Data Analysis and Physical Model of Electrochemical Impedance Spectroscopy for Corrosion Systems: Progresses and Challenges
GUO Yujie1, LI Yanhui2, XIA Da-Hai,1, HU Wenbin1
1 School of Materials Science and Engineering, Tianjin University, Tianjin 300350, China
2 Key Laboratory of Thermo-Fluid Science & Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China
Electrochemical impedance spectroscopy (EIS) is one of the most important methods for studying the electrochemical corrosion behavior and failure mechanisms of metallic materials and their coating systems. With the development of corrosion electrochemistry theory, numerical calculation, and corresponding fitting software, significant progress has been made in the analysis of EIS data. Through data fitting and analysis, key parameters such as the thickness of the passive film, the resistivity distribution of the passive film, and the resistivity distribution of the coating can be obtained. When the passive film breaks down, the expression of the Faraday impedance ZF can be derived through the kinetic model, correspondingly, the parameters such as the rate constants of each electrode reaction and the thickness of the diffusion layer can be analyzed. Taking passive metals and their organic coating systems as examples, this paper reviews the applications of the electrochemical equivalent circuit model (ECM), the point defect model (PDM), the electrochemical kinetic model, the power-law model (PLM), and the Young model in analyzing the properties of oxide films, the performance of coatings, and the kinetic parameters of electrode processes. Moreover, the advantages and disadvantages of each method are discussed. Finally, the development trends of EIS data analysis and physical models are pointed out.
Keywords：EIS
;
organic coating
;
electrochemical equivalent circuit
;
power-low model
;
Young model
GUO Yujie, LI Yanhui, XIA Da-Hai, HU Wenbin. Data Analysis and Physical Model of Electrochemical Impedance Spectroscopy for Corrosion Systems: Progresses and Challenges. Journal of Chinese Society for Corrosion and Protection[J], 2025, 45(5): 1143-1160 DOI:10.11902/1005.4537.2024.381
Fig.1
Proposed generation and annihilation reactions of defects at the interface of substrate metal and duplex passivation film in PDM-II and PDM-III models. Note: that reactions (1), (2), (4), (5) and (6) are lattice conservative processes (i.e. do not result in the movement of the interface), the reactions (3) and (7) are non-conservative[28]
Fig.3
Equivalent circuit model corresponding to the case of the formation of complete uniform passivation film on passive metal. Wherein, Re represents the solution resistance, Cdl represents the capacitance of the electrochemical double layer at the interface between the passive film and the electrolyte, is Faradaic resistance of oxygen reduction at the passive film/solution interface, Rox, i and Rox, e represent the resistances to the movements of ions and electrons in the passive film, respectively[39]
Fig.4
Equivalent circuit model of electrochemical behavior of sensitized 5083 Al-alloy in 3.5%NaCl solution under the condition of cracking of passivation film. This circuit contains four electrical components: Re, ZOX, ZF and Cdl[40]
Fig.5
Distribution of R//C elements corresponding to the impedance response of passivation film. Wherein, and represent differential capacitance and differential resistance, respectively[7]
Fig.10
Ohm resistance-corrected Bode plots of 5083-O Al-alloy under different conditions. The details of the samples and test conditions are shown in Table 1[40]
Fig.11
Nyquist (a) and Bode (b) plots of sensitized 5083-O Al-alloy under different conditions. The details of samples and test conditions are shown in Table 1[40]
Fig.13
