# Evaluation the Resistance Growth of Aged Vehicular Proton Exchange Membrane Fuel Cell Stack by Distribution of Relaxation Times

^{*}

## Abstract

**:**

^{−2}after running for 2000 h in the driving cycle. Mass transport is the main reason accounting for 66.1% of the resistance growth. The charge transfer resistance growth cannot be ignored, accounting for 30.23%. The resistance growth obtained by the DRT can quickly and accurately identify the main reason for stack decline and therefore promises to become an important diagnostic tool in relation to aging.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The PEMFC Stack and Test Bench

#### 2.2. Procedure of the Experimental Test

^{−2}to ensure the repeatability of the results. The operating variable of current densities for the EIS and polarization curve test of the new stack covers 20 mA cm

^{−2}to 1200 mA cm

^{−2}and the other operation conditions are referred to in Table 2. For the aged stack, the current densities range covers 20 mA cm

^{−2}to 800 mA cm

^{−2}. It operates for 15 min to ensure the validity of the test after changing the current density, and each point of current density is measured three times.

#### 2.3. Kramers–Kronig Validity Test

#### 2.4. Distribution of Relaxation Times

## 3. Results and Discussion

#### 3.1. Validity and Analysis of Measured EIS Data

^{−2}for a new stack in a frequency range of 0.4 Hz to 2 kHz. The Nyquist plot shows ${R}_{0}$ defined as a high-frequency intercept and ${R}_{\mathrm{pol}}$ defined as the subtraction of the low-frequency intercept from ${R}_{0}$. Since DRT requires high-quality EIS data, the validation of KK relations of each group of EIS data is required before DRT analysis. Figure 3b shows typical KK validation results at the current density of 400 mA cm

^{−2}of the new stack. The relative residuals between the imaginary part and the real part of the impedance are less than 0.5% in the whole frequency range.

^{−1}, there is a large overlap between the two peaks. Two obvious peaks are recognized with $\lambda $ values of 10

^{−2}to 10

^{−4}. From the relative residual distribution of the real part and the imaginary part in Figure 4b,c, the oscillation of the relative residual is more remarkable with the $\lambda $ of 10

^{−1}. Figure 4d depicts the SSR of the calculated DRT with $\lambda $ from 10

^{1}to 10

^{−7}. The SSR decreases exponentially with the decrease in the $\lambda $ value from 10

^{1}to 10

^{−2}. When reducing $\lambda $ to 10

^{−2}, the SSR tends to balance, and when the $\lambda $ is further reduced, the SSR is almost unchanged. This means that further decreasing $\lambda $ shows no notable improvement in DRT results or model accuracy while it increases the risk of system oscillation. Considering the residual and avoiding oscillation, it is reasonable to set the $\lambda $ value to 10

^{−3}.

#### 3.2. The Polarization Process Analysis of a New Stack with DRT

^{−2}to 1200 mA cm

^{−2}, covering low and high current densities. The other operating conditions are kept constant, according to Table 1.

^{2}to 355 mΩ cm

^{2}with the increase in current density at low current density regions (from 20 mA cm

^{−2}to 200 mA cm

^{−2}) and decreases gently from 340 mΩ cm

^{2}to 294 mΩ cm

^{2}at medium current density regions (from 300 mA cm

^{−2}to 600 mA cm

^{−2}). However, at high current density regions (from 800 mA cm

^{−2}to 1200 mA cm

^{−2}), the polarization resistance ${R}_{\mathrm{pol}}$ increases slightly from 276 mΩ cm

^{2}to 353 mΩ cm

^{2}with the increase in current densities. The main reason is that the mass transport limitation gradually dominates.

^{2}over the entire current densities range. In addition, at low current density regions, an obvious arc appears in the high-frequency region of the EIS data, which will be explained in the DRT analysis below.

