Journal of Minerals and Materials Characterization and Engineering, 2013, 1, 367-373
Published Online November 2013 (
Open Access JMMCE
Unification of the Quadratic Model Equations of the
Inhibition Characteristics of Acidified Ocimum Basilicum
on the Corrosion Behaviour of Mild Steel
Michael O. Nwankwo1, Paul A. Nwobasi2, Peter O. Offor3, Ndubuisi E. Idenyi1
1Department of Industrial Physics, Ebonyi State University, Abakaliki, Nigeria
2Department of Technology and Vocational Education, Ebonyi State University, Abakaliki, Nigeria
3Department of Metallurgical and Materials Engineering, University of Nigeria, Nsukka, Nigeria
Received September 3, 2013; revised October 14, 2013; accepted October 23, 2013
Copyright © 2013 Michael O. Nwankwo et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
An attempt has been made at unifying the resulting quadratic models from the study of the correlation behavior of the
inhibition characteristics of acidified ocimum basilicum on conventional mild steel. Weight-loss corrosion technique
was employed in obtaining the corrosion penetration rate using the equation: 87.6 w
. Subsequently, the quad-
ratic models were developed by using a computer-aided statistical modeling technique (International Business Machine
(IBM)’s SPSS version 17.0). The results obtained showed a nearly perfect positive correlation with a correlation coeffi-
cient in the range of 0.986 R 0.996 which depicts that R 1. Also, the coefficient of determination fell within the
range of 0.972 R2 0.992 showing that approximately 97% to 99% of the total variation in passivation rate was ac-
counted for by corresponding variation in exposure time, leaving out only between 3% and 1% to extraneous factors
that are not incorporated into the model equations. The equations were further unified into a generalized form using
MathCAD 7.0 and the resulting equation was 62
1.0320.0021.899 10
 t with a R2 value of 0.935 indicating a
well-correlated relationship. With this, a new frontier on corrosion studies has emerged typifying a classical departure
from previously long-held assumption that corrosion behaviours at room temperature were only logarithmic.
Keywords: Corrosion; Inhibition; Ocimum Basilicum; Correlation; Quadratic Models; Passivation
1. Introduction
Corrosion has been defined from the individual perspec-
tives of several authors. However, most authors insist
that the definition of corrosion should be restricted to
metals. More often than not, though, corrosion engineers
must consider both metals and nonmetals for solution of
a given problem. Accordingly, polymers (plastics, rub-
bers, etc.), ceramics (concrete, brick, etc.) or composites
(mechanical mixtures of two or more materials with dif-
ferent properties) and other nonmetallic materials are
generally included as materials that can corrode [1].
Reference [2] defined corrosion as the environmen-
tally induced degradation of a material that involves a
chemical reaction. Degradation implies deterioration of
physical properties of the material. This can be a weak-
ening of the material due to a loss of cross-sectional area;
it can be the shattering of a metal due to hydrogen em-
brittlement; or it can be the cracking of a polymer due to
sunlight exposure.
The deleterious effects of corrosion are well-known
and include among others: poor outward appearance of
material surfaces, high maintenance and operating costs,
frequent plant shutdowns, contamination of end products,
loss of valuable products, hazardous effects on safety and
reliability and burdensome product liabilities. As a result
of these, huge financial losses have always been recorded
annually as resulting from corrosion damage. As an in-
stance, in 1998 alone, the United States reported an esti-
mate of the cost of corrosion to be around $276 billion: a
figure that is however realistically put at $30 billion [1].
In fact, [3] has gone further to project that this figure
would reach $993 billion by March 2013, with a still
further increase to $1 trillion by June of the same year.
It is against this backdrop of financial losses that cor-
rosion engineers over the years have had to rely on the
concept of materials selection and economics to mitigate
corrosion. However, even with the proper selection of
base metals and well-designed systems or structures,
there is no absolute way to eliminate all corrosion.
Therefore, corrosion protection methods are used to ad-
ditionally mitigate and control the effects of corrosion.
Corrosion protection can be in a number of different
forms or strategies with perhaps multiple methods ap-
plied in severe environments [4]. The various forms of
corrosion protection include among others the use of in-
hibitors, surface treatments, coatings and sealants, ca-
thodic protection and anodic protection.
