Introduction

Corrosion inhibitors (CI’s) play a critical role in combating corrosion in various industrial applications1. For example, the oil and gas industry extensively uses CI’s for well acidizing wherein strong, corrosive acids such as HCl and/or HF are pumped through steel tubings and casings at high temperatures and pressures in order to enhance the permeability of the rocks and, thus, increase productivity2,3,4,5. Owing to increasingly stringent environmental norms and increasing depths of oil and gas wells, there is a need for design of newer and more efficient CI’s. However, the conventional CI design and discovery is a largely empirical, cost and time-intensive process, characterized by hundreds of trial-and-error experiments. Sometimes, it may cost millions of dollars and several years to come up with a single new CI molecule for a particular application. For instance, Meier and Xie6 indicate that it took them almost 4 years, and development & screening of more than 400 individual molecules to come up with a single new inhibitor molecule for copper corrosion inhibition in cooling water applications in the presence of halogen based oxidizing biocides (such as HOCl and HOBr).

Although, computational techniques (such as molecular modeling/ machine learning) have been in vogue for the last couple of decades, their use has been largely confined to predicting inhibition mechanisms of known CI’s rather than discovery of new CI molecules per se barring a few works especially by Winkler et al.7,8,9,10. In this paper, we highlight the use of first principles density functional theory (DFT) based approaches (Fig. 1) in order to expedite rational CI design and discovery (and thus, complement experiments). Specifically, our work elucidates the DFT-based discovery of naphthalene 1-thiocarboxamide (NTC) as an excellent CI for steels at both room as well as elevated temperatures (60 °C) in HCl environment. We have performed detailed DFT-based quantum chemical, adsorption and coverage studies followed by experimental gravimetric and electrochemical studies to conclusively establish our findings.

Fig. 1: Framework for rational screening/ design of new organic CI’s.
figure 1

Egap refers to HOMO-LUMO gap calculated using DFT.

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Results and discussion

Quantum chemical descriptors

Quantum chemical descriptors (QCDs) were calculated from the NWchem optimized geometries. QCDs such as the highest occupied molecular orbital (EHOMO), lowest unoccupied molecular orbital (ELUMO) and Egap (ELUMO- EHOMO) are important parameters to explain the reactivity of a molecule. HOMO and LUMO (Fig. 2) can be seen to be spread throughout the NTC molecule suggesting a flat orientation on the Fe surface to be more stable. EHOMO generally indicates the capacity of the molecule to donate electrons while ELUMO indicates its capacity to accept electrons11. As reported in literature, molecules having high EHOMO and low ELUMO (both close to metal EFermi) are generally considered to be good CI’s as these would allow easy flow of electrons from molecule to metal (EHOMO) and vice-versa (ELUMO)12. Similarly, lower Egap generally corresponds to better reactivity of the molecule13. The more reactive molecules are likely to adsorb on the metal surface to form a protective layer, which in turn prohibits the direct contact of the metal surface with corrosive elements.

Fig. 2: HOMO, LUMO plots of NTC molecule.
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Isovalue: ± 0.08 eV Å^−3.

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In our efforts to identify suitable CI’s for vapor phase corrosion inhibition (VCI), we tried to compare the Egap values for a few, hitherto untested, sulfur containing compounds with that of 11-mercaptoundecanoic acid—a known VCI for steels14. Among the list of molecules tried, we found NTC to show the lowest Egap (Table 1) and therefore, potentially, the best inhibition efficiency. Obviously, this list is not exhaustive, and there can be certainly many more S-compounds with potential as inhibitors. However, for practical purposes, we limited ourselves to these molecules.

Table 1 EHOMO, ELUMO and Egap of various sulfur containing compounds.
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Adsorption studies

QCDs may serve as a good screening aid for identifying potential inhibitor molecules. However, being metal surface agnostic, they may not always work for all metals; moreover, they do not provide insight into the underlying inhibition mechanisms15. Therefore, explicit adsorption studies become imperative to further probe and establish the nature and strength of the molecule-metal surface interactions.

