**4. Appendices**

524 Mass Transfer - Advanced Aspects

Fig. 8. Images taken with scanning electronic microscope, showing the electrode surface after the tests made in static conditions in the absence of oxygen (a) 25°C and (b) 60°C

The morphology of the film formed at 25°C is characteristic of a uniform corrosion process, noting in the first period of exposure an important amount of particles adhered to the electrode surface. The film formed at 60°C (Figure 8(b)) shows a rather compact morphology,

This difference can be seen in the response of the system, Tables 1 and 4. Despite the morphological differences in the diffusive barriers, the film shows good protective capacity. (Muñoz-Portero et al., 2006) indicate that the morphology of the corrosion products depend on the Br- concentration in the solution. According to their results, the diffusive barrier developed in the conditions of this project should show an amorphous and gelatinous

The records of current and potential noise, show other system characteristics. At 25°C, during the first period, a greater presence of an oxidizing agent in the interface causes an increase in copper dissolution which accelerates the production of CuBr. This substance accumulates on the electrode surface promoting the formation of a protective coating that inhibits the activity at the interface, due to its permeable nature, a pitting corrosion process

Under flow conditions at 45°C, as the solution velocity increases, the mass transport by diffusion contributes less to the dissolution process, Table 1. At higher velocities, the Ecorr develops at nobler conditions due to increased oxygen presence in the interface. The system behavior under these conditions clearly reflects the importance of oxygen and the diffusion

Given the conditions that occur at higher levels of velocity, greater involvement of an activation process of the cathodic fraction would be expected. A Tafelian behavior does not occur in these conditions. On the other hand, the behavior at higher levels is very similar

According to the records of the noise signal in current and potential (Figure 6), at 680 and 884 rpm the potential noise signal reaches the stationary state almost from the start of the test, showing no trend in both levels. Despite the difference in potential, ≈ 12 mV, the current noise signal at both levels is practically the same. This suggests that under these conditions the system is in a passive state. As mentioned above, the increase in the electrode

(a) (b)

morphology associated with a mixture of CuBr y CuBr2·3Cu(OH)2.

phenomenon of this element in the dissolution process of the alloy.

giving the impression of having reached the same level at the stationary state.

very different from the response of the system at 25°C.

takes place (Figure 5).

## **4.1 Appendix A**

Calculation of Gibbs free energy

Calculation of heat capacity <sup>o</sup> Cp (Heng & Johnston, 1952; Dean, 1989) in function of absolute temperature for pure substances CuBr.

$$\mathbf{C}\_{\mathrm{p}}^{\diamond} = 49.898 + 0.0169 \text{ T - 1.769} \times 10^{-6} \text{ T}^{-2} \tag{A1}$$

The method for determination the heat capacity <sup>o</sup> Cp of ionic species, - Br is that proposed by (Criss & Cobble, 1964; Taylor, 1978) for T< 200ºC, values of absolute entropy and the value of the parameters: a = -0.37 and b = 0.0055 (Roberge, 2000).

$$\mathbf{C}\_{\rm p}^{\rm o} = \left[ \left( \mathbf{4.186 \, a \, + \, b \, S\_{\rm (298 K)}^{\rm o}} \right) \left( \mathbf{T\_2 \, - 298.16} \right) \right] \Big/ \ln \left( \mathbf{T\_2 / 298.16} \right) \tag{A2}$$

Calculation of Gibbs free energy in the temperature range

$$\mathbf{G}^{0}\_{\mathrm{(T)}} = \mathbf{G}^{0}\_{\mathrm{(298 K)}} + \left(\mathbf{C}^{0}\_{\mathrm{p}} - \mathbf{S}^{0}\_{\mathrm{(298 K)}}\right) \left(\mathrm{T}\_{2} - \mathrm{298.16}\right) - \mathbf{C}^{0}\_{\mathrm{p}} \,\mathrm{T}\_{2} \ln\left(\frac{\mathrm{T}\_{2}}{\mathrm{298.16}}\right) \tag{A3}$$

Calculation of equilibrium potential <sup>o</sup> E for the reaction of copper dissolution

$$\text{Cu} + \text{Br}^{\cdot} \Leftrightarrow \text{CuBr} + 1 \text{ e}^{\cdot} \tag{A4}$$

$$\mathbf{E}\_{\text{(T)}}^{\text{o}} = \frac{\cdot \Delta \mathbf{G}^{\text{o}}}{\mathbf{n} \, \text{F}} \; ; \left( \mathbf{V}\_{\text{(SHE)}} \right) \tag{A5}$$

Calculation of the potential of equation A4

$$\mathbf{E}\_{\rm (T)} = \mathbf{E}\_{\rm (T)}^{o} + 0.0591 \log \left( \frac{1}{\mathbf{B} \mathbf{r}^{\cdot}} \right) \tag{A6}$$

Where Br is the activity of bromide ion

#### **4.2 Appendix B**

Physicochemical properties of the LiBr-H2O pair (Torres Merino, 1997) Calculation of the LiBr solution density based on the density of water, d `Alefeld equation

$$\rho\_{\left(X\_{\rm sol}, T\_{\rm sol}\right)} = \frac{\rho\_{H\_2O(T\_{\rm sol})}}{2} \left[ \exp\left(0.012X\_{\rm sol}\right) + \exp\left(\left(0.842 + 1.6414 \times 10^{-3} \text{ T}\_{\rm sol}\right) \left(\frac{X\_{\rm sol}}{100}\right)^2\right) \right] \tag{B1}$$

Where:

Mass Transfer in the Electro-Dissolution of

in ºC is given by the following equation

Where:

a = - 0.005 and b\* = 0.0085

**6. Acknowledgment** 

**7. References** 

translation of this document.

