Design of cathodic protection potentials and impressed current densities in ICCP systems for ships with coating defects

2.1 Materials

SS400 steel, commonly used for ship hulls, was used as specimens. The chemical composition (wt%) is as follow: C (0.18), Si (0.14), Mn (0.71), P (0.013), S (0.006), with Fe as the balance. Prior to testing, the specimens were sequentially abraded with SiC sandpapers up to 600 grit, rinsed with deionized water and ethanol, and airdried under ambient conditions. To ensure a consistent surface oxide film, all specimens were prepared within 10 minutes before electrochemical testing. The exposed surface area of the specimens was controlled using NITTOFLON 903 PTFE tape, which has outstanding electrical insulation properties and excellent chemical resistance, to replicate coating defects at levels of 10, 30, 50, and 100% and the specimens were designated as Coating Defect_10% (CD10%), Coating Defect_30% (CD30%), Coating Defect_50% (CD50%), and Coating Defect_100% (CD100%), respectively.

2.2 Electrochemical Tests

The effect of coating defects on the current distribution in cathodic protection systems in seawater was investigated through potentiodynamic polarization, potentiostatic, and EIS. All electrochemical tests were conducted using a potentiostat in a three-electrode system, comprising a Pt wire as the counter electrode, an Ag/AgCl electrode as the reference, and the specimen as the working electrode.

Potentiodynamic polarization tests were conducted to evaluate the intrinsic electrochemical behavior under varying coating defect conditions in a potential range of -1.0 to 0 V vs. Ag/AgCl at a scan rate of 0.166 mV/s in 3.5 wt% NaCl solution. EIS measurements were performed at E_corr, E_NACE, -0.7, and -0.8 V vs. Ag/AgCl across a frequency range of 100 kHz to 0.01 Hz, using a sinusoidal voltage with an amplitude 10 mV, to analyze surface characteristics and assess compliance with cathodic protection criteria (E_corr and E_NACE is determined based on the results and defined in Section 3.2). The EIS data were fitted to an appropriate equivalent circuit model using Gamry Echem Analyst software. Additionally, potentiostatic tests were conducted to simulate impressed current conditions, with the specimens cathodically polarized at -0.8 V vs. Ag/AgCl under simulated damaged coating conditions for 24 h. To ensure reproducibility, all tests were conducted at least three times.

2.3 Computer Simulation

Numerical simulations were performed using the finite element method (FEM) in COMSOL Multiphysics to analyze the distribution of current densities on ship’s hull. The ship model was constructed using the ship drawings provided by COMSOL [9]. The model was designed with dimensions of approximately 35 m in length, 5.7 m in width, and 5 m in height for the submerged portion. The anode was positioned 8 meters from the stern. Electrochemical reactions were incorporated into the simulation by applying realistic polarization curve data as boundary conditions. The polarization curve for steel was assigned to the ship’s hull. The primary electrode reaction occurring on the metal surface is oxygen reduction. As the transport of oxygen in the seawater is restricted by its diffusion rate to the surface, the current density is constrained to 5 A/m² based on electrode kinetics. Consequently, the local current density can be expressed as follows:

Where i_lim represents the diffusion-limited current density and i_kin accounts for the electrode kinetics.

All simulations assumed seawater with an electrical conductivity of σ = 4.5 S/m to replicate real seawater conditions. Additionally, an Ag/AgCl reference electrode was used to determine the protective potential. This setup enables a precise evaluation of the electrochemical behavior and the spatial distribution of potential and current across the ship’s surface under varying conditions.

2.4 Characterization

To assess the effectiveness of the cathodic protection potentials, scanning electron microscopy (SEM) combined with energy-dispersive spectroscopy (EDS) was employed to examine the surface morphology and chemical composition. The SEM/EDS analysis was performed at an accelerating voltage of 15.0 kV.

