1 Introduction

Mild steel due to its outstanding mechanical properties such as high tensile strength, impact strength, easy availability, low price is used in diverse industries such as construction or structural material, in chemical reactors, oil, and gas transport pipelines, manufacturing of automobiles, etc. [1]. The most commonly used acid solutions for removal of rust, de-scaling, and pickling before plating are hydrochloric acid and sulphuric acid [2]. Mild steel undergoes corrosion when exposed to acidic environments and hence their surface must be protected. Protection of metals from corrosion is important as corrosion leads to a great loss of material, as well as economy. The consequence of corrosion is tremendous, and its inhibition has been profoundly examined. It has been tracked down that perhaps the best strategy for protecting materials against electrochemical degradation includes the addition of inhibitors that are substances that minimize the rate of corrosion [3]. Subsequently, in the field of corrosion and industry, there is always a need to develop and use corrosion inhibitors which are an effective and reasonably low-cost method, to minimize the corrosive damage on materials. Literature reports indicated that usually compounds comprising of heteroatoms, unsaturated bonds, and aromatic or heterocyclic rings performed as inhibitors [4, 5]. Adsorption of inhibitor molecules on a material surface is responsible for corrosion inhibition. The adsorption relies fundamentally upon the electronic structure of the molecule. The effectiveness of the inhibitor relies upon its structure and the type of interaction with the metal surface [6].

To alleviate corrosion of mild steel in acid medium, hydrazide derivatives [7,8,9,10,11], thiosemicarbazide derivatives, acid hydrazide derivatives, and hydrazone derivatives [12,13,14,15] are reported. This is because of their exceptional structural features. The planarity of the whole structure of the compound dictates the formation of an adsorption film on the metal. [16]. As a part of our work on corrosion inhibition, we hereby report the corrosion rates of mild steel in 0.5 M H2SO4, determined by electrochemical techniques and its inhibition by (2E)-2-[Furan-2-ylmethylidene] hydrazine carbothioamide (FMHC) at three different temperatures. The synthesized inhibitor possesses a linear structure with active centers like heteroatoms, electron-donating groups, etc., which is the major requirement of efficient inhibitor.

2 Experimental details

2.1 Material

The composition of the test coupon of mild steel utilized for corrosion study is given in Table 1.

Table 1 Composition of specimen
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2.2 Test specimen preparation

The mild steel test specimen was readied by means of cold setting resin. The uncovered level surface (1 cm2) of the mounted part was subjected to polishing with different coarseness levels of emery papers and later the surface was finished by disc polishing with levigated alumina. Test coupon was washed with water, acetone and dried.

2.3 Preparation of medium

The stock of 1 M solution of H2SO4 was prepared from AR H2SO4. The solution was standardized by volumetric titration. As and when required from the stock, by proper dilution, the desired concentration was prepared.

2.4 Synthesis of (2E)-2-(furan-2-ylmethylidene) hydrazine carbothioamide (FMHC)

As per the reported literature, [17] (2E)-2-(furan-2-ylmethylidene) hydrazine carbothioamide (FMHC) was synthesized. An equimolar mixture of furan-2-aldehyde and thiosemicarbazide with sulphuric acid was refluxed on a boiling water bath for around 4 h. Ethanol was used for the recrystallization of the precipitated product. The scheme for the preparation of FMHC is given in Fig. 1. The characterization was done by IR and spectra is shown in Fig. 2.

Fig. 1
figure 1

Synthetic route for FMHC

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Fig. 2
figure 2

IR spectra of FMHC. C6H7N3OS m. p: 230—232 °C IR (KBr) [cm−1]: 3255.95 (OH str.), 3186 (NH str.), 3035 (Ar. CH str.), 1614(C = O), 1600 (C = N str.), and 1600 (Ar. C = C str.)