**5. Conclusions** 

90% Copper-10% Nickel Alloy in a Solution of Lithium Bromide 527

The calculation of the Kusik-Meissner parameter (Kusik & Meissner, 1978) for temperature t

Both the 90% Cu-10% Ni alloy and copper are dissolved, in the Tafel region, by a mechanism consisting of two steps that occur simultaneously. However, the kinetics of copper dissolution results in significant changes in the dissolution process of the alloy. Corrosion potential in more active regions and smaller corrosion rates due to the presence of

Due to the fact that the 90% Cu-10% Ni-X% LiBr system always polarized in comparison to the nickel equilibrium potential, and only sometimes compared to the copper equilibrium potential, the anodic reaction can not be considered reversible, and according to the

According to the proposed equivalent circuit, the dissolution process of the alloy is in fact under a mixed kinetic control, by activation and diffusion. However, the mass transport resistance under all experimental conditions is higher than that observed for charge transfer. On the other hand, as both elements are part of a series, the one representing the mass transport process is the one that shows a greater resistance to current flow. Thus, the

For the dissolution process to be maintained, the reacting species must match at the interface in an electrochemical process. In this sense the complex ion is generated at the interface of the film (equation 13) and spreads to the bulk of the solution. Therefore, oxygen is responsible for the diffusion phenomenon, and does not always follow the Levich relationship.

The authors acknowledge Consejo Nacional de Ciencia y Tecnología (CONACyT) for financial assistance for the realization of this work. Berenice Adame for her assistance in the

Bard A. J. & Faulkner L. R. (1980). *Electrochemical Methods Fundamentals and Applications*,

Barsoukov E. & Macdonald J. Ross. (2005). *Impedance Spectroscopy Theory, Experiment, and* 

Bockris J. O`M, Reddy A. K. N. & Gamboa-Aldeco M. (2000). *Modern Electrochemistry* 

0-471-64749-7, Hoboken, New Jersey. Published simultaneously in Canada. Beccaria A. M. & Crousier J. (1989). Dealloying of Cu-Ni alloys in natural sea water. *Br.* 

ISBN 0-471-04372-9 John Wiley & Sons, Inc., Published in the United States of

*Applicatons*, second edition. Wiley-Interscience. A John Wiley & Sons, Inc., Publication.

*Fundamentals of Electrodics*, *Vol. 2A (second edition),* Kluwer Academic/Plenum

diffusion phenomenon must be the process that controls the dissolution of the alloy.

nickel in the alloy, generate significant differences between these metals.

dissolution mechanism, is under activation control.

America simultaneously in Canada

*Corros. J*., Vol. 24, No. 1, (march 1988), pp. 49-52

( ( ) )( ) <sup>t</sup> <sup>25</sup> ( ) <sup>25</sup> q a q b t - 25 q <sup>∗</sup> =+ + (C8)

( ) <sup>2</sup> ρ *H O* Tsol , water density at the solution temperature, kg m-3; ( ) sol *Xsol* , T ρ , solution density, kg m-3; Xsol, (mass% LiBr)

Domain range: 40% ≤ Xsol ≤ 75%; 0ºC ≤ Tsol ≤ 190 ºC Calculation of dynamic viscosity µ d'Alefeld equation

$$\mu = \exp\left[\mathbf{A}\_1 + \frac{\mathbf{A}\_2}{\mathbf{T}\_{\text{sol}}} + \mathbf{A}\_3 \cdot \ln \mathbf{T}\_{\text{sol}}\right] \tag{B2}$$

Where:

A1 = - 494.122 + 16.3967 Xsol – 0.14511 (Xsol)2; A2 = 28606.4 – 934.568 Xsol + 8.52755 (Xsol)2; A3 = 70.3848 – 2.35014 Xsol + 0.0207809 (Xsol)2; µ = dynamic viscosity, cp; Tsol = Temperature solution, K; Xsol = mass %, LiBr

Domain: 45% ≤ Xsol ≤ 65% ; 30ºC ≤ Tsol ≤ 210ºC

#### **4.3 Appendix C**

Calculation of the activity of LiBr-H2O solution.

