Corrosion Inhibitors

#### **Chapter 3**

## Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature

*Mykhaylo Viktorovych Yarmolenko*

#### **Abstract**

Our investigations show that electrochemical corrosion of copper is faster than electrochemical corrosion of aluminium at temperatures below 100°C. Literature data analysis shows that the Al atoms diffuse faster than the Cu atoms at temperatures higher than 475°C, Al-rich intermetallic compounds (IMCs) are formed faster in the Cu-Al system, and the Kirkendall plane shifts towards the Al side. Electrochemical corrosion occurs due to electric current and diffusion. An electronic device working time, for example, depends on the initial copper cover thickness on the aluminium wire, connected to the electronic device, temperature, and volume and dislocation pipe diffusion coefficients, so copper, iron, and aluminium electrochemical corrosion rates are investigated experimentally at room temperature and at temperature 100°C. Intrinsic diffusivities ratios of copper and aluminium at different temperatures and diffusion activation energies in the Cu-Al system are calculated by the proposed methods here using literature experimental data. Dislocation pipe and volume diffusion activation energies of pure iron are calculated separately by earlier proposed methods using literature experimental data. Aluminium dissolved into NaCl solution as the Al3+ ions at room temperature and at temperature 100°C, iron dissolved into NaCl solution as the Fe2+ (not Fe3+) ions at room temperature and at temperature 100°C, copper dissolved into NaCl solution as the Cu<sup>+</sup> ions at room temperature, and as the Cu<sup>+</sup> and the Cu2+ ions at temperature 100°C. It is found experimentally that copper corrosion is higher than aluminium corrosion, and the ratio of electrochemical corrosion rates, *kCu*/*kAl* > 1, decreases with temperature increasing, although iron electrochemical corrosion rate does not depend on temperature below 100°C. It is obvious because the melting point of iron is higher than the melting point of copper or aluminium. It is calculated that copper electrochemical corrosion rate is approximately equal to aluminium electrochemical corrosion at a temperature of about 300°C, so the copper can dissolve into NaCl solution mostly as the Cu2+ ions at a temperature of about 300°C. The ratio of intrinsic diffusivities, *DCu*/*DAl* < 1, increases with temperature increasing, and intrinsic diffusivity of aluminium could be approximately equal to intrinsic diffusivity of copper at a temperature of about 460°C.

**Keywords:** electrochemical corrosion, metallic coatings, electrolysis, diffusion, intermetallic compounds, phases formation kinetics, copper, aluminium, iron, Kirkendall-Frenkel porosity, Kirkendall shift, activation energy

#### **1. Introduction**

An Al wire coated with a thin Cu cover (≈15-μm thickness), utilised near an automobile motor, is heated to temperatures about 373–473 K (100–200°C). Intermetallics (IMCs) can be formed at the Cu/Al interface and grow gradually during heating at such temperatures. The IMC layers are brittle and have high resistivity. Therefore, for assurance of the reliability of the product, information on the growth behaviour of the IMC layers during heating is essentially important [1]. **Figure 1** shows the problem: an electronic device working time, *t*0, depends on initial Cu cover thickness, *XCu*, and temperature. The electric conductivity of copper is higher than the electric conductivity of aluminium in approximately two times, but the formation of intermetallic phases induces a significant increase in contact resistance, which is found to increase linearly with the thickness of the intermetallics formed [2]. The temperature range used to produce the intermetallic phases was from 250 to 515°C. Moreover, the presence of an electrical field greatly accelerated the kinetics of formation of intermetallic phases and altered significantly their morphology, and the impaired mechanical integrity of the Al-Cu bimetallic joints treated by an electrical current was clearly demonstrated by an extensive cracking not only across the whole intermetallic bandwidth but also within different phases and at a neighbouring interface [2]. Three-phase thickness, *X*123, can be estimated in such a way. The mass conservation law gives

$$\begin{array}{l} \mathbf{X}\_{Cu}(t=0) \cdot \mathbf{1} = \frac{9}{9+4} \mathbf{X}\_{3}(t\_{0}) + \frac{\mathbf{1}}{\mathbf{1}+\mathbf{1}} \mathbf{X}\_{2}(t\_{0})\\ + \frac{\mathbf{1}}{\mathbf{1}+2} \mathbf{X}\_{3}(t\_{0}) \approx \frac{\mathbf{1}.526 \mathbf{X}\_{123}}{3} \approx 0.509 \mathbf{X}\_{123}, \text{and } \mathbf{X}\_{123} \approx 2 \mathbf{X}\_{\text{Cu}}, \end{array} \tag{1}$$

so three-phase general thickness is approximately greater in two times than the initial Cu cover thickness.

Otherwise, it was proved experimentally that a thin Al pad (≈1-μm thickness) can prevent gold and copper corrosion because the intermetallics formation rate in Au-Al system is much higher than the intermetallic formation rate in Cu-Al system, so it is possible to use Cu instead of Au for wire bonding in microelectronic packaging, and Cu has higher electric conductivity, higher thermal conduction, and

#### **Figure 1.**

*(a) Initial stage (t = 0): An electronic device is working, since the electric current, Ia = ICu + IAl, has optimal value; (b) final stage (t = t0): The electronic device is not working, because the electric current, Ib = I3 + I2 + I1 + IAl, has too small value, since pure Cu cover has disappeared.*

*Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature DOI: http://dx.doi.org/10.5772/intechopen.100279*

lower material cost than Au [3]. Corrosion and intermetallic rate formation in gold and copper wire bonding in microelectronics packaging were investigated in [3] at temperatures *T*<sup>1</sup> = 175°С,*T*<sup>2</sup> = 200°С, and *T*<sup>3</sup> = 225°С during 120, 240, 360, and 480 h. The authors have reported that cross-sectional analysis of the Cu ball on Al pad confirmed that corrosion occurred at temperatures about *T* = 200°С primarily beneath the Cu balls and did not initiate from the Al pad, formation of CuCl2 did not allow self-passivation of Cu to occur, so the rate of copper corrosion increased, and the rate of Cu-Al intermetallics formation was found to be three to five times slower than Au-Al intermetallic formation at all three annealing temperatures. So, copper dissolved into NaCl solution as Cu2+ ions at temperatures about *T* = 200°С, as we expected. They did not investigate corrosion rate dependence of copper and aluminium on temperature. Moreover, phase layers general thicknesses for Cu-Al system were calculated [3]:

$$\begin{split} \mathbf{X}\_{123}^{2} &= \mathbf{K}\_{123}\mathbf{t} + \mathbf{K}\_{01} = \mathbf{K}\_{0}\mathbf{e}^{-\mathbf{Q}\_{\prime}/(\mathbf{R}\mathbf{T})} + \mathbf{K}\_{01} \\ &= \mathbf{3.52} \cdot \mathbf{10}^{-4} \boldsymbol{\mu}\mathbf{m}^{2}\boldsymbol{\zeta}\_{\prime} \cdot \mathbf{e}^{-25500 \text{J} \cdot \text{mol}^{-1} \cdot (\mathbf{R}\mathbf{T})} \mathbf{t} + \mathbf{0.44} \boldsymbol{\mu}\mathbf{m}^{2}, \end{split} \tag{2}$$

where R ≈ 8.314 JK�<sup>1</sup> is the gas constant, and K01 is the constant related to initial IMC thickness. General reaction rates of IMC formation were calculated: K123(T1) = 3.57�10�<sup>7</sup> <sup>μ</sup>m2 /s, K123(T2) = 6.26�10�<sup>7</sup> <sup>μ</sup>m2 /s, and K123(T3) = 7.15�10�<sup>7</sup> <sup>μ</sup>m2 / s. The pre-exponential factor and IMC formation activation energy was calculated: K0 <sup>≈</sup> 3.52�10�<sup>4</sup> <sup>μ</sup>m2 /s, Q ≈ 25.5 kJ/mol. We can use these results to calculate the electronic device working time by Eq. (14) in [4] at different temperatures:

$$t\_0 \approx \frac{X\_{\text{Cu}}^2}{C\_3^2 K\_{123}} = \frac{169}{81} \frac{X\_{\text{Cu}}^2}{K\_{123}} \approx \frac{2X\_{\text{Cu}}^2}{K\_0} e^{\Psi(RT)} \approx 5900 \cdot X\_{\text{Cu}}^2 \left[\mu m^2\right] \cdot e^{\frac{25.5k\mu m^{-1}}{(kT)} \cdot (RT)\_5}; \quad \text{(3)}$$

$$t\_0(T\_1 = 175^\circ C = 448K) \approx 5900 \cdot 225 \cdot e^{2890(\text{s}\_3 \text{s}\_{4448})} \approx 40 years;$$

$$t\_0(T\_2 = 200^\circ C) \approx 28 years;$$

$$t\_0(T\_3 = 225^\circ C) \approx 21 years; t\_0(T\_4 = 300^\circ C) \approx 9 years; t\_0(T\_5 = 350^\circ C) \approx 6 years.$$

Other researchers have obtained [5]: K123(T4 = 300°C) = 4.2�10�<sup>4</sup> <sup>μ</sup>m<sup>2</sup> /s, K123(T5 = 350°C) = 3.4�10�<sup>3</sup> <sup>μ</sup>m<sup>2</sup> /s. Eq. (3) gives

$$t\_0(T\_4 = \text{300}^o \text{C}) \approx \frac{2X\_{Cu}^2}{K\_{123}} \approx 12days; \\ t\_0(T\_5 = \text{350}^o \text{C}) \approx \frac{2X\_{Cu}^2}{K\_{123}} \approx 1.5days.$$

We can calculate: Q <sup>≈</sup> 124 kJ/mol; K0 <sup>≈</sup> 8.5�10�<sup>5</sup> <sup>m</sup><sup>2</sup> /s = 8.5�10<sup>7</sup> <sup>μ</sup>m<sup>2</sup> /s;

$$t\_0(T = 175^{\circ}C) \approx 5.3 \cdot 10^{-6} \cdot e^{124fml^{-1}(448R)} \\ \approx 49 years; \\ t\_0(T = 200^{\circ}C) \approx 8.4 years;$$

$$t\_0(T = 225^{\circ}C) \approx \frac{2X\_{Cu}^2}{K\_0}e^{Q\_{(RT)}} \\ \approx 5.3 \cdot 10^{-6} \cdot e^{124fml^{-1}(498R)} \\ \approx 1.7 years.$$

It was reported in [1] that the growth of layer 1 is controlled predominantly by boundary diffusion, but that of layers 2 and 3 are governed mainly by volume diffusion at temperatures T = 483–543 K (210–270°C) for various periods up to 3.456Ms (960 h). The authors obtained: K01 <sup>≈</sup> 5.3�10�<sup>7</sup> <sup>m</sup><sup>2</sup> /s, Q1 ≈ 86 kJ/mol, K023 <sup>≈</sup> 4.2�10�<sup>5</sup> <sup>m</sup><sup>2</sup> /s, Q23 ≈ 146 kJ/mol. We can calculate: K123 (T6 = 210°C) = 1.5�10�<sup>6</sup> <sup>μ</sup>m<sup>2</sup> /s,

$$t\_0(T = 210^\circ C) \approx \frac{2X\_{\text{Cu}}^2}{K\_{123}} \approx 9.6 years... $$

The less temperature is, the higher contribution of grain-boundary diffusion and dislocation pipe diffusion to the layers growth is, so models of grain-boundary diffusion and dislocation pipe diffusion involving outflow into volume should be taken into account [6–8].

Diffusion activation energy of Al is less than diffusion activation energy of Cu (Q*Al* < Q*Cu*) at temperatures from 160–250°C for mutual diffusion in copper-a luminium thin film double layers, but the pre-exponential factors are different in 10 times [9]:

$$D\_{\rm Al}^{\*} = 4 \cdot 10^{-5} e^{-121 \text{k} \text{/} \text{mol}^{-1} / (\text{RT})} m^2 / \text{s}, \\ D\_{\rm Cu}^{\*} = 9.5 \cdot 10^{-4} e^{-135 \text{k} \text{/} \text{mol}^{-1} / (\text{RT})} m^2 / \text{s}, \tag{4}$$

in *θ*-phase (phase 1) CuAl2, *CAl* = 2/3 ≈ 0.67, *CCu* = 1/3 ≈ 0.33;

$$D\_{Al}^{\*} = \mathbf{1.5} \cdot \mathbf{10}^{-11} e^{-68klmd^{-1}/(RT)} m^2/\mathfrak{s},\\D\_{Cu}^{\*} = \mathbf{1} \cdot \mathbf{10}^{-6} e^{-106klmd^{-1}/(RT)} m^2/\mathfrak{s},\tag{5}$$

in *η*2-phase (phase 2) CuAl, *CAl* = *CCu* = 1/2 = 0.5;

$$D\_{\rm Al}^{\*} = \mathbf{1.7} \cdot \mathbf{10}^{-7} e^{-11 \text{S} \text{l} \text{l} \text{mol}^{-1} / (RT)} m^2/\text{s}, \\ D\_{\rm Cu}^{\*} = 2.4 \cdot \mathbf{10}^{-6} e^{-12 \text{S} \text{l} \text{l} \text{mol}^{-1} / (RT)} m^2/\text{s}, \tag{6}$$

in *γ*2-phase (phase 3) Cu9Al4, *CAl* = 4/13 ≈ 0.31, *CCu* = 9/13 ≈ 0.69.

We can calculate the mutual diffusion coefficient for each phase at temperature 160°C by the Darken equation [8, 10] and taking into account Eqs. (4)–(6):

$$D\_i^\* = \mathbf{C}\_{Al} D\_{\rm Cu}^\* + \mathbf{C}\_{\rm Cu} D\_{Al}^\*; i = 1, 2, 3; D\_1^\* = 6.64 \cdot 10^{-20} m^2/\text{s}; D\_2^\* = 1.3 \cdot 10^{-19} m^2/\text{s}; D\_3^\* = 1.8 \cdot 10^{-21} m^2/\text{s}.$$

We can calculate using the methods described in [4, 11]: K123(T7 = 160°C) <sup>≈</sup> 2.8�10�<sup>6</sup> <sup>μ</sup>m<sup>2</sup> /s, *<sup>t</sup>*<sup>0</sup> *<sup>T</sup>* <sup>¼</sup> <sup>160</sup>*<sup>o</sup>* ð Þ *<sup>C</sup>* <sup>≈</sup> <sup>2</sup>*X*<sup>2</sup> *Cu <sup>K</sup>*<sup>123</sup> ≈5*years*, so the problem remains unsolved.

