Adsorption Isotherm Modeling in Corrosion Inhibition Studies

Abstract

Metals and their alloys are useful structural materials in construction and building industry, due to their peculiar properties. The applications of metals and alloys are, however, bedeviled by corrosion problems. Among the many corrosion preventing methods available, the use of inhibitors stands out, of which their action of inhibitors in corrosion mitigation is through a number of ways, of which adsorption process is one. The knowledge of adsorption process can assist in understanding the mechanism of isotherm. Determination of isotherm best fit has been a subject of intensive debate. Two key parameters commonly employed for such determination are regression coefficient, R², and free energy, ΔG_ads value. Many authors have argued the inadequacy of these parameters for the determination. In this chapter, we provide a good insight into how to resolve ambiguity associated with isotherms best fit for adsorption of corrosion inhibitors unto.

1. Introduction

1.1 Corrosion science and inhibition

Metals and their alloys are hugely used for building and constructional materials on the account of numerous beneficial characteristics like high mechanical power and cost-effective nature. But these uses are bedeviled due to their high reactivity, as they are easily susceptible to corrosive degradation by their reaction with the constituents of environment [1]. Corrosion is simply defined as a deterioration process of any material on the account of its reaction with its surroundings. Corrosion, a common natural phenomenon, occurs in both metals and nonmetallic materials. Corrosion reactions are significant problems that we encounter daily, and such reactions result in the breaking down of essential properties of metals. The resultant effect is the production of new materials that are less desirable, making the materials to lose their functionality [2, 3]. Therefore, the protection of metals and other materials against corrosion is a typical subject always on front burner. This results in enormity of loss of natural resources and associated finances on account of corrosion process [4]. Aside economic effects, control of corrosion is also of importance on the account of environmental and from aesthetical angle. Phenomenon of corrosion is usually encountered in metal and their alloy products. Corrosion cost to the economy of any nation is usually huge. Many nations commit between 2 and 4% of their gross domestic product (GDP) into combating it [5]. Adding to the huge cost, corrosion process can also be blamed for number of the disasters that cause the loss of life and devastating pollution of the environment. Remarkable progress has been made in field of science and engineering of corrosion process, yet the menace of it remains a major challenge nations all nations are facing that have to be tackled.

Majority of metals are found in combined state with other elements and materials in the form of ores. Man obtained refined metals from these ores with the use of enormous energy, and as a result, they can be said to be in metastable state and ever ready to dissipate this energy to revert to materials more or less close to the original ore materials, which is corrosion [6, 7, 8]. The basic equation for metal corrosion can be represented in Eq. (1).

$$\mathrm{M}\to {\mathrm{M}}^{\mathrm{n}+}+\mathrm{n}{\mathrm{e}}^{-}$$E1

For the reaction to proceed from left to right, the electron produce must be consumed. This happens in a number of ways at the cathode. Few examples of such reactions are [7].

1. Hydrogen evolution reaction (HER), which can occur in acid or neutral solution

   1. in acid solution

      $$2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2$$E2

   2. in neutral solution

      $$2{\mathrm{H}}_2\mathrm{O}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2+2\mathrm{O}{\mathrm{H}}^{-}$$E3

2. Oxygen can pick up the electron either in acid or alkaline/neutral solution

   1. in acid solution

      $${\mathrm{O}}_2+4{\mathrm{H}}^{+}+4{\mathrm{e}}^{-}\to 2{\mathrm{H}}_2\mathrm{O}$$E4

   2. neutral solution

      $${\mathrm{O}}_2+2{\mathrm{H}}_2\mathrm{O}\to 4{\mathrm{e}}^{-}+4\mathrm{O}{\mathrm{H}}^{-}$$E5

3. Metal deposition or metal reduction is also a possible as cathodic reaction

   1. metal deposition

      $${\mathrm{M}}^{\mathrm{n}+}+\mathrm{n}{\mathrm{e}}^{-}\to \mathrm{M}$$E6

   2. metal reduction

      $${\mathrm{M}}^{3+}+{\mathrm{e}}^{-}\to {\mathrm{M}}^{2+}$$E7

4. Reduction of anion is another possible cathodic reaction; for example, nitrate ion can be reduced in acidic solution as shown in Eq. (8)

   $$2\mathrm{N}{\mathrm{O}}_3^{-}+4{\mathrm{H}}^{+}+4{\mathrm{e}}^{-}\to {\mathrm{N}}_2{\mathrm{O}}_4+2{\mathrm{H}}_2\mathrm{O}$$E8

For corrosion to occur, one or more of the following conditions must be fulfilled.