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2.5 Electrochemical studies

Electrochemical examinations were performed with a potentiostat (USA Model 604D with beta programming). Pyrex glass cell with 3 electrodes, namely, counter (platinum), saturated calomel reference electrode (SCE), and the working electrode (mild steel) was used. A finely polished mild steel test coupon was introduced to 0.5 M sulphuric acid in the absence and presence of the inhibitor at various temperatures (303–323 K) and endorsed to establish an open circuit potential (OCP). PDP plots were recorded by drifting the potential of the test specimen to – 250 mV cathodically and + 250 mV anodically with respect to the OCP for a sweep speed of 0.5 mV s−1 [18]. The impedance tests were done by applying in the periodic AC signal of 10 mV in the wide frequency range of 100 kHz to 0.01 Hz on the OCP [19].

2.6 Surface studies

Scanning electron microscopy (SEM) images of test specimen were noted using (JEOL JSM-6380 L) scanning electron microscope. The surface of the corroded sample was studied by dipping it in 0.5 M sulphuric acid solution for 3 h in absence and presence of FMHC.

2.7 Quantum chemical calculations

Schrodinger programming (Maestro Material Science) was utilized to do quantum chemical estimations. The DFT was used to optimize the geometry of inhibitor FMHC. Computations were done using the Hybrid functional with the correlation functional (B3LYP) and 6-31G** as the basis set. For neutral and protonated FMHC, frontier molecular orbital (FMO) energies were determined and explained in depth. Distinctive hypothetical parameters like the energy gap(∆E), hardness (η), softness(σ), electronegativity (χ), electrophilicity (ω), nucleophilicity (ε), and portion of electron transferred (ΔN) were assessed utilizing appropriate equations [20,21,22]. Mulliken charge population was assessed. The dipole moment of protonated and neutral FMHC was found and compared.

3 Results and discussion

3.1 Potentiodynamic polarization studies

The potentiodynamic polarization graphs for mild steel in 0.5 M H2SO4 at 313 K without and with the addition of FMHC are shown in Fig. 3. Electrochemical parameters such as corrosion potential (Ecorr), corrosion current density (icorr), cathodic slope (− βc), and anodic slope (βa) were noted and corrosion rate (CR) and percentage inhibition efficiency (%IE) were calculated [23] using Eqs. (1) and (2), respectively.

$${\text{CR}}\left( {{\text{mmy}}^{ - 1} } \right) = \frac{{3270 \times M \times i_{{{\text{corr}}}} }}{d \times n}$$
(1)
$$IE\% = \left( {\frac{{i_{{{\text{corr}}}} - i_{{{\text{corr}}\left( {inh} \right)}} }}{{i_{{{\text{corr}}}} }}} \right) \times 100$$
(2)
Fig. 3
figure 3

PDP plot for corrosion of mild steel in presence of diverse FMHC concentrations in 0.5 M H2SO4 at 313 K

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icorr and icorr(inh) are corrosion current density (μA cm−2) in the absence and presence of the inhibitor, 3270 is a constant, M is the atomic mass of corroding material [55.85], d = density of corroding material (7.725 g cm−3), and n is the number of electrons involved in the reaction (n = 2). Fraction of surface covered (θ) is calculated using Eq. (3)

$$\% {\text{IE}} = \theta \times 100$$
(3)

From Fig. 3, it was seen that the corrosion potential does not shift much with respect to blank. The slight difference in the cathodic and anodic slope shows the influence of the inhibitor FMHC on the reaction kinetics but not on the mechanism [24, 25]. The results of Tafel polarization are tabulated in Table 2.

Table 2 Results of PDP measurements
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From Table 2 it is evident that the corrosion rate of mild steel amplified with the upsurge in temperature in absence of FMHC. Added FMHC lessened the rate of corrosion. IE decreased with an increase in temperature. The exothermic nature of the adsorption process is suggestive of physical adsorption [26].

3.2 Electrochemical impedance spectroscopy

The Nyquist plot for the corrosion of mild steel in 0.5 M H2SO4 is shown in Fig. 4. The plot consists of two loops. One loop is high-frequency (HF) capacitive loop and another is small inductive loop at medium frequency (MF). Capacitive loop at high frequency stands for resistance for charge transfer. Diameter of the capacitive loop increased after the addition of inhibitor and increased further with increase in concentration of inhibitor. It clearly demonstrated the ability of inhibitor molecule to bring down the rate of charge transfer and hence corrosion [27]. Small inductive loop could be due to relaxation effect either due to hydrogen ion or corrosion product or metal ion inhibitor complex.