It was founded experimentally, that copper electrochemical corrosion is higher than aluminium electrochemical corrosion in approximately two times at room temperature [4, 11], so a thin Al layer can prevent copper electrochemical corrosion. It was reported also about the influence of hydrogen and the absence of a passive layer on the corrosive properties of aluminium alloys [12].

Besides, the soldered copper/tin-based contacts are the weakest part of the chip that can be related to intermetallics and the Kirkendall-Frenkel porosity formation in the contact zone [13]. One of the most common reasons for chip failure is the soldered. The typical range of packaging and operation of the integrated circuits is from room temperature to 250°C [14].

Hydrostatic pressure of Argon gas (≈10 MPa) can decrease Kirkendal-Frenkel porosity formation, but practically cannot decrease mutual diffusion coefficients, but hot isostatic pressing (p ≈ 100 MPa, Argon) removes porosity due to homogenisation heat treatment in alloy CMSX4 and superalloy CMSX10 [15].

It was clarified also that carbon steel-stainless steel with the environment of flowing sodium chloride does indeed produce synergetic corrosion instead of antagonistic corrosion [16].

Electric current can destruct wire bonding in microelectronics packaging, so we planned to investigate copper, iron, and aluminium electrochemical corrosion at room temperature and temperature 100°C. Direct current can dissolve metal anode into electrolyte, and we planned to do experiments under the same conditions: initial radii of Cu, Fe, and Al anodes should be approximately equal, electrolyte concentration should be the same, anodes lengths immersed into electrolyte should

*Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature DOI: http://dx.doi.org/10.5772/intechopen.100279*

be equal, graphite cathodes should be the same, direct electric current value should be practically the same. Aluminium can dissolve into electrolyte only as of the Al3+ ions, so the charge of aluminium ions should be exactly equal to 3, but copper can dissolve into electrolyte as the Cu<sup>+</sup> ions and the Cu2+ ions, and the charge of copper ions could be equal to 1 or 2, and iron can dissolve into electrolyte as the Fe2+ ions and the Fe3+ ions, and the charge of iron ions could be equal to 2 or 3. We need to find appropriate mathematical equations to calculate the charges of copper, iron, and aluminium ions dissolved into NaCl solution.

#### **2. Experimental results of copper, iron, and aluminium electrochemical corrosion**

#### **2.1 Investigation at room temperature**

Cylindrical anodes (99.99% Cu, 99.96% Fe, and 99.99% Al) were used for copper and aluminium [4, 11], and also iron electrochemical corrosion investigation. Sodium chloride (NaCl) solution was used as an electrolyte (**Figure 2**).

Direct electric current and anode mass decreasing were measured. First of all, we need to be assured that the Cu<sup>+</sup> ions (or the Cu2+), the Fe2+ (or the Fe3+), and the Al3+ were present in NaCl solution. The rate of anode dissolving into electrolyte can be calculated using Faraday's law of electrolysis:

$$\frac{dm}{dt} = \frac{MI}{zF}, dm = \rho \cdot L \cdot \pi \cdot d\left(\mathbb{R}^2(t)\right). \tag{7}$$

Here, *m* is anode mass dissolved into the electrolyte, *t* is a time of the experiment, *M* is molar mass, *I* is the direct electric current value, *F* is the Faraday constant (*F* ≈ 96,500 C mol�<sup>1</sup> ), *z* is a charge of ions, *R* is anode radius, *L* is anode length immersed into the electrolyte. Electric current value did not change, so one can calculate:

#### **Figure 2.**

*Scheme of experimental equipment at room temperature. Cu, Fe, and Al anodes dissolve into NaCl solution as Cu<sup>+</sup> , Fe2+, and Al3+ ions.*

where *ρ* is anode density. Charges of copper, iron, and aluminium ions were calculated:

$$\mathrm{Zr}\_{\mathrm{Cu}} = \frac{63.55 \cdot 10^{-3} \mathrm{kg}/\_{mol} \cdot 2.8 A \cdot 1.2 \cdot 10^3 s}{F \cdot \pi \cdot 8.9 \cdot 10^3 \mathrm{kg}/\_{m} \mathrm{J}\_{\mathrm{Cu}} \cdot \left(R\_{\mathrm{Cu}}^2(t=0) - R\_{\mathrm{Cu}}^2(t\_4)\right)} \approx 0.995 \approx 1,\tag{9}$$

$$z\_{Al} = \frac{27 \cdot 10^{-3} \text{kg/mol} \cdot 3.1A \cdot 1.2 \cdot 10^3 s}{F \cdot \pi \cdot 2.7 \cdot 10^3 \text{kg/}m^3 L\_{Al} \cdot \left(R\_{Al}^2(t=0) - R\_{Al}^2(t\_4)\right)} \approx 2.954 \approx 3,\tag{10}$$

$$z\_{\rm Fe} = \frac{55.847 \cdot 10^{-3} \text{kg} \,/\text{mol} \cdot 3.15 A \cdot 1.2 \cdot 10^3 s}{F \cdot \pi \cdot 7.86 \cdot 10^3 \text{kg} \,/\text{m}^3 L\_{\text{Fe}} \cdot \left(R\_{\text{Fe}}^2(t=0) - R\_{\text{Fe}}^2(t\_4)\right)} \approx 2.03 \approx 2,\tag{11}$$

where *LCu <sup>≈</sup> LAl <sup>≈</sup> LFe*: *LCu* <sup>=</sup> *LFe* = 5�10�<sup>2</sup> m, *LAl* = 4.5�10�<sup>2</sup> m; *R*0*Cu* = *R*0*Al* = 2.8 mm*, R*0*Fe* = 2.98 mm; *IAl ≈ ICu ≈ IFe*: *IFe* = 3.15A, *IAl* = 3.1A, *ICu* = 2.8A, so copper dissolved into NaCl solution as the Cu+ ions, iron dissolved into NaCl solution as the Fe2+ ions, and aluminium dissolved into NaCl solution as the Al3+ ions. Anodes radii-decreasing kinetics is shown in **Figure 3**. Experiments were carried during *t*<sup>1</sup> = 5 min*, t*<sup>2</sup> = 10 min*, t*<sup>3</sup> = 15 min*,* and *t*<sup>4</sup> = 20 min. Experimental results are as follows: *R*1*Cu* = 2.74 mm*, R*2*Cu* = 2.67 mm*, R*3*Cu* = 2.59 mm*, R*4*Cu* = 2.5 mm*; R*1*Al* = 2.77 mm*, R*2*Al* = 2.73 mm*, R*3*Al* = 2.68 mm*, R*4*Al* = 2.62 mm*, R*1*Fe* = 2.95 mm*, R*2*Fe* = 2.92 mm*, R*3*Fe* = 2.88 mm*, R*4*Fe* = 2.83 mm. Measurement precision was 0.01 mm or 10 micrometres.

Chemical reactions took place near the positive electrode (anode):

$$\text{Cu}^{0}-\text{e}^{-}=\text{Cu}^{+},\text{Al}^{0}-\text{3e}^{-}=\text{Al}^{3+},\text{Fe}^{0}-\text{2e}^{-}=\text{Fe}^{2+};$$

$$\text{Cu}^{+}+\text{Cl}^{-}=\text{CuCl}\downarrow,\text{Al}^{3+}+\text{3Cl}^{-}=\text{AlCl}\_{3}\downarrow,\text{Fe}^{2+}+\text{2Cl}^{-}=\text{FeCl}\_{2}\downarrow;\tag{12}$$

**Figure 3.** *Cu, Fe, and Al anodes radii decreasing kinetics at room temperature.*

*Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature DOI: http://dx.doi.org/10.5772/intechopen.100279*

$$Cl^- - e^- = Cl^0, \\ Cl^0 + Cl^0 = Cl\_2 \\ \uparrow.$$

Chlorine gas was formed near the anode.

Chemical reactions took place near the negative electrode (cathode):

$$\text{Na}^+ - e^- = \text{Na}^0, \text{2Na} + \text{2H}\_2\text{O} = \text{2NaOH} + \text{H}\_2\uparrow. \tag{13}$$

Hydrogen gas was formed near the cathode.

Anodes radii decreasing rate constants can be calculated as the average value of four experiments to increase calculation precise:

$$k\_{\rm Cu} = \frac{4R\_0^2 - \sum\_{i=1}^4 R\_i^2}{\sum\_{i=1}^4 t\_i} \approx 1.25 \cdot 10^{-9} m^2/\_\circ,\\ k\_{\rm Al} = \frac{4R\_0^2 - \sum\_{i=1}^4 R\_i^2}{\sum\_{i=1}^4 t\_i} \approx 7.29 \cdot 10^{-10} m^2/\_\circ,$$

$$k\_{\rm Fe} = \frac{4R\_{0Fe}^2 - \sum\_{i=1}^4 R\_{iFe}^2}{\sum\_{i=1}^4 t\_i} \approx 7.26 \cdot 10^{-10} m^2/\_\circ,\\ k\_{\rm Cu} \approx 1.71 k\_{\rm Al}; k\_{\rm Al} \approx k\_{\rm Fe},$$

so copper electrochemical corrosion is much higher than aluminium and iron electrochemical corrosion, despite *IFe* ≈ *IAl* ≥ *ICu*: *IFe* ≈ *IAl* ≈ 1.1*ICu*. It needs to point out that *kCu, kFe,* and *kAl* have dimensionalities as diffusion coefficients [m2 /s], because electrochemical corrosion occurs through anodes'surface.

#### **2.2 Investigation at temperature 100°C**

Experiments were carried also at temperature 100°C. Cylindrical anodes (99.99% Cu, 99.99% Al, and 99.96% Fe) were used for copper and aluminium [17] and also iron electric corrosion investigation. Sodium chloride (NaCl) solution was used as an electrolyte (**Figure 4**). Direct electric current and anodes' mass decreasing rate were measured (**Figure 5**).

Electric current value did not change, so one can calculate the following:

$$z\_{\rm Cu} = \frac{63.55 \cdot 10^{-3} \text{kg}/\text{mol} \cdot 3.05 \text{A} \cdot 1.2 \cdot 10^3 \text{s}}{F \cdot \pi \cdot 8.9 \cdot 10^3 \text{kg}/\text{m}^3 \text{L}\_{\text{Cu}} \cdot \left(R\_{\rm Cu}^2(t=0) - R\_{\rm Cu}^2(t\_4)\right)} \approx 1.47 \approx \frac{1+2}{2},\tag{15}$$

#### **Figure 4.**

*Scheme of experimental equipment at T = 100°C. Cu, Fe, and Al anodes dissolved into NaCl solution as Cu<sup>+</sup> , cu2+, Fe2+, and Al3+ ions.*

**Figure 5.** *Cu, Fe, and Al anodes radii decreasing kinetics at* T *= 100°C.*

$$z\_{Al} = \frac{27 \cdot 10^{-3} \text{kg} \langle \text{mol} \cdot 3.15 \text{A} \cdot 1.2 \cdot 10^3 \text{s}}{F \cdot \pi \cdot 2.7 \cdot 10^3 \text{kg} \langle \text{}\_{\text{m}} \text{L}\_{Al} \cdot \left( R\_{Al}^2 (t = \text{0}) - R\_{Al}^2 (t\_4) \right)} \approx 2.85 \approx 3,\tag{16}$$

$$z\_{\rm Fe} = \frac{55.847 \cdot 10^{-3} \text{kg/mol} \cdot 3.15 A \cdot 1.2 \cdot 10^3 s}{F \cdot \pi \cdot 7.86 \cdot 10^3 \text{kg/}m^3 L\_{\rm Fe} \cdot \left(R\_{\rm Fe}^2(t=0) - R\_{\rm Fe}^2(t\_4)\right)} \approx 2.01 \approx 2,\tag{17}$$

where *LCu* <sup>=</sup> *LAl* = 4�10�<sup>2</sup> m, *LFe* = 5�10�<sup>2</sup> m, *<sup>R</sup>*0*Cu* = 2.27 mm, *<sup>R</sup>*0*Al* = 2.6 mm, *R*0*Fe* = 2.83 mm, *IAl* = 3.15 A, *IFe* = 3.13 A, *ICu* = 3.05 A, so copper dissolved into NaCl solution as Cu+ and Cu2+ ions (copper dissolved into NaCl solution as Cu+ ions at room temperature), iron dissolved into NaCl solution as the Fe2+ ions (as at room temperature), and aluminium dissolved into NaCl solution as Al3+ ions (as at room temperature). Anode radii-decreasing kinetics is shown in **Figure 5**. Experiments were carried during *t*<sup>1</sup> = 5 min*, t*<sup>2</sup> = 10 min*, t*<sup>3</sup> = 15 min*,* and *t*<sup>4</sup> = 20 min. Experimental results are as follows: *R*1*Cu* = 2.2 mm*, R*2*Cu* = 2.12 mm*, R*3*Cu* = 2.03 mm*, R*4*Cu* = 1.92 mm; *R*1*Al* = 2.56 mm, *R*2*Al* = 2.51 mm, *R*3*Al* = 2.45 mm, *R*4*Al* = 2.38 mm; *R*1*Fe* = 2.80 mm, *R*2*Fe* = 2.76 mm, *R*3*Fe* = 2.72 mm, *R*4*Fe* = 2.67 mm. Measurement precision was 0.01 mm or 10 micrometres. We carried additional experiments, but the result was the same.

Chemical reactions are more complicated at 100°C than at room temperature near positive electrodes (anodes):

$$\text{Cu}^{0}-\text{e}^{-}=\text{Cu}^{+},\text{Cu}^{0}-2\text{e}^{-}=\text{Cu}^{2+},\text{Al}^{0}-\text{3}\text{e}^{-}=\text{Al}^{3+},\text{Fe}^{0}-2\text{e}^{-}=\text{Fe}^{2+};$$

$$\text{Cu}^{+}+\text{Cl}^{-}=\text{CuCl}\downarrow,\text{Al}^{3+}+\text{3Cl}^{-}=\text{AlCl}\_{3}\downarrow,\text{Fe}^{2+}+2\text{Cl}^{-}=\text{FeCl}\_{2}\downarrow;$$

$$\text{Cu}^{2+}+2\text{Cl}^{-}=\text{CuCl}\_{2}\downarrow,\text{Cl}^{-}-\text{e}^{-}=\text{Cl}^{0},\text{Cl}^{0}+\text{Cl}^{0}=\text{Cl}\_{2}\uparrow.$$

Chlorine gas and boiling water were formed near anodes. Chemical reactions took place near negative electrodes (cathodes):

$$\text{Na}^+ - e^- = \text{Na}^0, \text{2Na} + 2\text{H}\_2\text{O} = 2\text{NaOH} + \text{H}\_2\uparrow. \tag{19}$$

*Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature DOI: http://dx.doi.org/10.5772/intechopen.100279*

Hydrogen gas and boiling water were formed near cathodes.