Electrolyte resistance corrected impedance diagrams of 7050 Al-alloy during cavitation erosion in 3.5%NaCl solution with the gap widths of 0.5 mm (a), 1 mm (b) and 2 mm (c)[58]
Fig.14
Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model[58]
Fig.15
Proposed equivalent circuits for fitting resistance responses at metal/passive film/electrolyte interfaces based on EEC 1 of PLM (a) and EEC 2 of DBLM (b). Cdl represents the capacitance of the electrochemical double layer at the oxide/electrolyte interface, which can be ignored throughout the fitting process[59]
Fig.18
Schematic representation of a substrate/coating/electrolyte system (a) and corresponding equivalent circuit (b). Wherein, the upper box corresponds to Eq.(33) and the complete circuit is the one used for regression; CPE in the lower box is included considering the existence of oxide layer on the metal substrate[71]
Fig.19
EIS plots of 2024 Al-alloy with hybrid sol-gel coating after immersion in 0.5 mol/L NaCl solution for 72 h. The circles indicate experimental data, and the solid lines are regression results[71]
Fig.21
Schematic representation of the two-layer model. It is assumed that the coating is consist of an inner layer with uniform resistivity ρ = ρc and an outer layer with an exponential dependence of resistivity on position[72]
Fig.22
Resistivity vs. thickness curves for the coating after immersion in 0.5 mol/L NaCl solution for different time (a) and in 0.05 mol/L and 0.5 mol/L NaCl solution for 2 h and 504 h (b)[72]
Operando odd random phase electrochemical impedance spectroscopy (ORP-EIS) for in-situ monitoring of the Zr-based conversion coating growth in the presence of (in)organic additives
Odd random phase multisine electrochemical impedance spectroscopy to quantify a non-stationary behaviour: theory and validation by calculating an instantaneous impedance value
Localized corrosion: passive film breakdown vs. pit growth stability, part VI: pit dissolution kinetics of different alloys and a model for pitting and repassivation potentials
By anodic potentiostatic polarization and electrochemical impedance spectroscopy (EIS) measurements, the effect of temperature (200 degrees C, 250 degrees C, and 300 degrees C) on the electrochemical behavior of Alloy 690 was investigated in oxygenated borate buffer solution containing H3BO3 (2000 ppm B) + LiOH (2 ppm Li). The steady state passive current density was independent of the film formation potential at each temperature, indicating that the passive film is n-type in electronic character based on the predictions of the Point Defect Model (PDM). The passive current density increased and the absolute value of impedance decreased with increasing temperature, indicating a corresponding decrease in corrosion resistance. A mixed potential model (MPM), containing the PDM for describing the anodic passive dissolution of the alloy and the generalized Butler-Volmer equation for the cathodic oxygen reduction reaction was optimized on the experimental EIS data in order to extract model parameters, including kinetic parameters for the generation and annihilation of point defects in the barrier layer of the passive film. Metal (Cr, Ni, Fe) interstitials, which were found to have a higher concentration than oxygen vacancies, dominate the point defect structure of the barrier layer of the passive film at each temperature, thereby accounting for the n-type behavior of the passive film. With increasing temperature, the film thickness and defect density also increased, resulting in the decreased corrosion resistance of film. This indicates that the defect density of passive film plays a more important role on corrosion behavior of alloy than the film thickness. (C) 2019 Elsevier B.V.
SunL, ZhaoT Y, QiuJ, et al.