1. something that will corrode (metal-anode)

2. there must be a cathode, which could be another metal or another part of the same metal (cathode)

3. a conductive liquid/molten path (electrolyte)

4. a conductor to carry the flow of electrons.

Corrosion effects on our daily lives are both direct, in that it affects the useful service lives of our appliances, and indirect, as the costs incurred due to corrosion are passed to consumers from the producers and suppliers of goods and services. At home front corrosion is readily recognized on vehicle parts, charcoal grills, outdoor furniture, and metal tools. Preventive maintenance such as painting protects such items from corrosion. The reason behind replacement of vehicle parts like radiator coolant periodically is the replenishment of corrosion inhibitor which controls corrosion of the cooling system. Indeed, designing and building of major household appliances like water heaters, furnaces, ranges, washers, and dryers allowance must be made for corrosion protection/control measures [9]. Corrosion affects our lives during travel from home to work/school with huge consequences. The corrosion of steel reinforcing bar in concrete can take place unnoticed, but can result into failure of a section of highway, bridge, electrical towers, and damage to buildings, parking structures, etc. This can result into significant repair costs and even endangering public safety. Perhaps most dangerous of all is corrosion that occurs in major industrial plants, such as electrical power plants or chemical processing plants. Plant shutdowns can occur because of corrosion, with great repercussions. Few examples of well-known destructive actions of corrosion reaction to critical infrastructure and some with life lost are shown pictorially [10, 11]. Corrosion is of enormous cost to nations, in terms of resources, materials, energy as well as human life (Figures 1–3).

Figure 1.

(a) Prize-winning Berlin congress hall (b) the same congress hall in 1980 built in 1957 (https.//www.gettyimages.ae>detail>new-photo [Accessed: June 2, 2024]).

Figure 2.

Famous Aloha flight 243 after landing safely at Kahului airport in 1988 following fracture of part of the fuselage [11].

Figure 3.

Bridge collapse in Ogbia local government of Bayelsa state, Nigeria (https://dailytrust.com>the-curious-case-of-bayelsas-n2-3).

1.2 Corrosion prevention measures

Metallic materials find industrial applications and construction due to factors like availability, ease of fabrication, relatively low cost, perfect tensile strength, and their other important properties [12, 13]. However, the usage is bedeviled by the ease which they can corrode when in contact with environments like cleansing, transportation, storage, descaling, and other chemical processes. Plethora of corrosion control measures are available like material selection, coatings, application of inhibitors, cathodic protection, and design, and the most effective method has been found to be the use of inhibitors. A corrosion inhibitor can be defined as any substance that when added to corrosive environment in a small quantity reduces the corrosion rate, significantly [14]. Inhibitors reduce the rate of corrosion in one or combination of the following ways;

1. adsorption of molecules/ions onto the metal/material surface

2. decrease the anodic or cathodic reaction

3. decrease the diffusion rate of the reactants to the metal surface and/or

4. increase the electrical resistance of the metal surface.

The choice of any of the following processes in combating corrosion depends on number of factors like environment, materials, and cost. For years, great research efforts have been deployed to find suitable corrosion inhibitors, especially of organic origin in various corrosive media. In acid media, nitrogen-based materials and their derivatives, sulfur-containing compounds, aldehydes, thioaldehydes, acetylenic compounds, and various alkaloids, for example, papaverine, strychnine, quinine, and nicotine are useful for formulation of corrosion inhibitors [15]. In neutral media, benzoate, nitrite, chromate, and phosphate containing compounds can act as good inhibitors. Inhibitors act in the decrease or in prevention of metal reaction with the media by one or combination of the followings: adsorption of ions/molecules onto metal surface, increasing or decreasing the anodic and/or cathodic reaction, decreasing the diffusion rate for reactants to the surface of the metal, and decreasing the electrical resistance of the metal surface [16, 17].

The amount of inhibitor used is very important in corrosion formulation, as a good inhibitor is usually used in small concentrations and essentially minimizes the corrosion rate by inhibiting the reaction of metal with its environment. Synthetic inhibitors although are excellent in action, and they are, however, not commonly allowed nowadays as a result of their harmful effects on the human beings and the environment, as well as cost. This has generated much interest in the development of green/ecofriendly corrosion inhibitors (GCIs) among researchers [6], with much focus on green/benign inhibitors like plant extracts, due to their bio-degradability, ease of availability, low cost, renewability, as well as simplicity of their extraction procedures [18]. Many plant extracts and organic compounds/molecules have been tested as corrosion inhibitors with excellent results [2], as shown by few research work summarized below.