Fig. 4
figure 4

a Nyquist plots and b equivalent circuit fitment

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The appropriate equivalent circuit was used to simulate the impedance data with FMHC as shown in Fig. 4b. It consisted of 5 elements. They are solution resistance (Rs), charge transfer resistance (Rct), time constant phase element (Q), an inductive element (L), and inductive resistance (RL) [28].

The collective resistance due to the charge transfer and inductive loop is considered polarization resistance (Rp). It is calculated as per Eq. (4)

$$R_{{\text{p}}} = \frac{{R_{{{\text{ct}}}} \times R_{{\text{L}}} }}{{R_{{{\text{ct}}}} + R_{{\text{L}}} }}$$
(4)

The increase in the concentration of inhibitor added tends to decrease the double-layer capacitance (Cdl) because of the decrease in the double-layer thickness [29]. CPE acts as an ideal double-layer capacitance (Cdl). It was calculated from the frequency (fmax) at which the imaginary component of impedance becomes maximum (Zimp, max) using Eq. (5)

$$C_{{{\text{dl}}}} = \frac{1}{{2\pi R_{{{\text{ct}}}} f_{\max } }}$$
(5)

Calculation of percentage inhibition was done using Eq. (6)

$${\text{IE}}\left( \% \right) = \frac{{R_{{{\text{ct}}\left( {{\text{inh}}} \right) - }} R_{{{\text{ct}}}}^{0} }}{{R_{{{\text{ct}}\left( {{\text{inh}}} \right)}} }}$$
(6)

where Rct and \(R_{{{\text{ct}}}}^{0}\) show the charge transfer resistance in the presence and absence of inhibitor. Results are tabularized in Table 3

Table 3 Results of EIS measurements
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It is evident from Table 3 that the Cdl values decreased with a rise in inhibitor concentration at all studied temperatures. Increased Rct values at increased concentrations of FMHC resulted in improved corrosion resistance. This suggests the presence of a barrier layer on the electrode surface. The results obtained by the PDP and EIS method for the corrosion of mild steel in 0.5 M H2SO4 with FMHC were in good agreement at all studied temperatures.

3.3 Effect of temperature

Influence of temperature on the corrosion rate of mild steel and inhibition efficiency of inhibitor was studied at temperatures range of 303 K to 323 K. Figure 5 depicts the variation of % IE at varying concentrations of FMHC at different temperatures.

Fig. 5
figure 5

Variation of % IE with temperatures and FMHC concentrations

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Using Arrhenius equation (Eq. 7), calculation of the activation energy (Ea) was done

$$\ln \left( {{\text{CR}}} \right) = B - \frac{{E_{{\text{a}}} }}{RT}$$
(7)

where B = Arrhenius pre-exponential constant and R = universal gas constant.

The slope of the plot of ln CR vs 1/T (Fig. 6a) [30] is used to calculate the activation energy. Enthalpy of activation (∆Ha) and entropy of activation (∆Sa) were found out using the transition state Eq. (8)

$${\text{CR}} = \frac{RT}{{Nh}}\exp \left( {\frac{{\Delta S^{\# } }}{RT}} \right)\exp \left( {\frac{{ - \Delta H^{\# } }}{RT}} \right)$$
(8)
Fig. 6
figure 6

Plot of a ln(CR) Vs (1/T) and b ln(CR/T) vs 1/T

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Here h is Planck’s constant and N is Avogadro’s number. Plot of ln(CR/T) vs 1/T [Fig. 6b] gave a straight line. From slope and intercept, activation parameters were evaluated and recorded in Table 4.

Table 4 Activation parameters
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The increase in activation energy indicates an increase in the energy barrier for the corrosion reaction. Ea values increased with an increase in FMHC concentration suggesting the physisorption. The negative value of entropy of activation (∆Sa) indicates the association process during the formation of the activated complex [31, 32].

