complexes as antiwear and extreme pressure lubricant additives.^8–15 In general, additive molecules are physically and/or chemically adsorbed on interacting surfaces. The hetero-atoms and the aromatic rings present in the structure of these additives are the major adsorption centers during operating conditions. For this, several pieces of evidence using surface characterization techniques are available in literature.^1,4,5,16 The organic molecules usually promote the formation of a chelate on the metal surface by transferring electrons from the additive molecules to the metal and forming coordinate covalent bonds during chemical adsorption.¹⁷ In this way, the metal acts as an electrophile and the hetero-atoms of the organic additives, with lone pairs of electrons that are readily available for bond formation, act as nucleophilic centers.¹⁸ Recently, studies have been made regarding the relationship between the tribological performance and the structure of lubricant additives.^1–3 Lian et al.¹⁹ have correlated the tribological parameters of rare earth trifluorides with their electronic structures, bond parameters and thermodynamic parameters. This study indicates that the antiwear abilities of rare earth trifluorides increase gradually from lanthanum to europium with the increase in the number of electrons in the 4f orbitals. Ren et al.²⁰ have studied the effect of the molecular structure of heterocyclic compounds containing varying numbers of nitrogen atoms in a ring on their antiwear properties and found that the antiwear property of the compounds increases as the number of nitrogen atoms increases in a compound.

The study of quantitative structure–activity relationships has been one of the most active frontier research fields in chemistry worldwide. Now a days, quantum chemical calculations have been widely used in different areas of sciences to forecast the activity of compounds prior to experimentation; accordingly the design of the compounds can be improved. In the field of tribology, quantum chemical calculations have been performed to correlate the structure of additive molecules with their antiwear behavior.^{16,19,21–23} Once a correlation between structure and activity/property is found, any number of compounds, including those not yet synthesized, can be readily screened in order to select structures with the desired properties. It is then possible to select the most promising compounds, synthesize them and test in the laboratory. Thus, the aforesaid protocol is inexpensive, time-saving and does not require manpower towards the development of new kind of lubricant additives. Recently, our research group has reported theoretical investigations on SAPS-free Schiff base derivatives and successfully correlated their structures with their experimentally obtained wear-rates. Besides this, tribological behavior of various thiosemicarbazone Schiff's bases derived from the condensation of salicylaldehyde with substituted N-phenylthiosemicarbazides have also been reported.^24,25

The present communication reports a theoretical study of the thiosemicarbazone Schiff bases derived from the condensation of salicylaldehyde with N-phenylthiosemicarbazides. [(E)-1-(2-hydroxybenzylidene)-4-phenylthiosemicarbazide; H₂STC-Ph], N-p-tolylthiosemicarbazide [(E)-1-(2-hydroxybenzylidene)-4-p-tolylthiosemicarbazide; H₂STC-p-MePh] and N-(4-chlorophenyl)thiosemicarbazide, [(E)-1-(2-hydroxybenzylidene)-4-(4-chlorophenyl)thiosemicarbazide; H₂STC-p-ClPh] using quantum chemical calculations (QCC) based on density functional theory (DFT)²⁶ and correlation of the calculated parameters with the experimentally observed wear rates (see ESI S1†). The structural parameters such as dipole moment (μ), electronic properties, the frontier molecular orbital energies (E_HOMO, E_LUMO), energy gap (ΔE), mutual orbitals’ interactions between additive molecules and the metal surface (ΔE₁ and ΔE₂), and the global properties of the additives have been correlated with their antiwear efficiencies.

2. Theoretical studies

2.1. Theoretical background of structural parameters

According to Parr et al.²⁷ the Lagrangian multiplier (μ) in the Euler equation could be written as the partial derivative of the system's energy with respect to electron number at constant external potential; μ is commonly called the chemical potential and is characteristic of the system of interest.

Furthermore, by relating eqn (1) to Iczkowski and Margrave's definition of electronegativity,²⁸ a system's electronegativity (χ) and chemical potential (μ) were shown to be analogous.

