**3. Experimental methods for the evaluation of the inhibition activity of phosphonates and phosphonic acids**

Many experimental techniques and theoretical methods have been used to evaluate the corrosion inhibition activity of phosphonates and phosphonic acids. In this context, the most common and important of these techniques and methods are discussed below:

#### **3.1 Weight loss measurements**

The weight loss method is simple to implement and does not require significant equipment. Generally, the corrosion rate is determined after 24 h of immersion at a constant temperature equal to 25°C. In general, the operating protocol of this method consists in the first time the preparation of the metallic specimens used in weight loss tests. Then, we weigh the specimens before immersing them in the tested solutions. Also, each specimen was submerged in the tested solutions at constant temperature in absence and in presence of various concentrations of phosphonic inhibitors for a time of 24 h. After the expiration of the immersion time, the specimens have been recuperated from the tested solutions and rinsed with bi-distilled water. Finally, specimens were dried and weighed again.

The corrosion rate, surface coverage and inhibition efficiency are calculated by the following formulas:

$$A\_{corr} = \frac{\Delta W}{\mathcal{S} \times t} = \frac{W\_1 - W\_2}{\mathcal{S} \times t} \tag{1}$$

$$\theta = \frac{A\_{corr}^0 - A\_{corr}}{A\_{corr}^0} \tag{2}$$

$$E\_{\rm W}(\%) = \frac{A\_{\rm corr}^{0} - A\_{\rm corr}}{A\_{\rm corr}^{0}} \times 100\tag{3}$$

where:

*W*1: The mass of specimen before immersion in the tested solution.

*W*2: The mass of specimen after immersion in the tested solution.

*S*: The surface area of the specimen.

*t*: The immersion time of each test.

*Acorr*°: The corrosion rate in the absence of the phosphonate inhibitor.

*Acorr*: The corrosion rate in the presence of the phosphonate inhibitor.

Accordingly, the weight loss method is largely applied to evaluate the corrosion inhibition activity of phosphonates and phosphonic acids. In this context, many our published works on the use of weight loss method indicates that the phosphonates and phosphonic acids are good inhibitors of the corrosion of steel in various aggressive

#### **Figure 6.**

*Weight loss results for the inhibition activity of diethyl ((4-(dimethylamino)phenyl)(phenylamino)methyl) phosphonate obtained for the XC48 carbon steel in 0.5 Mol L*�*<sup>1</sup> H2SO4 at 25°C [16].*

media. **Figure 6** represents the weight loss results of the inhibition activity of diethyl ((4-(dimethylamino)phenyl)(phenylamino)methyl)phosphonate [16].

#### **3.2 Polarization curves**

The polarization curves technique is considered among the most widely used methods to determine the corrosion rate, the corrosion potential and the nature of the influence of the inhibitor on each of the elementary reactions, anodic and cathodic, at the electrode surface. Also, this method makes possible to determine the value of the corrosion current density by extrapolating the Tafel lines to the corrosion potential.

Generally, the following equation may be used to determine the inhibition efficiency obtained from the polarization curves (*E*p(%)):

$$E\_{\rm p}(\%) = \frac{i\_{\rm corr}^{\circ} - i\_{\rm corr(inh)}}{i\_{\rm corr}^{\circ}} \times 100\tag{4}$$

where:

*i* ° corr and *i*corr inh ð Þ: are the values of the corrosion current density in the absence and in the presence of the inhibitor, respectively.

On the other hand, the values of surface coverage ratio (*θ*) can be calculated using the following equation:

$$\theta = \frac{\dot{i}\_{\text{corr}} - \dot{i}\_{\text{corr}(\text{inh})}}{\dot{i}\_{\text{corr}}} \tag{5}$$

Concerning the application of the polarization curves technique in the evaluation of the corrosion inhibition activity of phosphonates and phosphonic acids, we observe from our previously published works that the majority of phosphonates and phosphonic acids derivatives inhibit corrosion by controlling the anodic and cathodic processes (mixed-type inhibitors) without affecting the dissolution of the metal in the anode or the evolution of hydrogen in the cathode [1]. Also, the adsorption of phosphonates and phosphonic acids on the metallic surfaces is responsible for the observed drop in *i*corr inh ð Þ and the observed rise in *E*p(%). As an example, **Figure 7**