1. Miralrio and Espinoza [19] in 2020 reviewed the use of extracts from plants as GCIs for different metal surfaces and corrosive media and found many plant extracts have excellent inhibitive action. Variables like concentration, extraction solvent, temperature, and immersion time can be explored to evaluate a plant extract as corrosion inhibitor: Theyadded that in order to complement the description on the corrosion inhibition many authorsinclude the study of the adsorption of corrosion inhibitor molecules on the metal surface. They review showed that constituent compounds of the plant extracts are mainly adsorbed onto the metal surface and obey the Langmuir isotherm model, by the processes of physical and chemical adsorption, and some even mixed adsorption mechanisms.

2. The toxicity of conventional corrosion inhibitors is the underlining factor behind many researchers into the study and developenvironmentally friendly inhibitor. Recently the rule is that any new inhibitor developed must conform to various regulations, in addition to upholding the general feature of good efficiency just like conventional industrial inhibitors. On that basis any good green inhibitor must be non-toxic, biodegradable, and with sign of no bioaccumulation in the environment. For the reasons, profound works to exploit the biodegradable nature of plant extracts and their efficacy as green have been initiated employing a number of laboratory techniques [20].

3. Zakeri and his co-researchers in 2022 reviewed plethora of works on plant extracts. They noted that parts like fruit, leaf, bark, peel, flower, root, seed, and even whole plant extracts have been utilized as green corrosion inhibitors (GCIs). Different types of phytochemicals and content were observed based on factor like plant extraction process. In the case of Sida acuta, contents vary by part; flavonoids, saponins, alkaloids, tannins, organic acid, and anthraquinones were found in leaves, while alkaloids, tannins, and anthraquinones were present in extract from the stem. They reported that leaf extracts exhibited the overall best inhibition performance under low concentrations for many plants. This could be attributed to the fact that many phytochemicals are produced in leaves. Among to the phytochemicals found, flavonoids, glycosides, alkaloids, saponins, phytosterol, tannins, anthraquinones, phenolic compounds, triterpenes, and phlobatannins were observed to have better inhibition performance. The primary reason for the action is because such compounds have polar functional groups that have features for adsorption. These groups are —CONH2, —OH, -OOC2H5, —COOH, and —NH2. In their conclusion, it was said that these substances present excellent option for replacing the toxic, harmful, and expensive corrosion inhibitors that have been in common use. However, the general snag with these types of inhibitors is how to identify the particular bioactive component that has the corrosive action. At the moment, this presents limitation to their full application as GCIs. They suggested directing future studies in such area [7].

4. In their 2018 study Verman et al., examined leaf extracts of Olea europaea, Taberaemontana divericata, Phyllanthus amarus, Croton rottleri, Eleusine aegyptiacca, etc., for their inhibitive action against corrosion of metals and their alloys. They concluded that plant extracts can be good candidates which can replace expensive and toxic inorganic and synthetic organic corrosion inhibitors in use. On modeling with adsorption isotherms, their observation was that many of such extract followed the Langmuir isotherm [9].

The choice of an inhibitor is usually guided by factors like quantity and cost, easy availability and most important safety to environment, whether the inhibitor is synthetic and plant-based.

In this chapter the inhibitive property of organic or plant-based inhibitor is elucidated by the use of adsorption isotherm models. This is as the result that basic information on the interaction between the inhibitor and the metal surface can only adequately be provided by the adsorption isotherms. The characterization is based on surface coverage (θ) at different concentrations and at particular temperature (and pH) [12]. In literature many authors pointed out the inadequacy of using thermodynamic parof plant extracts. This is due to the fact that an extract is a mixture of compounds of different molecular masses, but thermodynamic parameters are usually molar quantities [21]. But in reality adsorption process is very vital in understanding of electrochemical processes such as corrosion and its inhibition, electro-organic synthesis on the surface of metals, electro-kinetics, and double layer. Details of mechanism of inhibition of metallic corrosion, design, and development of new inhibitors will be possible only if adsorption process onto the metal surface is clearly understood [14]. Thus, inhibition efficiency of inhibitors demands an adequate understanding, evaluation, and optimization of the adsorption interactions between the inhibitor molecules and the metal surface.