The analytical definition of absolute or global hardness (η) of a chemical species as defined by Parr and Pearson²⁹ in terms of the second derivative of the system's ground-state energy with respect to electron number at constant external potential is given by

where E is the total energy, N is the number of electrons of the chemical species, and ν(r̄) is the external potential. The global hardness of a system is an indicator of its stability, and its half inverse is termed as global softness (S), which indicates the reactivity of the system.³⁰

Most widely accepted formulae to compute the chemical potential and global hardness make use of a three-point finite difference approximation (here I is the ionization potential and A the electron affinity).²⁹

Moreover, by considering Sanderson's principle of electronegativity equalization,^31,32 the following two equations have been derived which are basic statements of the HSAB theory.^29,33

Eqn (7) gives a first approximation to the fractional number of electrons transferred (ΔN) as two systems, X and Y, come together to react. The associated energy change is given by eqn (8), in fact, this is only a part of the total energy change which must include covalent bonding and ionic interactions. Nevertheless, eqn (7) and (8) are still very useful as chemical reactivity indices as they measure the initial interaction between species X and Y using properties of the isolated systems. For the two systems when metal and additive are brought together, electrons will flow from the lower χ to higher χ values until the chemical potentials become equal. The fraction of electrons transferred from additive molecules to the iron surface ΔN, is given by eqn (7).^34,35

Various quantum chemical parameters indicating the structural characteristics of these antiwear additive molecules such as the energy of highest occupied molecular orbital (E_HOMO), energy of lowest unoccupied molecular orbital (E_LUMO), energy gap (ΔE), energy gaps between metal and additives, dipole moment, ionization potential (I), electron affinity (A), were first calculated. DFT also provides a convenient theoretical framework for calculating global and local indices that describe the inherent reactivity of chemical species quantitatively. From the theoretical point of view, the electrophilic and nucleophilic nature of organic molecules can be characterized by using the reactivity indices. Thus, Parr et al.³⁶ introduced the following definition of the electrophilicity index ω as:

where μ is the chemical potential, and η is the global hardness. According to the Hartee–Fock theorem, the energy of the frontier molecular orbital (−E_HOMO) is considered to be equal to the ionization potential (I) while that of (−E_LUMO) is taken as electron affinity (A). The hard molecule has large energy gap between their HOMO and LUMO while soft molecule contains small energy gap between them. Soft molecules are more reactive than the hard ones because they may offer an electron to the acceptor easily.^33,37,38 Besides these quantum chemical indices, the most informative interaction parameters can be obtained by comparing the energy gap between the HOMO of additives and the LUMO of the metal (ΔE₁) and vice versa (ΔE₂).

2.2. Computational details

Density Functional Theory (DFT) is found to be a suitable method for such calculations. All the calculations were performed using B3LYP³⁹ that uses Becke's three-parameter functional (B3) and includes a mixture of Hartree–Fock with DFT exchange terms associated with the gradient corrected exchange-correlation functional of Lee, Yang and Parr (LYP).⁴⁰ It has fewer convergence problems than those found in the pure DFT methods. Thus, B3LYP has been used in this paper to carry out quantum calculations. Full geometry optimizations of all additives were carried out with the standard B3LYP/6-31G++(d,p) basis set⁴¹ using Gaussian 03, D.01.²⁶

