One‐dimensional Model of Oxygen Transport Impedance Accounting for Convection Perpendicular to the Electrode

A one‐dimensional (1D) model of oxygen transport in the diffusion media of proton exchange membrane fuel cells (PEMFC) is presented, which considers convection perpendicular to the electrode in addition to diffusion. The resulting analytical expression of the convecto‐diffusive impedance is obtained using a convection–diffusion equation instead of a diffusion equation in the case of classical Warburg impedance. The main hypothesis of the model is that the convective flux is generated by the evacuation of water produced at the cathode which flows through the porous media in vapor phase. This allows the expression of the convective flux velocity as a function of the current density and of the water transport coefficient α (the fraction of water being evacuated at the cathode outlet). The resulting 1D oxygen transport impedance neglects processes occurring in the direction parallel to the electrode that could have a significant impact on the cell impedance, like gas consumption or concentration oscillations induced by the measuring signal. However, it enables us to estimate the impact of convection perpendicular to the electrode on PEMFC impedance spectra and to determine in which conditions the approximation of a purely diffusive oxygen transport is valid. Experimental observations confirm the numerical results.     

An evaluation of the macro-homogeneous and agglomerate model for oxygen reduction in PEMFCs

The kinetics of oxygen reduction reaction on platinum/carbon powders in a Nafion film were evaluated with rotating disk electrode and gas diffusion electrode. The effects of the activation, mass transport and ohmic overpotentials were simulated via an “effectiveness factor” approach. The macro-homogeneous model was suitable to simulate the ORR kinetics at the RDE. On the other hand, it was found that the macro-homogeneous model does not simulate the operation of a porous gas diffusion cathode in PEMFC. With this model, the diffusion overpotential in the cathode is considerably overestimated. Conversely, the good agreement between calculated and experimental Tafel plots demonstrates the validity of the agglomerate model, even though the active layers of the PEMFC electrodes were thin and contained no PTFE. These results provided evidence for a two step transport process in the active layer of PEMFC electrodes.     

质子交换膜燃料电池二维全电池两相流综合数值模型

针对直通道质子交换膜燃料电池（PEMFC）建立了一个二维全电池综合数值模型,模型综合考虑参与电化学反应的三个要素反应物质、电子和质子的传输过程以及液态水的淹没和膜内水传输现象。研究了供气压力、液态水淹没对电池性能的影响;比较了不同输出电压、供气湿度等条件对阴极液态水饱和度分布以及电解质膜含水率的影响;预测了基准供气状态下电池的极化曲线和文献报道的实验结果吻合很好。计算结果显示：输出电压越小液态水淹没电极现象越严重;阴极液态水的生成有利于膜的浸润保持较高电导率,但是会淹没电极使有效电极面积减小,导致电池性能下降。     

A three-dimensional numerical simulation of the transport phenomena in the cathodic side of a PEMFC

A three-dimensional numerical model is developed to simulate the transport phenomena on the cathodic side of a polymer electrolyte membrane fuel cell (PEMFC) that is in contact with parallel and interdigitated gas distributors. The computational domain consists of a flow channel together with a gas diffusion layer on the cathode of a PEMFC. The effective diffusivities according to the Bruggman correlation and Darcy's law for porous media are used for the gas diffusion layer. In addition, the Tafel equation is used to describe the oxygen reduction reaction (ORR) on the catalyst layer surface. Three-dimensional transport equations for the channel flow and the gas diffusion layer are solved numerically using a finite-volume-based numerical technique. The nature of the multi-dimensional transport in the cathode side of a PEMFC is illustrated by the fluid flow, mass fraction and current density distribution. The interdigitated gas distributor gives a higher average current density on the catalyst layer surface than that with the parallel gas distributor under the same mass flow rate and cathode overpotential. Moreover, the limiting current density increased by 40% by using the interdigitated flow field design instead of the parallel one.     

