Prognostic Model for Corrosion-Inhibition of Mild Steel in Hydrochloric Acid by Crushed Leaves of Voacanga Africana

The weight-loss technique was used to study the inhibition of the corrosion of mild steel in 0.7M, 1.2M and 2.2M HCl by thoroughly crushed fresh-leaves of Voacanga Africana. The corrosion rate was observed to increase with increase in the concentration of acid. The maximum inhibition efficiency of 69.80% was obtained when thoroughly crushed leaves of Voacanga Africana was added at 15g per litre of 0.7M HCl with a corresponding decrease in corrosion rate from 2.6487mg.cm -2 .h -1 to 1.3684mg.cm -2 .h -1 . The prediction of the corrosion rate by the artificial neural network gave a minimal error and was closer to the experimental corrosion-rate value in comparison with the prediction by multiple regression. Upon the variation of temperature between 298K and 358K, the activation energy obtained for the corrosion of mild steel in the blank solution of 0.7M HCl was 20,908.68J while the addition of Voacanga Africana’s crushed leaves at 15g per litre of 0.7M HCl increased the activation energy to 26,710.26J. The corrosion inhibition of mild steel in hydrochloric acid by the addition of the crushed plant-leaves is in agreement with the Langmuir adsorption isotherm with R 2 = 0.992.


Introduction
Corrosion is the deterioration of a metal owing to its reaction with the environment [1,2]. This development involves a gradual reversion to the more stable state such as oxide, sulphide or carbonate [3]. Allowing corrosion to unabatedly occur may lead to catastrophic consequences. However, corrosion can be prevented through cathodic protection, anodic protection, addition of inhibitors, coating and proper selection of materials. The method of corrosion prevention by the addition of inhibitors is pertinent to this study.
An inhibitor should be able to reduce the degradation of a metal when added in small amount to the corrosive environment. Benzimidazole and triazole derivatives are well known corrosion inhibitors that showed more than 97% of inhibition against acid corrosion of mild steel [4], but they are also known for their toxicity [5,6,7]. Notably, the toxic nature of the known effective inhibitors of arsenate-and chromate-based has necessitated the search for an alternative inhibitor that would not only be efficacious but environmentally friendly. Previous research has revealed the effectiveness of some plant-extracts in inhibiting the corrosion of metals and alloys. This present work aims at investigating the effectiveness of thoroughly crushed leaves of Voacanga Africana in reducing the hydrochloric acidinduced corrosion of mild steel.
The various species of the Voacanga genus are evergreen trees. They grow to a height of 6m with a spread of 2m, but are usually kept smaller in cultivation. The stem is erect; the leaves are broadly oval and up to 30cm long. The berries contain several brown seeds which are irregularly shaped, and grow in a cluster that sometimes can resemble a brain. The various species of the genus are very similar to one another, featuring yellow or white flowers with five united petals [8,9]. A native of the West African rainforests, Voacanga Africana prefers rich soils in protected sunny to shady areas, and is tender to drought and frost. Propagation is from fresh seed or cuttings. Fresh seeds germinate much more quickly than older seeds [10].
The corrosion inhibition data are better understood by developing a mathematical model. Predictive models are produced using multiple regression and artificial neural network (ANN). In multiple regression, the relationship between the dependent variable (which is the corrosion rate in this study) and three independent variables (conc. of acid, quantity of crushed leaves and time of exposure) is evaluated. On the other hand, the working principle of the artificial neural network is similar to that of human nervous system [11].

Preparation of Crushed Leaves
Fresh leaves of Voacanga Africana were obtained within the surrounding of the Federal University of Technology Owerri. The leaves were thoroughly crushed with a manual blender before being added to different concentrations of acid at 15g per litre, 30g per litre and 45g per litre of 0.7M, 1.2M and 2.2M HCl.

Fabrication of Mild Steel Coupons
The Mild steel ((wt %) C=0.20%, Zn=0.75%, Ti=0.28, Mn=0.23%, S=0.04%, P=0.035% and Fe balance) coupons of 4cm by 4cm by 0.15cm dimensions were press cut from a sheet metal using a foot shear cutting machine. The mild steel coupons were ground down with coarse and fine emery papers and later cleaned with acetone before their initial weights were determined by the Ohaus electronic weighing balance.