2. Methods corrosion measurement

The corrosion measurement in a material is by the use of a probe which can be inserted in the process stream of the corrosion environment. The measurement, control, and prevention of corrosion cover a broad technical of activities. Common techniques available for the study inhibitors behavior in different media are the weight loss, gasometric, thermometric, electrical resistance, linear polarization resistance, electrochemical impedance spectroscopy, and a host of other techniques [20]. Each tone has its strengths and weaknesses; while some quite prone to errors, and others require expensive instrumentation.

Adejo and c0-workers demonstrated the use acidimetric technique for corrosion monitoring, adding to the list of techniques. The unique features of the method are simplicity of usage, less prone to error (measurement is done in situ, requiring no withdrawal and weighing), and inexpensive instrumentation. The method was used to study corrosion inhibition of mild steel in H₂SO₄ medium using urea as an inhibitor [5]. The inhibition efficiency and the efficacy of the technique were compared favorably with the weight loss technique, an established corrosion monitoring technique.

3. Adsorption isotherm

As defined by The International Adsorption Society (2004), adsorption is preferential partitioning of a substance from the gaseous or liquid phase onto the surface of a solid substrate. The Encyclopaedia Britannica (2013) explains adsorption to be capability of all solid substances to attract to their surface molecules of gaseous or solutions with which they are in contact. In adsorption process, the relationship between the amount of the adsorbed substance to the surface to its concentration in gas or solution phase at a particular temperature (and pH) is known as adsorption isotherm. Adsorption isotherm is simply the retention or mobility of a substance from aqueous porous media or aquatic environment to a solid phase at constant temperature and pH [1].

Adsorption isotherms are critical for optimization of the adsorption mechanism pathway, expression of the surface properties and capacities of adsorbents, and effective design of the adsorption systems [2]. Adsorption isotherms are useful for the elucidation of many processes. A process of the mechanism of inhibition in corrosion inhibition process can better be understood through the use of such isotherm [5, 6, 7]. Explanation of mechanism of inhibition of metallic corrosion, design, and even development of new and effective inhibitors will only be possible if adsorption of inhibitor onto the metal surface is clearly understood [22]. Kinetic, thermodynamic, and potential approaches are always used in formulating an isotherm. Freundlich in 1906 proposed the earliest known adsorption isotherm equation, through empirical deductions. Langmuir in 1916, through theoretical equilibrium, proposed isotherm which can be applied to non-ideal adsorption on heterogeneous surfaces as well as multilayer [3]. Thereafter, many isotherms have been put forward like Temkin, Frumkin, Flory-Huggins, El-Awady, Dubinin-Radushkevich, and Adejo-Ekwenchi models; all developed through empirical observations [5].

Insight into adsorption mechanism can be obtained through physico-chemical parameters and the underlying thermodynamic assumptions, surface properties, and the degree of affinity of the adsorbents. These factors are fundamentals in the characterization of adsorption process. The fundamental principle in isotherm derivation that, for any adsorption process, the rate of surface coverage depends on a number of factors. These are the heat of adsorption of the surface and the rate at which the molecules strike the surface (that is, to the pressure of the gas, or concentration in the case of molecules in liquid system) [23]. Adsorption isotherm derivation is purely empirical. The basis for the formulation is that the rate of surface coverage is dependent on a number of factors, mainly the heat of adsorption of the surface, the rate at which the molecules strike the surface (that is, to the pressure of the gas or concentration in the case of molecules in liquid system) [23]. Molecules would bind first to the more attracting sites, that is, those with greatest binding power having high negative Gibb’s free energy, ΔG_ads. As the binding sites on the surface get fill up, more active sites become used up, and therefore at higher surface coverage, ΔG_ads would be less negative, and the molecules uptake become less [8]. The Adejo-Ekwenchi isotherm is a good example of such empirical formulation. This isotherm is based on the fact that, for an adsorption process, the amount of adsorbate uptake from bulk concentration is inversely proportional to the difference between the total available surface on the adsorbent and the fraction that is covered by the adsorbate, prior to the attainment of maximum value of surface coverage at any given temperature. To sum this in clarity, the more the surface covered, the less the available surface. The expression for this is simply thus

$$\frac{1}{\left(1-\mathrm{\theta }\right)}\propto {\mathrm{C}}^{\mathrm{b}}$$E9

which can be written in nonlinear form;

$$\frac{1}{\left(1-\mathrm{\theta }\right)}={\mathrm{K}}_{\mathrm{AE}}{\mathrm{C}}^{\mathrm{b}}$$E10

Eq. (10) is the Adejo-Ekwenchi isotherm equation, which the linear form is

$$log\frac{1}{\left(1-\mathrm{\theta }\right)}=log{\mathrm{K}}_{\mathrm{AE}}+\text{blog}\left[\mathrm{C}\right]$$E11

The free energy for the adsorption process can be evaluated from the adsorption equilibrium constant, K_AE, as explained later.