3. Results and discussion

Quantum chemical calculations were performed to investigate the effect of different substituents on the basic skeleton of thiosemicarbazone Schiff bases towards their antiwear lubrication behavior. The chemical structures, IUPAC names and abbreviations of the studied compounds are mentioned in Fig. 1. The full geometry optimized structures of three Schiff bases H₂STC–Ph, H₂STC-p-MePh and H₂STC-p-ClPh are shown in Fig. 2. The calculated quantum chemical parameters like total energy, E_HOMO, E_LUMO and orbital energy gap (ΔE) between HOMO and LUMO of the additive molecules, dipole moment (μ), energy gap (ΔE₁) between HOMO_additive and LUMO_Fe and energy gap (ΔE₂) between HOMO_Fe and LUMO_additive are presented in Table 1. The interaction mechanism between lubricants or lubricant additives and the metal surface usually includes adsorption phenomenon. The strength of adsorption of lubricants on metallic surfaces depends on the nature of the adsorption, viz. physical adsorption and chemical adsorption which in turn, depends on the electrostatic attraction of the polar head of the additive molecules and the metal surface. The adsorption of molecular additives on the metal surface is not only a precursor of the surface chemical reaction but also provides important contributions to the tribological performance of the lubricants.^42,43 According to the frontier molecular orbital (FMO) theory, the energy of the highest occupied molecular orbital (E_HOMO) and the lowest unoccupied molecular orbital (E_LUMO) are the important indices for predicting the reactivity of any chemical species. This is because the adsorption of the additive molecule on the metal surface can be considered on the basis of the donor–acceptor interaction between the additive molecule and vacant d-orbitals of iron.⁴⁴ Therefore, increasing values of E_HOMO indicate that there is a high tendency of the additive molecules to donate electrons to the appropriate acceptor molecules having empty molecular orbitals. On the other hand, decreasing energy of E_LUMO indicates the ability of a molecule to accept the electrons. Therefore, the lower the value of E_LUMO, it is more probable that the molecule will accept electron.³⁴ The energy of the HOMO is directly related to the ionization potential and determines the susceptibility of the molecules to undergo electrophilic attack. Similarly, the energy of the LUMO is directly related to the electron affinity and determines the susceptibility of the molecules to undergo nucleophilic attack. Thus, according to the FMO theory of chemical reactivity, the formation of a transition state is due to the interactions between the frontier molecular orbitals of the reacting moieties. Therefore, an increase in E_HOMO and decrease in E_LUMO results in enhanced tribological properties of the additives due to their better adsorption on the metal surface forming a strong chemisorbed tribofilm.⁴⁵ On the other hand, the difference between E_LUMO and E_HOMO i.e., the energy gap (ΔE) is another important stability index that has been found to have excellent correlation with antiwear efficiencies in a tribological reaction. A large ΔE implies high molecular stability in a reaction.⁴² The ΔE has also been associated with the hardness and softness. The small energy gap (ΔE) between interacting HOMO and LUMO orbitals of the molecule is indicative of its soft nature i.e. it can be easily polarized, whereas large energy gap corresponds to its hard behavior. Therefore, it can be stated that antiwear efficiency of the additives would increase when the values of E_HOMO increase and those of E_LUMO and ΔE decrease. On the basis of E_HOMO, E_LUMO and ΔE for the studied compounds, the order of efficiency may be given as given below:

H₂STC–Ph < H₂STC-p-MePh < H₂STC-p-ClPh

Fig. 1 Chemical structures of the investigated Schiff base antiwear additives.

Fig. 2 Optimized structures of Schiff bases calculated with the B3LYP/6-31G++(d,p) basis set; (a) H₂STC–Ph, (b) H₂STC-p-MePh and (c) H₂STC-p-ClPh.

Table 1 Calculated quantum chemical parameters of Schiff base antiwear lubricant additives calculated with the B3LYP/6-31G++(d,p) basis set

Additives	Total energy (a.u.)	EHOMO (Hartree–Fock)	ELUMO (Hartree–Fock)	ΔE (Hartree–Fock)	ΔE1 (Hartree–Fock)	ΔE2 (Hartree–Fock)	μ dipole-moment	Wear rate ^2 (10^−4 × mm^3 h^−1)
Fe5 (ref. 43)		−0.18651	−0.06420	0.12231
H2STC–Ph	−1179.168	−0.00189	0.00954	0.01143	−0.06231	0.19605	4.3490	70.70
H2STC-p-MePh	−1218.460	−0.00170	0.00768	0.00938	−0.06250	0.19415	4.3661	61.14
H2STC-p-ClPh	−1638.790	−0.00142	0.00086	0.00228	−0.06278	0.18737	4.6791	53.00

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The above order is consistent with the experimentally found wear-rates.²

The dipole moment (μ) is an index that can be useful for predicting the antiwear behavior of a compound. The dipole moment is a measure of the polarity of a covalent bond, and it is related to the distribution of electrons in the molecules.⁴⁶ The obtained data (Table 1) indicate that the H₂STC-p-ClPh having the highest value of dipole moment exhibits highest antiwear behavior while H₂STC–Ph with the lowest value of μ has been found to show lowest antiwear properties. Thus, the dipole moment also supports the above order of antiwear behavior of different Schiff bases.