Weight-Loss Technique
The weighed coupons were immersed in various concentrations of hydrochloric acid to which different quantities of crushed leaves of Voacanga Africana had been added at 15g per litre, 30g per litre and 45g per litre of 0.7M, 1.2M and 2.2M HCl. Another experimental set-up which did not contain any inhibitor was prepared for the purpose of comparison. In every hour, a coupon was withdrawn from the study environment, thoroughly cleaned with acetone and reweighed to figure out the final weight. The experimentation lasted for eight hours. The above experimental procedure was repeated by varying the temperature between 298K and 358K.
The rate at which the mild steel corroded was computed using the formula [9,12]: Where, w = Weight-loss. A = Exposed area. t = Time of exposure. The inhibition efficiency occasioned by the addition of thoroughly crushed leaves of Voacanga Africana to the corrodent was obtained by the relationship: Inhibition efficiency, I.E (%) = (R corr1 -R corr2 /(R corr1 ))*100 (2) Where, R corr1 = Corrosion rate of the uninhibited environment. R corr2 = Corrosion rate of the inhibited environment.

Multiple Regression (MR)
Multiple regression is a statistical tool that generates a mathematical model by evaluating the relationship between the dependent variable and two or more independent variables. In this study, the dependent variable is the corrosion rate (mg.cm -2 .h -1 ) whilst the three independent variables are conc. of acid (M), quantity of crushed leaves (g) and time of exposure (h). Using the principle of multiple regression, the model can be obtained by employing the formula: R corr = k o + f 1 (time of exposure) + f 2 (conc. of acid) + f 3 (quantity of crushed leaves)

Artificial Neural Network (ANN)
Artificial neural network imitates the human brain in data analysis. It consists of a number of very simple and highly interconnected processors, also called neurons, which are similar to the biological neurons in the brain [13]. Figure 1 illustrates the artificial neural network for the prediction of corrosion inhibition of mild steel in hydrochloric acid by thoroughly crushed leaves of Voacanga Africana.
The artificial network neurons are joined by weighted links which pass signals from one neuron to another as displayed in Figure 2. Each neuron obtains several signals from its input links, computes a new activation level and transmits it as an output signal. The neuron calculates the weighted sum of the input signals and compares the result with a threshold value. The other input to the neuron, d j is referred to as the bias, which is an arbitrary selected value that oversees the input of the network as depicted in equation (4) [14].  According to [13], the neuron output is -1 if the net input is less than the threshold. But if the net input is greater than or equal to the threshold, the neuron becomes activated and its output attains a value +1. The net input of the network is computed by using the equation below: Where, p j = Net input. a i =Input of unit. w ij =Weight. d j =Bias of the unit.
The sigmoid function, f(p j ) transforms the input, which can have any value between plus and minus infinity, into a reasonable value in the range between 0 and 1 as given in equation (5) [14]. Neurons with this function are used in the back-propagation networks [13].
Where, p j = Net input.

Analysis of Error in Prediction
The importance of error analysis in prediction is to investigate how close the predicted value is to the actual or experimental value. The error in prediction can be obtained by using the mean standard error (MSE) and the mean absolute error (MAE) whose formulae are stated below: Where, N = Number of samples.

Effect of Addition of Thoroughly Crushed Leaves of Voacanga Africana on the Corrosion of Mild Steel Coupons Immersed in Hydrochloric Acid Solution
The average corrosion rate, CR and inhibition efficiency, I.E in the order CR (I.E) as presented in Table 1  .h -1 (42.40%) in 2.2M HCl. The addition of thoroughly crushed leaves of Voacanga Africana reduced the corrosion of mild steel coupons in hydrochloric acid medium. The corrosion rate was observed to increase with increase in the concentration of acid whilst the inhibition efficiency improved with time.
The corrosion rate-time curves for the mild steel coupons dipped in 0.7M, 1.2M and 2.2M HCl in the presence and absence of Voacanga Africana's crushed leaves are displayed in Figure 3. The corrosion-rate curves were observed to decrease progressively as the exposure time increased. On the other hand, the inhibition efficiency-time curves for the corrosion inhibition of mild steel coupons occasioned by the addition of Voacanga Africana's crushed leaves at 15g per litre, 30g per litre and 45g per litre of 0.7M, 1.2M and 2.2M HCl are shown in Figure 4. The inhibition efficiency curves increased as the experimentation progressed. The maximum inhibition efficiency of 69.80% was obtained when thoroughly crushed leaves of Voacanga Africana was added at 15g per litre of 0.7M HCl with a corresponding decrease in corrosion rate from 2.6487mg.cm -2 .h -1 to 1.3684mg.cm -2 .h -1 .

