Electrochemical-kinetics, MD-simulation and multi-input single-output (MISO) modeling using adaptive neuro-fuzzy inference system (ANFIS) prediction for dexamethasone drug as eco-friendly corrosion inhibitor for mild steel in 2 M HCl electrolyte.

In this research, the effect of Dexamethasone drug (DM) on mild steel corrosion  in  2 M HCl was analyzed using weight loss, potentiodynamic polarization, electrochemical impedance spectroscopy (EIS) and MD-simulation. In addition, Fourier transform infrared spectra (FTIR), scanning electron microscopy (SEM), Energy dispersive x-ray spectroscopy (EDX), and atomic force microscopy (AFM) were employed to inspect the mild steel surface in the blank and inhibited medium. For the optimization tool, adaptive neuro-fuzzy inference system (ANFIS) model was developed to predict the inhibition efficiency. The experimental data was categorized into two different sections for training and testing the ANFIS model. The developed model aimed to evaluate the fitness between the experimental and predicted values. From the results generated, optimum value (IE%) of DM was recorded as 80%, 81% and 83% at concentration of 0.4 g/L for weight loss, EIS and PDP respectively. Potentiodynamic polarization results reveal that Dexamethasone functions as a mixed-type inhibitor, whereas studies of EIS show that the inhibition mechanism is by the transfer of charges. Mild steel surface examination confirmed the presence of a protective adsorbed film on the mild steel surface. Thermodynamic parameters obtained imply that Dexamethasone is adsorbed on the steel surface by a physiochemical process and obeys Langmuir adsorption isotherm. Also the MD-simulation results evidenced that DM forms a metallic surface adsorbed film on the steel surface. From the ANFIS model, the sensitivity analysis shows that time and inhibitor concentration were the most important input variable while other input variables could not be neglected. ANFIS model coefficient of determination (R 2 0.993) was found between the observed and predicted values. ANFIS model gave optimum prediction (80%) with high degree accuracy and robustness. The outcomes of this investigation provide more information, simulation, and prediction about inhibition of metal corrosion.

Introduction

The destruction (or deterioration) of a metal and unwanted chemical or electrochemical attack by its environment starting at the surface is called corrosion. Corrosion can damage pipelines, bridges, public buildings, water and wastewater systems and if neglected can be catastrophic [1]. It is one of the most severe oil and gas industrial problems. Metal corrosion has caused huge economic losses in many industries, involving billions of dollars each year. The international corrosion prevention application and economic measure estimated global corrosion cost to 1–5% of an industrialized country's gross national product [2]. They suggested that implementing corrosion prevention could lead to global savings of 15–35%. Control measures or procedures therefore need to be introduced to minimize or prevent corrosion thereby prolonging the life span of metals [3]. Different methods for protection of metals from corrosion were suggested and implemented. One of these methods is the use of corrosion inhibitor which is one of the best corrosion control method. Corrosion inhibitors have been known to be an effective and simpler means of preventing corrosion [4], [5], [6].

A corrosion inhibitor is a chemical substance or a combination of substances that when applied to a corrosive environment in very limited amounts effectively reduce or inhibit corrosion without interacting significantly with the environmental components [7]. Corrosion inhibitors have found applications in different industries like oil and gas, chemical industries, heavy production processing and water treatment plants [8]. Corrosion inhibitors may be categorized as organic or inorganic compounds and can typically dissolved in corrosive environments. It should be noted that most organic and synthetic inhibitors are not biocompatible and economically cost effective. For this reason, these types of inhibitors became useless and outdated and current studies are directed towards application of inexhaustible, biocompatible, and nontoxic inhibitors [3].The growing understanding of health, safety and environment has drawn researcher's attention to develop very powerful and productive environmentally friendly inhibitors. Typical examples of such inhibitors that are environmentally friendly are fast green [9]. Fast green molecules have an aromatic ring with electroactive nitrogen and oxygen atoms while the Dexamethasone molecule has electroactive oxygen and carbon atoms with aromatic rings (rich electrons). Fig. 1 displays the molecular structure of the studied compound, these compounds are drug based and are adsorbed on the metal surface thereby blocking the active site of the metal resulting to decrease in the rate of corrosion and thus increasing the inhibition efficiency [10,11].

Fig. 1

Molecular structure of dexamethasone.

In the field of corrosion many researchers have agreed that drugs are inhibitors of corrosion, and can favorably compete with the natural products [12,13].