^{−2}to 200 mA cm

^{−2}), the P2 peak dominates the polarization process and rapidly decreases, and the characteristic frequency gradually shifts right from 3 Hz (20 mA cm

^{−2}) to 20 Hz (200 mA cm

^{−2}) with the increase in current density. In the enlarged view of Figure 5b, there is a P3 peak in the high-frequency region next to the P2 peak. The P3 peak has almost no correlation with the current density, and the characteristic frequency is about 300 Hz. The peak P3 in the high-frequency region is related to the process of the anode side and the proton transport of the cathode catalyst layer [23,35]. Due to the small peak of P3, the contribution for the polarization loss analysis can be ignored. The P1 peak begins to appear and the characteristic frequency is about 1.3 Hz (200 mA cm

^{−2}) in the low-frequency region left to peak P2.

^{−2}to 1200 mA cm

^{−2}), the P2 peak decreases slowly with the increase in current density, and the characteristic frequency continuously shifts right to 70 Hz (1200 mA cm

^{−2}). Due to the right shift of the P2 peak, the characteristics of the P3 peak are rolled inside the P2 peak; therefore, the P3 peak almost disappears in the high current density region. This phenomenon can also be verified from the high-frequency region of the Nyquist plot which has an obvious arc at the low current density region but disappears at the high current density region. With the increase in current density, the P1 peak gradually rises and dominates the polarization process. The characteristic frequency of P1 gradually shifts to the right of 6.5 Hz (1200 mA cm

^{−2}). The shift in the characteristic frequency of P1 is mainly due to the decrease in the polarization resistance.

^{−2}) from 2.3 to 1.4 (the other operating conditions refer to Table 3). According to the Nyquist plot in Figure 6a, as the air stoichiometry gradually decreases, the right arc gradually increases. It can be seen more clearly from the DRT spectrum in Figure 6b that the P1 peak is also gradually increasing. This conclusion is consistent with the air stoichiometry mainly affecting the cathode mass transport under high current density [56].

#### 3.3. The Polarization Process Analysis of the Aged Stack with DRT

^{−2}), 50% (400 mA cm

^{−2}), and 100% (800 mA cm

^{−2}) rated power. After that, the polarization curve of the aged stack is shown in Figure 7. Compared with the new stack, the voltage of the aged stack decreases significantly at each current density point. As can be seen from the I–V polarization curve, the voltage has been reduced from 0.89 V to 0.85 V even at a low current density (20 mA cm

^{−2}). The voltage recession also increases gradually with the increase in current density. The voltage is reduced from 0.67 V to 0.57 V at the rated current density of 800 mA cm

^{−2}with a recession rate of 15%. Furthermore, the voltage data of the stack at 100% rated power (800 mA cm

^{−2}) is extracted, and the average voltage of the stack at this operating point per day is used as the average cell voltage ${\overline{V}}_{\mathrm{cell}}$. The curve of ${\overline{V}}_{\mathrm{cell}}$ at 800 mA cm

^{−2}during the driving cycle is shown in Figure 7c. ${\overline{V}}_{\mathrm{cell}}$ gradually decreases from 0.65 V to 0.57 V. In the first 120 days, ${\overline{V}}_{\mathrm{cell}}$ undergoes large fluctuations but the overall decline is slight. This abnormal fluctuation is mainly due to the unsuitability of the operating conditions of the stack caused by the change in ambient temperature. For example, the capacity of the air compressor will decrease with an increase in ambient temperature, resulting in water management problems for the stack. After 120 days, ${\overline{V}}_{\mathrm{cell}}$ gradually decreases from 0.64 V to 0.57 V, and the ${\overline{V}}_{\mathrm{cell}}$ reaches its lowest point at 240 days. The EIS tests are carried out at 240 days.

^{−2}to 800 mA cm

^{−2}. The other operating conditions are kept constant, according to Table 2.

^{2}to 450 mΩ cm

^{2}with the increase in current density at low current density regions (from 20 mA cm

^{−2}to 300 mA cm

^{−2}); however, it remains constant at 410 mΩ cm

^{2}in the middle and high current density regions (from 400 mA cm

^{−2}to 800 mA cm

^{−2}). The polarization resistance ${R}_{\mathrm{pol}}$ increases by 48% compared with the new stack at 800 mA cm

^{−2}.