3.1. Interaction with metallic surface

The investigated Schiff base lubricant additives are the polar molecules which get adsorbed onto the metal surface through their active sites. Therefore, for the investigation of antiwear behavior it is important to correlate molecular orbital energies of the additive molecules to those energies of the metal. Huang et al.⁴³ have calculated the energy of frontier molecular orbitals of iron by considering iron as five-atom clusters. The interaction between additives and iron can be discussed on the basis of ΔE₁ (ΔE₁ = E_LUMO of iron − E_HOMO of additive) and ΔE₂ (ΔE₂ = E_LUMO of additive − E_HOMO of iron) as mentioned in Table 1. From these values it is evident that the additive molecules are electron donors while iron acts as an electron acceptor and there is nucleophilic interaction between iron and the additive molecules.⁴³ The results show that the difference between E_HOMO of H₂STC-p-ClPh and E_LUMO of iron is the smallest among the three additives, suggesting that the maximum interaction will take place between H₂STC-p-ClPh and iron. For a good antiwear additive, besides donation of electron from the HOMO of the additive molecules to the LUMO of the vacant d-orbitals of the iron atom, interaction between the HOMO of iron and LUMO of the additive molecules (reterodonation/backbonding) is equally important. Since the antiwear additives are polar molecules, the extent of interaction between the HOMO of the additives and the LUMO of iron may always be higher than the that of the HOMO of the iron and the LUMO of the additives i.e. ΔE₁ < ΔE₂.

A greater transfer of electron density from the additive molecules to the vacant d-orbital of the iron atom accumulates the electron density on the iron. The fraction of electrons transferred (ΔN) from the additive to the vacant d-orbital of the iron atom has been calculated using eqn (7) as suggested by Martinez⁴⁷ and the results are listed in Table 2. From Table 2, it can be clearly seen that the maximum amount of transferred electrons from the additive to iron has been found in the case of H₂STC-p-ClPh. Consequently, it develops a better tendency to donate back electrons to the vacant orbital of the additive. This favors the extent of back donation (synergistic bonding). It is evident from Table 1 that the values of interaction parameters ΔE₁ (E_LUMO of iron − E_HOMO of additive) are always lower than ΔE₂ (E_LUMO of additives − E_HOMO of iron) for all three additives. The order of antiwear efficiency of the additives emerging on the basis of the values of ΔE, ΔE₁, ΔE₂ and ΔN, is found to be exactly the same as that of their antiwear lubrication behavior evaluated experimentally with a four ball lubricant tester.²

Table 2 Quantum chemical descriptors for the studied Schiff bases as antiwear lubricant additives

Additives	I	A	χ	μ	η	S	ΔN	ω
Fe5 (ref. 43)	0.18651	0.06420	0.12535	−0.12535	0.06116	8.17
H2STC–Ph	0.00189	−0.00954	−0.00765	0.00765	0.00572	87.41	0.8948	0.005116
H2STC-p-MePh	0.00170	−0.00768	−0.00299	0.00299	0.00469	100.61	0.8960	0.000953
H2STC-p-ClPh	0.00142	−0.00086	0.00028	−0.00028	0.00114	438.59	0.9971	0.000035

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3.2. Mechanism of antiwear behavior using the HSAB principle and quantum chemical parameters