Anode radii-decreasing rate constants can be calculated as average value of four experiments to increase calculation precise:

$$k\_{\rm Cu} = \frac{4R\_{0\rm Cu}^2 - \sum\_{i=1}^4 R\_{i\rm Cu}^2}{\sum\_{i=1}^4 t\_i} \approx 1.154 \cdot 10^{-9} m^2/s, \{1.25.10^{-9} \text{ at room temperature}\},$$

$$k\_{\rm Al} = \frac{4R\_{0\rm Al}^2 - \sum\_{i=1}^4 R\_{i\rm Al}^2}{\sum\_{i=1}^4 t\_i} \approx 8.42 \cdot 10^{-10} m^2/s, \{7.29.10^{-10} \text{ at room temperature}\},\tag{20}$$

$$k\_{\rm F\varepsilon} = \frac{4R\_{0Fe}^2 - \sum\_{i=1}^4 R\_{iFe}^2}{\sum\_{i=1}^4 t\_i} \approx 6.83 \cdot 10^{-10} \text{m}^2/\text{s}, \left\{ 7.23.10^{-10} \text{ at room temperature} \right\}, \text{cm}$$

$$k\_{\rm Cu} \approx 1.37 k\_{\rm Al}, \{1.72 \text{ at room temperature } T\_1 \approx 27 \text{°C}\},$$

so copper electrochemical corrosion is higher at room temperature *T*<sup>1</sup> ≈ 27°C, aluminium electrochemical corrosion is higher at temperature *T*<sup>2</sup> = 100°C, and the ratio of electrochemical corrosion rates, *kCu*/*kAl*, decreases with temperature increasing, although iron electrochemical corrosion rate practically does not depend on temperature below 100°C. It is obvious, because of the higher melting point of iron than the melting point of copper or aluminium. We can conclude that the Cu2+ ions are less mobile than Cu<sup>+</sup> ions. It needs to point out that *kCu*, *kAl*, and *kFe* have dimensionalities as diffusion coefficients, *D*\* *Cu*, *D*\* *Al*, *D*\* *Fe* [m2 /s], because electrochemical corrosion occurs through anodes'surface.

Dislocation pipe and volume diffusion activation energies can be calculated in such a way. The Arrhenius law is valid for dislocation pipe diffusion and volume diffusion in ultra-high-purity samples [8, 18]:

$$D\_d^\* = D\_{0d} \mathfrak{e}^{-Q\_{\vartheta}(\mathbb{R}T)} \_{\text{or}} D\_d^\* = D\_{0d} \mathfrak{e}^{-E\_{\vartheta}(\mathbb{k}\_{\mathfrak{B}}T)}, \text{and} \ D\_V^\* = D\_{0V} \mathfrak{e}^{-Q\_{\vartheta}(\mathbb{R}T)} \_{\text{or}} D\_V^\* = D\_{0V} \mathfrak{e}^{-E\_{\vartheta}(\mathbb{k}\_{\mathfrak{B}}T)},\tag{21}$$

$$Q[J/mol] = F \cdot E[eV]. \tag{22}$$

Here, *R* ≈ 8.314 JK�<sup>1</sup> is the gas constant, *kB* is the Boltzmann constant, *Qd*(*Ed*) is the dislocation pipe diffusion activation energy (*Qd* = *FEd*), *F* ≈ 96,500 Cmol�<sup>1</sup> is the Faraday constant, *QV*(*EV*) is the volume diffusion activation energy (*QV* = *FEV*), *D*0*<sup>d</sup>* and *D*0*<sup>V</sup>* are the pre-exponential factors,*T* is the absolute temperature.

Our experimental results allow us to calculate:

$$\frac{k\_{\rm Cu}}{k\_{\rm Al}}(T) \approx \frac{D\_{\rm Cu}^{\*}}{D\_{\rm Al}^{\*}}(T) = \frac{D\_{0\rm Cu}^{\*}}{D\_{0\rm Al}^{\*}}e^{(Q\_{\rm Al} - Q\_{\rm Cu})/(RT)}\\\vdots\\\ln\left(\frac{D\_{0\rm Cu}^{\*}}{D\_{0\rm Al}^{\*}}\right) = -0.6; Q\_{\rm Al} - Q\_{\rm Cu} = 2.9 \text{kJ/mol}.\tag{23}$$

$$\frac{D\_{0\text{Cu}}^{\*}}{D\_{0Al}^{\*}} = 0.55, \frac{D\_{\text{Cu}}^{\*}}{D\_{Al}^{\*}}(T\_3) = \mathbf{1} \Rightarrow T\_3 = \frac{2900 \text{J/mol}}{0.6 \text{R}} \approx 583 \text{K} \approx 310^{\circ} \text{C},\tag{24}$$

so diffusion activation energy of Al, *QAl*, is higher than the diffusion activation energy of Cu, *QCu*, (*QAl> QCu*, *QAl*-*QCu* = 2.9 kJ/mol), at temperatures from 20 to 100°C, because the Cu<sup>+</sup> ions have higher mobilities than the Al3+ ions, and copper electrochemical corrosion rate can be approximately equal to aluminium electrochemical corrosion at temperature about *T*<sup>3</sup> ≈ 300°C due to the Cu2+ ions are less mobile than the Cu<sup>+</sup> ions. Moreover, the pre-exponential factors are approximately the same: *D*\* <sup>0</sup>*Al* ≈ 2*D*\* <sup>0</sup>*Cu*.

#### **3. Intrinsic diffusivities ratio and diffusion activation energy calculations**

#### **3.1 Intrinsic diffusivities ratio of Cu and Al analysis**

We can analyse described the experimental results in the Al-Cu system for bulk samples [19] since the ratio *D*\* *Al*/*D*\* *Cu* was not calculated in [19]:

$$\frac{D\_{\rm Cu}^{\*}}{D\_{\rm Al}^{\*}} \approx \frac{\sum\_{j=1}^{N} X\_{j} - X\_{K}(\mathbf{1} - \mathbf{C}\_{i})\sqrt{\pi}}{\sum\_{j=1}^{N} X\_{j} + \mathbf{C}\_{i} \mathbf{X}\_{K} \sqrt{\pi}} < \mathbf{1}, \mathbf{C}\_{i} = \mathbf{C}\_{\mathcal{H}}, \tag{25}$$

where *N* is formed phases quantity, *Xj* is phase *j*'s thickness, *Ci* is the average concentration of aluminium in phase *i*, and *XK* is the Kirkendall shift length.

Five phases are formed in the Al-Cu system at temperatures from 400 to 535°C in bulk samples [19]: θ-phase (phase 1) CuAl2 (*C*<sup>1</sup> = 2/3), η2-phase (phase 2) CuAl (*C*<sup>2</sup> = 1/2), ζ2-phase (phase 3*b*) Cu4Al3 (*C*3*<sup>b</sup>* = 3/7), δ-phase (phase 3*a*) Cu3Al2 (*C*3*<sup>a</sup>* = 2/5), and γ2-phase (phase 3) Cu9Al4 (*C*<sup>3</sup> = 4/13 ≈ 0.31 ≈ 1/3*, C* = *CAl*). Inert markers were in δ-phase (phase 3*a*) Cu3Al2 (*C*3*<sup>a</sup>* = 2/5 = 0.4) and moved to Al side during mutual diffusion. In general, inert markers move to the faster diffusivity component side. We can calculate (*C*3*<sup>a</sup>* = 0.4):

$$\begin{split} \frac{D\_{\text{Cu}}^{\*}}{D\_{Al}^{\*}}(T\_{1} = 535^{\circ}\text{C}) &\approx \frac{X\_{1} + X\_{2} + X\_{3b} + X\_{3d} + X\_{3} - X\_{K}\text{O.}\sqrt{\pi}}{X\_{1} + X\_{2} + X\_{3b} + X\_{3d} + X\_{3d} + X\_{3} + 0.4X\_{K}\sqrt{\pi}} \approx 0.814;\\ \quad y\_{1} = \frac{D\_{Al}^{\*}}{D\_{\text{Cu}}^{\*}} = \frac{1}{0.814} \approx 1.228, \\\\ \quad T\_{1} = 535^{\circ}\text{C} = 808\text{ K}, t = 40\text{ h}, X\_{K} \approx 20.5\text{ }\mu\text{m}, X\_{1} + X\_{2} + X\_{3b} + X\_{3d} + X\_{3} \approx 180\text{ }\mu\text{m}; \end{split} \tag{26}$$

$$\frac{D\_{Cu}^{\*}}{D\_{Al}^{\*}}(T\_{2} = 51\text{S}^{\prime}\text{C}) \approx \frac{X\_{1} + X\_{2} + X\_{3b} + X\_{3a} + X\_{3} - X\_{K}(1 - \text{C}\_{3d})\sqrt{\pi}}{X\_{1} + X\_{2} + X\_{3b} + X\_{3a} + X\_{3} + C\_{3d}X\_{K}\sqrt{\pi}} \approx 0.856;$$

$$\mathcal{Y}\_{2} = \frac{D\_{Al}^{\*}}{D\_{Cu}^{\*}} \approx \textbf{1.168},$$

*T*<sup>2</sup> = 515°C = 788 K, *t* = 40 h, *XK* ≈ 11 μm, *X*<sup>1</sup> + *X*<sup>2</sup> + *X*3*<sup>b</sup>* + *X*3*<sup>a</sup>* + *X*<sup>3</sup> ≈ 127 μm);

$$\frac{D\_{Cu}^{\*}}{D\_{Al}^{\*}}(T\_{3} = 495^{\circ}\text{C}) \approx \frac{X\_{1} + X\_{2} + X\_{3b} + X\_{3a} + X\_{3c} - X\_{K}\text{O.f}\sqrt{\pi}}{X\_{1} + X\_{2} + X\_{3b} + X\_{3a} + X\_{3c} + X\_{3} + 0.4X\_{K}\sqrt{\pi}} \approx 0.916;$$

$$\boldsymbol{\eta}\_{3} = \frac{1}{0.916} \approx 1.092,$$

*T*<sup>3</sup> = 495°C = 768 K, *t* = 40 h, *XK* ≈ 5 μm, *X*<sup>1</sup> + *X*<sup>2</sup> + *X*3*<sup>b</sup>* + *X*3*<sup>a</sup>* + *X*<sup>3</sup> ≈ 101 μm;

$$\frac{D\_{Cu}^{\*}}{D\_{Al}^{\*}}(T\_{4} = 47\text{S}^{\circ}\text{C}) \approx \frac{X\_{1} + X\_{2} + X\_{3b} + X\_{3u} + X\_{3} - X\_{K}(1 - 0.4)\sqrt{\pi}}{X\_{1} + X\_{2} + X\_{3b} + X\_{3u} + X\_{3} + 0.4\text{CX}\_{K}\sqrt{\pi}} \approx 0.969;$$

$$y\_{4} = \frac{D\_{Al}^{\*}}{D\_{Cu}^{\*}} \approx 1.032,$$

$$T\_4 = 47 \\ \mathbb{S}^o \mathbb{C} = 748 \text{ K}, t = 90 \text{ h}, X\_K \approx 2 \text{ }\mu\text{m}, X\_1 + X\_2 + X\_{3b} + X\_{3a} + X\_3 \approx 113 \text{ }\mu\text{m}.$$

*Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature DOI: http://dx.doi.org/10.5772/intechopen.100279*

We can use these four points to calculate by the least square method to increase calculation precise:

$$\Delta Q = Q\_{\mathcal{A}l} - Q\_{Cu} = \frac{4\sum\_{j=1}^{4} \left(\frac{1000}{RT\_j} \ln y\_j\right) - \sum\_{j=1}^{4} \ln y\_j \sum\_{j=1}^{4} \frac{1000}{RT\_j}}{4\sum\_{j=1}^{4} \left(\frac{1000}{RT\_j}\right)^2 - \left(\sum\_{j=1}^{4} \frac{1000}{RT\_j}\right)^2} \approx -13.4 \text{kJ/mol},\tag{30}$$

$$y\_0 = \exp\frac{\sum\_{j=1}^4 \left(\frac{1000}{RT\_j}\right)^2 \sum\_{j=1}^4 \ln y\_j - \sum\_{j=1}^4 \frac{1000}{RT\_j} \sum\_{j=1}^4 \left(\frac{1000}{RT\_j} \ln y\_j\right)}{4\sum\_{j=1}^4 \left(\frac{1000}{RT\_j}\right)^2 - \left(\sum\_{j=1}^4 \frac{1000}{RT\_j}\right)^2} \approx \exp\left(2.2\right) \approx 9.8\tag{31}$$

$$\frac{D\_{\rm Al}^{\*}}{D\_{\rm Cu}^{\*}}(T) = \frac{D\_{0\rm Al}^{\*}}{D\_{0\rm Cu}^{\*}}e^{(Q\_{\rm Al} - Q\_{\rm Cu})\_{\rm (RT)}} \approx \mathfrak{Re}^{-13.4k\rm mol^{-1}}{}^{\prime(RT)},\tag{32}$$

$$\frac{D\_{Al}^{\*}}{D\_{Cu}^{\*}}(T\_{5}) = \mathcal{y}\_{5} = \mathbf{1} \Rightarrow T\_{5} = \frac{13400 \text{J}/mol}{R \ln \text{9}} \approx 733 \text{K} \approx 460^{\circ} \text{C},\tag{33}$$

so *QAl* <sup>&</sup>lt; *QCu* (*QAl-QCu* <sup>=</sup> �13.4 kJ/mol) because the Cu2+ ions have less mobilities than the Al3+ ions, and we can conclude that the Kirkendall displacement changes sign at a temperature about *T*<sup>5</sup> ≈ 460°C for bulk samples. The pre-exponential factors are different in nine times: *D*\* <sup>0</sup>*Al* ≈ 9*D*\* <sup>0</sup>*Cu*.