^{2}to 90 mΩ cm

^{2}in the low current density regions and remains almost constant at 90 mΩ cm

^{2}in the high current density region. The ohmic resistance ${R}_{\mathrm{o}}$ increases by 4% compared with the new stack at 800 mA cm

^{−2}(Table 3).

^{−2}) to 21 Hz (200 mA cm

^{−2}) with the increase in current density. In the enlarged view of Figure 8b, the characteristic frequency of the P3 peak is 310 Hz.

^{−2}to 800 mA cm

^{−2}), the P2 peak decreases slowly with the increase in current density, and the characteristic frequency continuously shifts right to 38 Hz (800 mA cm

^{−2}). The P3 peak also disappears in the high current density region. With the increase in current density, the P1 peak gradually rises and dominates the polarization process. The characteristic frequency of P1 gradually shifts to the right to 4.7 Hz (800 mA cm

^{−2}). From the above analysis, the characteristic frequency of the P1 and the P2 peaks has slightly increased, but the distribution function has undergone a significant increase compared with the new stack.

#### 3.4. Individual Resistance Growth of the Aged Stack

^{−3}at the current density of 400 mA cm

^{−2}for the new stack. There are two obvious peaks, hence a two-order RC ECM is applied and compared with the DRT results in Figure 9c. Each peak region represents an independent polarization process, and the area within the span of each region from ${f}_{l}$ to ${f}_{u}$ represents the resistance, ${R}_{\mathrm{pol}-\mathrm{i}},$ of the polarization process [33].

^{2}to 139 mΩ cm

^{2}(from 60 mA cm

^{−2}to 800 mA cm

^{−2}). At each current density, the growth rate of ${R}_{\mathrm{ct}}$ is about 25% compared to the new stack. ${R}_{\mathrm{diff}}$ is basically 0 at a low current density and increases rapidly from 100 mΩ cm

^{2}to 250 mΩ cm

^{2}(from 200 mA cm

^{−2}to 800 mA cm

^{−2}) in the aged stack (Figure 10d). The growth rate of ${R}_{\mathrm{diff}}$ of the aged stack compared to the new stack is about 35%. It can be seen from Figure 10e that the ${R}_{\mathrm{ohm}}$ of the aged stack slightly increases compared with that of the new stack. The growth rate is about 5%. However, the growth rate is larger at a low current density, possibly because the gas humidity of the aged stack does not completely reach the preset humidity range. It can be seen from Figure 10f that the resistance value of ${R}_{\mathrm{an}}$ is relatively small and only exists in low current density regions. The growth rate of ${R}_{\mathrm{an}}$ is negative in the low current density range and ${R}_{\mathrm{an}}$ even disappears in the middle and high current density regions. This anomaly may be due to the fact that the characteristic frequency of the P2 peak of the aged stack is shifted to the right compared to the new stack. The P3 peak is more affected by the P2 peak and is rolled inside the P2 peak at a smaller current density, resulting in a decrease in the area of the P3 peak. With the increase in current density, the P2 peak shifts more to the right, resulting in the disappearance of the P3 peak. However, the P3 peak is relatively small and can be ignored without affecting the accuracy of the calculation. The resistance values of the new and aged stacks at different current densities are shown in Table 3.

#### 3.5. Recession Analysis of the Aged Stack

^{−2}are compared. As can be seen from Figure 11a, the sum of the resistance growth of each polarization process decomposed by DRT is 97 mΩ cm

^{2}, the resistance growth analyzed by the ECM of the measured EIS data is 89 mΩ cm

^{2}, and the equivalent resistance growth of the voltage decrease through the I–V polarization curve $\Delta {R}_{\mathrm{total}}$ is 99 mΩ cm

^{2}. The DRT method is closer to the actual resistance growth, and the deviation is about 3%. Therefore, it can be considered that the DRT method is effective in the analysis of the aged stack.