There are a large number of reports on the use of drug based compounds as corrosion inhibitor for metal corrosion prevention in aggressive environment. The impact of tobramycin drug on carbon steel in 2 M HCl solution was examined by Abeng et al. [14]. They reported the inhibition efficiency of 80% using 500 ppm inhibitor. The electrochemical and quantum chemical studies on adsorption of nifedipine as corrosion inhibitor at API 5LX-52 steel/ HCl acid interface was investigated by Ikpi and Abeng [15]. They found that nifepidine drug performed as a mixed type corrosion inhibitor and a maximum inhibition efficiency of 88.5% was determined with a 500 ppm solution of inhibitor. The adsorption process of the drug on API 5LX-52 steel was successfully interpreted by the Langmuir model. Also the quantum chemical studies revealed the feasible adsorption areas of the nifedipine molecule. El-Haddad et al. [16] studied the carbon steel corrosion rate in acidic medium containing cephapirin drug. They showed that the corrosion inhibitor molecules adsorption on the steel surface resulted in achievement of inhibition efficiency of 83% at 600 ppm and temperature of 303 K. The inhibitory action of expired asthalin drug on the corrosion of mild steel in acidic media was studied by Geethamani et al. [17]. They found that inhibition efficiency increases with the increase of inhibitor concentration, time and temperature. A mixed mode of inhibition mechanism was proposed for the effect of asthalin drug. The highest inhibition efficiency (73.68%) was retrieved for an inhibitor concentration of 9.0% v/v, also the adsorption thermodynamic was best interpreted by the Langmuir isotherm. Sumayah et al. [18] predicted the suitability of bronopol as a corrosion inhibitor for aluminum metal in 0.5 M HCl using weight loss data combined with the electrochemical measurement. They found that bronopol exhibits a maximum of 93.89% inhibition efficiency at 4000 ppm. Also the adsorption of bronopol on aluminum surface tends to obey Langmuir isotherm. The polarization measurement revealed bronopol to be a mixed sort inhibitor. Abdallah et al. [19] evaluates the performance of tramadol drug as a safe inhibitor for aluminum corrosion in 1 M HCl solution. They found that inhibition efficiency increases with the increase inhibitor concentration. Tramadol drug is a mixed inhibitor mainly anodic. They reported inhibition efficiency of 98% at temperature of 25 °C and inhibitor concentration of 500 ppm. Electrochemical and quantum chemical studies on corrosion inhibition performance of 2,2′-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] on mild steel corrosion in 1 M HCl solution was investigated by Iman et al. [20]. In their study, inhibition efficiency increased with an increase in inhibitor concentration. Maximum inhibition efficiency of 95% at 200 ppm was achieved. Polarization studies revealed that the drug molecule was a mixed type inhibitor.

The above literature analysis highlights the importance of identifying effective corrosion inhibitors for mild steel in order to increase safety, less maintenance costs and restricts the use of imported chemical inhibitors when it is adopted, especially, in the industries, for flow systems or chemical plants experiencing severe acidic conditions [21]. For the purpose of marketability of new discovered inhibitors, the latter should be closely examined by low cost, availability and near-to-zero environmental impact. Following this direction, this present work proposes the application of a novel drug (Dexamethasone) as a potential additive for mitigation of corrosion. Dexamethasone is a synthetic corticosteroid and derivative of cortisol. It is whitish in nature, odorless and a crystalline powder with molecular formula C22H29FO5, it helps in treatment of severe conditions like allergies and some common diseases. Dexamethasone is much cheaper and easy to procure. These outstanding characteristics have necessitated an ongoing research with a major breakthrough on the use of Dexamethasone in treatment of COVID 19.

In Chemical Engineering discipline to be precise, soft computing models and simulations have been enormously used in promising areas of research [22], [23], [24], [25], [26]. Modeling, simulation and solving complex nonlinear problems is one of the breakthrough applications of artificial intelligence like fuzzy inference programs, ASPEN HYSIS, artificial neural network (ANN), Genetic algorithm (GA) and RSM models. Some well-respected scientists with similar research interest have used different soft computing and modeling techniques and positive results were generated [27], [28], [29], [30], [31], [32], [33], [34], although the application of ANFIS is very scarce in this area. Thus, multi objective interest in this current research is to examine the interfacial adsorption and active sites of Dexamethasone drug at atomic and molecular rates using MD simulation concept, secondly for the first time, to use ANFIS model to predict the inhibition efficiency and to test the model application to pin point nonlinear complex interaction between independent variable and expected response.

Materials and method

Materials

Corrosion studies were performed on mild steel of compositions Mn (0.13%), P (0.22%), Si (0.05%), S (0.12%), C (0.24%), Cr (0.02%), Ni (0.07%), and Fe (99.15%). Prior to corrosion studies, the mild steel was mechanically cut (5 × 4 × 0.1 cm). Each coupon was abraded using 220, 600 and 800 emery papers to obtain a smooth / uniform surface area. The coupons were further degreased with acetone, rinsed with deionized water to remove debris and dried in warm air. This is in line with technique of previous report [35].

Methods

Preparation of 2 M HCl and inhibitor

171.82 HCl (37 wt%, specific gravity of 1.18) was added to 800 ml of distilled water in 1 liter measuring cylinder. The solution was made up to 1 liter with addition of distilled water. Dexamethasone drug (DM) used as inhibitor was obtained from G & I Pharmaceutical Company, Calabar, Nigeria without further purification. 5 g of ground Dexamethasone drug was dissolved in 1 liter of 2 M HCl solution. From the stock solution (5 g/L), Dexamethasone drug test solutions were prepared at concentrations of 0.1, 0.2, 0.3, 0.4 and 0.5 g/L respectively [36].

Weight loss measurements

We performed weight loss experiment at varying temperatures. Test coupons in triplicates were suspended freely in glass reaction vessels containing 200 ml of test solution (2 M HCl) without and with varying inhibitor concentrations. At the appropriate time, the mild steel samples were taken out, immersed in acetone, scrubbed with a bristle brush under running water, and dried in warm air before reweighing. The weight loss was calculated in grammes as the difference between the initial weight and the weight after the removal of the corrosion product. The experimental readings were recorded. The weight loss (∆w), corrosion rate (CR), inhibition efficiency (IE), and degree of surface coverage (θ) were calculated using Eqs. (1–4) [35]. where w1 and w2 are initial and final weight loss of mild steel respectively.CR blank and CR inhibitor are the corrosion rate of mild steel in absence and presence of inhibitor. ‘A’ is the total area of the mild steel sample and‘t’ is the time of immersion.