Diffusion activation energy of Al is less than the diffusion activation energy of Cu (*QAl < QCu*) at temperatures from 160–250°C for mutual diffusion in copper-a luminium thin film double layers, but the pre-exponential factors are different in 10 times [9]. Isolated W islands, 150 Å in diameter, have been deposited between Cu and Al thin film double layers to serve as inert diffusion markers. Marker displacements have been measured. We can calculate the ratio *D*\* *Al*/*D*\* *Cu* for each phase at different temperatures:

$$\begin{split} \frac{D\_{\text{Cu}}^{\*}}{D\_{\text{Al}}^{\*}}(T) &= \frac{D\_{\text{Cu}}^{\*}}{D\_{\text{24}}^{\*}}e^{(Q\_{\text{4}}-Q\_{\text{Ca}})}(RT) = 24e^{-14kfinal^{-1}}(RT) \text{ in } \theta\text{-phase (phase 1) CuAl\_2, C\_{\text{Al}}}\\ &= 2/3 \approx 0.67, \end{split}$$

$$\frac{D\_{\text{1Cu}}^{\*}}{D\_{\text{1Al}}^{\*}}(T = 250^{\theta}C = 523K) = 24e^{-140000 \text{J mol}^{-1}}(8.314 \kappa 523) \approx 24e^{-3.22} \approx 0.96,$$

$$\frac{D\_{\text{1Cu}}^{\*}}{D\_{\text{1Al}}^{\*}}(T = 160^{\theta}C = 433K) \approx 24e^{-3.89} \approx 0.49,$$

so the Al atoms diffuse faster than the Cu atoms in θ-phase at temperatures from 160 to 250°C;

$$\begin{array}{l} \frac{D\_{\text{Cu}}^{\*}}{D\_{\text{Al}}^{\*}}(T) = \frac{D\_{\text{Cu}}^{\*}}{D\_{\text{0} \text{Al}}^{\*}}e^{(Q\_{\text{d}\text{\textdegree}} - Q\_{\text{Cu}})(\text{RT})} = 7 \cdot 10^{4}e^{-38k\text{f}\text{mol}^{-1}} \text{(\textdegree T)} \text{ in } \eta\_{2}\text{-phase (phase 2)} \text{ CuAl}, \text{C}\_{\text{M}},\\ = 1/2 = 0.5, \end{array}$$

$$\frac{D\_{\text{2Cu}}^{\*}}{D\_{\text{2Al}}^{\*}}(T = 250^{\circ} \text{C}) = 7 \cdot 10^{4}e^{-38000 \text{J} \text{mol}^{-1}} \text{(\textdegree T)} \approx 11.2, \frac{D\_{\text{2Cu}}^{\*}}{D\_{\text{2Al}}^{\*}}(T = 160^{\circ} \text{C}) \approx 1.8,$$

so the Cu atoms diffuse faster than the Al atoms in *η*2-phase at temperatures from 160 to 250°C;

$$\frac{D\_{\text{Cu}}^{\*}}{D\_{\text{Al}}^{\*}}(T) = \frac{D\_{\text{Cu}}^{\*}}{D\_{\text{0Al}}^{\*}}e^{(\mathcal{Q}\_{\text{M}} - \mathcal{Q}\_{\text{Cu}})\_{\text{(RT)}}} = 14e^{-9k\text{J}mol^{-1}} \\ \begin{array}{l} \text{14}e^{-9k\text{J}mol^{-1}} \text{ in } \mathcal{V}\_{2}\text{-phase (phase 3)} \text{ Cu}\_{9}\text{Al}\_{4}, \text{C}\_{\text{0}} \\ \text{13} \approx \text{0.31}, \end{array}$$

$$\begin{split} \frac{D\_{3\text{Cu}}^{\*}}{D\_{3\text{Al}}^{\*}}(T = 250^{\circ}\text{C}) &= 1 \text{4e}^{-9000\text{J}mol^{-1}}(\text{RT}) \approx \mathbf{1.77}, \frac{D\_{3\text{Cu}}^{\*}}{D\_{3\text{Al}}^{\*}}(T = \mathbf{160}^{\circ}\text{C}) \\ &= \mathbf{14e}^{-9\text{kJ}mol^{-1}}(\text{RT}) \approx \mathbf{1.15}, \end{split}$$

so the Cu atoms diffuse faster than the Al atoms in *γ*2-phase at temperatures from 160 to 250°C.

The Cu-rich phases can be formed faster than the Al-rich phases at temperatures from 160 to 250°C, and the Cu atoms can diffuse faster than the Al atoms in the Al-Cu system at temperatures from 160 to 250°C. The Al-rich phases can be formed faster than the Cu-rich phases at temperatures from 400 to 535°C, and the Al atoms can diffuse faster than the Cu atoms in the Al-Cu system at temperatures from 400 to 535°C. It depends on the crystal structure of each phase, but, in general, it could depends on conclusions that the Cu2+ ions are less mobile than the Cu<sup>+</sup> ions, and the ratio *D*\* *Al/D*\* *Cu* depends on temperature.

#### **3.2 Diffusion activation energy calculation**

#### *3.2.1 Diffusion activation energy calculation in the Cu-Al system*

Mutual diffusion coefficients were calculated for all five phases [19]:

$$\begin{split} \tilde{D}\_{1}^{\*} &= 5.6 \cdot 10^{-5} e^{-127.6 \text{kJ} \cdot \text{mol}^{-1} / (RT)} m^{2}/\text{s}; \tilde{D}\_{2}^{\*} = 2.2 \cdot 10^{-4} e^{-148.5 \text{kJ} \cdot \text{mol}^{-1} / (RT)} m^{2}/\text{s}; \quad \text{(34)} \\ \tilde{D}\_{3b}^{\*} &= 1.6 \cdot 10^{2} e^{-230.5 \text{kJ} \cdot \text{mol}^{-1} / (RT)} m^{2}/\text{s}; \tilde{D}\_{3a}^{\*} = 2.1 \cdot 10^{-4} e^{-138.1 \text{kJ} \cdot \text{mol}^{-1} / (RT)} m^{2}/\text{s}; \tilde{D}\_{3}^{\*} \\ &= 8.5 \cdot 10^{-5} e^{-138 \text{kJ} \cdot \text{mol}^{-1} / (RT)} m^{2}/\text{s}. \end{split}$$

We can see that *Q*<sup>1</sup> < *Q*2, *Q*<sup>1</sup> < *Q*3, and *Q*<sup>3</sup> < *Q*<sup>2</sup> because of *K*<sup>1</sup> > *K*2, *K*<sup>1</sup> > *K*3, and *K*<sup>3</sup> > *K*2, and *D*<sup>01</sup> ≈ *D*<sup>02</sup> ≈ *D*03. Phase *j*'s rate formation is *Kj*. Three phases are formed in the Al-Cu system at temperatures 300 and 350°C [5]: CuAl2, CuAl, and Cu9Al4. Phases formation rates were experimentally measured: *K*<sup>1</sup> = 860x10�<sup>18</sup> m<sup>2</sup> /s, *K*<sup>2</sup> = 100x10�<sup>18</sup> m<sup>2</sup> /s, and *K*<sup>3</sup> = 360x10�<sup>18</sup> m<sup>2</sup> /s at temperature 350°C; *K*<sup>1</sup> = 77x10�<sup>18</sup> m<sup>2</sup> /s, *K*<sup>2</sup> = 18x10�<sup>18</sup> m<sup>2</sup> /s, and *K*<sup>3</sup> = 35x10�<sup>18</sup> m2 /s at temperature 300° C, so *K*<sup>1</sup> > *K*2, *K*<sup>1</sup> > *K*3, and *K*<sup>3</sup> > *K*2. We can calculate assuming *C*<sup>1</sup> = 2/3*, C*<sup>2</sup> = 1/2*, C*<sup>3</sup> = 1/3, *C* = *CAl* [11]:

$$D\_1 \approx \frac{1}{2} \left( C\_1 (\mathbf{1} - \mathbf{C}\_1) \mathbf{K}\_1 + C\_2 (\mathbf{1} - \mathbf{C}\_1) \sqrt{K\_1 K\_2} + C\_3 (\mathbf{1} - \mathbf{C}\_1) \sqrt{K\_1 K\_3} \right);\tag{35}$$

$$D\_2 \approx \frac{1}{2} \left( \mathbf{C\_2} (\mathbf{1} - \mathbf{C\_2}) \mathbf{K\_2} + \mathbf{C\_2} (\mathbf{1} - \mathbf{C\_1}) \sqrt{K\_1 K\_2} + \mathbf{C\_3} (\mathbf{1} - \mathbf{C\_2}) \sqrt{K\_2 K\_3} \right); \tag{36}$$

$$D\_3 \approx \frac{1}{2} \left( C\_3 (1 - C\_3) K\_3 + C\_3 (1 - C\_1) \sqrt{K\_1 K\_3} + C\_3 (1 - C\_2) \sqrt{K\_2 K\_3} \right);\tag{37}$$

$$\begin{split} D\_1(T\_2 = 350^0 \text{C}) \approx \frac{1}{9} K\_1 + \frac{1}{12} \sqrt{K\_1 K\_2} + \frac{1}{18} \sqrt{K\_1 K\_3} \approx 150 \\ \cdot 10^{-18} m^2/s, D\_1(T\_1 = 300^\circ \text{C}) \approx 15 \cdot 10^{-18} m^2/s; \end{split} \tag{38}$$

*Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature DOI: http://dx.doi.org/10.5772/intechopen.100279*

$$\begin{split} D\_2(T\_2 = 350^\circ \text{C}) &\approx \frac{1}{8} K\_2 + \frac{1}{12} \sqrt{K\_1 K\_2} \\ &+ \frac{1}{12} \sqrt{K\_2 K\_3} \approx 50 \text{\textdegree } 10^{-18} m^2/\text{s}, D\_2(T\_1 = 300^\circ \text{C}) \approx 8 \cdot 10^{-18} m^2/\text{s}; \end{split} \tag{39}$$

$$\begin{split} D\_3(T\_2 = 350^\circ C) &\approx \frac{1}{9} K\_3 + \frac{1}{18} \sqrt{K\_1 K\_3} + \frac{1}{12} \sqrt{K\_2 K\_3} \approx 90 \\ &\quad \cdot 10^{-18} m^2 / \text{s}, D\_3(T\_1 = 300^\circ C) \approx 12 \cdot 10^{-18} m^2 / \text{s}. \end{split} \tag{40}$$

Moisy et al. [5] did not calculate diffusion activation energies and the pre-exponential factors, so we can do it:

$$Q\_i = \frac{RT\_1T\_2}{T\_2 - T\_1} \ln \left(\frac{D\_i(T\_2)}{D\_i(T\_1)}\right),\\D\_{0i} = D\_i(T\_1)e^{Q\_i(\mathbb{R}T\_1)} = D\_i(T\_2)e^{Q\_i(\mathbb{R}T\_2)};\tag{41}$$

$$\tilde{D}\_1 = 4.3 \cdot 10^{-5} e^{-13 \text{€} \text{(kJ/mol}^{-1} / (RT)} m^2 / \varsigma,\\ \tilde{D}\_2 = 6.6 \cdot 10^{-8} e^{-108.8 \text{kJ/mol}^{-1} / (RT)} m^2 / \varsigma, \quad \text{(42)}$$

$$\tilde{D}\_3 = 9.6 \cdot 10^{-7} e^{-119.6 \text{kJ/mol}^{-1} / (RT)} m^2 / \varsigma.$$

Eq. (42) correspond to Eq. (34). We can use several, *N*, points to calculate by the least square method to increase calculation precise:

$$Q\_i = -\frac{N\sum\_{j=1}^{N} \left(\frac{1000}{RT\_j} \ln D\_i(T\_j)\right) - \sum\_{j=1}^{N} \ln D\_i(T\_j) \sum\_{j=1}^{N} \frac{1000}{RT\_j}}{N\sum\_{j=1}^{N} \left(\frac{1000}{RT\_j}\right)^2 - \left(\sum\_{j=1}^{N} \frac{1000}{RT\_j}\right)^2} [kf/mol], \tag{43}$$

$$D\_{0i} = \exp\frac{\sum\_{j=1}^{5} \left(\frac{1000}{RT\_j}\right)^2 \sum\_{j=1}^{5} \ln D\_i(T\_j) - \sum\_{j=1}^{5} \frac{1000}{RT\_j} \sum\_{j=1}^{4} \left(\frac{1000}{RT\_j} \ln D\_i(T\_j)\right)}{5 \sum\_{j=1}^{5} \left(\frac{1000}{RT\_j}\right)^2 - \left(\sum\_{j=1}^{5} \frac{1000}{RT\_j}\right)^2} [m^2/s]. \tag{44}$$

Eqs. (43) and (44) give Eq. (41) for only two points (*N* = 2).

#### *3.2.2 Diffusion activation energy calculation in pure iron*

A method of dislocation pipe diffusion parameter determination during the type B diffusion kinetics was suggested by the model of dislocation pipe diffusion involving outflow [6, 20]. The method involves diffusion dislocation pipe kinetics for two different annealing times at the same temperature during the type B kinetics and dislocation pipe kinetics for one annealing time at other lower temperature during the type C kinetics. Transition time for type B kinetics to type A kinetics (volume diffusion) and kinetics law *t* 1/6 [7] for cone top rate are used in this method.