3.1 Corrosion of Ship’s Hull with Coating Defects

Potentiodynamic tests were conducted to investigate the electrochemical properties of a ship’s hull with damaged coatings. From the polarization curves, electrochemical parameters, such as corrosion potentials (E_corr), corrosion current densities (i_corr), anodic Tafel slope (β_a), and cathodic Tafel slope (β_c), were obtained using EC-Lab software. Figure 1 presents the polarization curves for coated steels with damages, while the electrochemical parameters derived from these tests are summarized in Table 1. The slight variations in E_corr were attributed to the formation of oxide films during the potentiodynamic tests, though they remained within the range of -400 to -500 mV. In addition, the corrosion current densities increased with increased coating defects due to the enlarged areas for electrochemical reactions. On the other hand, since the tested specimens were composed of the same material and subjected to identical conditions, the kinetics of anodic and cathodic reactions were found to be similar. The obtained β_a and β_c values were approximately 75 mV/decade and 635 mV/decade, respectively.

Figure 1:

Potentiodynamic polarization curves of coated steel as a function of coating defects in 3.5 wt% NaCl solution

Table 1:

Electrochemical parameters obtained from the potentiodynamic polarization tests under different coating defect conditions in 3.5 wt% NaCl solution

To evaluate the severity of corrosion in the damaged areas, corrosion rates were calculated based on Faraday’s law using the following equation:

where a is the atomic weight, i is the corrosion current density, n is the number of electrons transferred per metal atom, and D is the density of the metal. As shown in Table 1, the corrosion rates of CD10%, CD30%, CD50%, and CD100% were 0.050, 0.078, 0.137, and 0.235 mm/yr, respectively. These values exceed the low corrosion rate threshold (0.025 mm/yr) recommended by NACE, indicating the necessity of implementing ICCP systems to mitigate corrosion.

3.2 Investigation on Cathodic Protection Potential and Impressed Current Density

According to the international standard ISO 12473: General Principles of Cathodic Protection in Seawater, the recommended cathodic protection potential range is -0.8 to -1.1 V vs. Ag/AgCl [10]. To minimize the required current density for cathodic protection (i_cp), the lowest cathodic potential that satisfies the NACE criterion for low corrosion rates (E_NACE) was determined from polarization curves. Figure 2 presents the potentiodynamic polarization curve, anodic Tafel line, and i_cp for each cathodic potential. CD100% was presented as a representative. The E_NACE was calculated to be -0 .58 V. additionally, 27.44, 36.15, and 43.36 μA/cm² of current densities were required to maintain the potential of CD100% at -0.58, -0.7, and -0.8 V, respectively. The corresponding corrosion rates were reduced to 0.025, 6.65 × 10^-10, and 3.16 × 10^-11 mm/yr, indicating that -0.58 and -0.7 V could also be considered effective cathodic protection potentials. Other calculated applied current densities and corrosion rates are summarized in Table 2.

Figure 2:

Calculated applied current density for cathodic protection (icp) and the anodic Tafel line of CD100% derived from the potentiodynamic polarization curve

Table 2:

Calculated applied current densities for cathodic protection and corrosion rates at the potentials as a function of coating defect levels

Potentiostatic tests were performed to replicate ICCP-applied environments and validate the calculated i_cp values, assessing the applicability to ICCP conditions. Figure 3 presents the recorded current densities of CD100% during the tests. Impressed current densities initially decreased sharply due to the formation of oxide films, which reduced the active surface area, as shown in the inset. However, as the oxide films continued to grow, their low electrical conductivity led to an increase in the required impressed current density. After around 20,000 s, the surface of CD100% stabilized, requiring 17.50, 29.62, and 34.30 μA/cm² of i_cp at E_NACE, -0.7, and -0.8 V, respectively.