相对湿度对质子交换膜燃料电池性能影响的模型研究

采用全电池催化层模型建立一个沿流道方向的燃料电池二维综合数值模型,研究不同供气湿度条件下膜内水迁移过程及其对输出性能的影响。计算结果显示：阴极进口相对湿度从100%变为10%,阴极侧膜失水导致电解质膜欧姆极化损失由0.15 V增大至0.36 V;随着相对湿度减小氧气浓度增大,阴极活化极化损失由0.45 V减小为0.22 V。模型预测的不同相对湿度条件下极化曲线和文献中实验数据吻合很好。     

Dynamic Simulation of Oxygen Transport Rates in Highly Ordered Electrodes for Proton Exchange Membrane Fuel Cells

Highly ordered Pt electrode has been recognized as an important technology for reducing Pt usage in fuel cells due to its improved oxygen transport capability. However, ordered Pt electrode can lead to the decrease in roughness of electrode, which in turn makes it unclear whether the improved oxygen transport can offset the decreased roughness of ordered electrode. Herein, we theoretically investigate the oxygen distribution, generated current, and minimum Pt loading of ordered Pt electrode based on kinetic model of oxygen transport. The results reveal that ordered Pt electrodes do not exhibit concentration polarization with the electrode thickness up to 100 μm. For ordered Pt electrode with diameter of nanorod of 60 nm, the limited current density reaches 110.2 A cm⁻² that is much higher than that for conventional electrode without considering Ohmic loss and mass transport loss outside electrode. To generate a current of 1.5 A cm⁻² at 0.67 V for fuel cell, the minimum Pt loading of cathode in PEMFC reaches 0.029 mg cm⁻² assuming that the electrocatalyst nanorods contain 1 nm Pt layer at the outmost surface.     

A “proton pump” concept for the investigation of proton transport and anode kinetics in proton exchange membrane fuel cells

A novel concept for the measurement of proton transport properties and electrode kinetics in proton exchange membrane fuel cells (PEMFC) is presented. The “proton pump” is essentially a fuel cell operated with pure nitrogen or very low hydrogen partial pressure instead of oxygen-containing gas on the cathode side, avoiding the complicated electrode kinetics of oxygen reduction. In this first study using this concept, we investigated the proton transport in high temperature PEMFC based on polybenzimidazole (PBI)/phosphoric acid membranes. The impedance spectra of the proton pump allow the clear distinction between anode and cathode kinetics and proton transport in the membrane. Identifying and analyzing the contribution of the anodic processes in the impedance spectra enabled the quantitative investigation of anode kinetics based on the Butler-Volmer equation. The proton transport was investigated in more detail in the current saturation region, where proton transport turned out to be the limiting process in case of sufficient H₂ supply at the anode. The maximum proton transport capacity of the PBI/phosphoric acid membrane was found to be comparable to those of Nafion^® membranes.     

Effect of membrane-electrode-assembly configuration on proton exchange membrane fuel cell performance

Four different membrane-electrode-assemblies (MEAs) with single and dual-layer gas diffusion layers (GDLs) at the anode and the cathode were prepared to examine polarization characteristics that rely on MEA configuration. Porous structure of single and dual-layer GDLs was investigated using a mercury porosimeter. An MEA with dual-layer GDLs at each electrode demonstrated higher performance with an air feed. To comprehend the improvement, the impedance behavior at various current densities and polarization behavior under back pressure were analyzed in terms of oxygen diffusion processes that control catalyst utilization in the gas diffusion electrode.     

A Simple and Accurate Method for High‐Temperature PEM Fuel Cell Characterisation

A set of basic parameters for any polymer electrolyte membrane fuel cell (PEMFC) includes the Tafel slope b and the exchange current density j_* of the cathode catalyst, the oxygen diffusion coefficient D_b in the cathode gas‐diffusion layer and the cell resistivity R_cell. Based on the analytical model of a PEMFC [A. A. Kulikovsky, Electrochim. Acta (2004) 617], we propose a two‐step procedure allowing to evaluate these parameters for a high‐temperature PEMFC. The procedure requires two polarisation curves measured at different oxygen (air) stoichiometries. The method is validated using the experimental data obtained with the in‐house designed cell. High quality of fitting confirms validity and accuracy of this approach. The physical background of the method is discussed.     

球形团聚物模型在质子交换膜燃料电池过程模拟中的应用

在建立直通道质子交换膜燃料电池(PEMFC)的二维全电池数学模型中,将球形团聚物模型应用至两极的催化剂层。通过调节团聚物中质子传导介质的比例和催化层孔隙率,预测了基准供气状态下单电池的极化曲线,与文献报道的实验数据吻合良好。研究了电池运行过程中,膜电极内各化学组分和电流密度的分布情况及流向,比较了不同供气压力、催化剂铂颗粒尺寸等参数对电池性能的影响。计算结果表明,在阴极及时排出反应产生的水,并在阳极对燃料气进行加湿是保证单电池正常运行的前提,提高阴极的氧化剂气体压力,可显著改善PEMFC单电池性能,特别是在受浓差极化影响较大的大电流密度区;在催化剂铂载量相同的情况下,减小铂颗粒的尺寸可以提高电池的性能。     