**Figure 7.**

*Polarization curves for the inhibition activity of 4-(2-{[ethoxy(hydroxy)phosphonyl](3-nitrophenyl)methyl} hydrazinyl)benzoic acid obtained for the carbon steel in 0.5 Mol L*�*<sup>1</sup> H2SO4 at 20°C [1].*

represents the obtained polarization curves of the inhibition activity of 4-(2-{[ethoxy (hydroxy)phosphonyl](3-nitrophenyl)methyl}hydrazinyl)benzoic acid [1].

#### **3.3 Electrochemical impedance spectroscopy (EIS)**

In this technique, we measure the response the response of an electrode to a sinusoidal modulation of low amplitude of the potential as a function of the frequency. The strength of this technique is that it completely analyzes the mechanism of action of inhibitor on the metallic surface. So, the role of the inhibitor in the different processes occurring at the electrode such as charge transfer, diffusion, adsorption, etc., can be studied in detail, and values such as those of the transfer resistance and the polarization resistance can provide access to the measurement of the corrosion rate even in the case where the metal is covered with a protective layer [17]. Generally, to study the anticorrosion activity of phosphonates and phosphonic acids, the electrochemical impedance (EIS) measurements were performed around in the frequency range from 100 kHz to 10 mHz, with a signal of 5 mV sinusoidal amplitude. In this context, the inhibition efficiency (*E*R(%)) can be calculated applying the electrochemical impedance spectroscopy results by using the following equation:

$$
\eta\_{\rm R}(\%) = \frac{R\_{\rm t(inh)} - R\_{\rm t(0)}}{R\_{\rm t(inh)}} \times 100\tag{6}
$$

Concerning the application of EIS study for the phosphonate derivatives inhibitors, we take as an example the Nyquist plot of [(2-hydroxy-5-methoxy-1,3-phenylene)bis (methylene)]bis(phosphonic acid) obtained for the carbon steel in 1 mol L�<sup>1</sup> HCl at 25°C in the absence and in the presence of different concentrations of the inhibitor (**Figure 8**) [18]. Note that the diameter of the Nyquist diagram increases with the

*Phosphonates and Phosphonic Acids: New Promising Corrosion Inhibitors DOI: http://dx.doi.org/10.5772/intechopen.109499*

addition of the inhibitor, suggesting that the corrosion of carbon steel in acidic media is mainly controlled by a charge transfer process [19]. Also, it is clearly observed in **Figure 8** that the Nyquist diagrams of all tested concentrations present similar semicircle shapes. This means that there is no significant change in the corrosion mechanism due to the addition of the inhibitor [20]. On the other hand, we observe that the obtained diagrams are not perfect semi-circles, because of the frequency dispersion which can be attributed to a surface heterogeneity which generates a frequency distribution. In general, this heterogeneity is due to the roughness of the surface and the chemical composition of carbon steel [21].

Also, the analysis of the results presented in **Figure 8** show that the charge transfer resistance (*R*ct) values increase and the double layer capacitance (*C*dl) values decrease with increasing the concentration of the phosphonate derivative. The increase in *R*ct may be due to the formation of a protective film at the metal/solution interface. On the other hand, the decrease in *C*dl values is due to the increase in the thickness of the electrical double layer, which indicates that the phosphonate derivative act by adsorption on the metal surface.

**Figure 8.**

*EIS results for the inhibition activity of [(2-hydroxy-5-methoxy-1,3-phenylene)bis(methylene)]bis(phosphonic acid) obtained for the carbon steel in 1 mol L<sup>1</sup> HCl at 25°C [18].*

#### **3.4 Scanning electron microscopy (SEM)**

The Scanning Electron Microscopy (SEM) technique is largely used in the corrosion inhibition field. The main objective of this technique is to visualize the surface morphology of metals in the absence and in the presence of inhibitory molecules. Briefly, a scanning electron microscope uses a very fine beam of electrons which scans, point by point, the surface of the sample to be observed. In this context, this

technique allows researchers to visualize what is happening on the metal surface at the microscopic scale and to know what changes are made on the surface of the metal after the addition of the inhibitor (e.g. the addition of phosphonates and phosphonic acids inhibitors).