Electrochemical measurements

Electrochemical measurement was performed in 2 M HCl solution in absence and presence of different concentrations of inhibitor at 30 °C. Within the context of this study two components of epoxy resin were used to mount the mild steel in a PVC holder connected with a copper wire forming a working electrode with a surface area of 1cm2. The electrochemical study was done using a VERSASTAT 400 full set DC Voltammetry and a Potentiodynamic/ Galvanostat corrosion system with E-chem software for polarization study. The procedures for the electrochemical measurement are as follows: electrochemical cell assembly comprising of mild steel known as working electrode, 1 cm × 1 cm platinum foil used as counter electrode, and the saturated calomel electrode representing the reference electrode [37]. The entire electrochemical measurement was performed in a 200 ml glass filled with the test solution. Prior to each experimental measurement the test solution was stabilize at 100 s. EIS measurement was carried out over the frequency range of 100 KHz to 10 MHz with signal amplitude of 5 mV. Zsimpwin 3.0 software was used to analyze the impedance data. Potentiodynamic polarization measurements were performed at the scan rate of 0.33 mV/s. The potential range was ± 250 mV versus corrosion potential. The experiment was run in triplicates to scrutinize and justify the reproducibility of average values obtained for further statistical analysis. The following Equations were used for the calculation of inhibition efficiency.

Where R and R represent the charge transfer resistance in uninhibited and inhibited solution and corrosion current densities in uninhibited and inhibited solution represented as  i and i respectively.

Molecular dynamics and simulation

The quantum chemical calculations and MD-simulation were performed using the DFT electronic structure programs Forcite and DMol3 as embedded in the materials studio 4.0 software. The electronic parameters for the simulation include unrestricted spin polarization using DND basis set and perdew-Wang (PW) local correlation density functional. The Fe slab for the simulations was cleaved along the (110) plane. The calculations were performed in a 12 × 10 super cell using a Compass force field (condensed phase optimized molecular potential simulation studies) and the Smart algorithm with NVE (micro canonical) ensemble, a time step of 1 fs and simulation time of 5 ps. The temperature was fixed at 303 K. The system was quenched automatically at intervals of 250 steps.

MISO modeling with adaptive-neuro fuzzy inference system (ANFIS)

ANFIS is a unique optimization tool as it has the capability to model and scrutinize stochastic values with high level of accuracy. ANFIS modeling requires data for independent variables (MI) and dependent variable (SO). The coding or network program focuses on Takagi-Sugeno fuzzy inference system [23]. ANFIS program uses back-propagation and least square evaluation for prediction of membership function. The adaptive network normally consists of nodes and directional links, which are the connectors of the node. The nodes are purely adaptive because they depend on the node parameters, and during learning; these parameters are changed based on the learning rules with a target on minimizing a prescribed error measure. The Takagi-Sugeno program is used in ANFIS where every rule's output is constant. The ANFIS rule is categorize into two as given below.

:A1,A2,B1andB2 are nonlinear numbers whilep 1,p 2,q 1,q 2 and r 1andr 2 are linear numbers.

A statistical criterion R 2was employed for predicting the model's order. R 2evaluates the conformity (fitness) between the experimental and predicted data set using the following equation:

Prior to ANFIS analysis and prediction, 14 runs of experiment were considered. The experimental data were normalized. Normalization is refers to changing the experimental data to values between 0 and 1. It is pertinent to normalize such data to ensure error free (zero) on completion of system analysis. The Z-score normalization method through mean and standard deviation of training data for normalizing the input values was done using the following equation

Wherexis input data set, μ is mean ofxσ standard deviation of x(n) is normalized variablexas input to ANFIS environment.

Surface film analysis of mild steel and FTIR studies

The mild steel coupons were immersed in test solution at 303 K for duration of one day. The coupons were then taken out and dried after one day. The nature of the film formed on the metal surface was analyzed by Fourier transform infrared (FTIR), Scanning electron microscope in combination of energy dispersive x-ray SEM-EDX, For the SEM analysis, the electron beam acceleration takes place through the voltage system 15 kV. The electron beam gets narrowed after passing through the apertures and electromagnetic lens. Afterwards the beam scans the metal surface with the help of scan coils. The images are generated after production of SEM types of signals from the area of beam and specimen interaction. In addition, atomic force microscope (AFM) was used to estimate the mean roughness (Ra) on mild steel specimens [38].

Results and discussion

Weight loss measurement

Effect of immersion time

When characterizing corrosion inhibitor, time is a standout factor used in the determination of the inhibitor film stability and the rate at which inhibitor adsorption occur. The periods of immersion varied between 1 and 5 h. The findings are shown in Table 1 , which indicates the impact of time on the inhibition performance of Dexamethasone drug. The inhibition efficiency systematically increased from the early immersion period, which was 2–4 h. This was due to the inhibitor's rapid adsorption to the mild steel surface due to the maximum number of active inhibitor molecules available for the surface coating. The inhibition efficiency was observed to decline slightly after 4 h of immersion, this could be associated with more dissolution energy effect acquire by the corrosive agents within the aggressive environment [39].

Table 1

Effect of independent variables (time, IC, temperature) and the expected responses.