The adsorption equilibrium constant, K_ads, can be obtained for any adsorption isotherm; Langmuir, Freundlich, Temkin, Frumkin, Flory-Huggins, El-Awady, Dubinin-Radushkevich, Adejo-Ekwenchi, etc. [9]. These isotherms were all formulated through kinetic, thermodynamic, and potential approaches. The inhibitive action of a compounds is due to the formation of surface layers and films on the metal surface, reducing the accessibility of the corrodent to the metal surface. Adsorption isotherms have been used to characterize this inhibitive action. Commonly used isotherms are the Langmuir, Freundlich, Frumkin, Temkin, Flory-Huggins, El-Awady, and Adejo-Ekwenchi [24, 25]. The linear forms of these isotherm equations are represented by Eqs. (12–19) [23, 25, 26, 27].

Langmuir

$$\frac{\mathrm{C}}{\mathrm{\theta }}=\frac{1}{\text{Kads}}+\mathrm{C}$$E12

Freundlich

$$\text{logθ}=log{\mathrm{K}}_{\mathrm{F}}+{\mathrm{n}}_{\mathrm{F}}\text{logC}$$E13

Frumkin

$$log\frac{\mathrm{\theta }}{\left[\left(1-\mathrm{\theta }\right)\right]\mathrm{C}}=\text{logK}+\frac{2\mathrm{a\theta }}{2.303}$$E14

Flory-Huggins

$$log\frac{\mathrm{\theta }}{\mathrm{C}}=\text{logK}+\text{xlog}\left[1-\mathrm{\theta }\right]$$E15

Temkin

$$-2\propto \mathrm{\theta }=\text{lnKC}$$E16

El-Awady

$$log\frac{\mathrm{\theta }}{1-\mathrm{\theta }}=log{\mathrm{K}}^{\prime }+\text{ylog}\left[\mathrm{C}\right]$$E17

Sips

$$log\frac{\mathrm{\theta }}{1-\mathrm{\theta }}=\text{logA}+\text{xlog}\left[\mathrm{C}\right]$$E18

Adejo-Ekwenchi

$$log\frac{1}{1-\mathrm{\theta }}=log{\mathrm{K}}_{\mathrm{AE}}+\text{blog}\left[\mathrm{C}\right]$$E19

The positive value of equilibrium constant K_ads indicates favorable adsorption. Through this parameter, the free energy, ∆G_ads, of the adsorption process can be calculated.

$$∆{\mathrm{G}}_{\mathrm{ads}}=-2.303\text{RTlog}\left[55.5{\mathrm{K}}_{\mathrm{ads}}\right]$$E20

$${\mathrm{K}}_{\mathrm{ads}}=\frac{\mathrm{\theta }}{\left[1-\mathrm{\theta }\right]\mathrm{C}}$$E21

where C is the extract concentration, and 55.5 is concentration of water expressed in moles (i.e., ∼ 1000 g/dm³ [21]).

4. Isotherm modeling in corrosion inhibition

Many authors have, indeed, challenged the adequacy of thermodynamic parameters in the discussion of the adsorption behavior of plant extracts as inhibitors. Thermodynamic parameters are molar quantities, but extracts are usually mixtures of many components of different molecular masses. Knowing the exact molecule acting to inhibit is really difficult to identify in such a mixture; the use of adsorption isotherms is of immeasurable value in this regard. Regression coefficient, R², has been employed by many authors to determine the fitness of adsorption data into an isotherm, and ∆G_ads value is known whether the process is physical adsorption process (physisorption or chemical adsorption process (chemisorption). Employing the R² has a snag due to the fact that most isotherm equations are nonlinear, which means their transformation to linear forms alters their error structure and may as well violates the error variance and normality assumptions of standard least squares [28]. Again a number of authors have put forward argument that the value of ΔG_ads below −20 kJ/mol indicates physisorption, and value above −40 kJ/mol is chemisorption. Popova and Co-workers [28, 29] have argued against total dependency on ΔG_ads criterion only for such distinction. There is the possibility of Coulombic interaction between charged species, for cases involving adsorption of charged species. There is therefore that possibility of increase in the value of ΔG_ads, even though new chemical bonds are not formed. This then creates ambiguity in the use of these parameters as sole criteria for modeling and the determination of isotherm best fit of adsorption process. Here lines the importance of the Adejo-Ekwenchi isotherm, which unambiguously clears the ambiguity.