Several conformations (conf1-4) of NTC were considered on Fe (001) surface in order to arrive at the most stable adsorption geometry. The initial and optimized adsorption geometries are shown in Fig. 3 while the corresponding ΔEads are shown in Fig. 4. It can be seen that the flat conformations strongly adsorb on Fe surface via Fe—C, Fe—N and Fe—S chemical bonds while vertical conformations adsorb via only Fe—S bonds. The average bond lengths of Fe—C, Fe—N and Fe—S are 2.16, 2.18 and 2.25 Å respectively. These bond lengths are close to the sum of the covalent radii of respective bond-forming atoms (rcFe + rcC = 1.32 + 0.76 = 2.08 Å; rcFe + rcN = 1.32 + 0.71 = 2.03 Å; rcFe + rcS = 1.32 + 1.05 = 2.37 Å) suggesting that the bonds are of covalent type. Despite having similar initial conformations, conf1 and conf2 lead to significantly different final conformations and ΔEads values. On the other hand, conf3 and conf4 exhibit similar optimized adsorption geometries and ΔEads values; however, these ΔEads values are almost half that of the flat geometries (conf1 and conf2).

Fig. 3: Initial and optimized adsorption geometries of NTC on Fe surface.
figure 3

Violet, Yellow, Pale Yellow, Blue and Aqua represent Fe, C, S, N, and H atoms respectively.

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Fig. 4: Adsorption energies of different configurations of NTC adsorbed on Fe surface.
figure 4

Conf1 with flat orientation shows the highest magnitude of adsorption energy (|ΔEads|).

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Clearly, the flat orientation of the molecule in Conf1 facilitates extensive interactions between practically all the atoms of the NTC molecule and the underlying surface Fe atoms. In fact, a comparison of the |ΔEads | ( = 4.54 eV) values for NTC with that of another commonly used inhibitor, trans-cinnamaldehyde (TCA) ( | ΔEads | = 3.89 eV), reported in our earlier publication16 suggests that the former adsorbs much stronger ( ~ 17%) and, therefore, can be a promising inhibitor for steels.

Further, to shed some light on the interaction mechanism of NTC with Fe surface, electron density difference (EDD) and projected density of states (PDOS) were plotted for the most stable adsorption geometry (conf1). In the EDD plot (Fig. 5-Upper panel), blue regions show electron depletion while reddish-brown regions show electron accumulation. It is evident from the EDD plot that there is a significant charge redistribution happening between the molecule and the Fe surface because of strong hybridization of Fe-3d orbitals with C/N/S-2p orbitals. Moreover, the charge accumulation is occurring between C/N/S atoms of molecule and Fe atoms of the surface, thus, signifying that the bond formed between F—C/N/S is of covalent type17. The large perturbation of the electronic structure due to adsorption of NTC on Fe (001) also induces the sp2 to sp3 rehybridization of the molecular electronic structure—indicated by the shifting of H-atoms above the plane of the aromatic rings18.

Fig. 5: Electron density difference (top panel) and projected density of states (bottom panel) plots for the most stable Fe (001)-NTC adsorption conformation.
figure 5

In the top panel, blue regions indicate electron depletion while reddish-brown regions indicate electron enrichment. Isovalue: ± 0.003 eV Å^−3.

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Lower panel of Fig. 5 shows the PDOS of C/N/S-atoms adsorbed on Fe surface. For isolated or unadsorbed molecule, the molecular peaks are quite sharp and discrete.However, post adsorption, the molecular peaks broaden and become continuous. Furthermore, it can also be seen that there are significantly higher number of overlapping peaks in Fe—S and it goes on decreasing from S to C to N. Thus, it can be concluded that the interaction between Fe—S is the strongest while Fe—N is the weakest among the three bonds.

The Bader charges (Table 2) were calculated using projector-augmented-wave (PAW) potentials and a charge density kinetic energy cutoff of 800 Ry, for the most stable optimized configuration (conf1, DFT-D3), employing the algorithm developed by Henkelman’s group19. Analysis of Table 2 revealed a net transfer of charge (Δ = 1.74 e) from the Fe surface to the NTC molecule. Notably, the S atom of NTC receives the highest amount of charge (−0.193e), while the C atoms receive −0.135e charge on an average. This suggests that S/C atoms play a significant role in the strong NTC-Fe interactions validating the PDOS results above.