Electrochemical impedance spectroscopy evidence of dimethyl-silicon-oil enhancing O2 transport in a porous electrode

Faster oxygen transport is critical to guarantee reliable power output of polymer electrolyte membrane fuel cells (PEMFCs). In order to enhance oxygen transfer in a porous electrode especially in the case of water flooding, water-proof oil (dimethyl-silicon-oil (DMS)) was introduced into the conventional Pt/C electrode. Owing to the capability of electrochemical impedance spectroscopy (EIS) in discriminating individual contribution of ohmic, kinetic, and mass transport from all PEMFC processes, EIS was carried out to evaluate the effect of the DMS on the oxygen reduction reaction (ORR). The equivalent circuits corresponding to the EIS spectra were employed. The parameters in the equivalent circuits were obtained by curve fitting to the EIS spectra with the aid of the frequency response analysis software (FRA) attached in the electrochemical station Autolab PGSYAT302. The EIS analysis has shown that the introduction of DMS reduces the oxygen diffusion resistance as well as the charge transfer resistance in the flooded state. The single cell tests show that even in the case of normal operating condition the accumulated water with PEMFC operation also worsens the oxygen transfer in the conventional Pt/C gas diffusion electrode (GDE) with more and more water produced at the cathode. GDE containing DMS, which is defined as a flooding tolerant electrode (FTE), is fortunately quite good at alleviating water flooding. Success of the FTE in alleviating water flooding is ascribed to (1) its high oxygen transfer flux due to the higher solubility of oxygen in DMS than in water as long as parts of pores are occupied beforehand by DMS rather than by water, and (2) enhanced hydrophobic property of the FTE with DMS adsorption on the walls of the pores, which makes more hydrophobic pores be open to oxygen transport.     

Cobalt coated electrodes for high efficiency PEM fuel cells by plasma sputtering deposition

Proton exchange membrane (PEM) fuel cell electrodes coated with ultra-thin Co layer have been successfully fabricated via plasma sputter-deposition. In order to investigate the influence of Co layers on the oxygen reduction reaction, a series of Co layers with different nominal thickness have been deposited into the cathode–membrane interface. The polarization curves confirmed visible enhancement in cell performance when a 5 nm Co layer on cathode gave rise to a high current density of 750 mA cm⁻² at 0.6 V. Scanning electron microscopy showed that the sputter deposited 5 nm Co layer formed nanosized island structures on the porous electrode, while electrochemical impedance spectra confirmed that a reduction in the total impedance of the electrode led to the improvement of the membrane electrode assembly (MEA) performance.     

In situ grown carbon nanotubes on carbon paper as integrated gas diffusion and catalyst layer for proton exchange membrane fuel cells

In situ grown carbon nanotubes (CNTs) on carbon paper as an integrated gas diffusion layer (GDL) and catalyst layer (CL) were developed for proton exchange membrane fuel cell (PEMFC) applications. The effect of their structure and morphology on cell performance was investigated under real PEMFC conditions. The in situ grown CNT layers on carbon paper showed a tunable structure under different growth processes. Scanning electron microscopy (SEM) and Brunauer–Emmett–Teller (BET) demonstrated that the CNT layers are able to provide extremely high surface area and porosity to serve as both the GDL and the CL simultaneously. This in situ grown CNT support layer can provide enhanced Pt utilization compared with the carbon black and free-standing CNT support layers. An optimum maximum power density of 670 mW cm⁻² was obtained from the CNT layer grown under 20 cm³ min⁻¹ C₂H₄ flow with 0.04 mg cm⁻² Pt sputter-deposited at the cathode. Furthermore, electrochemical impedance spectroscopy (EIS) results confirmed that the in situ grown CNT layer can provide both enhanced charge transfer and mass transport properties for the Pt/CNT-based electrode as an integrated GDL and CL, in comparison with previously reported Pt/CNT-based electrodes with a VXC72R-based GDL and a Pt/CNT-based CL. Therefore, this in situ grown CNT layer shows a great potential for the improvement of electrode structure and configuration for PEMFC applications.     