Point defect model for passivity breakdown on hyper-duplex stainless steel 2707 in solutions containing bromide at different temperatures
A seawater corrosion test platform to simulate the dynamic seawater/air interface is constructed, comprising an electric putter, a time relay, and four corrosion electrochemical sensors. The localized corrosion mechanism of 2024 aluminum alloy in a simulated dynamic seawater/air interface is investigated by corrosion potential monitoring, electrochemical impedance spectroscopy (EIS), electrochemical noise (EN) measurements, and the analysis of the surface and cross-section morphology. The differences in the corrosion behavior at the seawater/air interfacial region and that of full immersion region are discussed. The results showed that the corrosion products at the dynamic seawater/air interfacial region are continuously distributed, which is mainly due to the dissolved Al3+ flowing from the pits and reacting with the oxygen in the dynamic seawater/air interfacial region. The distribution of corrosion products in the entire leaching area is more dispersed. As aluminum alloy is immersed and removed from water periodically, the corrosion potential fluctuates periodically with an amplitude of 5-10 mV. Due to the high corrosion potential in the seawater/air interfacial region, the aluminum alloy above the waterline behaves as the cathode, and that below the waterline acts as the anode. However, because of the subtle difference in the corrosion potential, the galvanic corrosion effect is not obvious. The results of EIS revealed that the high-frequency capacitive arc radius of both seawater/air interfacial region and full immersion zone increased first and then decreased, and the corrosion product film in the interface zone had better corrosion resistance than that in the full immersion zone. The results of the EN test showed that the fluctuation amplitude of current noise decreased first and then increased, indicating that the local corrosion sensitivity decreased first and then increased. The slope of the high-frequency linear region of the power spectral density of current noise was less than -20 dB/dec, indicating that the corrosion type was local corrosion. The pit size at the seawater/air interface was much smaller than that in full immersion region, because the oxygen in the seawater/air interface region could be easily reduced within the pits by consuming H+, thereby increasing the pH value within the pits.
A mechanistic study on stress corrosion cracking of sensitized AA5083 in a simulated waterlevel fluctuation zone: combined impedance analysis and tensile tests
TribolletB, VivierV, OrazemM E. EIS Technique in Passivity Studies: Determination of the Dielectric Properties of Passive Films [M]. Oxford: Elsevier, 2018: 94
The study of passive film's resistivity distribution to crystalline Fe-based pseudo high entropy alloys: The use of measurement model and Cole-Cole regression
Passivity breakdown on 436 ferritic stainless steel (FSS) has been investigated in solutions containing different concentrations of chloride at 25 °C and interpreted in terms of the point defect model (PDM). The measured near-normal distributions of passivity breakdown potentials for 436 FSS under experimental conditions are in good agreement with the calculated results according to the PDM. The linear dependence of breakdown potential on the square root of potential scanning rate, which was described by the PDM, provides the estimation of the critical concentration of condensed vacancies at the metal/film interface, which leads to the passivity breakdown. This value is in good agreement with that calculated from the microstructure properties of the alloy substrate and the barrier layer of the passive film. This study demonstrates the validity of the PDM in describing the passivity breakdown on 436 FSS in NaCl solutions.
BaconR C, SmithJ J, RuggF M.
Electrolytic resistance in evaluating protective merit of coatings on metals
Electrochemical test methods for evaluating organic coatings on metals: an update. Part III: multiple test parameter measurements
[J]. Prog. Org. Coat., 1997, 31: 375
MurrayJ N.
Electrochemical test methods for evaluating organic coatings on metals: an update. Part I. introduction and generalities regarding electrochemical testing of organic coatings
To realize a rapid evaluation of coating degradation under alternating hydrostatic pressure (AHP), appropriate physical models of electrochemical impedance spectroscopy (EIS) data fitting were respectively developed for epoxy coatings with and without pigments, based on their different water absorption behaviours. Power-law model was selected to evaluate the anti-permeability of epoxy varnish (EV) coating, which tends to form through pores in the coating structure. On the other hand, two-layer model based on Young theory was developed to evaluate the anti-permeability of pigmented epoxy coating. Consequently, the resistivity profile with coating thickness was calculated as a critical parameter to describe the anti-permeability of coating at different immersion time. The interpretation of water diffusion dynamics based on different coating structures was also given, which is responsible for the choice of distribution models.
LiY N, WangJ, ZhangW.