In the Adejo-Ekwenchi model of isotherm, value of the parameter b clearly settles the ambiguity [23]. A decrease in the value of b with rise in temperature means the adsorption process is of physical mechanism, while increase or fairly constant value with increase in temperature is a sign of chemical adsorption mechanism. Also, low value of b signifies small variation of the adsorbate concentration (that is small change of performance) with increase in adsorbate concentration. This implies that the ability of the adsorbate molecules to accumulate onto the surface of the adsorbent with change in concentration is small. High value of b is an indication that more of the adsorbate is accumulated onto the adsorbent surface with change in its concentration [23, 25]. To give credence to the appropriateness of the use of Adejo-Ekwenchi isotherm in such determination, values ΔG_ads obtained through it are found to compare favorably with those obtained through the Langmuir iostherm [23].

Adejo and Akukwa [30] investigated the corrosion inhibition of Securinega virosa modified nano-chitosan (SVMCNP) particles in acidic medium through acidimetric method and obtained parameters of various isotherm are as presented in Tables 1–3 show the data obtained for corrosion rate, inhibitor efficiency, and parameters evaluated for some common adsorption isotherm.

	CR (CR (moldm^−3cm^−2h^−1))
Conc. /(g/dm^3)	301 K	305 K	309 K	313 K
Blank	4.4693 x10–^3	5.2851 x 10^−3	6.1491 x 10^−3	6.9474 x 10^−3
0.1	3.3728 x 10^−3	3.7588 x 10^−3	4.0614 x 10^−3	4.1316 x 10^−3
0.2	3.1360 x 10^−3	3.5526 x 10^−3	3.6974 x 10^−3	3.8772 x 10^−3
0.3	2.7983 x 10^−3	3.1798 x 10^−3	3.1842 x 10^−3	3.2763 x 10^−3
0.4	2.5614 x 10^−3	2.7105 x 10^−3	2.8509 x 10^−3	2.7807 x 10^−3
0.5	2.3158 x 10^−3	2.4868 x 10^−3	2.3728 x 10^−3	2.1886 x 10^−3

Table 1.

Corrosion rate (CR) of the inhibitor at different temperature.

%I.E
Conc./(g/dm^3)	301 K	305 K	309 K	313 K
0.1	24.50	28.92	33.98	40.56
0.2	29.80	32.81	39.88	44.21
0.3	37.40	39.84	48.23	52.82
0.4	42.71	48.71	53.61	59.95
0.5	48.22	52.98	61.42	68.48

Table 2.

Inhibition efficiency (% IE) of the inhibitor on corrosion of mild steel at varying temperatures.

Isotherm	Tempt.; (K)	R^2	Slope	Intercept	Kads	Isotherm constant	-ΔGads; (kJ/mol)
Langmuir
	301	0.9637	1.5237	0.3140	3.1847		12.95
	305	0.9416	1.4076	0.2724	3.6711		13.48
	309	0.9660	1.2842	0.2103	4.7551		14.32
	313	0.9527	1.1818	0.1783	5.6085		14.94
Freundlich						nf
	301	0.9798	0.4254	−0.2016	0.6286	0.4254	8.89
	305	0.9379	0.3896	−0.1746	0.6690	0.3896	9.17
	309	0.9708	0.3642	−0.1208	0.7572	0.3642	9.60
	313	0.9210	0.3239	−0.0929	0.8074	0.3239	9.90
Temkin						B
	301	0.9514	0.1469	0.5628	46.1179	0.1469	19.64
	305	0.9051	0.1529	0.6120	54.7403	0.1529	20.33
	309	0.9391	0.1659	0.6972	66.8500	0.1659	21.11
	313	0.8874	0.1691	0.7593	89.1400	0.1691	22.14
El-Awady						y
	301	0.9661	0.6558	0.1341	1.3618	0.6558	10.82
	305	0.9079	0.5516	0.1311	1.3524	0.5516	10.95
	309	0.9429	0.6806	0.3509	2.2434	0.6806	12.29
	313	0.8802	0.6943	0.4643	2.9127	0.6943	13.23
Adejo-Ekwenchi						b
	301	0.9285	0.2297	0.3355	2.1652	0.2297	11.98
	305	0.8788	0.2583	0.3828	2.4144	0.2583	12.42
	309	0.8992	0.3163	0.4716	2.9621	0.3163	13.11
	313	0.8366	0.3704	0.5572	3.6075	0.3704	13.79

Table 3.