Bulk diffusion coefficients, *DV*, for the diffusion of 59Fe in the high-purity iron were calculated in [21] using type B ! A kinetics: *DV* = 1.5\*10�<sup>18</sup> <sup>m</sup><sup>2</sup> s �<sup>1</sup> at *T*<sup>1</sup> = 973 K for tB ! <sup>A</sup> = 67.5ks (*Tm/T*<sup>1</sup> = 1.86,*Tm* is melting point of iron). Only one experiment was carried out at the same temperature for two annealing times *t*<sup>1</sup> and *t*<sup>2</sup> (*t*<sup>1</sup> < < *t*2, *t*<sup>2</sup> = 40 *t*1). Dislocation diffusion coefficients for the diffusion of 59Fe in the iron were calculated in [21] using type C kinetics: *Dd* = 3\*10�<sup>16</sup> m<sup>2</sup> s �<sup>1</sup> at *T*<sup>2</sup> = 753 K for *tC* = 2.4ks (*Tm*/*T*<sup>2</sup> = 2.4). One can find ratio *Dd/DV*: *y t*ð Þ¼ *<sup>C</sup>*!*<sup>B</sup>* ffiffiffiffiffi *Dd* 6*D* q *δ*, where δ = 1 nm, *Dd <sup>D</sup>* <sup>¼</sup> <sup>4</sup>*:*3*x*106. Ratio *Dd*/*DV* increases remarkably for lower temperature. Dislocation pipe and volume diffusion activation energies and pre-exponential factors were not calculated in [21]. It is possible to calculate *Ed* and *<sup>D</sup>*0: *Ed* <sup>¼</sup> ln *Dd*ð Þ *<sup>T</sup>*<sup>1</sup> *Dd*ð Þ *T*<sup>2</sup> *kB T*1*T*<sup>2</sup> *T*1�*T*<sup>2</sup> , *<sup>D</sup>*<sup>0</sup> <sup>¼</sup> *Dd*ð Þ *<sup>T</sup>*<sup>1</sup> exp *Ed kBT*<sup>1</sup> ,*Ed* <sup>¼</sup> <sup>1</sup>*:*1*eV*; *Qd* <sup>¼</sup> <sup>106</sup>*kJ=mol*, *<sup>D</sup>*<sup>0</sup> <sup>¼</sup> <sup>6</sup>*:*<sup>85</sup> � <sup>10</sup>�9*m*2*<sup>s</sup>* �1. One can calculate dislocation pipe diffusion coefficient for temperature 973 K directly (*T*<sup>1</sup> = 753 K and *T*<sup>2</sup> = 693 K (type C kinetics)): *Dd* ≈ 10�<sup>14</sup> m<sup>2</sup> s �1 . Such value corresponds to value calculated using the proposed method. The Fisher law (*t* 1/4) gives *Dd* ≈ 10�<sup>16</sup> ÷10�<sup>15</sup> m<sup>2</sup> s �1 . Such value is in two orders lower than experimentally obtained in [21]. The volume diffusion activation energy *EV* can be calculated: *EV* <sup>¼</sup> ln *<sup>D</sup>*<sup>0</sup> *DV*ð Þ *T*<sup>1</sup> *kBT*1, *EV* <sup>¼</sup> <sup>1</sup>*:*85*eV*; *QV* <sup>≈</sup>179*kJ=mol*. Ratio *Ed EV* ¼ 0*:*6 as described in [8].

#### **4. Conclusions**

The Al atoms diffuse faster than the Cu atoms at a temperature higher than 475°C, but the Cu atoms diffuse faster than the Al atoms at a temperature lower than 100°C. The diffusion activation energy of Al is less than the diffusion activation energy of Cu at a temperature higher than 475°C, but diffusion activation energy of Cu is less than the diffusion activation energy of Al at a temperature lower than 100°C. Our investigations show that it is possible because the Cu2+ ions are less mobile than Cu+ ions.

Volume diffusion activation energy of Fe is higher than volume diffusion activation energy of Cu or Al, but dislocation pipe diffusion activation energy of Fe is smaller than volume diffusion activation energy of Cu or Al, so the Fe atoms diffuse faster along the dislocation line, but the Cu or Al atoms diffuse faster in volume.

#### **Author details**

Mykhaylo Viktorovych Yarmolenko Faculty of Market, Information and Innovation Technologies, Kyiv National University of Technologies and Design, Cherkasy, Ukraine

\*Address all correspondence to: yarmolenko.mv@knutd.edu.ua

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Copper, Iron, and Aluminium Electrochemical Corrosion Rate Dependence on Temperature DOI: http://dx.doi.org/10.5772/intechopen.100279*

#### **References**

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[2] Braunovic M, Alexandrov N. Intermetallic compounds at aluminumto-copper electrical interfaces: Effect of temperature and electric current. IEEE Transactions on Components, Packaging, and Manufacturing Technology: Part A. 1994;**17**(1):78-85. DOI: 10.1109/95.296372

[3] Goh CS, Chong WLE, Lee TK, Breach C. Corrosion study and intermetallics formation in gold and copper wire bonding in microelectronics packaging. Crystals. 2013;**3**(3):391-404. DOI: 10.3390/cryst3030391

[4] Yarmolenko MV. Copper and aluminum electric corrosion investigation and intermetallics disappearance in Cu-Al system analysis. Phys. Chem. Solid St. 2020;**21**(2): 294-299. https://journals.pnu.edu.ua/ index.php/pcss/article/view/3055

[5] Moisy F, Sauvage X, Hug E. Investigation of the early stage of reactive interdiffusion in the Cu-Al system by *in-situ* transmission electron microscopy. Materialia. 2020;**9**:100633. DOI: 10.1016/j.mtla.2020.100633

[6] Yarmolenko MV. Method of dislocation and bulk diffusion parameters determination. Metallofizika i Noveishie Tekhnologii. 2020;**42**(11): 1537-1546. https://mfint.imp.kiev.ua/ article/v42/i11/MFiNT.42.1537.pdf

[7] Yarmolenko MV. Intermediate phase cone growth kinetics along dislocation pipes inside polycrystal grains. AIP Advances. 2018;**8**:095202. DOI: 10.1063/ 1.5041728

[8] Mehrer H. Diffusion in Solids. New York: Springer; 2007. 651p. http://users. encs.concordia.ca/tmg/images/7/79/ Diffusion\_in\_solids\_Helmut\_Mehrer. pdf

[9] Hentzell HTG, Tu KN. Interdiffusion in copper–aluminum thin film bilayers. II. Analysis of marker motion during sequential compound formation. Journal of Applied Physics. 1983;**54**:6929-6937. DOI: 10.1063/1.332000

[10] Darken LS. Diffusion, mobility and their interrelation through free energy in binary metallic systems. Transactions AIME. 1948;**175**:184-201. http://garfield. library.upenn.edu/classics1979/ A1979HJ27500001.pdf

[11] Yarmolenko MV. Intermetallics disappearance rate analysis in double multiphase systems. DDF. 2021;**407**: 68-86. DOI: 10.4028/www.scientific. net/ddf.407.68

[12] Włodarczyk PP, Włodarczyk B. Effect of hydrogen and absence of passive layer on corrosive properties of aluminium alloys. Materials. 2020;**13**(7): 1580-1593. DOI: 10.3390/ma13071580

[13] Kumar S, Handwerker CA, Dayananda MA. Intrinsic and interdiffusion in Cu-Sn system. JPEDAV. 2011;**32**:309-319. DOI: 10.1007/s11669-011-9907-91547-7037

[14] Tu KN. Electronic Thin-Film Reliability. 1st ed. New York: Cambridge University Press; 2010. 392p. DOI:h ttps://www.amazon.com/Electronic-Thin-Film-Reliability-King-Ning-Tuebook-dp-B00QIT3LXA/dp/ B00QIT3LXA/ref=mt\_other?\_ encoding=UTF8&me=&qid=

[15] Epishin A, Chyrkin A, Camin B, Saillard R, Gouy S, Viguier B. Interdiffusion in CMSX-4 related Nibase alloy system at a supersolvus

temperature. DDF. 2021;**407**:1-10. DOI: 10.4028/www.scientific.net/ddf.407.1

[16] Prawoto Y. Synergy of erosion and galvanic effects of dissimilar steel welding: Field failure analysis case study and laboratory test results. Journal of King Saud University – Engineering Sciences. 2013;**25**:59-64. DOI: 10.1016/j. jksues.2011.12.001

[17] Yarmolenko MV. Intrinsic diffusivities ratio analysis in the Al-Cu system. Phys. Chem. Solid St. 2020; **21**(4):720-726. https://journals.pnu.edu. ua/index.php/pcss/article/view/4440

[18] Yarmolenko MV. Intermetallics disappearance rates and intrinsic diffusivities ratios analysis in the Cu-Zn and the Cu-Sn systems. Phys. Chem. Solid St. 2021;**22**(1):80-87. https:// journals.pnu.edu.ua/index.php/pcss/ article/view/4744

[19] Funamizu Y, Watanabe K. Interdiffusion in the Al–Cu system. Transactions of the Japan Institute of Metals. 1971;**12**(3):147-152. DOI: 10.2320/matertrans1960.12.147

[20] Yarmolenko MV. Analytically solvable differential diffusion equations describing the intermediate phase growth. Metallofizika i Noveishie Tekhnologii. 2018;**40**(9):1201-1207. https://mfint.imp.kiev.ua/article/v40/ i09/MFiNT.40.1201.pdf

[21] Shima Y, Ishikawa Y, Nitta H, Yamazaki Y, Mimura K, Isshiki M, et al. Self-diffusion along dislocations in ultra high purity iron. Materials Transactions. 2002;**43**(2):173-177. https://www.jim.or. jp/journal/e/43/02/173.html

#### **Chapter 4**

## Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods and Molecular Dynamics Simulation

*Şaban Erdoğan and Burak Tüzün*

### **Abstract**

Many experts working in the field of corrosion work in laboratories experimentally with long-term procedures and high costs by making changes in the structures of new corrosion inhibitors or existing inhibitors. Advances in computational chemistry and computer software in recent years combine corrosion prevention studies with theoretical chemistry, enabling fast, cheap and highly accurate research. Researchers working in this field can now predict the electronic, molecular and adsorption properties of anti-corrosion molecules at the molecular level with density functional theory (DFT) and Molecular Dynamics Simulation. This section includes: introduction, corrosion mechanisms, introduction to corrosion inhibitors, density functional theory (DFT) and corrosion applications, Molecular Dynamics Simulation, DFT and Molecular Dynamics Simulation applications of the effectiveness of the selected corrosion inhibitor and results. The theoretical data obtained by both the DFT approach and the molecular dynamics simulation approach showed that the corrosion inhibition efficiency order against iron corrosion for the studied Schiff bases and derivatives can be presented as: DBAMTT> SAMTT> AMTT. HOMO energy value of DBAMTT has 8,18144, HOMO energy value of SAMTT has 8,09001, and AMTT has 8,01518 in HF/6–31++G\*\* basis set.

**Keywords:** Corrosion, DFT, Molecular Dynamics Simulation, Fe(110), Corrosion inhibitor

#### **1. Introduction**

Corrosion prevention studies have been intensified in recent years by the use of many organic compound classes as corrosion inhibitors for metals in acidic environments [1–3]. Both experimental and theoretical studies are carried out on this subject, but due to the fact that experimental studies are expensive and timeconsuming, emphasis is placed on theoretical chemistry with software systems that have developed considerably in recent years [4, 5]. Some quantum chemical methods and molecular modeling techniques are carried out to characterize the molecular structure of the inhibitors by determining the effectiveness of corrosion inhibitors and to suggest the mechanisms of their interaction with surfaces [6–8].

Corrosion inhibitors, which are one of the easiest methods of protecting metals against corrosion, are gaining importance day by day [9–11]. The adsorption of

```
Figure 1.
Chemical molecular structures of studied Schiff bases derivatives.
```
these molecules depends on many physicochemical properties of the molecules [12–14]. There are many physicochemical properties for the studied molecules to be good inhibitors, such as aromaticity, steric factors, electron density etc. [15–17].

It has been stated in many studies that organic inhibitors contain heteroatoms such as nitrogen, sulfur or oxygen and that congenital double bonded heterocyclic aromatic ring systems are quite good inhibitors for mild steel [18, 19]. Schiff bases are also a very good inhibitor because they have these properties, and many experimental studies are carried out on Schiff bases. In this study, salicylideneamino-3-methyl-1,2,4-triazole-5-thi one26 (SAMTT) and 4- (2,4-dihydroxybenzylideneamino) -3-methyl-1,2,4-triazole-5-thione (DBAMTT) and methyl-1,2,4-triazole-5-thion27 (AMTT) compounds are theoretically studied [20].

The use of Conceptual density functional theory (DFT) to describe the structure and effectiveness of inhibitors in corrosion processes is becoming a well-known use. With this theory, using the energy of the highest filled molecular orbitals (EHOMO) and the lowest empty molecular orbitals (ELUMO), global chemical descriptors such as hardness [21], electronegativity [22], softness [23], electrophilicity [24] and chemical potential are calculated for corrosion. It provides information about the effectiveness of inhibitors. In this section, determination of the corrosion inhibition efficiency and best inhibitor of the molecules in **Figure 1** on iron corrosion is explained using quantum chemical calculations and molecular dynamics simulations approach.

#### **2. Theory and computational details**

Density Functional Theory (DFT), the most common method used to determine the chemical reactivity of molecules, aggregates, and solids, seems to be getting more popular day by day [25]. DFT calculations in this study were made with Gaussian View 5.0.8 program [26] for the preparation of Gaussian 09 [27] input files. The structures of the compounds in the study are calculated with functional B3LYP

*Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods… DOI: http://dx.doi.org/10.5772/intechopen.98968*

[28, 29] based on density functional theory (DFT). High-level 6–311 ++ G (d, p) foundation sets were used in the calculations. This basic sebum is one of the most accurate basic sets. Calculations in both gas and aqueous phases were also made using SDD, 6–31 ++ G (d, p) and 6-31G base sets, as well as HF and DFT/B3LYP methods, using other levels of theory. One of the reasons to investigate the liquid phase in the study is that the corrosion is higher than the liquid phase. For the liquid phase calculations in the study, Tomasi's polarized continuity model (PCM) and selfconsistent reaction area (SCRF) theory were used. These methods model the solvent as a uniform dielectric constant (DC = 78.5) continuity and define the cavity in which the solute is placed as a uniform series of interlocking atomic spheres.

In recent years, DFT methods have been found to be successful in providing insight into chemical reactivity indices such as chemical hardness (η), energy gap (ΔEgap = HOMO–LUMO), electronegativity (χ), chemical potential (μ). Fukui functions *f(r)* [30] in terms of proton affinity (PA), electrophilicity (ω) and nucleophilicity (ε) and selectivity [25], spherical descriptors and local descriptors.