3.4 Adsorption isotherm

Adsorption isotherm provides evidence for interaction among inhibitor and metal surface. It enables the understanding of the mechanism of corrosion inhibition. FMHC adsorbs on the metal surface and forms a barricade over it and isolates the metal surface from the medium. The efficiency of the inhibitor depends on the degree of surface coverage (θ). Linear fit of parameters to several adsorption isotherms in the temperature range was considered, and Langmuir's adsorption isotherm was obeyed. It is given by the expression (9)

$$\frac{{C_{{{\text{inh}}}} }}{\theta } = \frac{1}{K} + C_{{{\text{inh}}}}$$
(9)

where the K value indicates the equilibrium constant for metal-inhibitor interaction, Cinh is the inhibitor concentration, and θ is the degree of surface coverage [33]. The plots of Cinh/θ versus Cinh for different temperatures give a straight line with intercept 1/K as shown in Fig. 7

Fig. 7
figure 7

Langmuir adsorption isotherm

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Standard free energy of adsorption \(\left( {\Delta G_{{{\text{ads}}}}^{0} } \right)\) is related to adsorption/desorption constant (K) by relation (10)

$$K = \frac{1}{55.5}\exp \left( {\frac{{ - \Delta G_{{{\text{ads}}}}^{0} }}{RT}} \right)$$
(10)

where R is the universal gas constant, T is absolute temperature, and 55.5 is the concentration of water in solution in mol dm−3 [34].

As per the reported literature [35, 36] \(\Delta G_{{{\text{ads}}}}^{0}\) more negative than − 40 kJ mol−1 is suggestive of chemical adsorption. However, in the present study value of \(\Delta G_{{{\text{ads}}}}^{0}\) is found to be between − 33 kJ mol−1 and − 35 kJ mol−1.. It is clearly suggestive of physical adsorption. In order to get a clear-cut picture of the nature of adsorption, detailed quantum chemical calculations are done and discussed in Sect. 3.6

3.5 Role of FMHC in corrosion inhibition

Adsorption of FMHC is a consequence of the replacement of water molecules which is usually adsorbed on the metal surface.

$${\text{Inh}}_{{({\text{sol}})}} + n{\text{H}}_{{2}} {\text{O}}_{{\left( {{\text{ads}}} \right)}} \leftrightarrow {\text{Inh}}_{{({\text{ads}})}} + n{\text{H}}_{{2}} {\text{O}}_{{({\text{sol}})}}$$
$${\text{6H}}_{{2}} {\text{SO}}_{{4}} + {\text{3Fe}} \to {\text{3Fe}}\left( {{\text{HSO}}_{{4}} } \right)_{{2}} + {\text{3H}}_{{2}}$$
$${\text{3Fe}}\left( {{\text{HSO}}_{{4}} } \right)_{{2}} \to {\text{Fe}}_{{3}} \left( {{\text{SO}}_{{4}} } \right)_{{2}} + {\text{4H}}_{{2}} {\text{SO}}_{{4}}$$

The metal surface is positively charged when in contact with H2SO4 [37]. Because of the accumulation of positive charges at the interface, sulfate ions get adsorbed here because of electrostatic interaction, leading to the formation of the electrical double layer. These negative charges will allure protonated FMHC for adsorption. In this way, protonated FMHC gets electrostatically adsorbed on mild steel, which was previously covered with sulfate ions. Likewise, at cathodic regions also, protonated FMHC gets adsorbed thereby decreasing the rate of hydrogen evolution [38, 39]. Schematic illustration of corrosion inhibition mechanism of FMHC is depicted in Fig. 8.