Table 2 Bader charges before and after adsorption of NTC on Fe surface. S, C and N atoms showing the largest change are marked in bold.
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Coverage studies

In addition to adsorption, corrosion inhibition also involves the creation of a compact, protective layer. The molecules must strongly adhere to the surface at high coverage to promote the formation of a protective film20. Therefore, it is essential to model coverage effects for a given CI molecule using DFT16,21. For this purpose, we have carried out detailed surface coverage studies for NTC on Fe (001) surface. The optimized structures for different coverages, viz. 1/48, 2/48, 3/48, and 4/48 in ML (where monolayer, ML, is the ratio of the number of inhibitor molecules to the number of metal atoms in the first layer of the surface) are displayed in Fig. 6. As shown in Fig. 7, the ΔEads decreases only slightly (~0.2 eV, 4.4%) with increase in coverage implying weak lateral repulsions between the molecules and therefore, formation of a more compact layer under actual conditions.

Fig. 6: Optimized structures of NTC on Fe (001) surface at various coverages.
figure 6

a 0.021 (1/48), b 0.042 (2/48), c 0.062 (3/48), d 0.083 (4/48) ML. Legend: Silver, Yellow, Pale Yellow, Blue, and Aqua represent Fe, C, S, N, and H atoms respectively.

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Fig. 7: Variation of ΔEads (-eV) with surface coverage (ML).
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Figure shows the influence of surface coverage on adsorption energy of NTC molecule on Fe (001) surface.

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Apart from ΔEads computations at different coverages, we have also computed the adsorption surface free energy, γads, which is the ΔEads normalized to a unit surface area and plotted as a function of the molecular chemical potential μ. This is done because as per Kokalj22, γads as a function of μ is a better indicator of stability. The γads is given by the following correlation (Eq. (1)):

$${{\rm{\gamma }}}_{{ads}}\approx \frac{n\left(\varDelta {E}_{{ads}}-\mu \right)}{A}$$
(1)

Where n is the number of NTC molecules adsorbed on the Fe surface with an area, A.

Fig. 8 shows the relationship between γads and μ at varying coverage levels. The coverage at which γads is most negative is considered to be the most stable. It is evident from Fig. 8 that the highest coverage (4/48) is most stable at μ > ~ −4.15 eV.

Fig. 8: Adsorption surface free energy (γads) versus molecular chemical potential (µ) at different coverages.
figure 8

Coverages studied: 1/48, 2/48, 3/48 and 4/48 ML, where monolayer, ML, is the ratio of the number of NTC molecules to the number of Fe atoms in the first layer of the surface.

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Thus, starting from the computation of quantum chemical descriptors of 9 sulfur containing compounds, followed by detailed adsorption and coverage studies for the best molecule (NTC) on Fe (001) surface, it has taken a total of only around 225 h (<10 days) of computations on a high-performance computer having the following specifications: 2x AMD EPYC 7532 32-Core Processor (64 cores per node), Frequency: 3.2 GHz. This is comparatively much faster (and also cheaper!) than what would have been otherwise required to identify this molecule using conventional empirical approaches. In the next section, we describe the successful experimental validation of this molecule based on simple weight loss and electrochemical studies.

Weight-loss tests

The values of inhibition efficiency (IE) for various concentrations of NTC were calculated using the below formula (Eq. (2)):

$${\rm{IE}}\left( \% \right)=\left[1-\frac{{\rm{corrosion}}\; {\rm{rate}}\; {\rm{with}}\; {\rm{inhibitor}}}{{\rm{corrosion}}\; {\rm{rate}}\; {\rm{without}}\; {\rm{inhibitor}}}\right]\,{\rm{x}}\,100$$
(2)

An increase in inhibition efficiency could be seen with increasing concentration, as shown in Table 3. In general, the cathodic reaction for steel corrosion in HCl is hydrogen evolution reaction (HER) characterized by bubble formation and evolution. The rapidity of bubble evolution was observed to decrease with increasing concentration, and could not be noticed at all, for 0.2, 0.7, and 1 mM concentration values suggesting very low corrosion rates, as also, indicated in Table 3 and the lack of metallic lustre loss at these concentration values. This is also consistent with our DFT coverage studies which hint towards the formation of a compact layer with very little lateral repulsion between the molecules.

