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Polymer Electrolyte Membrane Cell Performance and Phenomena
General layout on PEM devices’ performance
One of the most common methods used to analyze the PEM devices behaviors and performance is the polarization curves. It represents the cell voltage as a function of the current density. Using usually a potentiostat that applies a current and measures the voltage. The curves are later compared to other data found in the literature to characterize the performance. Each PEM device has a specific pattern that the measurements frequently revolves around. The variations around the theoretical shape is due to variation of the temperature, the relative humidity, the catalyst loading thickness and material, the types of membranes used, and so on.
Figure 1.13 exhibits the theoretical polarization curves frequently presented in the literature for (a) PEMWE and (b) PEMFC. Several phenomena contribute to the performance and thus to the obtaining of this Voltage-Current curve. The thermodynamic potential imposed by the redox couple determines the minimum potential in the case of the PEMWE and the maximum in the case of the PEMFC. When the current flows, the ohmic losses and the activation over potential appear, they are added to the thermodynamic potential in the case of the PEMWE. However, in the case of the PEMFC, the ohmic losses and activation over potential are deducted. For the PEMFC, the over potential appear due to the mass transport on the active sites at high current.
The methods of characterization like the polarization curves are needed to understand better the areas that still need to be improved in these devices. Even though they reached remarkably high performances in the market, these PEM cells still have many drawbacks which limits their efficiency.
For EHC, Casati et al. [60] have investigated some fundamental aspects in the EHC using a PEMFC; this work has unveiled some performing parameters of the system, such as:
• The membrane hydration is a critical issue: galvanostatic operating conditions can damage the membrane due to the improper water management. Therefore, potensiostatic operating conditions must be favored.
• The feed flow has an important impact on the amount of hydrogen recovered. The recovered fraction rises when the inlet hydrogen flow rate decreases. The recovery rate is maximum when the inlet flow of hydrogen is equal to the flow rate through the membrane (determined by the cell current). Therefore, this maximum is determined by the hydrogen production (at the outlet).
• The specific energy consumption depends only on the applied voltage, which is divided into:
o Thermodynamic potential: due to the compression ratio of the hydrogen
o Kinetic potential: that depends on cell current, or in other words the flowrate of hydrogen treated across the MEA (overvoltage)
o Dissipative potential: defined by the useless forces (Ohmic drop)
Water management in PEMFC and EHC
Water transport through a proton electrolyte membrane (PEM) is a critical issue for both a fuel cell and an electrochemical compressor. Most of the studies that focused on water management were related to the case of fuel cells (FC). Water transport inside the membrane is induced by three mechanisms: the electro-osmotic drag caused by proton transport (from the anode to the cathode side), the back-diffusion flux (from the cathode to the anode side) due to gradient of water content and the Darcy like flux involved with the pressure gradient due to the pressure rise of the compression at the cathode side (in the case of EHC). The difference between the FC and the EHC for this particular issue is that at the cathode side of a FC, water is produced by the electrochemical reaction, which might cause an excess of water in the system (flooding); in the case of an EHC water is not involved in any of the reactions at stake; this does however not mean that water is useless to the operation of an EHC. Indeed, the lack of water production coupled to the need for non-negligible proton transport in the PEM from the anode to the cathode (being admitted that protons are accompanied by water molecules and that the present membranes need to be well-hydrated to promote fast proton transport) might cause a water drainage in the membrane; if uncontrolled, it will eventually stop any proton transport, hence the compression process.
The water content parameter is used to describe the water quantity in the membrane. Both Zawodzinksi et al. [61] and Springer et al. [41] have presented a correlation between the equilibrium water vapor pressure and the water content value for Nafion® at atmospheric pressure and a temperature of T = 30°C. Hinatsu et al. [62] demonstrated an empirical formula describing the previous correlation at a temperature of T = 80°C and Ge et al. [63] gave an equation predicting the water content in a PEM for 30 < T < 80°C. As for Kusoglu et al. [64], they talked about the internal balance between chemical and mechanical forces determining the water content in Nafion® membranes. For the diffusion coefficient, it is also a function of the water content; Majsztrik et al. [65] have provided insight into the different measurement methods considered in the literature to quantify water diffusion, whilst distinguishing sorption and desorption effects. For PEMFC, PEMWE and EHC many equations must be solved such as thermodynamic equilibrium, mass, momentum, and charge balance. Therefore, steady-state mass balance in the membrane for incompressible fluid flow simplifies the water equation as follows (equation (1.12)):
where H2O is the bulk concentration of water in the membrane (mol.m-3), ⃗m is the velocity inside the membrane (m s-1) and the term H2O is the effective diffusion coefficient of water (m².s-1).