Figure 3:

Records of applied current densities of CD100% during potentiostatic tests conducted at ENACE, -0.7 V, and -0.8 V in 3.5 wt% NaCl solution

To simulate i_cp on ICCP-applied ships under different cathodic potentials, which is challenging to measure in full-scale experiments, COMSOL Multiphysics was employed. Figure 4(a) presents a 3D simulation of the current density distribution at a cathodic protection potential of -0.8 V, while Figure 4(b), (c), and (d) illustrate the required i_cp values across the hull under cathodic potentials of E_NACE, -0.7, and -0.8 V, respectively. In the ship modeling, the position and number of anodes were not optimized, resulting in a high current density near the 8 m region where the anodes are located. Hence, the current density values obtained from the simulation were selected from a spatial coordinate where the potential was stably maintained to establish the cathodic potential. The acquired impressed current densities at E_NACE, -0.7, and -0.8 V were 27.84, 33.68, and 39.76 μA/cm², respectively.

Figure 4:

(a) Computational model of the current density distribution on a ship with CD100% hull and the corresponding icp values across the hull at cathodic potentials of (b) ENACE, (c) -0.7 V, and (d) -0.8 V

The calculated, measured, and simulated i_cp at E_NACE, -0.7, and -0.8 V were summarized in Table 3 and the trend lines and coefficient of determination (R²) are presented in Figure 5. The R² was calculated based on the square of the Pearson correlation coefficient. When the trend line was plotted based on the calculated values, the simulation and experimental results exhibited high R² of 0.996 and 0.962, respectively. The experimentally obtained current density was lower than the calculated and simulated values, likely due to the lengthy duration of the potentiostatic tests. As observed in the potentiostatic tests, a higher current density was initially required before stabilizing over time, suggesting that prolonged exposure led to surface changes affecting current demand. Nevertheless, the results exhibited a strong correlation, indicating that cathodic protection potentials and required current densities can be reliably estimated through calculations and simulations.

Table 3:

Calculated, experimental, and simulated applied current densities for cathodic protection of CD100% as a function of cathodic protection potentials

Figure 5:

Trend line and R2 values of the calculated, measured, and simulated icp for cathodic protection of CD100% at ENACE, -0.7 V, and -0.8 V of cathodic protection potentials

3.3 Verification of Cathodic Potentials

To investigate the surface characteristics and evaluate the effectiveness of the applied cathodic potentials, EIS tests were conducted. The Nyquist plots of CD100% at E_corr, E_NACE, -0.7, and -0.8 V are presented in Figure 6(a). A depressed capacitive loop, which is commonly associated with charge transfer during the corrosion process, was observed at all cathodic potentials [11][12]. The semicircle diameter, representing charge transfer resistance (R_ct), increased as the cathodic potential became more negative, enabling a comparative assessment of corrosion resistance. In contrast, an inductive loop at low frequency was only observed at E_corr, E_NACE. The presence of this inductive loop indicates that the adsorption of intermediate species, such as metal hydroxides, oxygen species, or H⁺_ads, is actively occurring. This suggests that insufficient cathodic protection at E_corr and E_NACE has led to the accumulation of corrosion products on the surface of CD100% [13]. Conversely, at -0.7 and -0.8 V, where no inductive loop was observed, the system appears to be under effective cathodic protection, minimizing surface adsorption effects and stabilizing the electrode-electrolyte interface.

Figure 6:

(a) Nyquist plots of CD100% at cathodic protection potentials of Ecorr, ENACE, -0.7 V, and -0.8 V and equivalent circuits of CD100% at (b) Ecorr and ENACE and (c) -0.7 V and -0.8 V

As the distinct characteristics depending on the cathodic potentials were exhibited, different equivalent electrical circuit (EEC) models were used. The impedance parameters of CD100% at E_corr and E_NACE were identified using the EEC shown in Fig. 6 (b). The circuit consists of the following components: R_s represents the solution resistance; R_L and L correspond to the inductive elements; R_ct denotes the charge transfer resistance; and C_dl (CPE) signifies the double layer capacitance. To achieve a more accurate fit, a constant phase element (CPE) was introduced instead of an ideal capacitor [12]. The impedance parameters of CD100% at -0.7 and -0.8 V, which demonstrated sufficient cathodic protection, were determined using the electrical equivalent circuit model shown in Figure 6(c). The circuit consists of the following components: R_s represents the solution resistance; R_film and C_film (CPE₁) denotes the electrical resistance and capacitance of the oxide film, respectively; R_ct is the charge transfer resistance; C_dl (CPE₂) is the double layer capacitance.