Time	Wo (g)	CRo (mg/cm−2h−1)	W1 (g)	CR1 (mg/cm−2h−1)	IE (%)	Ɵ
1 hr.	0.10	11.11	0.07	7.778	30.00	0.3000
2	0.18	10.00	0.09	5.000	50.00	0.5000
3	0.26	9.63	0.10	3.704	61.54	0.6154
4	0.41	11.39	0.11	3.056	80.17	0.8017
5	0.42	9.333	0.13	2.889	69.05	0.6905
Effect of Dexamethasone drug (inhibitor concentration)
0.0 g/L−1	0.41	11.39	–	–	–	–
0.1			0.31	8.611	24.39	0.2439
0.2			0.22	6.111	46.34	0.4634
0.3			0.18	5.000	56.10	0.5610
0.4			0.11	3.056	80.17	0.8017
0.5			0.12	3.333	70.73	0.7073
Effect of Temperature
303 K	0.09	2.500	0.07	1.944	22.22	0.2222
313	0.17	4.722	0.09	2.500	47.06	0.4706
323	0.28	7.778	0.12	3.333	57.14	0.5714
333	0.41	11.39	0.11	3.056	80.17	0.8017
343	0.42	11.67	0.13	7.778	69.05	0.6905

Effect of dexamethasone drug concentration

The dissolution of mild steel in acidic media over a period of five hours was demonstrated in the form of electrochemical reactions [40]. The dexamethasone drug concentration varied with inhibition efficiency is shown in Table 1. With the increase in dexamethasone concentration, the inhibition efficiency expedite due to the existence of vast amounts of adsorption sites caused by other concentrations of macromolecules. Calculation of the inhibition efficiencies from corrosion rates was shown by Eqs. (2) and (3) whereas surface coverage was calculated by Eq. (4). The optimum inhibition efficiency of dexamethasone was recorded as 80.17% at the concentration of 0.4 g/L. This is attributed to the availability of C and O in the drug compound that participates as active centers and electrostatic forces in the inhibitory action between dexamethasone and the steel surface. The active functional groups which are carbonyl in the studied compound and other groups interact with the surface of MS by electron donation to the d-orbital of Fe, thus enabling the adsorption of Dexamethasone to the surface of the mild steel [41], [42].

Effect of temperature

Weight loss experiments were also used to test temperature effects on mild steel corrosion with the aid of corrosion inhibitor. The findings are listed in Table 1. The findings were used to quantify metal dissolution activation energy and Gibbs energy of inhibitor adsorption onto the mild steel surface. The inhibition efficiency was observed to increase rapidly at mild temperature increase and gradually decline after 333 K. The reduction in the inhibition efficiency at 343 K demonstrated Dexamethasone's instability when it is exposed to higher temperatures, which implies that Dexamethasone adsorption onto MS surface was a process of exothermia, heat is released during adsorption. In keeping with the theory of Le Chatelier when the reaction that occurs is exothermic, the temperature rise will induce the reverse of the reaction. The same is true of endothermic reactions as well [43]. Dexamethasone was found to function better at low to medium temperatures than at higher temperatures. Also, the desorption of adsorbed inhibitor molecules due to increased solution agitation by higher rates of hydrogen gas evolution at elevated temperature is possible and may cause the ability of the inhibitor to be adsorbed on the mild steel surface to reduce [44].

Activation energy, heat of adsorption and adsorption isotherm studies

E andQin 2 M HCl with Dexamethasone for mild steel protection are shown in Table 2. The measuredEvalue for the inhibited solution with Dexamethasone ranges from 6.5437 to 21.7149 kJmol-1 in the presence of 0.1 and 0.3 g/L-1 inhibitor concentrations, while the activation energies range from 9.1619 to 16.4986 kJmol-1 in the 0.2 and 0.5 g/L-1 inhibitor concentrations. This work shows that the inhibited partial reaction of mild steel is due to the adsorption of the film layer on the metal surface. This is due to the nature of the studied heterocyclic compounds which shield the metal from further dissolution [27]. In general,Qnegative values imply that Dexamethasone molecules' surface attachment was exothermic and spontaneous. In same vain the interaction of adsorbed molecules with the metal surface can be explained by various adsorption models. The essential step of the adsorption process of Dexamethasone molecule onto the mild steel surface is shown in Eq. (11), where (θ) is the surface coverage which was calculated from weight loss [45]. As revealed by the plot of as a function of log C indicates a linear graph [46], with a mathematical model of slope values 0.311 to 0.3149 and intercepts 0.0895 to 0.1057 respectively. The regression factor (R 2) ranges from 0.929 to 0.930.During the analysis, adsorption model from Langmuir was tested and the model offered the best fit as shown in Fig. 2 and was used for calculating the free energy of adsorption according to Eq. (12). where C is the concentration of inhibitor, R, T andKis the molar gas constant, absolute temperature and equilibrium constant. The free threshold value for free energy of adsorption is   – 40 kJ/mole which is more than the free energy of the present study 34.2 kJ/mole reflecting physical adsorption mechanism of the corrosion reaction [47].

Table 2

Activation energy, heat of adsorption and adsorption isotherm studies.