The momentum balance is described by a form of Schlögl’s equation of motion, electric potential and pressure gradients generate convection within the pores of the ion-exchange membrane [66], as expressed by equation (1.13).
where μ denotes the water viscosity (kg m-1 s-1), κФ is the electro-kinetic permeability (m2), f is the fixed-charge number in the membrane, f is the fixed-charge concentration (mol.m-3), κp is the hydraulic permeability (m2), σ is the ionic conductivity (Ω-1 m-1) and ⃗ is the current density inside the membrane (A m-2).
This type of equation can be difficult to solve due to the different parameters that should be considered, such as the current density, the pressure, the water concentration, and the membrane characteristics.
Modeling of the EHC properties therefore requires a clear distinction between the internal driving forces for water fluxes and external conditions [67]. According to them, the hydrogen dehumidification is an interesting issue observed during compression. Compression of the gases leads to the pressure rise of the hydrogen at the cathode side unlike for water vapor that is condensed.
Gas permeation
As two compartments with different partial pressures are separated by a membrane, permeation of any species could occur downward the partial pressure gradient. Gas permeation is therefore driven by partial pressure gradient, and depends on the operating conditions, such as temperature and relative humidity (water management) and is determined by the nature of the membrane and its thickness. Kocha et al. described the principle of gas permeation and gave the expression of gas permeation rate Ni (mol s-1 m-2) of species i (equation (1.14)):
and the definition of ki, the gas molar permeability coefficient, (mol m-1 s-1 Pa-1) (equation (1.15)):
with Hi the solubility coefficient, (mol m-3 Pa-1), Di the effective diffusion coefficient in the membrane, m2 s-1, pi the partial pressure of gas (Pa), and the thickness of the membrane. These expressions demonstrate that the solubility and diffusion coefficient of the species are of equal importance in the permeation phenomenon.
Hydrogen crossover
A lot of study exists on hydrogen crossover in PEMFC ([68], [69], [70], [71], [72], among others), due to its severe impact on both the efficiency and durability of the fuel cell. For example, Brunetti et al [71] evaluated mass-transport, including hydrogen crossover, for Nafion® 117. The gas permeability coefficient depends on temperature, relative humidity, and nature of the membrane, while the transport is strongly depending on the water content and on the hydrothermal history of membrane. Truc et al.
[70] proposed a numerical model including hydrogen crossover and the dependence of permeability with membrane water content and temperature.
Table of contents :
1. State of art on Polymer Electrolyte Membrane devices for hydrogen carrier
1.1.1. Polymer Electrolyte Membrane Water Electrolysis
1.1.2. Polymer Electrolyte Membrane Fuel cells
1.1.3. Polymer Electrolyte Membrane compressor/concentration
1.2.1. Single Cell Design
1.2.2. Polymer Electrolyte Membrane
1.2.3. Catalyst Layer
1.2.4. Gas Diffusion Layer (GDL)
1.2.5. Bipolar Plates
1.2.6. Polymer Electrolyte Membrane Cell Performance and Phenomena
1.3.1. Purification methods
1.3.2. Comparison of Hydrogen Compression
1.3.3. Applied aspect of electrochemical compression/purification
1.3.4. Operating conditions
2. Modeling of Polymer Electrolyte Membrane cells (steady state, DC modeling)
2.2.1 Charge balance in the catalytic layer
2.2.2 Charge balance in the membrane
2.2.3 Mass balance in the membrane
2.3.1 Dimensionless equations
2.3.2 Analytical solution of the dimensionless equations
2.4.1 Dimensionless ionic current density distribution in catalyst layer
2.4.2 Dimensionless water content distribution in membrane
2.4.3 Dimensionless over potential variation
3. Polymer Electrolyte Membrane Cells Experimental Application: Electrochemical hydrogen compression/concentrator (or purification)
3.1.1 Conductivity measurement Setup
3.1.2 Electrochemical Hydrogen Compression Setup
3.2.1 Conductivity measurements for PEM membrane Nafion®
3.2.3 Measurements for PEM membrane Nafion® N117: Ammonia (NH3) effects
3.3.1 Online results: Pressure variation
3.3.2 Membrane resistance analysis for in situ experiment of EHC
3.4.1 Entropy analysis
3.4.2 Electrochemical Impedance Spectroscopy (EIS) comparison
3.6.1 Pressure variation for low hydrogen concentration
3.6.2 Pressure variation with methanol contamination
4. Polymer Electrolyte Membrane Cells Electrochemical Impedance Spectroscopy Modeling
4.1.1 The Principle of the Electrochemical Impedance Spectroscopy
4.1.2 The Electrochemical Impedance Spectroscopy approach methodology
4.1.3 Resolution example:
4.1.4 Equivalent electrical circuit
4.2.1 The equation system development at the active layer
4.2.2 Analytical solution of the equation
4.3.1 Electrochemical Impedance Spectroscopy: Frequency behaviors
4.3.2 Electrochemical Impedance Spectroscopy: Influence of σ and Rf
4.3.3 Electrochemical Impedance Spectroscopy: Experimental analysis