Reactivity indices such as electronegativity (χ), chemical hardness (η), and chemical potential (μ) are defined as derivatives of electronic energy (E) with respect to the number of electrons (N) at external potential, *υ(r).* Mathematical operations related to these concepts are given through the following Equations [31].

$$
\mu = -\chi = \left(\frac{\partial E}{\partial \mathbf{N}}\right)\_{\nu(r)}\tag{1}
$$

$$\eta = \frac{1}{2} \left( \frac{\partial^2 E}{\partial \mathbf{N}^2} \right)\_{\nu(r)} = \frac{1}{2} = \left( \frac{\partial \mu}{\partial \mathbf{N}} \right)\_{\nu(r)} \tag{2}$$

Pearson and Parr were presented the operational and approximate definitions depending on electron affinity (A) and ionization energy (I) of any chemical species (atom, ion or molecule) for chemical hardness, which measures of the resistance of a chemical species to charge transfer, softness (σ) electronegativity and chemical potential in the light of finite differences method [32].

$$
\chi = -\mu = \left(\frac{I+A}{2}\right) \tag{3}
$$

$$
\eta = \frac{I - A}{2} \tag{4}
$$

The global softness [33] is defined as the inverse of the global hardness and this quantity is given as in Eq. (4).

$$
\sigma = \frac{1}{\eta} \tag{5}
$$

Molecular Orbital Theory and Conceptual Density Functional Theory gained a new dimension with the Koopmans theorem [34] presented in the 1930s, and to predict the ionization energy and electron affinities of chemical species, the ionization energy and electron affinity of a molecule approximate the negative values of the orbital energies of HOMO and LUMO, respectively. He predicted that it was equal. Equations (6) and (7) were obtained using Eqs. (3) and (4) to calculate hardness, electronegativity, and chemical potential with the Koopmans theorem.

$$\chi = -\mu = \left(\frac{-E\_{\rm HOMO} - E\_{\rm LUMO}}{2}\right) \tag{6}$$

*Corrosion - Fundamentals and Protection Mechanisms*

$$\eta = \left(\frac{E\_{LUMO} - E\_{HOMO}}{2}\right) \tag{7}$$

The concept of electrophilicity (ω) as a global reactivity index similar to the chemical hardness and chemical potential has been introduced by Parr et al. [35]*.* This new reactivity descriptor measures the stabilization in energy when the system acquires an additional electronic charge ΔN from the environment. The electrophilicity is defined as in Eq. (8).

$$
\rho = \frac{\mu^2}{2\eta} = \frac{\chi^2}{2\eta} \tag{8}
$$

The global electrophilicity index (ω) is a descriptor of reactivity that allows a quantitative classification of the global electrophilic nature of a molecule within a relative scale. From the light of this index, electrophilic power of a chemical compounds is associated with its electronegativity and chemical hardness. Nucleophilicity (ε) is physically the inverse of the electrophilicity as is given in the equation below (Eq. (9)).

$$
\varepsilon = \mathbf{1}/w \tag{9}
$$

The solvent effect in the study was examined using the polarized continuity model (PCM) model [36].

#### **3. Results and discussion**

The experimental values of the Schiff bases in the study, 4-Amino-3-methyl-1,2,4-triazole-5-thione (AMTT) and its Derivatives (SAMTT and DBAMTT) were obtained by the study [20]. Experimentally, the inhibition activity of these bases was determined as follows: AMTT <SAMTT< DBAMTT*:*

Quantum chemical descriptors such as EHOMO, ELUMO, Energy gap (ΔE=ELUMO - EHOMO), chemical hardness, softness, electronegativity, chemical potential, proton affinity, electrophilicity and nucleophilicity were calculated and corrosion inhibition was discussed through these parameters. Numerical values of all calculated parameters of Schiff bases and derivatives and their protonated states are given in **Tables 1**–**4** in gas and water solution.

We will discuss all the parameters in detail below.

#### **3.1 Non-protonated inhibitors**

According to the boundary molecular orbit theory FMO, a function of the interaction between HOMO and LUMO levels of the reacting species is defined as chemical reactivity [37]. The molecule's ability to donate electrons to a suitable acceptor with empty molecular orbitals is called EHOMO, and its ability to accept electrons is called ELUMO. The higher the value of the inhibitor's EHOMO, the greater the inhibition efficiency and its presenting electrons to the empty d-orbit of the metal surface. The larger the molecule's ability to accept electrons depends on the lower the value of ELUMO [9]. As a result of the calculations, among the molecules investigated, the lowest energy EHOMO, AMTT had the lowest and DBAMTT the highest corrosion inhibition (**Table 2**). This situation is compatible with causal results. This means that the molecule that tends to adsorb the most on the metal surface is DBAMTT. SAMTT, on the other hand, has a lower number of OH groups


**Table 1.** *Calculated quantum chemical parameters for non-protonated molecules in gas phase (eV).*

#### *Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods… DOI: http://dx.doi.org/10.5772/intechopen.98968*


#### *Corrosion - Fundamentals and Protection Mechanisms*


*Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods… DOI: http://dx.doi.org/10.5772/intechopen.98968*

> **Table 3.**

*Calculated quantum chemical parameters for protonated molecules in gas phase*

 *(eV).*


**Table 4.** *Calculated*

 *quantum chemical parameters*

 *for protonated*

 *molecules in aqueous solution (eV).*

#### *Corrosion - Fundamentals and Protection Mechanisms*

**58**

*Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods… DOI: http://dx.doi.org/10.5772/intechopen.98968*

than DBAMTT, so its corrosion inhibition efficiency is less than DBAMTT. **Figure 2** shows the areas where the activities of molecules are high. It is seen that these areas are the regions where nitrogen is present.

The ΔE approach, defined as the HOMO - LUMO energy deficit, is a very important stability index and provides the necessary theoretical models to make explanations about the structure and conformation in molecular systems. In order to have a high inhibition efficiency, the ΔE value should be low [38–40]. When the investigated molecules were compared, it was seen that there was a DBAMTT molecule in the smallest HOMO-LUMO gap (8,68921 eV obtained by HF method) as seen in **Table 2**. This means that the DBAMTT molecule has a tendency to adsorb more on the metal surface than other molecules and can be expected to be a very good corrosion inhibitor.

Electronegative indicates the strength of atoms in a molecule to attract bonding electrons [41]. The higher the electronegativity value of the molecule, the more the atoms in the molecule will attract the bond electrons. This will cause the inhibitor activity of the molecule to decrease [42].

The reason for not making a detailed analysis on the dipole moment μ, it should be stated first that there is no consensus on the relationship between dipole moment and inhibition efficiency in literature [7, 11, 43–46]. The results obtained in the

#### **Figure 2.**

*The optimized structures, HOMOs, LUMOs and electrostatic potential structures of nonprotonated inhibitor molecules using DFT/6–311++G\*\* calculation level.*

study also show that there is no significant result between μ and inhibition efficiency and that it confirms the previous studies.

One of the ways to measure molecular stability and reactivity is Absolute hardness, η, and softness σ, where a hard molecule has a fairly large energy gap and a soft molecule has a small energy gap. Soft molecules are more reactive than hard molecules because they easily donate electrons to the receiver. While performing a simple electron transfer from the adsorption molecule, the transfer takes place from the part where the σ value of the molecule is highest [47]. In corrosion systems, the metal behaves like a lewis acid and while it is soft acid, the inhibitor acts as a lewis base and the more soft base inhibitors are, the more these metals have an effect on acidic corrosion. In this case, when **Table 2** dec-I data were examined, it was seen that the DBAMTT inhibitor had the highest σ value and this was an expected result when compared with the experimental results.

When iron and inhibitor approach each other, electrons flow from low χ (inhibitor) to high χ (iron) until their chemical potential or electronegativity is equal. As a first approximation, the fraction of electrons transferred, N, is given by Eq. (10).

$$
\Delta N\_{\text{max}} = \frac{\chi\_{Fe} - \chi\_{inh}}{2(\eta\_{Fe} + \eta\_{inh})} \tag{10}
$$

In the Hard Soft Acid Base (HSAB) theory [48], it was determined that iron behaves like lewis acid, so the difference in electronegativity drives the electron transfer and the sum of the hardness parameters acts as a resistance. This is calculated using the fraction of transferred electrons assuming I = A for a metallic mass, using a theoretical value χ Fe = 7 eV [49] for cast iron's electronegativity and a global hardness Fe = 0. [50] In this study, the number of electrons transferred (ΔNmax) of the compounds under the probe is calculated and the results are shown in **Tables 5** and **6**. According to Lukovits et al. [51], if ΔN <3.6, inhibition efficiency increased with increasing ability to donate electrons at the metal surface. A value of ΔNmax < 3.6 eV indicates the tendency of a molecule to donate electrons to the metal surface. The results in **Tables 5** and **6** revealed that the molecules under the probe act as electron donors outside the protonated AMTT, SAMTT, and DBAMTT species in the gas phase and at the B3LYP/6–31 ++ G (d, p) theory level. Acting as an electron acceptor. The results show that the highest fraction of transferred electrons, ΔNmax, is associated with the best inhibitor (DBAMTT), while the least fraction is associated with the inhibitor with the least inhibitory activity (AMTT). In any case, the ability of inhibitor molecules to donate electrons follows the order DBAMTT> SAMTT> AMTT. These results are in good agreement with experimental studies.

Recently, according to the theory presented by Gomez et al. [38], provided that both electron transfer to the molecule and recycling from the molecule are simultaneously, the energy change and the hardness of the molecule change in direct proportion (Eq. (11)).

$$
\Delta E\_{back-donation} = -\frac{\eta}{4} \tag{11}
$$

Eq. (11) implies that when>0 or ΔEb-d < 0, back-donation from molecule to metal is energetically preferred. The results reported in **Table 5** show that ΔEb-d < 0, therefore charge transfer to a molecule followed by re-release from the molecule is energetically favorable. Assuming that the inhibition efficiency should increase when the molecule has better adsorption on the metal surface, the inhibition efficiency should increase when the stabilization energy resulting from the interaction between the metal surface and the inhibitor increases. As expected and


#### *Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods… DOI: http://dx.doi.org/10.5772/intechopen.98968*

**Table 5.**

*Calculated quantum chemical parameters (ΔNmaz, Δψ, and ΔEb-d (in eV) and the optimized energies (E in hartree) of the non-protonated molecules under probe in gas phase and in aqueoussolution (eV).*


#### *Corrosion - Fundamentals and Protection Mechanisms*

**Table 6.** *Calculated*

*chemical*

*and*

*and*

*the*

 *energies (E in hartree) of the protonated*

 *molecules under probe in gas phase and in aqueous solution*

*Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods… DOI: http://dx.doi.org/10.5772/intechopen.98968*

in line with the experimental results [39], the calculated values of ΔEb-d tend to: DBAMTT> SAMTT> AMTT.

In the theoretical studies, the ESP calculations of the molecules show the regions where the electron density is high in the molecule [40]. For this reason, molecules interact chemically by donating electrons on atoms with higher electron density. It is seen that the electron density of the sulfur atom is higher than the other atoms in the calculated molecules. For this reason, they try to be good inhibitors by interacting chemically over the molecular sulfur atom [41].

Apart from these, another important property, Sastri and Perumareddi [40] discovered by using the following equation molecule-metal interaction energy (Δψ) can be calculated (14).

$$
\Delta \psi = -\frac{\left(\chi\_{Fe} - \chi\_{inh}\right)^2}{4\left(\eta\_{Fe} + \eta\_{inh}\right)}\tag{12}
$$

When the results are examined, molecule-metal interaction Δψ|, is respectively as DBAMTT> SAMTT> AMTT (**Tables 5** and **6**). In addition, the initial moleculemetal interaction energy (Δψ) order is again DBAMTT> SAMTT> AMTT.

#### **3.2 Protonated inhibitors**

The enthalpy of the reaction of a chemical species in the gas phase with the H + ion is defined as the affinity of protons (PA) [41, 52]. PA gives information about the ability of chemical compounds to donate or accept electrons and the degree of alkalinity. Compounds containing hetoroatoms such as oxygen and nitrogen tend to protonate very well in acidic environments and aqueous solutions. **Tables 7** and **8** shows the PA values of the compounds in this study with different calculation methods in gas and aqueous solution. When PA values and excision activities were compared, it was determined that the efficiency ranking was DBAMTT> SAMTT> AMTT and was consistent with the experimental result.


**Table 7.**

*Calculated proton affinity values of studied quinoline derivatives in gas phase using different calculation levels.*


#### **Table 8.**

*Calculated proton affinity values of studied quinoline derivatives in aqueous solution using different calculation levels.*

The following equation is used to calculate the PA values of Schiff bases compounds.

$$PA = E\_{\text{(pro)}} - \left(E\_{\text{(non-pro)}} + E\_{H^{+}}\right) \tag{13}$$

In the above equation, Enon-pro and Epro are energies of non-protonated and protonated inhibitors, respectively. EH + is the energy of the H + ion and is calculated in the figure below.

In the high calculation methods selected in the study, the protonated inhibitors have lower EHOMO values compared to their non-protonated states, and the order is respectively DBAMTT, SAMTT, AMTT, and these results given in **Table 3** are consistent with the experimental inhibition efficiency.

Agreement of EHOMO values with experimental data ELUMO and T.E. and there is a correlation between these parameters and the inhibition efficiency. When the ΔE values were examined, it was seen that the lowest value belonged to DBAMTT and it was determined that it was the most intrusive (9,8405 eV).

In addition, when **Tables 2** and **3** are examined, it is seen that protonated compounds have higher μ than non-protonated compounds. Similarly, this verification was made for chemical hardness. The results show that the calculations show that non-protonated inhibitors have a more positive ΔN value than the protonated inhibitor. The DBAMTT molecule, on the other hand, has the highest ΔN value in each round, confirming that it has the same highest inhibitory properties as experimental data.

#### **3.3 Solvent effect**

The greater occurrence of the corrosion phenomenon in the solvent phase indicates that the solvent phase in the process may be important. Inhibitors may show different properties in a vacuum or in another solvent [1, 27, 41, 42]. In the study, the solvent effect on the molecular structure of the solute was calculated by the polarized continuity model (PCM) model [50]. In the PCM model, the solvent is treated as a continuous dielectric medium, and the solute is considered a molecule trapped in a cavity surrounded by the solvent. In the Gaussian 09 program, CPCM, a special version of PCM based on integral equation formalism, was used together with HF/6– 31 ++ G (d, p) to examine the solver effect.). When the results are examined, a small increase is shown for the values of EHOMO, ELUMO, ΔE, T.E., Pi, MV, i and g, while a rather small decrease is shown for values of v and ΔN. For the molecular in this study, it was determined that the quantum chemical parameters calculated in the presence of a solvent (water) and in the gas phase did not differ significantly (**Table 5**).