Comparative studies on the deterioration process of organic coatings under immersed and cyclic wet-dry conditions by EIS
Electrochemical behaviors of organic coating/matal substrate under simulated deep sea environment Part Ⅰ. effects of seawater pressure on transportation behavior of water through coating and coating's protective performance
Distribution of <i>R</i>//<i>C</i> elements corresponding to the impedance response of passivation film. Wherein, <span class="formulaText"><inline-formula><math id="M48"><msub><mrow><mi>C</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span></inline-formula></span> and <span class="formulaText"><inline-formula><math id="M49"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span></inline-formula></span> represent differential capacitance and differential resistance, respectively<sup>[<xref ref-type="bibr" rid="R7">7</xref>]</sup>Fig.5
Operando odd random phase electrochemical impedance spectroscopy (ORP-EIS) for in-situ monitoring of the Zr-based conversion coating growth in the presence of (in)organic additives
Odd random phase multisine electrochemical impedance spectroscopy to quantify a non-stationary behaviour: theory and validation by calculating an instantaneous impedance value
Localized corrosion: passive film breakdown vs. pit growth stability, part VI: pit dissolution kinetics of different alloys and a model for pitting and repassivation potentials
... [28]Proposed generation and annihilation reactions of defects at the interface of substrate metal and duplex passivation film in PDM-II and PDM-III models. Note: that reactions (1), (2), (4), (5) and (6) are lattice conservative processes (i.e. do not result in the movement of the interface), the reactions (3) and (7) are non-conservative<sup>[<xref ref-type="bibr" rid="R28">28</xref>]</sup>Fig.1
... [39]Equivalent circuit model corresponding to the case of the formation of complete uniform passivation film on passive metal. Wherein, <i>R</i><sub>e</sub> represents the solution resistance, <i>C</i><sub>dl</sub> represents the capacitance of the electrochemical double layer at the interface between the passive film and the electrolyte, <span class="formulaText"><inline-formula><math id="M16"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">F</mi><mo>,</mo><mtext> </mtext><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></math></span></inline-formula></span> is Faradaic resistance of oxygen reduction at the passive film/solution interface, <i>R</i><sub>ox, i</sub> and <i>R</i><sub>ox, e</sub> represent the resistances to the movements of ions and electrons in the passive film, respectively<sup>[<xref ref-type="bibr" rid="R39">39</xref>]</sup>Fig.3
... [39]Equivalent circuit model corresponding to the case of the formation of complete uniform passivation film on passive metal. Wherein, <i>R</i><sub>e</sub> represents the solution resistance, <i>C</i><sub>dl</sub> represents the capacitance of the electrochemical double layer at the interface between the passive film and the electrolyte, <span class="formulaText"><inline-formula><math id="M16"><msub><mrow><mi>Z</mi></mrow><mrow><mi mathvariant="normal">F</mi><mo>,</mo><mtext> </mtext><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></math></span></inline-formula></span> is Faradaic resistance of oxygen reduction at the passive film/solution interface, <i>R</i><sub>ox, i</sub> and <i>R</i><sub>ox, e</sub> represent the resistances to the movements of ions and electrons in the passive film, respectively<sup>[<xref ref-type="bibr" rid="R39">39</xref>]</sup>Fig.3
A mechanistic study on stress corrosion cracking of sensitized AA5083 in a simulated waterlevel fluctuation zone: combined impedance analysis and tensile tests
Equivalent circuit model of electrochemical behavior of sensitized 5083 Al-alloy in 3.5%NaCl solution under the condition of cracking of passivation film. This circuit contains four electrical components: <i>R</i><sub>e</sub>, <i>Z</i><sub>OX</sub>, <i>Z</i><sub>F</sub> and <i>C</i><sub>dl</sub><sup>[<xref ref-type="bibr" rid="R40">40</xref>]</sup>Fig.4