The model for calculating the activity of strong electrolytes in aqueous solution is proposed by (Meissner et al., 1972; Meissner & Tester, 1972). The calculation of the activity coefficient for a strong electrolyte solution at 25°C is as follows

$$
\Gamma^{\rm o} = \left[ \mathbf{1} + \mathbf{B} \left( \mathbf{1} + 0.1 \, \mathbf{I} \right)^{g} - \mathbf{B} \right] \Gamma^{\*} \tag{C1}
$$

With:

$$\mathbf{B} = \mathbf{0}.\mathbf{75} \text{-} \mathbf{0}.\mathbf{0} \mathbf{65} \text{ q} \tag{\text{C2}}$$

$$\left(1\log\Gamma^\*\right) = \left(\text{-5107 }\sqrt{\text{I}}\right)\left(1 + \text{C}\sqrt{\text{I}}\right) \tag{C3}$$

$$\mathbf{C} = \mathbf{1} + 0.055 \mathbf{q} \exp\left(\text{-}0.023 \,\text{I}^3\right) \tag{\text{C4}}$$

where <sup>o</sup> Γ is the reduced activity coefficient of the pure solution at 25°C, q is the Meissner parameter (q = 7.27 for LiBr) I is the ionic strength of electrolyte

$$\mathbf{I} = \begin{array}{c} \sum \mathbf{m}\_i \ Z\_i^2 \\ \mathbf{2} \end{array} = \mathbf{m}\_{\text{LiBr}} \tag{\text{C5}}$$

Z is the number of charges on the cation or anion (Z = 1 for LiBr) The average ionic activity coefficient for LiBr-H2O solution

$$\mathcal{N}\_{\pm} = \left(\Gamma^{\bullet}\right)^{Z\_{+} Z\_{-}} = \Gamma^{\bullet} \tag{C6}$$

Finally, the activity of the LiBr solution is given by the expression

$$\mathbf{a}\_{\text{(LiBr)}} = \frac{\mathbf{m}\_{\text{LiBr}}}{\mathbf{m}^{\text{o}}} \ \chi\_{\pm} \tag{C7}$$

Where mo is the standard solution molality (1 mol LiBr/kg H2O)

The calculation of the Kusik-Meissner parameter (Kusik & Meissner, 1978) for temperature t in ºC is given by the following equation

$$\mathbf{q}\_{\rm t} = \left(\mathbf{a}\,\mathbf{q}\_{\rm (25)} + \mathbf{b}^\*\right) \mathbf{(t-25)} + \mathbf{q}\_{\rm (25)} \tag{C8}$$

Where:

526 Mass Transfer - Advanced Aspects

2 1 3sol

⎡ ⎤ = + +⋅ <sup>⎢</sup> <sup>⎥</sup> <sup>⎣</sup> <sup>⎦</sup>

sol A exp A A ln T <sup>T</sup>

A1 = - 494.122 + 16.3967 Xsol – 0.14511 (Xsol)2; A2 = 28606.4 – 934.568 Xsol + 8.52755 (Xsol)2; A3 = 70.3848 – 2.35014 Xsol + 0.0207809 (Xsol)2; µ = dynamic viscosity, cp; Tsol = Temperature

The model for calculating the activity of strong electrolytes in aqueous solution is proposed by (Meissner et al., 1972; Meissner & Tester, 1972). The calculation of the activity coefficient

where <sup>o</sup> Γ is the reduced activity coefficient of the pure solution at 25°C, q is the Meissner

2 i

( ) o o Z-

LiBr

γ

m

m Z I m 2

*<sup>Z</sup>*

LiBr o m

<sup>+</sup>

( )

a

LiBr

ρ

( ) o 1 B 1 0.1 I B <sup>⎡</sup> *<sup>q</sup>* <sup>⎤</sup> <sup>∗</sup> <sup>Γ</sup> = + + −Γ <sup>⎣</sup> <sup>⎦</sup> (C1)

log -5107 I 1 C I ( ) ( ) <sup>∗</sup> Γ = + (C3)

( ) <sup>3</sup> C 1 0.055 q exp -0.023 I = + (C4)

B 0.75 - 0.065 q = (C2)

*<sup>i</sup>* <sup>=</sup> ∑ <sup>=</sup> (C5)

<sup>±</sup> = Γ =Γ (C6)

= <sup>±</sup> (C7)

, solution density,

(B2)

*H O* Tsol , water density at the solution temperature, kg m-3; ( ) sol *Xsol* , T

Domain range: 40% ≤ Xsol ≤ 75%; 0ºC ≤ Tsol ≤ 190 ºC Calculation of dynamic viscosity µ d'Alefeld equation

μ

( ) <sup>2</sup>

kg m-3; Xsol, (mass% LiBr)

solution, K; Xsol = mass %, LiBr

Domain: 45% ≤ Xsol ≤ 65% ; 30ºC ≤ Tsol ≤ 210ºC

Calculation of the activity of LiBr-H2O solution.

for a strong electrolyte solution at 25°C is as follows

parameter (q = 7.27 for LiBr) I is the ionic strength of electrolyte

Z is the number of charges on the cation or anion (Z = 1 for LiBr) The average ionic activity coefficient for LiBr-H2O solution

Finally, the activity of the LiBr solution is given by the expression

Where mo is the standard solution molality (1 mol LiBr/kg H2O)

γ

ρ

Where:

With:

**4.3 Appendix C** 

a = - 0.005 and b\* = 0.0085