#### **3.4 Molecular dynamic simulations**

Monte Carlo simulations can be used to predict interactions between inhibitor molecules and metal surface. In the study, the most stable low energy adsorption configurations of AMTT, SAMTT, DBAMTT on the Fe (110) surface were induced by Monte Carlo simulation and the configurations are shown in **Figure 3**. Outputs and descriptors, including total adsorption, solid adsorption and deformation energies are given in **Table 9**. Adsorption energy is attributed to the energy released during relaxed adsorbate components adsorbed on the substrate. Adsorption energy is the addition of solid adsorption and deformation energies of the adsorbate component. Higher values of negative adsorption energy indicate the presence of a more stable and stronger interaction between a metal and an inhibitor molecule. Monte Carlo simulation and DFT calculation results showed

*Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods… DOI: http://dx.doi.org/10.5772/intechopen.98968*

#### **Figure 3.**

*Top and side views of the most stable low energy configurations for the adsorption of three inhibitors on Fe (110) interface obtained using Monte Carlo simulations.*


#### **Table 9.**

*Experimental inhibition efficiencies, IE (%) and the outputs and descriptors calculated by the Mont Carlo simulation for adsorption AMTT, SAMTT, DBAMTT of on Fe (110) (in kcal Mol<sup>1</sup> ).*

us once again that the corrosion inhibition efficiency was in the form of DBAMTT, SAMTT and AMTT, respectively, and it was seen to confirm the experimental results [28].

#### **4. Conclusions**

DBAMTT, SAMTT, and AMTT molecules used in this theoretical study were synthesized by M. Saravana Kumar et al. In order to predict the corrosion inhibition activities of Schiff bases and derivatives against the corrosion of iron metal, density functional theory with different basic sets and molecular dynamics simulation approach were used in Hartree Fock (HF), B3LYP. Quantum chemical calculations of the non-protonated and protonated structures of the molecules examined in this study were made in both gas phase and aqueous solution. At the end of the study, the following results are given in summary.


order against iron corrosion for the studied Schiff bases and derivatives can be presented as: DBAMTT> SAMTT> AMTT.


### **Acknowledgements**

This research was made possible by TUBITAK ULAKBIM, High Performance and Grid Computing Center (TR-Grid e-Infrastructure).

#### **Authors Contribution**

Şaban Erdoğan performed the calculations. Şaban Erdoğan and Burak Tüzün discussed and analyzed the results. All authors equally contributed to preparation of the manuscript. All the authors have read and approved the final manuscript.

#### **Funding information**

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

#### **Compliance with ethical standards**

Conflict of interest the authors declare that they have no conflict of interest.

#### **Avaibility of data and materials**

The datasets generated during the current study are available from the corresponding author on reasonable request.

*Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods… DOI: http://dx.doi.org/10.5772/intechopen.98968*

#### **Author details**

Şaban Erdoğan<sup>1</sup> \* and Burak Tüzün<sup>2</sup>

1 Department of Nutrition and Dietetics, Faculty of Health Sciences, Yalova University, Yalova, Turkey

2 Department of Chemistry, Faculty of Science, Cumhuriyet University, Sivas, Turkey

\*Address all correspondence to: saban.erdogan@yalova.edu.tr

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **References**

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*Applications of the Effectiveness of Corrosion Inhibitors with Computational Methods… DOI: http://dx.doi.org/10.5772/intechopen.98968*

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#### **Chapter 5**

## Corrosion and Natural Corrosion Inhibitors: A Case Study for *C. microphyllus*

*Dwarika Prasad*

#### **Abstract**

Worldwide, corrosion causes the value of the gross domestic product to decrease in industrialized countries by 4.26% and causes significant losses to industries including infrastructure. As a result, corrosion prevention and research related to it are extremely important. Some researchers are working to develop plant-based natural corrosion inhibitors, and experimental and computational studies are being conducted widely to prevent corrosion through cheap and environmental friendly coatings. A case study of *Convolvulus microphyllus* (*C. microphyllus*) extract was examined as eco-friendly for bio-corrosion inhibitor of mild steel in 0.5 M H2SO4 by using conventional weight loss, electrochemical polarization measurements, and electrochemical impedance spectroscopy (EIS) techniques. The compounds responsible for decreasing the rate of corrosion are kaempferol and phydroxycinnamic acid present in the extract. This inhibitor slows down the corrosion rate. Out of many observations, the best result 89.87% corrosion resistance efficiency was obtained at 600 mg/L of *C. microphyllus as* extract for mild steel in 0.5 M H2SO4 by applying electrochemical and weight loss measurements. The presence of a heteroatom in the main component of *C. microphyllus as* extract is believed to be an excellent inhibitor. Theoretical research revealed an entirely important report about comparative inhibition effect of different phytochemicals.

**Keywords:** adsorption, spontaneous reaction, natural inhibitors, electrochemical study, computational study

#### **1. Introduction**

The process of deposition of oxide layer on the surface of metals is called corrosion. It usually occurs when metal is exposed to moisture or water and gases such as dioxygen, dihydrogen, dichloride, hydrogen sulfide. It is a spontaneous chemical reaction with a slow rate. It usually occurs over days or weeks, and as a result of corrosion, the refined metal is turned into a more stable form such as oxide, hydroxide, or sulfide. The net worth of the corrosion prevention industry was estimated to be around \$2.5 trillion (USD) in 2018 and is expected to cross \$3.0 trillion (USD) by 2022, as per the National Association of Corrosion Engineers [1, 2]. The electrochemical phenomenon of degradation of material over course of time due to exposure toward the environment is called corrosion. Common types of corrosion for rusting of steel and internal polymeric pipeline are wet corrosion and dry corrosion [3]. In today's world, corrosion is no longer merely a chemical degradation of metals, but also of semiconductive materials, insulating materials, and polymeric materials after exposure to the environment. It is a surface phenomenon, where at the material surface formed oxide or hydroxide or sulfide layer [4].

Mild steel is a low-priced material with properties that are suitable for most general engineering applications. That's why it is high in demand, but it contains very poor corrosion resistance. Corrosion produces very harmful effects on commercial industries such as paper mills, oil, and gas construction, and electronics used in a multitude of processes. When materials and structures are attacked by corrosion, they lose many of their useful properties. Some useful tools and machinery made from metal can become useless because of corrosion, many disaster situations such as chemical plant leaks, bridges can collapse and oil or gas pipelines can break and can produce a dangerous effect on the life of human beings. They also produce economical losses. Acid pickling is used for removing the impurities, scale, and sludge deposits on the metal surface. Acid pickling contains strong acid due to this, that process may cause a great economic loss. In the presence of inhibitors, the rate of acidic attack decreases on the metallic surface and it prevents metallic corrosion [5]. Decades of years many organic inhibitors, for example, phosphate esters, quaternary ammonium salts, amidoethyl imidazolines, as well as an inorganic inhibitor, for example, sulfate of Mg, Mn, Ni, and Zn are being used. Corrosion of steel has been inhibited by them. These types of inhibitors are generally costly and toxic and they might be harmful to the living organisms that is why the study of eco-friendly and non-toxic green inhibitors is important to prevent steel from corrosion nowadays. Natural corrosion inhibitors are biodegradable, non-toxic eco-friendly, and low cost. Phytochemical substances obtained from plants that reduce corrosion reaction rates are termed inhibitors. The plant extract is organic in its nature, and it contains secondary-metabolized compounds such as alkaloids, amino acids, pigment, and flavonoids etc behave like inhibitors.

These types of natural products contain N, O, S, and multiple bonds so that their lone pair electrons or pi-electrons are adsorbed on the metal surface and form a protective layer to prevent metal from corrosion.

The experimental outcomes come from weight-loss study and electrochemical impedance spectroscopy studies and to support a better understanding of the adsorption of phytochemicals, computational studies were needed to operate. The quantum chemical calculations have been performed as a part of computational studies. It is well known that plant extract contains more than one phytochemical constituent. In this computational evaluation, we chose the phytochemicals present in the plant extract. The selected molecules or phytochemicals have been operated using density functional theory (DFT) using Gaussian 09 program. To decide the intensity and interaction properties of phytochemicals molecules on the metal surface Fe (110), Monte Carlo (MC), and molecular dynamics (MD) have been carried out.

#### **2. Corrosion**

Corrosion is a surface process where the oxide layer is formed on the surface of the metal. There is various types of corrosion such as oxidation corrosion, corrosion by other gases such as Cl2, SO2, H2S, NOx, liquid metal corrosion, differential metal corrosion, differential aeration corrosion, crevice corrosion, and pitting corrosion. If we discuss pitting corrosion as an example, it is due to the formation of small holes or pits on the metal surface. Pitting corrosion is highly destructive as pits are very small to be observed and usually covered with corrosion products. The pitting corrosion is the result of depassivation of a small area on the metal surface, which acts as an anode, while the rest of the undefined and large surface acts as a cathode. It is preceded by a spontaneous galvanic reaction with very limited diffusion of ions (**Figure 1**) [6].

*Corrosion and Natural Corrosion Inhibitors: A Case Study for* C. microphyllus *DOI: http://dx.doi.org/10.5772/intechopen.100505*

**Figure 1.** *Corrosion in water pipeline.*

#### **2.1 Electrochemical aspects of corrosion**

Most of the metals that we humans commonly use are unstable in the atmosphere as they were obtained from respective ores by artificial reduction through a chemical process. Thus, such metals undergo a reaction very easily to get converted into a stable form. The chemical reactions that do not require any external medium or reagent like energy or catalyst to proceed but occur on their own are called as spontaneous reactions. For spontaneous reactions, the formed products are more stable than reactants. The value for change in Gibb's free energy is always negative, and change in enthalpy is also negative, while the change in entropy is positive for such reactions.

The reactions in which oxidation and reduction both occur simultaneously are called as redox reactions. Corrosion also involves a redox reaction in which one specie or metal or part of the metal is oxidized and it acts as an anode, while the other specie or metal or part of the metal is reduced and acts as a cathode. At anode loss of electrons takes place and loss of mass occurs, while at cathode gain of electron takes place and deposition of corrosion products occurs.

The most primitive corrosion is where anodic oxidation reactions involve a pure iron when it is exposed to a strong acid such as hydrochloric acid. The reaction occurs with the formation of bubble violently. It is given as follows:

$$\text{Fe} + 2\text{H}^+ + \text{Cl}\_2^- \rightarrow \text{Fe}^{\*2} + \text{Cl}^{2-} + \text{H}\_2\uparrow\tag{1}$$

$$\text{Fe} + 2\text{HCl} \rightarrow \text{FeCl}\_2 + \text{H}\_2\uparrow\tag{2}$$

Another example is the exposure of iron toward moisture or water (**Figure 2**).

**Figure 2.** *Anode and cathode formation.*

$$Fe \rightarrow Fe\_2 + +2e^- \tag{3}$$

$$\text{O}\_2 + \text{H}\_2\text{O} + 4\text{e}^- \rightarrow 4\text{OH}^- \tag{4}$$

$$\text{Fe}^{2+} + 2\text{OH}^- \rightarrow \text{Fe}(\text{OH})\_2 \tag{5}$$

$$\text{Fe}^{3+} + \text{3OH}^{-} \rightarrow \text{Fe}(\text{OH})\_{3} \tag{6}$$

Some other reactions involve in the formation of anode and cathode that leads to corrosion are given below.

Examples of anode reactions:

$$\text{Zn} \left( \text{s} \right) \rightarrow \text{Zn}^{\ast 2} \left( \text{aq} \right) + \text{2e} \tag{7}$$

$$Al\,(\text{s}) \to Al^{\ast 3}\,(aq) + \text{3e} \tag{8}$$

$$Fe^{\ast 2} \text{ (s)} \rightarrow Fe^{\ast 3} \text{ (aq)} + \text{e} \tag{9}$$

An examples of cathode reaction:

$$\text{H}^+\left(aq\right) + \text{e} \to \text{1}/2\text{H}\_2\left(\text{g}\right) \tag{10}$$

Corrosion reactions are often electrochemical in nature. The reaction is timeconsuming and may take few weeks to months to occur, it is a time and temperature-dependent reaction.

If corrosion reactions occur in aqueous media, then they are similar to that of Leclanche cell. As shown in **Figure 3**, a zinc container act as an anode, it gets oxidized. Graphite rod coated with carbon and MnO2 paste acts as a cathode, it gets reduced, whereas both anode and cathode are joined by means of NH4Cl and ZnCl2 paste that serves the role of electrolyte. The greater the flow of electrons, the greater is the corrosion of the zinc electrode [7, 8].

*Corrosion and Natural Corrosion Inhibitors: A Case Study for* C. microphyllus *DOI: http://dx.doi.org/10.5772/intechopen.100505*

#### **2.2 Local cell formations**

#### *2.2.1 Dissimilar electrode cells*

When two dissimilar metals come in direct contact with each other and an electrolytic substance is present between them, then dissimilar electrode cells are formed. It is basically a Galvanic cell, for example, we have a Daniel cell in which zinc and copper are in contact. In daily life, a copper pipe connected to a steel pipe provides an example of this type of corrosion cell. This cell is also referred to as galvanic coupling cell, the less noble metal becomes the anode whereas others act as a cathode (**Figure 4**).

**75**

*Daniel cell.*

**Figure 6.** *Differential aeration cell.*

#### *2.2.2 Concentration cells*

When two similar electrodes dipped in solutions of different compositions come in contact, then concentration cells are formed. The electrode dipped in dilute solution acts as an anode, while the electrode that is in contact with concentrated solution acts as a cathode (**Figure 5**).

#### *2.2.3 Differential aeration cells*

When two similar electrodes exposed to different aeration conditions come in contact with one another, then differential aeration cells are formed. The electrode exposed to lesser aeration conditions will act as an anode, while the electrode exposed to higher aeration conditions will act as a cathode. This type of corrosion is very common and is responsible for the significant economic loss (**Figure 6**) [9, 10].

#### **3. Natural corrosion inhibitors**

Natural corrosion inhibitors reduced or controlled the rate of corrosion by the addition of a natural product in cleaning or pickling solution. It reduces the rate of corrosion either by inhibiting oxidation at the anode or inhibiting reduction at the

*Corrosion and Natural Corrosion Inhibitors: A Case Study for* C. microphyllus *DOI: http://dx.doi.org/10.5772/intechopen.100505*

cathode, or both. It forms a protective layer at the metal surface, either by physical (means electrostatic attraction between natural product and metal surface) adsorption or chemisorption (means coordination bonds between natural product and metal surface).

Studies of natural corrosion inhibitors are one of the methods for protecting metal from corrosion. So here I am discussing a specific plant *C. microphyllus* as a natural corrosion inhibitor.

#### **3.1 Experimental studies**

#### *3.1.1 Preparation of materials*

The *C. microphyllus* is a hairy herb from the *Convolvuaceae* family, which is also known as Shankhpushpi and wind weed. The leaves are linear to oblong, small, and subsessile. About 1–3 flowers are produced, which are stalked. It is easily available all over the world. *C. microphyllus* contains alkaloids kaempferol, and p-hydroxycinnamic acid as its main phytochemical constituent [11, 12]. **Figure 7** shows the image of *C. microphyllus* aerial parts and its main phytochemicals.