^{−2}. In Figure 11b, $\Delta {R}_{\mathrm{diff}}$ overwhelmingly dominates the resistance growth of 66.1%, which means that the oxygen mass transport performance of the aged stack undergoes a severe decline and the possible influencing factors include the GDL/MPL and the catalyst layer (CL). The low temperatures at which the PEMFC operates mean that the product water is almost liquid. This liquid water can accumulate in the pores of the CL and must be removed to keep the gas pathways to the active sites of the CL unblocked [57]. Many researchers have reported that the GDL interacts with the changes in water during durability tests. These changes appear to occur at the microstructural level [58,59]. The GDL gradually changes from hydrophobic to hydrophilic and gas diffusion and convection are blocked after the durability test [60]. In addition, liquid water covers the catalyst–ionomer phase in the CL, limiting the flow of gas to the active platinum sites [61]. As a result, the performance of the PEMFC decreases drastically under high current densities. Keeping the hydrophobic properties of the GDL/MPL hydrophobic gradient constant is important for maintaining mass transport during the durability test. $\Delta {R}_{\mathrm{ct}}$ also makes a great contribution to the resistance growth of 30.23%. Carbon corrosion and the dissolution and aggregation of platinum catalysts may be the main reasons for the increase in ORR polarization resistance [1,14,17,62]. $\Delta {R}_{\mathrm{ohm}}$ has little effect on resistance growth, which is only 3.67%.

## 4. Conclusions

^{−2}declines by about 15%. The resistance growth method based on the DRT is proposed to determine the reason for the decline of the stack.

^{−2}were compared to verify the accuracy of the DRT method. The DRT method has been found to yield a result closer to the actual resistance growth, with a deviation of about 3%, which verifies the effectiveness of the DRT method. The increase in mass transport resistance is the main reason for the resistance growth, accounting for 66.1% at rated power. We believe that optimizing the oxygen mass transport performance is the key factor in improving the lifetime of the stack. The charge transfer resistance of the ORRs also makes a great contribution to the resistance growth of 30.23% at rated power. The ohmic resistance has little effect on resistance growth.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**(

**a**) Nyquist plot of EIS data at a current density of 400 mA cm

^{−2}of a new stack. (

**b**) Relative residual of the KK transformation.

**Figure 4.**(

**a**) Calculated DRTs with $\lambda $ values from 10

^{−1}to 10

^{−4}. (

**b**) Relative residual of the real part of the impedance. (

**c**) Relative residual of the imaginary part of the impedance. (

**d**) SSR of the calculated DRT with a $\lambda $ value from 10

^{1}to 10

^{−7}.

**Figure 5.**(

**a**) Nyquist plot of low current densities of the new stack. (

**b**) Relevant DRT spectra. (

**c**) Nyquist plot of middle and high current densities of the new stack. (

**d**) Relevant DRT spectra.

**Figure 6.**(

**a**) Nyquist plot with different air stoichiometries from 1.4 to 2.3 (800 mA cm

^{−2}). (

**b**) Relevant DRT spectra.

**Figure 7.**(

**a**) The drive cycle of the stack on the bus. (

**b**) The polarization curve of the new and aged stacks. (

**c**) The average cell voltage of 800 mA cm

^{−2}during the driving cycle.

**Figure 8.**(

**a**) Nyquist plot of low current densities of the aged stack. (

**b**) Relevant DRT spectra. (

**c**) Nyquist plot of middle and high current densities of the aged stack. (

**d**) Relevant DRT spectra.

**Figure 9.**(

**a**) ECM for standard RC elements. (

**b**) DRT spectra for standard RC elements. (

**c**) ECM developed by DRT with a λ value of 10

^{−3}.