Fig. 8
figure 8

Schematic representation of the mechanism of corrosion inhibition by FMHC

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3.6 Quantum chemical study

As per Pearson’s Hard Soft Acid–Base (HSAB) theory, the energy gap is difference between the highest occupied molecular orbital (EHOMO) and lowest unoccupied molecular orbital (ELUMO) of the inhibitor molecule [40]. Further, EHOMO is directly connected to ionization energy and ELUMO is directly linked to electron affinity. Hence liability of a molecule toward electrophilic attack is designated by EHOMO, while the vulnerability of a molecule toward nucleophilic attack is shown by ELUMO [41]. Optimized structures of FMHC and frontier orbital electron density distribution for neutral FMHC are shown in Fig. 9.

Fig. 9
figure 9

Optimized structure and frontier orbital electron density distribution for neutral FMHC

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FMHC gets protonated in an aqueous acidic medium and involves in the physical adsorption process. Optimized structure and frontier orbital electron density distribution for protonated FMHC are shown in Fig. 10.

Fig. 10
figure 10

Optimized structure of protonated inhibitor molecule and its frontier electron density distribution

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It becomes essential to know the electron population or electron density distribution within the inhibitor molecule. The preferred site for protonation of FMHC is heteroatom with remarkably high negative Mulliken charges. [42, 43]. Mulliken charge distribution in various heteroatoms present in FMHC is given in Fig. 11 and Table 5.

Fig. 11
figure 11

Mulliken charge distribution

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Table 5 Mulliken charges on heteroatoms of FMHC
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Table 6 reports the various parameters of the quantum chemical study of FMHC (for neutral and protonated molecules) [44,45,46,47].

Table 6 Quantum chemical parameters of the neutral and protonated FMHC
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When EHOMO of the neutral molecule is associated with that of protonated FMHC, there is a diminution in the value showing that electron-donating ability decreased significantly after protonation. Further, the ELUMO value also reduced to a significant extent suggesting that the electron-accepting capacity of the FMHC increased. After protonation, the global electronegativity \((\chi )\) increased twofold. Electrophilicity index \((\omega )\) increased, and nucleophilicity (\(\epsilon )\) decreased to a large extent in the case of protonated FMHC. This led to stable layer formation on the surface of mild steel as a decrease in the energy gap \((\Delta E,)\) between EHOMO and ELUMO. For a neutral FMHC, the fraction of electron transferred \((\Delta N)\) is 0. 26, whereas for protonated FMHC molecule, it is − 1.63. This suggested that a neutral molecule can give electrons, whereas after protonation, its electron giving capacity is reduced and its tendency to receive electrons increased many folds [44]. This again reaffirmed the physisorption of protonated FMHC molecules onto the surface of mild steel.

The dipole moment (μ) of the neutral FMHC is 1.150 Debye. After protonation, the dipole moment is 8.811 Debye. The large increase in the value of dipole moment for protonated molecule compared to that of water molecule confirmed its physical adsorption on metallic surface replacing water molecule [48].

3.7 Surface morphology studies

The impact of FMHC on corrosion of mild steel was evaluated by recording the SEM pictures. Mild steel was immersed in 0.5 M H2SO4 for 3 h with and without inhibitor. Figure 12a shows the pits because of the destructive activity of 0.5 M H2SO4 on the mild steel surface with cracks and unpleasant, uneven, in homogeneous surface. Figure 12b depicts steel surface after immersion in 0.5 M H2SO4 containing 2.5 × 10–4 M FMHC. It is quite evident that surface has become relatively smooth in large area due to the adsorption of FMHC.

Fig. 12
figure 12

SEM images: a MS + 0.5 M H2SO4 and b MS + 0.5 M H2SO4 + 2.5 × 10–4 M of FMHC

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4 Conclusions

  1. 1.

    The effectiveness of FMHC increased with its concentration and lessened at elevated temperatures.

  2. 2.

    FMHC performed as a moderate mixed type of inhibitor, endured physical adsorption, and adapted Langmuir’s adsorption isotherm.

  3. 3.

    FMHC showed inhibition efficiency of 60% at concentration of 2.5 × 10–4 M at 303 K.

  4. 4.

    Surface studies confirmed the adsorption of FMHC on the metal.

  5. 5.

    Quantum chemical calculations supported the mechanistic aspect of corrosion.