Inhibitor	Ea(KJ/mol)	Qads(KJ/mol)
0.1 g/L−1	6.54	−2.83
0.2	9.16	−3.96
0.3	21.71	−13.41
0.4	17.86	−7.77
0.5	16.49	−7.14
Langmuir model parameters
Log C	Log (C/θ) 323 K	Log (C/θ) 333 K
−1	−0.38721	−0.37676
−0.69897	−0.36493	−0.35449
−0.52288	−0.27184	−0.24204
−0.39794	−0.26227	−0.25182
−0.30103	−0.15063	−0.14019

Fig. 2

Langmuir isotherm plot of Log(C/θ) versus Log C for M-steel in 2 M HCl containing DM at different temperatures.

Electrochemical measurements

Electro-kinetics and phenomenal nature of the electrochemical practice concerned in the corrosion and corrosion inhibition of mild steel in 2 M HCl solution was appreciated by electrochemical impedance spectroscopy (EIS). The EIS study was carried out in the uninhibited and inhibited solution. The spectra impedance present in 2 M HCl solution at 303 K are shown in Fig. 3 a-3c as nyquist, bode phase angle and bode modulus plots accordingly. The blank was used as a reference point in comparing the results with that of the inhibited solution shown in Fig. 3a. The spectra exhibited an imperfect semicircle with double hump nature throughout the frequency study [35]. In the Nyquist impedance spectra, the solution resistance (Rs) represent the high frequency intercept with the real axis and charge transfer resistance (Rct) is the low frequency intercept with the real axis. The data for the impedance were fitted with circuit model shown as an inset in Fig. 3a. The model consists of C andRct representing the impedance effect due to the corrosion product species from the blank, fractal geometry, electrode geometry and porosity as describe by Eq. (13) [48].where Qand n are associated with CPE and exponent respectively, j 2= − 1 is regarded as imaginary axis, ωstand for angular frequency inrads −1,(ω = 2πfexplain frequency in H), Rsignifies solution resistance, Wdenotes the Warburg parameter and n is the considered shifting factor, it is in assortment of −1 to 1. If n = −1(an inductor),n = 0(real resistor) and n = 1(capacitor) [47], [48], [49]. Double layer (C) and film capacitance (Cf) are evaluated and defined byY 0,n, ω as shown in Eq. (14) [49].

Fig. 3

Electrochemical impedance plot of MS in 2 M HCl solution in the absence and presence DM of (a) Nyquist (b) Bode phase angle plot and (c) Bode modulus plot (d) OCP plot (e) fitting curve.

The goodness of EIS data fit to model isχ2 factor, described as [50] where ω aare the experimental data points,is a factor connected with the proposed model andZ′andZ ′′ are expected data points (calculated). As listed in Table 3 the χ2 values are slightly small (∠1×10–3), showing excellent fitness of available EIS plot (Fig. 3d) to proposed circuit model [51]. Close scrutiny of Fig. 3a revealed that the addition of inhibitor results in an increase in the diameter of the semi-circle in the Nyquist plot. An increase in the diameter of the semi-circle in the Nqyuist plot is attributed strengthening of the adsorbed film formed by the active molecules of dexamethasone drug. The formation of the protective film layer on the steel surface is believed to be the culprit of the observed suppression in the cathodic and anodic partial reactions [52]. The increase in the diameters and in the low frequency impedance magnitude (/Z/0.05 Hz) was found to depend on concentration of Dexamethasone compound. In high frequency region the presence of DM in the phase angle maximal became higher than that of the uninhibited solution which results to the formation of protective film and increase in surface coverage on the steel surface [53]. The OCP versus time plot for mild steel in the blank solution and with different concentrations of the Dexamethasone drug is shown in Fig. 3d. From the plot, the OCP of 2 M HCl acid solution was found to be −0.55 V. For an increase in concentration of inhibitor from 0.1 g/L to 0.4 g/L, the OCP shifted towards the noble direction from −0.51 to −0.52 V, indicating that Dexamethasone controls mainly anodic metal dissolution reaction. Further observation revealed that the blank solution stabilizes from the point of immersion. Also the inhibited medium 0.1 g/L-1 reaches a steady state condition after 19 s while that of 0.4 g/L-1 stabilizes after 80 s, suggesting that the potential evolves towards the stable values during the period of study. Table 3 shows the results obtained from the EIS, noticeably the R(Ωcm2) values and the efficiency of the inhibitor (IE%) is seen to increase on addition of the drug compound. One unique observation is that as the consistence of DM increases, C andCexhibited opposite trend, which reveal on the MS surface adsorb DM molecule and charge transfer phenomenon. Also the numerical values of the shifting factor “n” evaluates the non-ideal capacitive trend due to unevenness of the electrode and surface micro-defects. The constant phase element represented by double layer capacitance values confirmed the presence of the Dexamethasone compound on the surface of the steel leading to the decrease in the dielectric constant and increasing the thickness of the double layer. This is because organic species shown minimum dielectric influence than inorganic species [54].

Table 3

Electrochemical parameters of mild steel in 2 M HCl in absence and presence of DM.