**Figure 10.**(

**a**) Nyquist plot of the new and aged stacks at different current densities. (

**b**) Relevant DRT spectra. (

**c**) Relevant ${R}_{\mathrm{ct}}$. (

**d**) Relevant ${R}_{\mathrm{diff}}$. (

**e**) Relevant ${R}_{\mathrm{ohm}}$. (

**f**) Relevant ${R}_{\mathrm{an}}$.

**Figure 11.**(

**a**) The resistance growth obtained by the DRT, ECM and I–V of the aged stack at a rated current density of 800 mA cm

^{−2}. (

**b**) Relevant proportions of each polarization resistance growth obtained by the DRT.

Parameters | Values |
---|---|

Specification | S2 |

Pitch number | 216 |

Electrochemical active area | 195 cm^{2} |

Cathode/anode Pt loading | 0.4 mg cm^{−2}/0.1 mg cm^{−2} |

Rated output power of stack | 22.6 kW |

Rated current of stack (0.67 V) | 156 A |

Maximum output power of stack | 30.3 kW |

Maximum current of stack (0.6 V) | 234 A |

Working temperature | 70~80 °C |

Bipolar plate | Metal |

Flow field | Counter flow |

Parameters | Values |
---|---|

Operating temperature | 70 °C |

Anode relative humidity | 60% |

Current density | 20~800 mA cm^{−2} |

Cathode relative humidity | 80% |

Anode stoichiometry | 1.5 |

Cathode stoichiometry | 2 |

Anode pressure | 0.85 bar |

Cathode pressure | 0.75 bar |

Current Density | Type | New Stack | Aged Stack | Growth Rate |
---|---|---|---|---|

60 mA cm^{−2} | ${R}_{\mathrm{ct}}$ | 693 mΩ cm^{2} | 854 mΩ cm^{2} | 23% |

${R}_{\mathrm{diff}}$ | 0 | 0 | - | |

${R}_{\mathrm{ohm}}$ | 81.5 mΩ cm^{2} | 104 mΩ cm^{2} | 22% | |

${R}_{\mathrm{an}}$ | 24.3 mΩ cm^{2} | 6 mΩ cm^{2} | −75% | |

200 mA cm^{−2} | ${R}_{\mathrm{ct}}$ | 292 mΩ cm^{2} | 372 mΩ cm^{2} | 27% |

${R}_{\mathrm{diff}}$ | 78 mΩ cm^{2} | 105 mΩ cm^{2} | 35% | |

${R}_{\mathrm{ohm}}$ | 84.8 mΩ cm^{2} | 90 mΩ cm^{2} | 6% | |

${R}_{\mathrm{an}}$ | 4.7 mΩ cm^{2} | 0 | - | |

400 mA cm^{−2} | ${R}_{\mathrm{ct}}$ | 183 mΩ cm^{2} | 220 mΩ cm^{2} | 20% |

${R}_{\mathrm{diff}}$ | 146 mΩ cm^{2} | 195 mΩ cm^{2} | 34% | |

${R}_{\mathrm{ohm}}$ | 83 mΩ cm^{2} | 85.4 mΩ cm^{2} | 3% | |

${R}_{\mathrm{an}}$ | 0 | 0 | - | |

800 mA cm^{−2} | ${R}_{\mathrm{ct}}$ | 109 mΩ cm^{2} | 139 mΩ cm^{2} | 28% |

${R}_{\mathrm{diff}}$ | 190 mΩ cm^{2} | 254 mΩ cm^{2} | 34% | |

${R}_{\mathrm{ohm}}$ | 82 mΩ cm^{2} | 86 mΩ cm^{2} | 4% | |

${R}_{\mathrm{an}}$ | 0 | 0 | - |

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## Share and Cite

**MDPI and ACS Style**

Zhu, D.; Yang, Y.; Ma, T.
Evaluation the Resistance Growth of Aged Vehicular Proton Exchange Membrane Fuel Cell Stack by Distribution of Relaxation Times. *Sustainability* **2022**, *14*, 5677.
https://doi.org/10.3390/su14095677

**AMA Style**

Zhu D, Yang Y, Ma T.
Evaluation the Resistance Growth of Aged Vehicular Proton Exchange Membrane Fuel Cell Stack by Distribution of Relaxation Times. *Sustainability*. 2022; 14(9):5677.
https://doi.org/10.3390/su14095677

**Chicago/Turabian Style**

Zhu, Dong, Yanbo Yang, and Tiancai Ma.
2022. "Evaluation the Resistance Growth of Aged Vehicular Proton Exchange Membrane Fuel Cell Stack by Distribution of Relaxation Times" *Sustainability* 14, no. 9: 5677.
https://doi.org/10.3390/su14095677