In recent times, however, the hazardous consequences
of the somewhat traditional or conventional methods of
corrosion control, has made it imperative to source for
cost-effective and environmentally-friendly corrosion
control measures to eliminate or at least reduce these
effects. In this respect, the use of natural plants as corro-
sion inhibitors has expectedly become the current fron-
tiers of most research activities in corrosion engineering.
Inhibitors are chemicals that react with the surface of a
material decreasing the material’s corrosion rate, or that
interact with the operating environment to reduce its
corrosivity [4]. They can be added into the corrosion
medium as solutions or dispersions to form a protective
film, or as additives in coating products, or further still
into waters used for washing vehicle, system or compo-
nent. When added, they interact with the metal, thus
slowing the corrosion process by shifting the corrosion
potential of the metal’s surface toward either the cathodic
or anodic end; preventing permeation of ions into the me-
tal; or increasing the electrical resistance of the surface [4].
Africa, and particularly Nigeria, with her favourable
tropical climatic conditions is home to a vast number of
natural plants that are continuously been investigated as
profitable alternatives to synthetic inhibitors because of
their inherent advantages amongst which are their ready
availability, biodegradability, non-toxicity, non-pollutan-
cy and eco-friendliness [5,6]. It is on the strength of these
that ocimum basilicum was chosen for this work.
Ocimum basilicum is itself a vegetable plant believed
to be of Indian origin [7-9]. It belongs to a popular plant
species called basil. There are several varieties of basil in
existence, some of which have been used in previous
works [10-13]. However, basilicum species have not
been investigated previously in relation to mild steel to
the best of the authors’ knowledge.
Reference [14] used statistical tools (particularly re-
gression analysis) as a novel approach in corrosion stud-
ies. Since then, several other works have been done to
develop models for predicting the corrosion behavior of
engineering materials using specific parameters [15-18].
The findings from these works show that corrosion pro-
files correlated better in the quadratic models than the
logarithmic models at room temperatures.
This work therefore is an attempt to reinforce the find-
ings of [14] with regards to the regression behavior of
corrosion rates at room temperatures; and then unifying
the resultant regression equations into a single model
equation that would satisfy the conditions as a frame-
work for futuristic corrosion predictions particularly dur-
ing design considerations.
2. Experimental Techniques
2.1. Materials/Equipment
The materials and equipment used for the work include
10mm diameter mild steel rods sourced from a local steel
stockiest in Enugu, Nigeria, beakers, digital weighing
balance, tetraoxosulphate (VI) acid, leaves of ocimum
basilicum, acetone, nylon strings, emery cloth, distilled
water, hacksaw, vernier caliper, measuring cylinder, and
volumetric flask.
2.2. Materials Preparation
The mild steel rods were cut to sizes, each averaging
94.5 cm2 in surface area. They were thoroughly brushed
with emery cloth to reveal the metal surface. Thereafter,
they were washed with distilled water and rinsed with
The tetraoxosulphate (VI) acid was prepared to 0.5 M
and 1.0 M concentrations using standard procedures.
The ocimum basilicum leaves were washed with cold
tap water, dried under room temperature after which they
were subjected to soxhlet extraction process in ethanol
for about 80 hours to obtain the extract.
2.3. Experimentation
The mild steel coupons were tied with nylon strings and
then suspended in beakers containing the acid and the
acidified extracts. Each beaker contained 5 coupons and
the entire set up were allowed to stand for 30 days. After
6 days a coupon was withdrawn from each beaker, rinsed
in distilled water and swabbed in acetone. Thereafter,
they were weighed for weight loss determination and
corrosion rate calculation using the formula:
87.6 w
The pH value of the ocimum basilicum extract was eva-
luated and noted.
2.4. Unification of the Model Equations
Using MathCAD 7.0, the model equations were plotted
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Open Access JMMCE
and the best line of fits was taken. The equation corre-
sponding to this line was then noted with all of its neces-
sary parameters.
3. Results
Tables 1-6 show the corrosion penetration rate values
obtained from weight loss measurements; while Figures
1 and 2 are the quadratic model fits from regression
analysis of the corrosion penetration rates. Table 8 is the
quadratic model equations obtained from the regression
4. Discussion
4.1. Corrosion Trends
Looking at Tables 1-6, the corrosion rates obtained de-
pict those of passivating metals: beginning with an initial
steep rise, peaking at a maximum and then subsequently
decreasing as exposure time increased. On interaction
with the corrosion medium, the metal surface normally
reacts swiftly with it, forming an oxide film that coats the
entire surface acting as a barrier, thereby preventing fur-
ther reactions [19].