System	RS(Ωcm2)	Rct(Ωcm2)	n	Cf(μFcm−2)	Cdl(Fcm2)	IE(%)	χ2(x 10–4)
2 M HCl	1.659	50.8	0.86	21.02	2.343E−5	–	8.16
0.1 g/L DM	2.820	94.1	0.88	10.53	3.919E−5	60	9.50
0.4 g/L DM	3.306	157.8	0.89	9.19	3.216E−5	81.8	9.30

Potentiodynamic polarization

Polarization plot for mild steel in the blank and inhibited solution (0.1 g/L-1- 0.4 g/L-1) of DM at   30°C is shown in Fig. 4. The nature of the plot in the blank and at varying DM concentrations is comparable [55]. Increase in DM concentration obstructs the anodic and cathodic reactions. Vital parameters considered in this investigation includes; corrosion potential (E), tafel slopes   and corrosion current density (I) as well as (IE%) are presented in Table 4. The  (E)values were marginally modified by adding 0.1 g/L-1- 0.4 g/L-1DM in 2 M HCl, which shows that the impact of DM is significant. However, literature findings suggested that for an inhibitor to be categorized as a cathodic or anodic mode, a precise range or acceptable deviation in corrosion potential(E) should be ± 85 mV/SCE [56]. From our investigation, the(E) values were less than 85 mV, postulating that DM was a mixed type inhibitor [57], [58]. The description of our findings denotes that the active molecules of DM adsorbed by impeding the active sites of mild steel surface, resulting in a significant reduction in the area needed for corrosion. As listed in Table 4, the numerical values fordecline bit by bit with rise in DM concentration. The trend of bandbscrutinizes the symmetry of the activation energy for both side reactions [59]. Thus the DM thin film had a positive influence on anodic and cathodic axis with predominant anodic effect. (I) value also decline slightly from 0.1 g/L-1–0.4 g/L-1 DM, signifying that (IE%) is promoted with increase in DM concentration.

Fig. 4

Potentiodynamic polarization curves of mild steel in 2 M HCl solutions in the absence and presence of Dexamethasone (DM).

Table 4

Polarization data for mild steel in 2 M HCl in the absence and presence of DM.

	ECorr	ICorr	bC	ba	sc	IE(%)
System	(mV vs. SCE)	(µA cm-2)	(mV dec‑1)	(mV dec‑1)	(θ)
2 M HCl	−466.3	312.7	120.1	95.0	–	–
0.1 g/L DM	−459.3	85.4	108.7	78.1	0.72	72
0.4 g/L DM	−463.8	53.6	101.2	73.2	0.83	83

MD-simulation concept

MD-simulation was used to explain the details of mechanism of the corrosion inhibition process of the study molecule [60]. For the neutral form, the optimize structure, HOMO, LUMO, electron density and the snap shot are shown in Fig. 5 while the protonated form are shown in Fig. 6 . Donor-acceptor relationship is due to the adsorption of organic molecules on the metallic surface. The ability of the molecule to donate electron or accept electron is represented by HOMO and LUMO. The vital parameters of the quantum chemical study include energy of highest occupied molecular orbital EHOMO, energy of lowest unoccupied molecular orbital ELUMO, energy gab ΔE, electronegativity χ, global hardness η, global softness σ and the number of electron transfer ΔN are shown in Table 5 . The high electron donating and accepting abilities of the Dexamethasone are associated with high values of EHOMO and low value of ELUMO respectively which shows bonding between the inhibitor molecule and the surface of the steel [61]. The energy gab parameter describes the relationship between metal-inhibitor interactions. The smaller the value of energy gab ΔE is associated with a global softness of the studied molecule which indicated a good inhibition efficiency of the molecule, while the higher value of energy gab ΔE is associated with global hardness, reflecting that the inhibitor is not capable of performing well as a corrosion inhibitor. The important parameters required for the calculation of electronegativity χ, global hardness η, global softness σ are the ionization potential (IP) and electron affinity (EA) obtained from the EHOMO and ELUMO according to equations below [62].

Fig. 5

Electronic structures of neutral form of Dexamethasone (a) Optimized structure (b) HOMO (c) LUMO (d) Electron density and (e) Snapshot of DM molecule.

Fig. 6

Electronic structures of protonated form of Dexamethasone (a) Optimized structure (b) MEP (c) HOMO (d) LUMO (e) Electron density and (f) Snapshot of DM molecule.

Table 5

Calculated quantum chemical parameters of the Dexamethasone molecule.

EHOMO	ELUMO	ΔE (eV)	IP(eV)	EA (eV)	χ(eV)	η(eV)	σ	Eads	ΔN/e
Neutral form
−6.284	−6.280	4 × 10–3	6.284	6.280	6.282	2 × 10–3	500	137.3	7.2 × 10–3
Protonated form
−5.045	−2.347	2.698	5.045	2.347	3.696	1.349	0.741	168.7	0.4166

The values of electronegativity χ and global hardness η were used in estimating the number of electrons transfer ΔN based on Eq. (19) [63].

The derive work function (φ), theoretical value given as φ= 4.82 according to [64]. The number of electrons transfer always take place from the inhibitor molecule to the metal surface. When the value of electron transfer ΔN is greater than zero it signifies a greater electron donating ability of the inhibitor to the metal surface, also when the value of the electron transfer ΔN is less than 3.6 it reflect the effectiveness of the Dexamethasone molecule. In our present study the value of ΔN is positive showing better performance in the neutral form. The estimated value for the energy gap also supported inhibitory performance of the DM molecule. Also the chemistry of Dexamethasone is very vital, DM is a fluorinated steroid that is replaced by hydroxyl groups at positions 11, 17 and 21, a methyl group at position 16 and oxo groups at positions 3 and 20. It is a member of the type of glucocorticoids. DM has electro-active oxygen and carbon atoms with aromatic ring (rich electrons). From the quantum chemical point of view, Figs. 5a and 6a show the optimized structure of DM and Fig. 6b illustrates the molecular electrostatic potential (MEP) plot for the DM molecule. As shown, the colors for the MEP surface are according to red for     (−ve) charge; blue for (+ve) charge; light blue represents slightly electron rich areas; green for neutral respectively. In case of our results, the partial negative charges are mainly localized over the carbonyl group (red color), the site where HOMO is located which can interact with the mild steel, while the LUMO level is seen at the carbon atom having the tendency of accepting electrons. Total electron density plot for the most stable configuration is displayed in Fig. 6e.   As can be easily seen from Fig. 6e, a significant charge transfer has occurred due to the interaction of the DM molecule with the mild steel. Also the carbonyl groups conjugated with a double bond undergo adsorption in comparison with the isolated carbonyl group. The adsorption of unconjugated carbonyl group is activated by the neighboring hydroxyl groups. The carbonyl group at position 20 is activated by the hydroxyl groups present at position 17 and 21.