**Figure 9** represents the SEM image of mild steel specimen in the presence of 10<sup>3</sup> mol/L of Ethyl hydrogen [(2-methoxyphenyl)(methylamino) methyl] phosphonate [22]. The examination of the obtained SEM image of the tested phosphonate compound shows an observed reduce in roughness of the surface of mild steel. So, we can say that the metallic surface has been protected against corrosion when the phosphonate derivatives have been added to the corrosive medium. This phenomenon is explained by the formation of an adsorbed layer (thin protective film) of the phosphonate derivative on the metal surface.

#### **Figure 9.**

*SEM image of mild steel in the presence of 10<sup>3</sup> mol/L of ethyl hydrogen [(2-methoxyphenyl)(methylamino) methyl]phosphonate [22].*

#### **3.5 Atomic force microscopy (AFM)**

Atomic force microscopy (AFM) is another useful microscopic technique which is extensively used in corrosion inhibition studies. Especially, this technique makes to determine the formation of a protective layer of the inhibitor on the metal surface by measuring the variation in the roughness values of the metal surface before and after the addition of the inhibitor molecule.

An example of the use of the AFM technique as a useful way to illustrate the formation of adsorbed layers of phosphonic derivatives on the metal surface is demonstrated in **Figure 10**, which is shows the obtained AFM images of carbon steel in the presence of diethyl((4-(dimethylamino)phenyl)(phenylamino)methyl)phosphonate and 4-(2-{[ethoxy(hydroxy)phosphonyl](3-nitrophenyl)methyl}hydrazinyl)benzoic acid [1, 16].

The analysis of the achieved AFM images indicates that the addition of phosphonates or phosphonic acids makes a significant modification on the surface morphology of the metal indicating the formation of a protective adsorbed layer of *Phosphonates and Phosphonic Acids: New Promising Corrosion Inhibitors DOI: http://dx.doi.org/10.5772/intechopen.109499*

#### **Figure 10.**

*AFM images of mild steel in the presence of 10<sup>3</sup> mol/L of diethyl ((4-(dimethylamino) phenyl) (phenylamino) methyl) phosphonate (a) and 4-(2-{[ethoxy(hydroxy)phosphonyl](3-nitrophenyl)methyl}hydrazinyl)benzoic acid (b) [1, 16].*

phosphonate molecules. This phenomenon can be explicated by the diminution of the measured values of the roughness of metal after the addition of phosphonates or phosphonic acids to the corrosive media.

#### **3.6 Density functional theory (DFT)**

Recently, the quantum chemical calculations by applying DFT method are extensively used to correlate the experimental results of corrosion inhibition efficiencies with some quantum descriptors, electronic and structural proprieties of the inhibitive molecule such as the energy of the Highest Occupied Molecular Orbital (*E*HOMO), the energy of the Lowest Unoccupied Molecular Orbital (*E*LUMO), the energy gap (Δ*E*gap), the absolute electronegativity (*χ*), the hardness (*η*), the softness (*σ*), and the dipole moment (*μ*). Basing on our previously published works, the DFT results indicated that the high corrosion inhibition activity of phosphonates and phosphonic acids is related to the presence of phosphonate or phosphonic acid functional groups in their molecular structure. Also, DFT calculations on phosphonates and phosphonic acids proved that the active sites responsible for the anticorrosion activity of these derivatives are located on the heteroatoms such as P, O, N and S. On the other hand, the DFT study demonstrates that the most negative sites responsible for the electrophilic attacks are located on the oxygen atoms of the phosphonate groups. The **Table 1** summarized the calculated quantum chemical descriptors of two phosphonate derivatives [22].



#### **Table 1.**

*Some calculated quantum chemical descriptors of ethyl hydrogen [(2-methoxyphenyl)(methylamino) methyl] phosphonate and ethyl hydrogen [(3-methoxyphenyl) (methylamino) methyl]phosphonate [22].*