Table 1. Corrosion penetration rates of mild steel sample in 0.5 m H2SO4.
Exposure time (hrs) Initial weight (g) Final weight (g) Weight loss (g) Corrosion rate (mm/yr)
144 26.76 20.46 6.30 0.5178
288 26.34 19.59 6.75 0.2774
432 26.87 19.77 7.10 0.1945
576 26.51 19.00 7.51 0.1543
720 27.01 15.93 11.11 0.1826
Table 2. Corrosion penetration rates of mild steel sample in 0.5 m H2SO4 with 25 cm3 of ocimum basilicum.
Exposure time (hrs) Initial weight (g) Final weight (g) Weight loss (g) Corrosion rate (mm/yr)
144 25.14 19.04 6.10 0.5013
288 28.82 22.29 6.53 0.2683
432 28.36 21.80 6.56 0.1767
576 27.61 20.67 6.94 0.1422
720 26.90 17.80 9.10 0.1596
Table 3. Corrosion penetration rates of mild steel sample in 0.5 m H2SO4 with 50 cm3 of ocimum basilicum.
Exposure time (hrs) Initial weight (g) Final weight (g) Weight loss (g) Corrosion rate (mm/yr)
144 28.02 22.46 5.56 0.4560
288 27.24 21.05 6.19 0.2544
432 27.93 21.63 6.30 0.1745
576 27.41 20.36 7.08 0.1444
720 27.38 17.38 10.00 0.1454
Table 4. Corrosion penetration rates of mild steel sample in 1.0 m H2SO4.
Exposure time (hrs) Initial weight (g) Final weight (g) Weight loss (g) Corrosion rate (mm/yr)
144 25.70 14.84 10.86 0.8926
288 25.64 12.69 12.95 0.5322
432 25.50 12.35 13.15 0.3603
576 24.47 9.82 14.65 0.2900
720 26.63 10.63 16.00 0.2630
Table 5. Corrosion penetration rates of mild steel sample in 1.0 m H2SO4 with 25 cm3 of ocimum basilicum.
Exposure time (hrs) Initial weight (g) Final weight (g) Weight loss (g) Corrosion rate (mm/yr)
144 26.58 17.03 9.55 0.7849
288 26.40 16.36 10.04 0.4126
432 26.81 15.53 11.28 0.3090
576 24.80 12.69 12.11 0.2488
720 25.10 6.08 17.02 0.2305
Table 6. Corrosion penetration rates of mild steel sample in 1.0 m H2SO4 with 50 cm3 of ocimum basilicum.
Exposure time (hrs) Initial weight (g) Final weight (g) Weight loss (g) Corrosion rate (mm/yr)
144 27.71 18.42 9.29 0.7635
288 27.22 16.85 10.37 0.4261
432 26.86 15.29 11.57 0.3170
576 25.19 12.97 12.22 0.2318
720 24.73 10.63 14.10 0.2511
0.7930.002 x
1.998 106
0.7710.002 x
1.922 106
0.6820.002 x
1.567 106
1.3020.003 x
2.647 106
1.1550.003 x
2.588 106
1.1320.003 x
2.540 106
1 10480006000 4000200002000 40006000 80001104
Figure 1. Graphical plots of the quadratic model equations using mathcad 7.0.
Figure 2. Line of best fits from the model equations.
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Open Access JMMCE
4.2. Model Summary
From Table 7 , it can be seen that R (coefficient of corre-
lation) values ranged from 0.986 to 0.996 showing that R
1, which is a near-perfect correlation; while the R2 (co-
efficient of determination) values ranged from 0.972 to
0.992, implying that approximately between 97% to 99%
of the entire variation in passivation rate is dependent on
exposure time, leaving only a maximum of 3% to extra-
neous sources such as errors of measurements, experi-
mental procedures and test locations.