Mechanism of corrosion inhibition

From the experimental results obtained from different techniques. It can be inferred that   dexamethasone drug inhibits the corrosion of mild steel in 2 M HCl by adsorption of active molecules at metal /solution interface. It is generally known that the adsorption of inhibitors at the metal surface is the first stage in the mechanism of the inhibitor action. Active molecules of an inhibitor may be adsorbed on the metal surface in different ways; (i) electrostatic /mutual interaction between the protonated form of the inhibitor and adsorbed counter chloride ion (physisorption),(ii) donor–acceptor relationship between electron pairs of heteroatoms and vacant d-orbital of Fe surface atoms (chemisorption), (iii) donor–acceptor relationship between the       π – electrons of aromatics rings and multiple bonds and vacant d-orbitals of Fe surface atoms (chemisorption) and a combination of types (I and III). The inhibition of active dissolution sites of the metal is attributed to the adsorption of dexamethasone active molecules on the MS surface forming a dense film layer. The active molecules can be adsorbed onto the MS surface through electron transfer from adsorbed species to the vacant electron orbital of low/ minimum energy in the metal to form a co-ordinate type of bond. Inhibitory action of an inhibitor depends on many factors [35] including number of feasible adsorption areas, mode of interaction with metal surface, molecular size and the heterocyclic structure. The schematic illustration of adsorption orientation of Dexamethasone drug on MS surface is shown in Fig. 7 . The active molecules can share their lone pair with empty orbitals of metal cations, so the steel surface can be shield by a protective film layer. This results in the formation of a barrier film with capability of ions, oxygen and water diffusion restrictions on the steel surface.

Fig. 7

Schematic representation of the adsorption of DM molecule against MS corrosion.

Adaptive-Neuro fuzzy inference system prediction

ANFIS program in MATLAB was used to design a model to predict the efficiency of DM drug as a potential inhibitor. In ANFIS environment, the experimental data was split into 3 sections for training, testing and validation. Gaussian membership was used for input and linear membership used for output. Training section comprises of 80% data while 20% was attributed to testing section [65]. Number of iterations required to achieve minimum steady state error was 30 epochs and two triangular membership functions attached to each of the independent variables. With a total of 3 independent variables, the total number of constant membership functions used for the dependent variable was eight membership functions as seen in Table 6 which resulted in generation of eight inference rules (the yellow color region denote the membership function of the input data while blue region is the second phase of the fuzzy rule as presented in Fig. 8 ). The ANFIS response was obtained and de-normalized to obtain accurate ANFIS prediction. ANFIS prediction based on the R2 is presented in Table 7 considering 14 runs. From the ANFIS architecture (Fig. 9 ) the input neuron is 3 (each neuron denotes the independent variables) with the input neuron attached to 2 neurons indicating 2 membership functions used for each independent variable. The hidden neurons correspond with the output neurons where each of the neurons in the hidden layer is connected to the neurons in the output layer. The single neuron at the extreme right indicates the dependent variable which is one. The model systematically gave accurate prediction with optimum value of 80%. The accuracy/conformity of the predicted values is clearly affirmed by the statistical factor R 2 0.993 which denotes excellent model status as shown in Fig. 10 a. Since the proposed ANFIS model obeyed the criteria of having its R 2-value greater than 90%, it made it the most preferred model to carry out further test [66]. As such, surface viewer plots of ANFIS prediction with respect to the interaction parameters were also considered vital. The surface viewer plots pin points the effect of interaction parameters     (coding the independent variables as x and y axis of the 3D plots) against inhibition efficiency. It is pertinent to graphically obtain the independent parameters that gave the optimal value via ANFIS prediction. Thorough inspection of Fig. 10b explain that systematic increase in DM concentration increases the inhibition efficiency (IE%), on the contrary a slight diminution curve was evidently seen at elevated temperatures, The decline in (IE%) from 333 to 343 K temperatures demonstrated Dexamethasone's instability when it is exposed to higher temperatures, which also prove that the DM active molecule was disperse at elevated corrosive conditions. Fig. 10c gives additional insight on the nature of interaction between temperature and time. At early immersion period of adsorption phenomenon, the positively charge DM molecules initiates spontaneous competition with H+ for electrons on the MS thereby impeding the chloride ions that necessitates corrosion [35]. This led to a near perfect or uniform surface coverage by DM molecules. The efficiency declined slightly after 4 h of immersion. Further insight shows that the corrosion rate (CR) increased rapidly with prolonged immersion period at 343 K due to dispersion of DM active molecules. The interactive effect between time and inhibitor is highlighted in Fig. 10d. The DM efficiency rises and consequently attains equilibrium point of 80% at 4 h of study at optimum range of DM. Furthermore, it slightly decline afterwards. This implies that the Max IE% is attainable within 4 h of immersion. However, taking into consideration of both independent factors, efficiency of DM drug is attainable and stable at optimum range and medium immersion time.