Ohm resistance-corrected Bode plots of 5083-O Al-alloy under different conditions. The details of the samples and test conditions are shown in Table 1<sup>[<xref ref-type="bibr" rid="R40">40</xref>]</sup>Fig.10
Nyquist (a) and Bode (b) plots of sensitized 5083-O Al-alloy under different conditions. The details of samples and test conditions are shown in Table 1<sup>[<xref ref-type="bibr" rid="R40">40</xref>]</sup>Fig.11
Nyquist (a) and Bode (b) plots of sensitized 5083-O Al-alloy under different conditions. The details of samples and test conditions are shown in Table 1<sup>[<xref ref-type="bibr" rid="R40">40</xref>]</sup>Fig.11
... [40]Nyquist (a) and Bode (b) plots of sensitized 5083-O Al-alloy under different conditions. The details of samples and test conditions are shown in Table 1<sup>[<xref ref-type="bibr" rid="R40">40</xref>]</sup>Fig.11
<strong>C</strong>alculated Bode plots from Eqs.(31) and (32) with exponent <i>γ</i> as a parameter based on power-law impedance model<sup>[<xref ref-type="bibr" rid="R44">44</xref>]</sup>Fig.6
Calculated normalized resistivity as a function of dimensionless position based on Eq. (31) with <span class="formulaText"><inline-formula><math id="M66"><mi>γ</mi></math></span></inline-formula></span> as a parameter<sup>[<xref ref-type="bibr" rid="R44">44</xref>]</sup>Fig.7
Calculated normalized resistivity as a function of dimensionless position based on Eq. (31) with <span class="formulaText"><inline-formula><math id="M66"><mi>γ</mi></math></span></inline-formula></span> as a parameter<sup>[<xref ref-type="bibr" rid="R44">44</xref>]</sup>Fig.7
... [44]Calculated normalized resistivity as a function of dimensionless position based on Eq. (31) with <span class="formulaText"><inline-formula><math id="M66"><mi>γ</mi></math></span></inline-formula></span> as a parameter<sup>[<xref ref-type="bibr" rid="R44">44</xref>]</sup>Fig.7
Calculated phase angle vs. frequency curves from Eq.(41) with <i>δ</i>/<i>λ</i> as a parameter based on Young impedance model<sup>[<xref ref-type="bibr" rid="R44">44</xref>]</sup>Fig.8
Calculated normalized resisitivity vs. dimensionless position curves from Eq.(40) with <i>δ</i>/<i>λ</i> as a parameter<sup>[<xref ref-type="bibr" rid="R44">44</xref>]</sup>Fig.9
Calculated normalized resisitivity vs. dimensionless position curves from Eq.(40) with <i>δ</i>/<i>λ</i> as a parameter<sup>[<xref ref-type="bibr" rid="R44">44</xref>]</sup>Fig.9
... [44]Calculated normalized resisitivity vs. dimensionless position curves from Eq.(40) with <i>δ</i>/<i>λ</i> as a parameter<sup>[<xref ref-type="bibr" rid="R44">44</xref>]</sup>Fig.9
The study of passive film's resistivity distribution to crystalline Fe-based pseudo high entropy alloys: The use of measurement model and Cole-Cole regression
... [58]Nyquist (a-c) and Bode (d-f) plots of 7050 Al-alloy in 3.5%NaCl solution with the gap widths of of 0.5 mm, 1 mm and 2 mm<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.12
Electrolyte resistance corrected impedance diagrams of 7050 Al-alloy during cavitation erosion in 3.5%NaCl solution with the gap widths of 0.5 mm (a), 1 mm (b) and 2 mm (c)<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.13
Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
Electrolyte resistance corrected impedance diagrams of 7050 Al-alloy during cavitation erosion in 3.5%NaCl solution with the gap widths of 0.5 mm (a), 1 mm (b) and 2 mm (c)<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.13
Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
... [58]Electrolyte resistance corrected impedance diagrams of 7050 Al-alloy during cavitation erosion in 3.5%NaCl solution with the gap widths of 0.5 mm (a), 1 mm (b) and 2 mm (c)<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.13
Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
