#
Physico-Chemical Modelling of Chloride Migration in Cement-Based Materials Considering Electrode Processes^{ †}

^{*}

^{†}

## Abstract

**:**

^{−}in the cathode and H

^{+}in the anode allows for the monitoring of the electroneutrality. The modelling considers all the ions of the pore solution. Ion fluxes are calculated using Nernst–Planck equation. The Langmuir model is used to simulate the chloride isotherms. The thermodynamic equilibrium in the material is considered, which reflects the liquid–solid interactions during the migration. The ion profiles with and without considering the electrode processes are presented.

## 1. Introduction

^{−}, Na

^{+}, K

^{+}, OH

^{−}and Ca

^{2+}. The diffusion, migration and chemical activity were considered. The chemical activity was calculated using the Pitzer model. The numerical results highlighted the influence of the composition of the pore solution and the chemical activity on the chloride penetration.

^{−}and H

^{+}in the cathode and anode, respectively. The electrode processes ensure the electroneutrality in the migration cell (sample and compartments). The concentrations of OH

^{−}and H

^{+}are calculated from the current density measured during the test, using Faraday’s law. The charge passed is deduced from the current density measured. Ion fluxes are calculated by the Nernst–Planck equation, which describes the diffusion and migration of the species. The Langmuir model is used to simulate the chloride chemical fixation by the material (chloride isotherms). The chemical activity is neglected according to [3]. The considered ions are Cl

^{−}, Na

^{+}, K

^{+}, OH

^{−}, H

^{+}, Ca

^{2+}and SO

_{4}

^{2−}. The migration cell used is composed of two compartments: (1) upstream containing 25 mM NaOH and 83 KOH and 500 mM NaCl; (2) downstream containing only 25 mM NaOH and 83 KOH (boundary conditions). The composition of the pore solution of the material tested was considered the initial condition. An electrical field of 300 V∙m

^{−1}was applied at the sample boundaries and monitored using two calomel reference electrodes. The latter were placed at each side of the sample tested in order to maintain the electrical field constant modelling outputs are as follows:

- The ion profiles in the material that can be used for the calculation of the ion diffusion coefficients in the non-steady state (from the ion-penetration depth), with and without the electrode processes.
- The electroneutrality in the sample tested with and without integrating the electrode processes in order to highlight the need for the consideration of the electrode processes in the chloride migration modelling proposed.

## 2. Methodology

#### 2.1. Modelling Principle

_{i}) during the migration test is calculated by using the mass balance equation (Equation (1)), which takes into account the porosity of the material tested (φ), the chloride concentration bonded to the cement matrix (C

_{i,b}) calculated by the Langmuir’s model and the ion flux (J

_{i}) calculated by the NP equation (see Equation (2)). The internal electrical potential between ions is neglected in front of the applied electrical field of 300 V∙m

^{−1}. The mass exchange term (q

_{i}), added to the mass balance equation, describes the ion gain/loss in the pore solution due to the dissolution/precipitation of the solid phases considered (C-S-H, portlandite, monosulfoaluminates and trisulfoaluminates). Further details about the calculations of the term (q

_{i}) and the thermodynamic equilibrium constants used are shown in [8]. The ions considered in this study are: Cl

^{−}, Na

^{+}, K

^{+}, OH

^{−}, H

^{+}Ca

^{2+}and SO

_{4}

^{2−}. Note that the proposed modelling concerns ion transport in saturated materials that do not require coupling with convection and moisture transfer.

_{E,i}[m².s

^{−1}] is the effective diffusion coefficient of the ion i, z

_{i}is the valence of the ion i, F [C∙mol

^{−1}] is the Faraday constant, E [V∙m

^{−1}] is applied electric field, R [J∙K

^{−1}∙mol

^{−1}] is the ideal gas constant and T [K] is the temperature γ

_{i}is the ion activity coefficient.

^{−}in the catholyte (upstream) and H

^{+}in the anolyte (downstream) are given in the following. Note that non-corrodible Platine electrodes were used.