The CPE impedance is expressed as:

Where Y₀ is the magnitude of the CPE and n is the deviation from ideal capacitive behavior due to the surface roughness, porosity, or electrode heterogeneity [14].

The conversion of the CPE to capacitance was performed using the equation below [15]:

Where ω_max = 2πf_max, f_max is the frequency where the imaginary part of the impedance reaches its maximum.

The impedance parameters of CD100% at E_corr and E_NACE, -0.7 and -0.8 V are listed in Table 4. It can be noted that R_ct increased as the cathodic protection potential became more negative. This aligns with the ICCP principle, where a more negative potential enhances the suppression of anodic dissolution by shifting the surface further into the cathodic region. As a result, R_ct, which represents the difficulty of electron transfer in corrosion reactions, increases due to the reduced corrosion activity and the stabilization of the passive film on the metal surface. The R_film at -0.7 V was larger than that at -0.8 V, indicating that the suppression of anodic reactions at more negative potentials reduced oxide film formation, thereby decreasing R_film.

Table 4:

Impedance parameters of CD100% at cathodic protection potentials of Ecorr, ENACE, -0.7 V, and -0.8 V

The capacitance related to oxide film (C_film) and electrical double layer (C_dl) can be represented by:

Where ε is the dielectric constant, ε₀ is the vacuum permittivity, A is the surface area of the electrode, and d is the thickness.

At cathodic protection potentials of -0.7 and -0.8 V, C_film showed nearly identical values, suggesting that the oxide film thickness was similar. This indicates that -0.7 V provides corrosion protection performance comparable to that of -0.8 V. C_dl at E_corr and E_NACE were lower than those at -0.7 and -0.8 V, which can be attributed to the increased corrosion reactions generating intermediate species. These species likely contributed to a thicker double layer, reducing the overall capacitance. On the other hand, the C_dl at -0.7 V was higher than that at -0.8 V. At more negative cathodic potentials, the cathodic reaction (O₂ + 2H₂O + 4e^- → 4OH^-) becomes more dominant, leading to a greater concentration of ions at the electrode surface. As a result, the electrical double layer thickens, causing a reduction in C_dl.

To further evaluate the effectiveness of cathodic potentials, SEM/EDS analysis was performed on the surface of CD100% after the potentiostatic tests. As depicted in Figure 7, the surfaces of CD100% at -0.7 and -0.8 V remained clear, whereas corrosion products were observed on CD100% at E_corr and E_NACE. Additionally, EDS mapping revealed that the Fe content in CD100% was 58.9, 69.7, 91.9, and 94.3 at%, while the O content was 41.1, 30.3, 8.1, and 5.7 at% at E_corr, E_NACE, -0.7, and -0.8 V, respectively. The lower Fe content and higher O content observed at E_corr and E_NACE indicate extensive oxide film formation, suggesting significant corrosion. Therefore, -0.7 V and -0.8 V can be considered effective cathodic protection potentials. These findings are consistent with the calculated corrosion rates and EIS results, further confirming the effectiveness of the cathodic potentials.

Figure 7:

SEM images and EDS mapping of CD100% after potentiostatic tests

Author Contributions

Conceptualization, U. Kim and S. Lee; Methodology, U. Kim; Software, U. Kim; Validation, U. Kim and S. Lee; Formal Analysis, U. Kim; Investigation, U. Kim, N. Kim; Resources, J. Sin, Y. Maeng, and S. Lee; Data Curation, U. Kim, N. Kim; Writing—Original Draft Preparation, U. Kim, N. Kim; Writing—Review & Editing, S. Lee; Visualization, U. Kim; Supervision, S. Lee; Project Administration, S. Lee; Funding Acquisition, J. Sin, Y. Maeng, and S. Lee.