Prediction of Corrosion Inhibition of Mild Steel in Hydrochloric Acid by Thoroughly Crushed Leaves of Voacanga Africana
Multiple regression and artificial neural network were used to predict the corrosion inhibition of mild steel in hydrochloric acid by Voacanga Africana's crushed leaves.
The predicted values are illustrated in Appendix 1. Using multiple regression as presented in Table 2 On the other hand, the prediction of the experimental corrosion rate of mild steel by artificial neural network revealed the importance of the following independent variables: (time of exposure (h), concentration of acid (M) and quantity of crushed leaves (g)) in the prediction of the dependent variable (Corrosion rate, CR (mg.cm -2 .h -1 ) as illustrated in Table 3. The time of exposure was found to largely influence the prediction of the corrosion rate by 49.6%, followed by the quantity of crushed leaves, 26.2% and finally the concentration of acid, 24.2%.
The comparison of error results for the prediction of corrosion inhibition of mild steel by Voacanga Africana's crushed leaves in hydrochloric acid using multiple regression and artificial neural network are presented in Table 4 and displayed in Figures 5 and 6. The results show that predictions by the artificial neural network gave a minimal error and were closer to the experimental corrosion rate values in comparison with predictions by multiple regression.

Effect of Variation in Temperature on the Corrosion of Mild Steel Coupons Immersed at 15g of Voacanga Africana's Thoroughly Crushed Leaves Per Litre of 0.7M HCl
The result of the variation in temperature between 298K and 358K on the corrosion of mild steel without and with the addition of thoroughly crushed leaves of Voacanga Africana at 15g per litre of 0.7M HCl is presented in Table 5 and displayed in Figure 7. The activation energy obtained for the corrosion of mild steel in the blank solution of 0.7M HCl was 20,908.68J while the addition of Voacanga Africana's crushed leaves at 15g per litre of 0.7M HCl increased the activation energy to 26,710.26J. The higher value of activation energy obtained by the introduction of the crushed leaves of Voacanga Africana to the corrodent suggests that more energy needs to be attained before further corrosion can take place.

Adsorption Isotherm for the Corrosion Inhibition of Mild Steel in Hydrochloric Acid by Thoroughly Crushed Leaves of Voacanga Africana
Langmuir, Freundlich, Temkin and El-Awady adsorption isotherm models were tested and presented in Table 6 and Figure 8 for the corrosion inhibition of mild steel in hydrochloric acid by thoroughly crushed leaves of Voacanga Africana. Of all the tested models, only the Langmuir adsorption isotherm (R 2 = 0.992) was obeyed. This development reveals that corrosion inhibition was achieved by the adsorption of a monolayer of the inhibitive constituents of Voacanga Africana's crushed leaves on the surface of mild steel. The Langmuir adsorption isotherm model is expressed by the relationship: Where, C inhibitor = Concentration of the inhibitor. ϴ = Fraction of surface coverage. k = Equilibrium constant for the adsorption process.

FTIR Analysis of the Corrosion Inhibition of Mild Steel in Hydrochloric Acid by Thoroughly Crushed Leaves of Voacanga Africana
The FTIR spectrum of the adhered constituents of Voacanga Africana's crushed leaves on the surface of mild steel coupon immersed at 30g per litre of 0.7M HCl for eight hours is shown in Figure 9. The O-H functional group is spotted around 3652.8cm -1 . The presence of carbon-carbon triple bond of alkynes is indicated at 2117.8cm -1 . The display of a sharp band around the frequency, 2117.8cm -1 reveals a very polar functional group. The amide functional group of C=O bond is found at 1676cm -1 whilst the two spikes around 1676cm -1 depicts the existence of primary amides.

SEM Micrograph for the Corrosion Inhibition of Mild Steel in Hydrochloric Acid by Thoroughly Crushed Leaves of Voacanga Africana
The SEM image shows that the deterioration of the surface of mild steel in an uninhibited solution of 0.7M HCl is not uniform (Figure 10(a)) but, is somewhat protected by the addition of thoroughly crushed leaves of Voacanga Africana at 30g per litre of 0.7M HCl as shown in Figure 10(b).

Conclusion
The maximum inhibition efficiency of 69.80% was obtained when thoroughly crushed leaves of Voacanga Africana was added at 15g per litre of 0.7M HCl with a corresponding decrease in corrosion rate from 2.6487mg.cm -