_{2}O + 2 e

^{−}→ H

_{2}+ 2 OH

^{−}

_{2}O → 0.5 O

_{2}+ 2 H

^{+}+ 2 e

^{−}

#### 2.2. Case Study

^{−1}is applied at the sample boundaries. Concrete samples of 1 cm thickness are used (1D modelling). In this study, the numerical results show the ion profiles in the material tested that are useful for the calculation of the diffusion coefficient at the non-steady state [4,35].

## 3. Results and Discussion

^{−}, Na

^{+}, K

^{+}, OH

^{−}, H

^{+}, Ca

^{2+}and SO

_{4}

^{2−}in the sample at the end of the migration test (after 15 days) with and without considering the electrode processes, respectively. The free chloride concentration in the pore solution is maximum along the sample depth (~459 mol∙m

^{−3}) because of their migration from the upstream to the sample. The max concentration is relatively different compared to the literature’s data without considering the thermodynamic equilibrium (the participation of chloride with the other ions in the pore solution to form salts). For these models in the literature, the max concentration is equal to the boundary condition on the side of the upstream (500 mol∙m

^{−3}) [2]. Bulleted lists look like this:

^{+}and K

^{+}in the pore solution due to their migration from the downstream to the sample tested. The increase in Ca

^{2+}and SO

_{4}

^{2−}concentrations are due to the dissolution of the portlandite, monosulfoaluminates, and trisulfoaluminates under the electrical field [36,37].

^{+}and OH

^{−}with and without considering the electrode processes is noticed. This is reflected by the electroneutrality ensured in the case of the migration modelling with electrode processes and not ensured in the case of the modelling without electrode processes (see Figure 3). This impacts also the concentration of the other ions in the pore solution. The electroneutrality was calculated using Equation (5). The results obtained confirm the need of considering the electrode processes in the chloride migration modelling.

## 4. Conclusions

- The modelling proposed allowed us to simulate the standard migration test at the steady and non-steady states considering the real pore solution of the material tested and the dissolution/precipitation phenomena during the migration. The modelling was applied to OPC-based materials.
- Outputs of the modelling proposed are the ion profiles in the material tested during the migration test.
- The numerical results show the need of considering the electrode processes in the chloride migration modelling in order to better simulate the standard migration test. The model proposed could be improved by considering more solid phases of the material such as C-S-H, oxychloride, etc.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Profiles of Cl

^{−}, Na

^{+}, K

^{+}, OH

^{−}, H

^{+}, Ca

^{2+}and SO

_{4}

^{2−}in the sample at the end of the migration test (15 days) considering electrode processes.

**Figure 2.**Profiles of Cl

^{−}, Na

^{+}, K

^{+}, OH

^{−}, H

^{+}, Ca

^{2+}and SO

_{4}

^{2−}in the sample at the end of the migration test (15 days) without considering electrode processes.

**Figure 3.**Electrochemical imbalance in the pore solution of the sample, deduced from ion concentrations in the steady state with and without considering electrode processes.

Cement [kg∙m^{−3}] | Sand [kg∙m^{−3}] | Coarse Aggregate [kg∙m^{−3}] | Water [kg∙m^{−3}] | W/C | |
---|---|---|---|---|---|

Concrete | 300 | 710 | 1242 | 180 | 0.6 |

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**MDPI and ACS Style**

Kribes, Z.-E.; Cherif, R.; Aït-Mokhtar, A.
Physico-Chemical Modelling of Chloride Migration in Cement-Based Materials Considering Electrode Processes. *Mater. Proc.* **2023**, *13*, 37.
https://doi.org/10.3390/materproc2023013037

**AMA Style**

Kribes Z-E, Cherif R, Aït-Mokhtar A.
Physico-Chemical Modelling of Chloride Migration in Cement-Based Materials Considering Electrode Processes. *Materials Proceedings*. 2023; 13(1):37.
https://doi.org/10.3390/materproc2023013037

**Chicago/Turabian Style**

Kribes, Zine-Eddine, Rachid Cherif, and Abdelkarim Aït-Mokhtar.
2023. "Physico-Chemical Modelling of Chloride Migration in Cement-Based Materials Considering Electrode Processes" *Materials Proceedings* 13, no. 1: 37.
https://doi.org/10.3390/materproc2023013037