Table 3 Results of weight-loss experiments.
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At 60 °C, the steel underwent rapid corrosion; however, in the presence of 1 mM NTC, the corrosion rate dropped to a value almost 2 orders of magnitude lower. The exceptionally high inhibition efficiency values at both room temperature (97.23%) as well as at 60 °C (98.54%) using merely 1 mM concentration, indicate that NTC can be a highly effective inhibitor for steels in acidic media.

Based on the above experimental data, different adsorption isotherms (like Langmuir, Temkin, and Frumkin) were evaluated. It was found that the adsorption of NTC on mild steel follows the Langmuir isotherm (Fig. 9):

$$\frac{C}{\theta }=\frac{1}{{{\rm{K}}}_{{\rm{ads}}}}+C$$
(3)

where Kads represents the equilibrium constant for adsorption, C and θ (IE/100) represent the inhibitor concentration (mM) and surface coverage respectively.

Fig. 9: Langmuir adsorption isotherm plot for NTC adsorption on mild steel in 1 M HCl.
figure 9

Here C indicates the concentration of NTC in mM and θ represents surface coverage (IE/100).

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From the obtained Kads value using the above expression (Eq. (3)), the free energy of adsorption (ΔGads) was calculated using the expression (Eq. (4)):

$$\Delta {{\rm{G}}}_{{\rm{ads}}}=-R{\rm{T}}\mathrm{ln}\left(55.5{{\rm{K}}}_{{\rm{ads}}}\right)$$
(4)

Where, R is the universal gas constant and T is the absolute temperature in Kelvin.

A ΔGads value of −22.16 kJ mol^−1 was calculated from the above expression. The negative value indicates a spontaneous adsorption of NTC on mild steel. Generally, ΔGads > −20 kJ mol^−1 (< −40 kJ mol^−1) are considered to indicate physisorption (chemisorption) while intermediate values of ΔGads ∈ [−20, −40] kJ mol^−1 indicate mixed physisorption/chemisorption. Based on the intermediate value of ΔGads so obtained, it appears that adsorption of NTC on mild steel is via both physical and chemisorption. However, as discussed by Kokalj23 recently, the value of ΔGads is not a very reliable criteria to distinguish between physisorption and chemisorption. Instead, he suggests the molecule-surface distance and the electronic structure analysis of the molecule-surface bonding readily available from computational studies as better options. From our DFT computed bond lengths and electron density difference plots (as reported in the previous sections), it is clear that NTC adsorbs via chemisorption on Fe surface.

Additionally, one of the inherent assumptions in Langmuir adsorption isotherm is that there are no lateral interactions between the adjacent adsorbing molecules. Thus, the heat of adsorption of the corrosion inhibitor ΔHads is independent of fractional coverage of the inhibitor24. Using our DFT computed ΔEads values as indicators of the experimental ΔHads values (as reported in earlier section), the small changes in ΔEads as a function of coverage are validated by the observation of a Langmuir-type adsorption isotherm. It must be mentioned that in our previous publication on trans-TCA20, our DFT computations indicated a Temkin-type isotherm consistent with the experiments.

Potentiodynamic polarization

NTC seems to be a mixed inhibitor for the current system, as can be deduced from Fig. 10. The polarization plots were analyzed using VersaStudio software to arrive at corrosion current densities (Icorr) which are directly proportional to corrosion rates. Table 4 confirms the excellent inhibition efficiencies at all the concentrations tested, in agreement with the weight loss results reported in the previous section. The following equation (Eq. (5)) was employed to calculate the IE’s at various concentrations:

$${\rm{IE}}\left( \% \right)=\left[1-\frac{{{\rm{I}}}_{{\rm{corr}}}{\rm{with}}\; {\rm{inhibitor}}}{{{\rm{I}}}_{{\rm{corr}}}{\rm{without}}\; {\rm{inhibitor}}}\right]\,{\rm{x}}\,100$$
(5)
Fig. 10: Polarization curves.
figure 10

Change in current density (A cm^-2) in response to applied potential (V) at various NTC concentrations.