Initially the iron surface is exposed to air, therefore, there is formation of iron oxides on the surface due to its oxidation. According to Pearson's HSAB principle,^29,35 “hard acid prefers to react with hard base and soft acid prefers to react with soft base”. Thus, it is supposed that there was no interaction in the beginning between the oxidized iron surface containing Fe³⁺ (hard acid) and sulfur containing additives (soft base). Later on, under operating conditions as the time and/or load increases, the oxide film may rupture and thus nascent iron surface (soft acid) was generated which further oxidized into Fe²⁺ (borderline acid). Consequently, at this stage the sulfur containing additive molecules (soft base) may strongly interact with Fe (soft acid)/Fe²⁺ (borderline acid) through the appropriate energies of their HOMO and LUMO resulting in the formation of an adherent tribochemical film.⁴⁸ This newly generated tribofilm prevents direct asperity–asperity contact between the metal surfaces and hence reduces wear. According to Cavdar and Ludema⁴⁹ the formation of a tribofilm is time dependent under operating conditions; therefore, some time exposure is required to form a durable tribofilm on sliding surfaces. It is evident from the findings of the present communication also that a strong tribofilm is produced when there is significant interaction between the corresponding acid and base. Among the studied Schiff bases, maximum softness is exhibited by p-chlorothiosemicarbazone, thus maximum interaction with Fe/Fe²⁺ is expected to occur in this case forming a strong tribofilm resulting in an appreciable reduction in wear rate. The formation of the tribofilm has been further confirmed by EDX analysis in our previous work.² The wear rate in the absence of an additive was found to be 71.43 × 10⁻⁴ mm³ h⁻¹ which reduces to 53.00 × 10⁻⁴ mm³ h⁻¹ in presence of the said additive due to formation of a strong tribofilm.

Fig. 3 shows the highest occupied (HOMO) and the lowest unoccupied (LUMO) frontier molecular orbital (FMO) density distribution of the three Schiff bases H₂STC–Ph, H₂STC-p-MePh and H₂STC-p-ClPh. From these figures, it is evident that all the three additives exhibit a significant contribution of their p-orbitals related to a thiosemicarbazide moiety on their HOMO whereas phenyl rings along with thiosemicarbazide moiety have contributed to their respective LUMO.

Fig. 3 Frontier molecular orbitals (HOMO and LUMO) diagrams of investigated Schiff base antiwear additives respectively: (a and b) H₂STC–Ph, (c and d) H₂STC-p-MePh and (e and f) H₂STC-p-ClPh.

4. Conclusion

In order to investigate the reactivity of Schiff bases as antiwear additives with metal surfaces and correlate it with experimentally found wear rates, B3LYP/6-31++G(d,p) level calculations based on density functional theory have been performed. Various molecular orbital indices including the energy of the frontier molecular orbitals (E_HOMO and E_LUMO), energy gap (ΔE), ΔE₁, ΔE₂, dipole moment (μ), global softness (S) and the fraction of electrons transferred (ΔN) have been used as the criteria to study the interactions between the lubricant additives and the metal surface. The interactions of E_HOMO of the additives with the E_LUMO of iron (ΔE₁) and E_HOMO of the iron with E_LUMO of the additive (ΔE₂) have shown the occurrence of a synergistic bonding between the additive molecules and iron. On the basis of various quantum chemical parameters, the effectiveness of the studied antiwear additives was observed as:

H₂STC–Ph < H₂STC-p-MePh < H₂STC-p-ClPh

Among all the three Schiff bases H₂STC-p-ClPh has shown maximum wear reduction by lowering the wear rate. The density distributions of the frontier molecular orbitals (HOMO & LUMO) of the additive molecules have shown that the thiosemicarbazide moiety and phenyl rings are the preferential sites for chemical reaction with the surface of iron which is in accordance with the experimental observations.

Appendix

Energy gap, ΔE = E_LUMO − E_HOMO.

ΔE₁ = E_LUMO of iron − E_HOMO of additive.

ΔE₂ = E_LUMO of additive – E_HOMO of iron.

Ionization potential, I = −E_HOMO.

Electron affinity, A = −E_LUMO.

Absolute electronegativity, χ = (I + A)/2.

Global hardness, η = (I – A)/2.

Global softness, S = 1/2η.

Global electrophilicity index, ω = χ²/2η.

Fraction of electron transferred,

Acknowledgements

The authors are thankful to the Head, Chemistry Department, Faculty of Science, Banaras Hindu University, Varanasi, India for carrying out quantum chemical calculation studies.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3ra45806g

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