Table 6

8 Membership functions selected for ANFIS modeling.

Membership functions	Error value
trimf	2.1685
trapmf	1.6195
gbellmf	1.4547
guassmf	1.5466
guass2mf	1.6194
pimf	1.6342
dsigmf	1.6264
psigmf	1.6274

Fig. 8

ANFIS rules for input and output response.

Table 7

Experimental and ANFIS prediction.

No of runs	Expected	ANFIS Pred.
1	30	30.9197
2	50	47.6779
3	61.54	63.7874
4	80.17	80.4107
5	69.05	69.4095
6	24.39	24.6766
7	46.34	44.603
8	56.1	58.7618
9	80.17	80.4107
10	70.73	70.759
11	22.22	21.8933
12	47.06	47.9118
13	80.17	80.4095
14	69.05	69.4095

Fig. 9

Architectural design of ANFIS model.

Fig. 10

(a) Exp. vs. ANFIS Pred. (b) Surface viewer plots for independent variables with expected response.

Surface characterization analysis

Earlier researchers have reported that the FTIR spectrometer is a strong instrument which can be used to prove the form of organic inhibitors bonding adsorbed on the metal surface [67]. The protective film formed on a metal surface was analyzed using FTIR spectra. FTIR of pure Dexamethasone is given in Fig. 11 a. It evidenced the existence of O—H, N—H, C—O, CO groups. The FTIR spectra of the film layer formed on the metal surface after immersion for 5 h in     2 M HCl containing 0.4 g/L of Dexamethasone is shown in Fig. 11b. Nearly all the peaks observed for the pure compounds were also present in the adsorbed specie (corrosion products), with some slightly changes or modification after molecular adsorption. Further observation reveals that after adsorption of the molecules most of the peaks appeared weaker. The FTIR bands of the compounds with slight changes and the absence of few bands suggest an interaction between the compounds and the metal surface resulting in the formation of a protective film layer [27, 68].

Fig. 11

FTIR spectra for (a)Dexamethasone drug and (b) adsorbed  molecules on MS surface.

SEM, EDX and AFM studies

So as to understand the level of protection of MS surface by DM more clearly, micrographs of the steel in blank and inhibited system were closely scrutinized using SEM technique. In the blank solution (Fig. 12 a) a coarse, dark pits and uneven surface fractions were observed with various macro pores. The corrosion topography is visible enough due to hostile nature of chloride ions in the facial dissolution layer of the steel [69]. Inversely, the micrograph of the steel from inhibited medium (Fig. 12c) evidently differs from the control sample (appears smooth). The level of iron oxide form is suppressed due to the physical formation of a dense film on the facial layer of the steel [70]. The great deal of activeness of DM is enormously dependent on dosage of the studied inhibitor. Also EDX is a vital analytical instrument for evaluation of elemental composition on the steel surface prior to and after DM immersion. In Fig. 12b the densely particles deposited on the steel enormously comprises of iron oxides in devoid system. On the contrary, in the inhibited area Fig. 12d several peaks like O, Ca, Si and Fe were added and an increase in Fe peaks evidently describe that DM molecules obstruct the invading of electrolyte species [71]. Atomic force microscope (AFM) is an effective method for examining surface morphology, and it is also useful in corrosion inhibition studies to evaluate the nature of film formation on metal surface. Fig. 12e and 12f indicates the AFM images of polished mild steel in 2 M HCl with and without the presence of 0.4 g/L−1 Dexamethasone molecule. In HCl, the AFM picture of the mild steel surface appears more degraded than in HCl with 0.4 g/L-1Dexamethasone drug. In addition, the typical average roughness of polished mild steel in a blank solution of 2 M HCl was calculated to be 238 nm, peak to valley was recorded as 78.4 nm and the average roughness was reduced to 98 nm, peak to valley was 43.7 nm when the inhibitor (DM) was added to the blank solution which indicated the formation of a film layer on the mild steel surface [72], [73].

Fig. 12

SEM Micrographs, EDX and AFM images of mild steel  in (a-b) 2 M HCl (c-d) 2 M HCl + 0.4 g/L DM (e) AFM / MS in 2 M HCl ( f) AFM /MS in 2 M HCl + 0.4 g/L DM.

Concluding remarks

From the available data set obtained, the following points can be inferred.

DM is a strong corrosion inhibitor in 2 M HCl solution for protection of mild steel by intercepting both anodic and cathodic reactions (Mixed type inhibitor).

The inhibitory action of DM drug depends on its concentration. For appropriate safety this inhibitor should be applied at high concentrations.

Langmuir adsorption isotherm best reflects that the process of inhibition of corrosion occurs only by physical adsorption.

MD-simulation concept provides detailed information on feasible adsorption areas of DM drug.

Measurements of surface analysis are in good agreement with the experimental findings and indicate a safe and well distributed film over the metal surface. In the 2 M HCl solution containing inhibitor, a substantial diminution in surface roughness was seen as opposed to the solution without DM.

ANFIS model best predicted the non-linear interactions between the multi input and single output response with optimum value of 80% and R 2 0.993.

Declaration of Competing Interest

The authors declare that they have no conflict of interest.