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Table 4 Results of potentiodynamic polarization experiments.
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The polarization resistance was calculated using the Stern-Geary equation (Eq. (6)):

$${{\rm{R}}}_{{\rm{p}}}=\frac{{{\rm{\beta }}}_{{\rm{c}}}\cdot {{\rm{\beta }}}_{{\rm{a}}}}{2.303\cdot {{\rm{I}}}_{{\rm{corr}}}\cdot \left({{\rm{\beta }}}_{{\rm{c}}}+{{\rm{\beta }}}_{{\rm{a}}}\right)}$$
(6)

where, βa and βc correspond to the anodic and cathodic slopes in the polarization curve for a particular NTC concentration.

The corrosion current densities show a decrease of corrosion by at least twenty times in 1 M HCl due to the molecule. It is remarkable that the current density at 1 mM NTC (2.93 µA cm^−2) is almost one-fourth of that for the industrially used inhibitor, TCA at 7.5 mM (1000 ppm) for the same steel as reported in our previous publication16. This again reinforces our weight-loss results’ inference that NTC can be a promising inhibitor for steels in acidic media. Cathodic branches clearly show similarity in behaviour at lower concentrations, which is different from the behaviour at higher concentrations indicating an influence of molecule on the HER beyond 0.2 mM concentration. The anodic branches at three higher concentrations (0.2, 0.7, and 1 mM) differ from that of the lowest concentration (0.05 mM) indicating a change in inhibition mechanism.

Electrochemical impedance spectroscopy

The impedance studies with the molecule at different concentrations resulted in Nyquist plots as shown in Fig. 11, which are analyzed using the ZSimpWin software to understand the influence of the molecule at the metal-solution interface. The behavior of the interface for blank and with various concentrations of inhibitor could be understood using the equivalent electrical circuits R(QR) and R(Q(R(QR))). The IE’s at various concentrations of the molecule were calculated using the charge transfer resistance, Rct, with the help of the below equation (Eq. (7)):

$${\rm{IE}}\left( \% \right)=\left[1-\frac{{{\rm{R}}}_{{\rm{ct}}}{\rm{without}}\; {\rm{inhibitor}}}{{{\rm{R}}}_{{\rm{ct}}}{\rm{with}}\; {\rm{inhibitor}}}\right]\,{\rm{x}}\,100$$
(7)
Fig. 11: Nyquist plot showing the impedance response of mild steel in various concentrations of NTC.
figure 11

The increase in diameter of the semi-circle shows increased charge transfer resistance and thereby increased corrosion inhibition with NTC concentration.

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The impedance due to constant phase element, Q was evaluated using the equation25 (Eq. (8)):

$${{\rm{Z}}}_{{\rm{Q}}}=\frac{1}{{{\rm{Y}}}_{{\rm{o}}}{\left({\rm{j}}\omega \right)}^{n}}$$
(8)

The increasing Rct values suggest an increasing inhibition with concentration (Table 5). A very high Rct (6187 Ω cm^2) as seen with 1 mM implies outstanding protection, thus further supporting the observations from weight-loss and polarization studies.

Table 5 EIS results for various concentrations of the inhibitor.
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To summarize, in this paper we highlight the use of first principles density functional theory (DFT) based approaches in order to expedite rational CI design and discovery (and thus, complement experiments). Specifically, our work elucidates the DFT-based discovery of naphthalene 1-thiocarboxamide (NTC) as an excellent CI for steels at both room as well as elevated temperatures (60 °C) in HCl environment. The computed quantum chemical descriptors gave preliminary indication of the promising adsorption ability of NTC. This was further validated with explicit adsorption studies which reveal strong flat chemisorption of NTC onto the Fe (001) surface, forming covalent bonds Fe- S/C/N, further corroborated by EDD and PDOS analyses. Coverage studies also suggest that NTC forms a compact monolayer (essential for good corrosion inhibition) on Fe surface with little lateral repulsions between the adjacent molecules. Gravimetric, potentiodynamic polarization, and Electrochemical Impedance Spectroscopy studies, all confirmed NTC as a remarkable inhibitor for mild steel, thus, testifying the powerful role of DFT in screening & design of new, more efficient corrosion inhibitors.

Methods

Computational methodologies

Molecular structure of NTC was created in Avogadro −1.2.026 and subsequently optimized using NWchem −6.827. For the geometry optimization, the exchange-correlation functional and basis set used were B3LYP28 and 6-311 + + G**29, respectively. Energy and force cutoffs of 0.0027 meV and 0.027 meV Å^−1 respectively were used during the optimization. The NTC molecule (Fig. 12) was fully relaxed without any constraints.