Parameters of various adsorption isotherm studies for adsorption of SVMCNP unto metal surface for acidimetric method [Adejo acidimetric].

The corrosion rate of the mild steel sample in the acidic medium as presented in Table 1 increases with the rise in temperature for the blank and significantly dropped upon the introduction of the inhibitor. This shows that the nanoparticle has inhibitive action against the corrosion of the mild steel in H₂SO₄. Observation from the table shows that the corrosion rate increases with rise in temperature and dropped with the introduction of the nanoparticle. Using the data from the corrosion rate, the inhibition efficiency was calculated as shown in Table 2. The trend of the inhibition efficiency shows an increase with rise in temperature. As has been pointed out in literature, such trend is suggestive of chemisorption. Table 3 shows parameters of commonly used adsorption isotherms in characterization of behavior of corrosion inhibitors.

On the account of R² values (Table 3), the adsorption behavior SVMNCP can be modeled using the Langmuir, Freundlich, Temkin, El-Away, and Adejo-Ekwenchi isotherms, as the values are close to unity. However, there are discrepancies in the values of ΔG_ads., bringing about the usual ambiguity. That the value of parameter b of the Adejo-Ekwenchi increases with rise in temperature is a clear feature that the adsorption is chemisorption. But R² values for this isotherm cannot be said to be too good. Temkin isotherm mostly is followed by chemisorption, an indication of interaction of uncharged molecules on a heterogeneous surface. The adherence of this adsorption process to Temkin adsorption isotherm (through R² values), coupled with ΔG_ads above −20 kJ/mol, is suggestive of participation of molecular species in adsorption process. The inhibition efficiency was indeed observed to increase with rise in temperature, further evidence of chemisorption. The R² for the Langmuir isotherm, although good, ΔG_ads values are far from −20 kJ/mol for chemisorption. For the Freundlich isotherm, the parameter n is related to the intensity of the adsorption process and depends on the heterogeneity of the material. It has a typical positive value of 0.6 [21]. The fact that the obtained values have average value of 0.376, which is less than 0.6 is clear suggestion that the adsorption process cannot be modeled by Freundlich isotherm [24]. Turning to El-Awady isotherm model, the parameter y determines whether an adsorption process is multilayer or an inhibitor molecule occupies more than one active site. When y > 1, it means multilayer, while y < 1 means a single molecule occupies more than one active site on the surface of the metal. From Table 3, values of y are less than 1, indicating monolayer (typical of chemisorption). Going by all these argument, the adsorption of the studied inhibitor molecules for the system can best be modeled by Temkin isotherm, and the adsorption is chemisorption. The outline clearly shows how such ambiguity is perfectly resolved. More of such resolutions are given by Adejo and co-worker [27].

5. Conclusion

Corrosion reaction is very destructive reaction to metals and alloys in environment. The use of inhibitors is one major way commonly employed to stop or slow down such reaction. One way inhibitors perform such action is through adsorption. And to have a good understanding of adsorption process, isotherms are used for their modeling. Regress coefficient, R², and free energy, ∆G_ads, values, are two common parameters usually employed to determine the isotherm best fit of adsorption process. Many authors have clearly asserted the inadequacy of these two parameters in such determination. This chapter outlines clearly the way to go about resolving ambiguity usually arising from modeling inhibitor behavior in corrosion systems, through the engagement of the Adejo-Ekwenchi isotherm model.

Acknowledgments

Authors profoundly thank the Tertiary Education Fund of Nigeria (tetFund-Nigeria) for the sponsorship of the chapter production. Indeed, the doctoral thesis of the lead Author sponsored by the Agency culminated into the chapter production. Also in a very special way, the authors wish to acknowledge the immeasurable support and encouragement of the Benue State University to its staff and students in achieving academic excellence.