PEMFC流道横截面二维两相流数学模型(Ⅰ)模型建立

建立了质子交换膜燃料电池（PEMFC）流道和脊横截面的二维两相流数学模型（across-the-channel model）。模型描述了PEMFC主要的传递和反应过程,包括阴、阳两极反应气的质量传递、动量传递、电子和质子的传递以及电化学反应等。模型细致地描述了水（液态和气态）在扩散层、催化层以及质子交换膜中的传递过程。模型可以用来研究流场、扩散层、催化层以及膜等对电池性能的影响,进而达到优化电池结构的目的。     

Modelling Approach for Planar Self‐Breathing PEMFC and Comparison with Experimental Results

This paper presents a model‐based analysis of a proton exchange membrane fuel cell (PEMFC) with a planar design as the power supply for portable applications. The cell is operated with hydrogen and consists of an open cathode side allowing for passive, self‐breathing, operation. This planar fuel cell is fabricated using printed circuit board (PCB) technology. Long‐term stability of this type of fuel cell has been demonstrated. A stationary, two‐dimensional, isothermal, mathematical model of the planar fuel cell is developed. Fickian diffusion of the gaseous components (O₂, H₂, H₂O) in the gas diffusion layers and the catalyst layers is accounted for. The transport of water is considered in the gaseous phase only. The electrochemical reactions are described by the Tafel equation. The potential and current balance equations are solved separately for protons and electrons. The resulting system of partial differential equations is solved by a finite element method using FEMLAB (COMSOL Inc.) software. Three different cathode opening ratios are realized and the corresponding polarization curves are measured. The measurements are compared to numerical simulation results. The model reproduces the shape of the measured polarization curves and comparable limiting current density values, due to mass transport limitation, are obtained. The simulated distribution of gaseous water shows that an increase of the water concentration under the rib occurs. It is concluded that liquid water may condense under the rib leading to a reduction of the open pore space accessible for gas transport. Thus, a broad rib not only hinders the oxygen supply itself, but may also cause additional mass transport problems due to the condensation of water.     

质子交换膜燃料电池膜中气态水管理模型

分析质子交换膜燃料电池的膜水含量与运行参数的关系,从工程方法的角度建立水传输模型.模型分析得到,要提高膜的水合程度,需要通过增湿反应气体.过高的增湿反应气体又会引起阴极扩散层水的泛滥,需通过调节反应气体流量来缓解水的泛滥.为保证膜的高水合程度和低的阴极扩散层水的泛滥,建立了膜水含量的神经网络控制模型,为电池水管理奠定了基础.     

Performance degradation studies on PBI/H3PO4 high temperature PEMFC and one-dimensional numerical analysis

Five hundred hours continuous aging test at constant discharge current (640 mA cm⁻²) was performed on PBI/H₃PO₄ high temperature PEMFC unit cell, electrochemical techniques-linear sweep voltammetry (LSV) and AC impedance measurement were used to investigate the changes of electrochemical surface area (ESA) and high frequency resistance (internal resistance) with time. Initial experimental results showed that during 500 h continuous aging test the main reason for cell performance degradation is the decrease of ESA caused by sintering. In addition, a one-dimensional mathematical model was constructed, the concentration distributions of cathode reactant gases (O₂ and gaseous H₂O) were calculated and polarization curves recorded during aging test were simulated based on the model, the simulated polarization curves compare well with the experimental results.     

PEMFC流道截面对气体浓度在催化层分布影响的数值分析

以蛇形流场质子交换膜燃料电池阴极为研究对象,取其中一部分建立三维、稳态的数学计算模型,利用CFD（计算流体动力学）方法研究了质子交换膜燃料电池阴极内的流动和传质过程,得到了阴极内氧气和水蒸气的质量分数的分布情况,探讨了流道宽度和深度对气体在催化层空间分布的影响,为燃料电池流场的设计和改进提供了参考依据。     

PEMFC阴极扩散层结构特性对水淹影响的数值分析

建立质子交换膜燃料电池一维两相传递模型,通过达西定律和菲克定律的联立求解得到扩散层中的液体饱和度和氧气浓度分布。考察扩散层特性参数孔隙率、厚度、接触角、渗透率对阴极水淹的影响,结果表明扩散层表面憎水将有助于液态水移出,但当达到憎水条件后,增大接触角对液态水传输和氧气传质的影响逐渐变小。憎水条件下孔隙率和厚度对液态水传输的影响不是很明显,但孔隙率增大和扩散层厚度减小均有利于氧气传质,实际应用中孔隙率增大的同时,厚度也要适当增大,极限电流密度相差不大。模型计算结果与文献中不同PTFE含量条件下实验的Tafel斜率和极限电流密度比较,吻合较好。