... [58]Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
... [58]Nyquist (a-c) and Bode (d-f) plots of 7050 Al-alloy in 3.5%NaCl solution with the gap widths of of 0.5 mm, 1 mm and 2 mm<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.12
Electrolyte resistance corrected impedance diagrams of 7050 Al-alloy during cavitation erosion in 3.5%NaCl solution with the gap widths of 0.5 mm (a), 1 mm (b) and 2 mm (c)<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.13
Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
Electrolyte resistance corrected impedance diagrams of 7050 Al-alloy during cavitation erosion in 3.5%NaCl solution with the gap widths of 0.5 mm (a), 1 mm (b) and 2 mm (c)<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.13
Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
... [58]Electrolyte resistance corrected impedance diagrams of 7050 Al-alloy during cavitation erosion in 3.5%NaCl solution with the gap widths of 0.5 mm (a), 1 mm (b) and 2 mm (c)<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.13
Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
... [58]Impedance diagrams of 7050 Al-alloy after 1 h (a), 2 h (b) and 4 h (c) cavitation erosion in 3.5%NaCl solution with the gap width of 0.5 mm. All data are fitted based on Young model<sup>[<xref ref-type="bibr" rid="R58">58</xref>]</sup>Fig.14
Proposed equivalent circuits for fitting resistance responses at metal/passive film/electrolyte interfaces based on EEC 1 of PLM (a) and EEC 2 of DBLM (b). <i>C</i><sub>dl</sub> represents the capacitance of the electrochemical double layer at the oxide/electrolyte interface, which can be ignored throughout the fitting process<sup>[<xref ref-type="bibr" rid="R59">59</xref>]</sup>Fig.15
Electrochemical test methods for evaluating organic coatings on metals: an update. Part III: multiple test parameter measurements
0
1997
Electrochemical test methods for evaluating organic coatings on metals: an update. Part I. introduction and generalities regarding electrochemical testing of organic coatings
... [71]Schematic representation of a substrate/coating/electrolyte system (a) and corresponding equivalent circuit (b). Wherein, the upper box corresponds to Eq.(33) and the complete circuit is the one used for regression; CPE in the lower box is included considering the existence of oxide layer on the metal substrate<sup>[<xref ref-type="bibr" rid="R71">71</xref>]</sup>Fig.18
EIS plots of 2024 Al-alloy with hybrid sol-gel coating after immersion in 0.5 mol/L NaCl solution for 72 h. The circles indicate experimental data, and the solid lines are regression results<sup>[<xref ref-type="bibr" rid="R71">71</xref>]</sup>Fig.19
Resistivity profiles of 2024 Al-alloy with hybrid sol-gel coating after immersion for 24 h, 72 h and 168 h<sup>[<xref ref-type="bibr" rid="R71">71</xref>]</sup>Fig.20
Resistivity profiles of 2024 Al-alloy with hybrid sol-gel coating after immersion for 24 h, 72 h and 168 h<sup>[<xref ref-type="bibr" rid="R71">71</xref>]</sup>Fig.20
... [71]Resistivity profiles of 2024 Al-alloy with hybrid sol-gel coating after immersion for 24 h, 72 h and 168 h<sup>[<xref ref-type="bibr" rid="R71">71</xref>]</sup>Fig.20
Schematic representation of the two-layer model. It is assumed that the coating is consist of an inner layer with uniform resistivity <i>ρ = ρ</i><sub>c</sub> and an outer layer with an exponential dependence of resistivity on position<sup>[<xref ref-type="bibr" rid="R72">72</xref>]</sup>Fig.21
... [72]Resistivity vs. thickness curves for the coating after immersion in 0.5 mol/L NaCl solution for different time (a) and in 0.05 mol/L and 0.5 mol/L NaCl solution for 2 h and 504 h (b)<sup>[<xref ref-type="bibr" rid="R72">72</xref>]</sup>Fig.22<strong>4.3</strong> 模型的适用性和局限性讨论
Electrochemical behaviors of organic coating/matal substrate under simulated deep sea environment Part Ⅰ. effects of seawater pressure on transportation behavior of water through coating and coating's protective performance