The soxhlet apparatus is used for plant extraction. Fresh *C. microphyllus* aerial parts were collected from our surrounding and then put them in a shaded area for few days, and after drying them properly, they were grinded to convert into powder material. Now, the powder was packed in a soxhlet apparatus and refluxed for 72 hours; then, the diluted extract was collected in the round bottom flask and transformed into a gel like extract by distillation. In the next step, the gel extract is kept in the desiccators packed with silica for few days so that the extract converts

**Figure 8.** *Soxhlet apparatus.*

#### **Figure 9.** *Desiccators.*

into solid extract without moisture. After that, it is preserved in other desiccators for experimental studies.

In this work, for weight loss measurement and electrochemical impedance studies a piece of 1 cm2 dimension is taken as a sample. These samples were mechanically polished with emery paper of different grades and subsequently cleaned with acetone, once again clean distilled water before inserting them into the pickling or cleaning solution. Here for study of *C. microphyllus* diluted solution of conc. H2SO4 having a molarity of 0.5 is used as a corrosive medium (**Figures 8** and **9**).

#### *3.1.2 Weight loss studies*

The best method for this measurement is the ASTM standard G 31–72 [13]. In this method, all measurements are carried out at room temperature in the thermostat.


*Corrosion and Natural Corrosion Inhibitors: A Case Study for* C. microphyllus *DOI: http://dx.doi.org/10.5772/intechopen.100505*

#### **Table 1.**

*Corrosion rate and efficiency of mild steel in 0.5 M H2SO4 absence and presence of C. microphyllus for 24 hours at room temperature.*

Here minimum three times repeating the same measurement for the average value. The weight loss values, surface coverage (θ), inhibition efficiency (η%), and corrosion rate (CR) are shown in **Table 1** at different concentrations of *C. microphyllus* extract for mild steel. At different concentrations of *C. microphyllus* extract, the value of weight loss, surface coverage (θ), inhibition efficiency (η%), and corrosion rate (CR) for mild steel were calculated by equations that are as follows:

$$\mathbf{C}\_{\aleph} = \frac{\mathbf{K} \times \mathbf{W}}{A \times t \times \rho} \tag{11}$$

$$IE(\%) = \frac{C\_{R-}^{0}C\_{R}^{\prime}}{C\_{R}^{0}} \times 100\,\tag{12}$$

$$\boldsymbol{\theta} = \frac{\mathbf{C}\_{\text{R}-}^{0} \mathbf{C}\_{\text{R}}^{i}}{\mathbf{C}\_{\text{R}}^{0}} \tag{13}$$

where,


From the above data, it is clear that the concentration of *C. microphyllus* extract is inversely proportional to the rate of corrosion, which is used as an inhibitor.

Adsorption of active phytochemicals of *C. microphyllus* extract occurs on the surface of mild steel, which reduces the surface area available for corrosion that is why the rate of corrosion decreases. The highest inhibition efficiency 88.08% is obtained at 600 mg/L.

#### *3.1.3 Electrochemical measurements*

An electrochemical workstation is used for the electrochemical measurement. The workstation is made up of three electrodes: (a) the working electrode of metal which works like anode (b) saturated calomal electrode as the reference electrode work like cathode, and (c) platinum electrode as the counter electrode for collect current. In this measurement, metal or alloy was immersed in cleaning or pickling solutions and different concentrations of *C. microphyllus* aerial part extract were added immersed for a specific time. At room temperature, the values of the open circuit potential (OCP) were noted with respect to the reference electrode. The scanning frequency from 100 kHz to 0.01 Hz is used for recording the Nyquist plot. A 5 mV signal amplitude perturbation at OCP was considered in EIS measurement. The authentic values were taken after three-time repeat measurement.

In **Figure 10** shown Nyquist plot explained that 600 mg/L *C. microphyllus* extract provided larger radius semicircles. The diameter of the capacitive loop was enlarged by increasing *C. microphyllus* extract concentration, highest at 600 mg/L explaining also the highest inhibition effect. The radiuses of the semicircles in the case of using the *C. microphyllus* extract were larger than the blank. Because of same shapes of semicircles, it means the mechanism is not change. Calculated EIS results from the following equation provided the percentage inhibition efficiency of bioinhibitor in the electrolytes [14]:

$$IE\left(\%\right) = \frac{R\_{\rm cr} - R\_{\rm cr}^{0}}{R\_{\rm cr}} \times 100\tag{14}$$

**Figure 10.** *Nyquist plot of mild steel in 0.5 M H2SO4 solution in the absence and presence of C. microphyllus extract.*

*Corrosion and Natural Corrosion Inhibitors: A Case Study for* C. microphyllus *DOI: http://dx.doi.org/10.5772/intechopen.100505*


**Table 2.**

*EIS parameters of mild steel in 0.5 M H2SO4 without and at different concentrations of C. microphyllus at 298 K.*


#### **Table 3.**

*The HOMO and LUMO energies (eV), ELUMO-EHOMO energy gap (*Δ*EL-H), electron affinity (A), ionization potential (I), electronegativity (χ), hardness (η), and a fraction of electrons transferred (∆N) for extract compounds.*

where, *R*ct and <sup>0</sup> *Rct* represent the charge transfer resistance in inhibitor and blank, respectively [15].

From **Table 2**, it is clear that maximum inhibition efficiency of 89.87% was obtained at 600 mg/L of *C. microphyllus* extract, where the highest Rct value was 155.13 [15]. In **Table 3**, value of the double-layer capacitor (Cdl) gradually decreasing means protective layer gradually form at the metal surface [16].

#### **3.2 Computational studies**

#### *3.2.1 DFT optimization*

For the evaluation of electronic features of *C. microphyllus* extract molecules (including hydroxylcinnamic acid and kaempferol shown in **Figure 11**), the structures were initially optimized by density functional theory (DFT) using Gaussian 09 program. Optimization was done *via* widely used functional of B3LYP, which was combined with 6-311G\*\* basis function. By a combination of SCRF theory and PCM formula, these calculations were continued in the liquid phase. After optimization, the following properties were analyzed: graphics, energies, and gap of molecular orbitals of highest occupied and lowest unoccupied (HOMO, LUMO, EHOMO, ELUMO, and ELUMO-EHOMO = ΔEL-H) and partial charges [17].

Electronic level calculations (i.e., DFT) were performed so as to obtain insights into the reactive sites of hydroxylcinnamic acid and kaempferol molecules. The optimized hydroxylcinnamic acid and kaempferol geometries resulted from chemical DFT calculations are plotted in **Figure 11**. For these energy-minimized geometries, the analysis of frontier orbitals was done as these orbitals play a crucial role in

**Figure 11.**

*The B3LYP/6-311G\*\* optimized geometry, HOMO, and LUMO of kaempferol and hydroxycinnamic acid compounds.*

donor-acceptor interactions of inhibiting extract molecules. The HOMO and LUMO pictures of hydroxylcinnamic acid and kaempferol are provided in **Figure 11**. As displayed, the phenyl ring, carbonyl/hydroxyl O atoms, and ethylene bond of hydroxylcinnamic acid appeared in the role of HOMO implying their strong electron supplying affinity toward a potential electron acceptor, for instance metal atoms containing unoccupied orbitals. According to the LUMO plot, all carbon and oxygen atoms of hydroxylcinnamic acid contributed to LUMO distribution, which is a signification of their tendency for getting electrons provided by filled orbitals of metal atoms. In the case of the kaempferol compound, it is seen that the HOMO placed over the entire aromatic heterocyclic skeleton and on the other hand the carbon as well as oxygen atoms behaved as reactive LUMO locations. As a consequence, the kaempferol component is able to involve in electronic interactions (i.e., donor-acceptor) with the metal surface through the donation of electrons (lone pair in hydroxyl/carbonyl O and π electrons of heterocycles) and receiving of electrons from filled iron orbitals by its C and O atoms. The eigenvalues of HOMO/LUMO and the energetic gap of frontier orbitals were examined, and the quantitative results are tabulated in **Table 3** for hydroxylcinnamic acid and kaempferol. From this table, it is evident that the kaempferol species have higher EHOMO and lower ELUMO in comparison with the other compound (i.e., hydroxylcinnamic acid). These results suggest the stronger electron donation and receiving capacity of kaempferol. In addition, the optimized kaempferol molecule owned a lower energetic gap (ΔEL-H), an observation reflecting better electron sharing and subsequent stronger corrosion inhibition manner of this compound of *C. microphyllus* extract. This trend of DFT calculated electronic parameters and simulated adsorption energies discloses the stronger kaempferol interactions and adsorption on the steel surface leading to its more effective corrosion prevention influence as compared with the inhibiting molecule of hydroxylcinnamic acid [18, 19].

*Corrosion and Natural Corrosion Inhibitors: A Case Study for* C. microphyllus *DOI: http://dx.doi.org/10.5772/intechopen.100505*

**Figure 12.** *The simulated Fukui indices of kaempferol and hydroxycinnamic acid compounds.*

The electrophilic/nucleophilic interactions of studied molecules are summarized in **Figure 12**. From the given pictures, it is obvious that the electrophilic nature of hydroxylcinnamic acid is graphically distributed on benzene ring and double bond of carbon atoms (with a rich source of π electrons) and heteroatom of O (owing lone pair electrons). These electrons could be donated to an appropriate acceptor of electrons like metal atoms that are composed of empty orbitals. Moreover, similar to LUMO distribution, almost all carbon atoms along with three O heteroatoms are the most reactive sites for nucleophilic behavior clarifying electron getting affinity of these atomic sites. Also, the electrophilic interactions of equilibrated kaempferol compound could likely happen *via* its electron-rich places including heterocycles and the oxygen atoms of surrounding oxygenated fragments. On the other side, the O and C atoms of the whole backbone could accept electrons when attacked by a nucleophile [20, 21].

#### *3.2.2 Molecular simulations*

The hydroxylcinnamic acid and kaempferol adsorption and their interactions with the substrate (i.e., steel) were examined applying molecular simulations. These atomic simulations include Monte Carlo (MC) and molecular dynamics (MD). For the representation of steel substrate in these simulations, the frequently applied iron surface Fe (110) was used. The thickness, vacuum region, and periodic replication of this surface were set as 1.5 nm, 4 nm, and (14 × 14), respectively. To examine the adsorption preference of extract components, which are output from DFT calculations, on the iron substrate the MC-based simulation was carried out by adsorption Locator module (Materials Studio software). The MC simulations convergency was controlled with a level of fine. The last cell with the lowest potential energy generated by MC was the starting simulation box of the next modeling, that is, MD. For performing this simulation in solution phase-like experiments, water molecules were also added to the MC-generated cell. Thereafter, an optimization of 20,000 steps and NVT MD simulation of 1 ns were successively performed *via* COMPASS force field and Forcite module. The time step and temperature of NVT were set as 1 fs and 298 K. The electrostatic interactions of hydroxyl cinnamic acid and kaempferol were modeled by the Ewald scheme along with their charges calculated by DFT. The interactions of van der Waals form were evaluated by the atom-based cutoff. All metal atoms of the substrate were kept fixed [22, 23].

#### *3.2.3 Molecular simulation*

Simulations at molecular scale namely MC and MD were conducted for the analysis of the ability of *C. microphyllus* extract molecules adsorption above the metal surface (Fe (110)). The equilibrated cells of hydroxyl cinnamic acid and kaempferol generated by MC-based molecular simulations are displayed in **Figure 13**. The depicted MC snapshots clearly demonstrate that the *C. microphyllus* extract species have the ability of approaching and adsorption to iron surfaces. It is observed from the presented top views that hydroxylcinnamic acid and kaempferol adsorption on the surface happened through preferred flat orientation. The aromatic backbones of these adsorbed *C. microphyllus* extract molecules aligned parallel relative to the outmost iron atoms. The adsorption of hydroxylcinnamic acid and kaempferol took place with energies of −96.65 and − 165.51 kcal/mol, respectively. The adsorption energies of hydroxyl cinnamic acid and kaempferol with negative values further declare their adsorption over the steel substrate. The molecular adsorption was more evaluated through conducting liquid-phase dynamics (MD) simulations. The resulting snapshots of such simulations for hydroxyl cinnamic acid and kaempferol compounds are depicted in **Figure 13**. The obtained side views of ultimate simulation snapshots indicate that the chosen *C. microphyllus* extract compounds equilibrated in the vicinity of the crystalline surface (i.e., Fe (110)) under the wet conditions of the interface. This observation points to the fact that hydroxyl cinnamic acid and kaempferol as organic constituents of the green extract could bind to the surface of iron even in the presence of water molecules. Such surface adsorption affinity

#### **Figure 13.**

*The final snapshots of kaempferol and hydroxycinnamic acid compounds over Fe (110) surface obtained from MC and MD simulations.*

*Corrosion and Natural Corrosion Inhibitors: A Case Study for* C. microphyllus *DOI: http://dx.doi.org/10.5772/intechopen.100505*

was quantified by corresponding adsorption energy values. The energies related to hydroxyl cinnamic acid and kaempferol adsorption were estimated as −137.53 and −208.02 kcal/mol, respectively. The negative MD-calculated adsorption energies further reflect the adsorption propensity of extract components on the metallic adsorbent. In summary, the MC and MD snapshots together with predicted adsorption energies propose that the *C. microphyllus* extract compounds of hydroxyl cinnamic acid and kaempferol are capable of adsorbing on the steel substrate. The surface adsorption enables the organic extract molecules to form corrosion-preventing films over the surface, which is in support of experimental results [24, 25].

#### **4. Conclusion**

This chapter covers the corrosion problem and due to corrosion worldwide loss. This chapter discusses the importance of mild steel and discusses corrosion as a spontaneous electrochemical process. This chapter also explains of formation of different type of cells, due to different types of conditions, then start electrochemical corrosion process at the anode. In this chapter, I have discussed new developments as an example of natural corrosion inhibitor *C. microphyllus*, here I have discussed preparing inhibitors and explain experimental methods such as weight loss and electrochemical study for calculating their corrosion inhibition efficiency. After that, I have discussed computational studies of their main phytochemicals with help of DFT, molecular simulations, and molecular simulation to understand their relative adsorption properties.

#### **Conflict of interest**

The authors declare no conflict of interest.

#### **Author details**

Dwarika Prasad Department of Chemistry, Shri Guru Ram Rai University, Dehradun, Uttarakhand, India

\*Address all correspondence to: dwarika.maithani@gmail.com

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Section 3