Fig. 12: Molecular structure of NTC.
figure 12

a Chemical structure and b DFT optimized molecular geometry of NTC molecule. Legend: Yellow, Pale Yellow, Blue, and Aqua represent C, S, N, and H atoms respectively.

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The adsorption and coverage studies for NTC on Fe (001) surface were investigated using Plane-Wave, spin-polarized DFT method as implemented in the PWscf code of Quantum Espresso −6.730. The exchange-correlation functional was described using the Perdew-Burke-Ernzerhof (PBE)31 scheme within the framework of the generalized gradient approximation (GGA). All calculations were performed with a kinetic energy cut-off of 35 Ry and a charge density cut-off of 300 Ry. The van der Waals interactions were taken into account by using Grimme’s semi-empirical correlation (DFT-D3)32 as built in the PWscf code. The bulk Fe was fully optimized using a uniform Monkhorst-Pack k-points mesh33 of 8x8x8. A 5 × 4 supercell containing 5 layers of Fe-atoms was created, and then fully relaxed until the force on each atom dropped below 0.0025 eV Å^−1. For the surface coverage studies, a larger supercell size of 6 × 8 was employed to accommodate larger number of molecules (1/48, 2/48, 3/48, 4/48 ML). Due to the large system sizes, the surface relaxations and subsequent NTC adsorption on Fe surface were carried out at Γ-point. Further details on this section can be found in Kumar et al.17. The adsorption energies (ΔEads) were computed using the expression (Eq. (9)):

$$\Delta {{\rm{E}}}_{{\rm{ads}}}=\frac{1}{N}[{{\rm{E}}}_{{\rm{complex}}}-\left({{\rm{E}}}_{{\rm{slab}}}+N* {{\rm{E}}}_{{\rm{mol}}}\right)]$$
(9)

where, Ecomplex, Eslab, and Emol are the total energies of the NTC-Fe (001) complex, Fe (001) slab and the NTC molecule respectively, while N represents the number of NTC molecules.

Experimental studies

NTC was evaluated for its acid corrosion inhibition characteristics on mild steel using weight-loss tests, potentiodynamic polarization and electrochemical impedance spectroscopy (EIS) in 1 M HCl. The electrochemical tests were carried out at ambient atmospheres i.e. ~27 °C, on 1 cm^2 area of mild steel in 300 ml electrolyte with the help of Ametek K0235 flat cell comprising Pt mesh counter electrode, Ag/AgCl with Vycorr® tip as reference electrode. Ametek PARSTAT 1000 AC/DC Potentiostat was used for electrochemical tests.

Materials

NTC (>97%, CAS: 20300-10-1), Sigma-Aldrich—make was used in all the tests as received. The molecule was evaluated on the coupons of mild steel grade IS2062 with a composition shown in Table 6. Surfaces of metal coupons were prepared on emery papers of grits 80, 150, 240, 400, and 600, following which the coupons were cleaned with acetone and preserved in a desiccator to avoid contact with moisture and/or any corrosion. Tetrahydrofuran was used as a solvent for the molecule.

Table 6 Composition of IS2062 mild steel used for experimental study.
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Weight-loss tests

NTC was tested at various concentrations such as 0.05, 0.2, 0.7, and 1 mM on metal coupons in 1 M HCl under room temperature conditions i.e. ~27 °C. In addition, similar tests were conducted at 60 °C for 1 mM concentration. The coupons were washed with distilled water, followed by air drying, after 2 h of immersion in test solution. The weight-loss was calculated from the observed weights of the coupons before and after the tests.

Potentiodynamic polarization studies

A scan rate of 1 mV s^−1 was used for potentiodynamic polarization studies to increase the potential from −250 mV to +250 mV with respect to Open Circuit Potential (OCP). The results were analysed using VersaStudio, a proprietary software provided by Ametek Scientific Instruments.

Electrochemical impedance spectroscopy

A perturbation voltage of 10 mV was used for impedance studies between the frequencies 105 and 10−1 Hz of AC signal. The results were analysed using ZSimpWin, a proprietary software provided by Ametek Scientific Instruments.