Also, the standard error of estimation fell between
0.021 - 0.054 which is significantly less than 0.1. The
implication of this very narrow error margin is that the
use of quadratic models to characterize corrosion rates at
room temperature is justifiable and therefore could be
employed. That being the case, a classical departure from
the long-held assumptions that corrosion rate behaviours
are only logarithmic at room temperatures has been es-
These claims are corroborated by the line patterns of
Figure 1 where the lines of best fits agree with the near
perfectness of the correlation data obtained.
4.3. Model Equations
From Table 8, the model fit equations show that each
had a non-negligible quadratic element that must be ac-
counted for during corrosion rate evaluation. Since time
and media are critical considerations in corrosion moni-
toring, for a given medium therefore the exposure time
becomes the overriding factor for corrosion progression,
hence our time-dependent quadratic models subsist in
this present study.
Furthermore, looking at the equations in the order in
which they appeared, both the constant term and the co-
efficient of t2 decreased as the volume of the extracts
increased in each of the acid molarities. This confirms
further that inhibition has taken place and that an in-
crease in the inhibitor concentration caused a decrease in
corrosion penetration rate.
4.4. Unified Model Equation
From Figure 2 we see the best line of fits from the plots
of all the model equations represented in Table 8 and as
plotted in Figure 1. The model parameters in Table 9
clearly show that the coefficient of determination, R2 of
0.935 is very high indicating in similar manner that about
94% of the determining factors are dependent on expo-
sure time of the corrosion process, whilst 6% is ac-
count-ed for by extraneous factors which in this case may
include errors of mathematical measurements and eva-
luations. Based on the foregoing, the unified model equa-
1.0320.0021.899 10cprt t
is adjudged a suitable and correct corrosion predictor for
the present study.
Table 7. Model equations of the various quadratic fits.
Corrosion medium Model equations
0.5 M H2SO4 only 62
0.7930.0021.998 10tt
0.5 M H2SO4 + 25 cm3 ocimum basilicum 62
0.5 M H2SO4 + 50 cm3 ocimum basilicum 62
0.6820.0021.567 10tt
1.0M H2SO4 only 62
1.3020.0032.647 10tt
1.0 M H2SO4 + 25 cm3 ocimum basilicum 62
1.1550.0032.588 10tt
1.0 M H2SO4 + 50 cm3 ocimum basilicum 62
1.1320.0032.540 10tt
Table 8. Model parameters.
Corrosion Medium R R2 Adjusted R2 Standard Error of Estimation
0.5M H2SO4 0.994 0.988 0.976 0.023
0.5 M H2SO4 + 25 cm3 Ocimum basilicum 0.995 0.990 0.980 0.021
0.5 M H2SO4 + 50 cm3 Ocimum basilicum 0.994 0.988 0.975 0.021
1.0M H2SO4 0.996 0.992 0.984 0.033
1.0 M H2SO4 + 25 cm3 Ocimum basilicum 0.986 0.972 0.944 0.054
1.0 M H2SO4 + 50 cm3 Ocimum basilicum 0.993 0.986 0.972 0.037
Table 9. Model summary and parameter estimates of the unified equation.
Dependent Variable: Y
Model Summary Parameter Estimates
Equation R Square F df1 df2 Sig. Constant b1 b2
Quadratic 0.935 171.551 2 24 0.000 1.032 0.002 1.889E-6
The independent variable is T.
Regression Equation: 62
1.0320.0021.899 10
 .
5. Conclusion
The conclusion that can be drawn from the foregoing
discussions is that ocimum basilicum is a good corrosion
inhibitor since its pH value of 6.7 falls within the region
in which passivation occurs in the Poubaix diagram [20].
Again the quadratic model which fits each with a nearly
perfect correlation suggest in strong terms that room tem-
perature corrosion progression can no longer be said to
be only logarithmic but also has a significant quadratic part
that must be accounted for during corrosion characteriza-
tions. Additionally, the unification of the model equa-
tions into a single generalized form also shows that it is
henceforth possible and accurately so, to use the equation
to make futuristic computations of corrosion penetration
rates for engineering mild steel in acidic environments
with ocimum basilicum serving as a veritable inhibitor.
6. Acknowledgements
The authors wish to acknowledge the Department of In-
dustrial Chemistry of Ebonyi State University for grant-
ing them the permission to use their facilities for the
work. Dr. S. O. Maliki of the Department of Industrial
Mathematics, Ebonyi State University is also acknowl-
edged for his immense contributions.
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