Modeling of Polymer Electrolyte Membrane cells (steady state, DC modeling)

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 Polymer Electrolyte Membrane devices

The most common Proton Electrolyte Membrane devices are Proton Electrolyte Membrane Fuel Cells (PEMFCs) and Proton Electrolyte Membrane Water Electrolysis (PEMWEs). As shown in Figure 1.2, unlike the fuel cell, the polarity of the water electrolysis on the anode is positive and on the cathode is negative [12]. The Electrochemical Hydrogen Compressor (EHC) is one of the devices that will be also discussed in this paragraph (subsection 1.1.3). Its cell has the same structure as these two previous devices and the reactant gas feed consists of a hydrogen gas mixture at low pressure and the product is high pressure hydrogen. The core of the system is usually called membrane electrode assembly (MEA).
Figure 1.2: Comparison between Proton Electrolyte Membrane Fuel Cells and Proton Electrolyte Membrane Water Electrolysis [13]
PEMFC, EHC and PEMWE are currently developing to be an alternative for hydrocarbon fuel demands and environmental concerns [14]. These devices will play a substantial part in the sustainable advancement in the hydrogen and fuel cell technology (HFCT) market in international industries via transportation, stationary and portable applications.

Polymer Electrolyte Membrane Water Electrolysis

Water electrolysis for hydrogen production has many advantages, the first one is the simple process: only water and electricity are required to produce hydrogen. Several technologies are available: Solid oxide electrolysis, alkaline electrolysis, PEM electrolysis. According to Joshua Mermelstein and Oliver Posdziech [15] an electrochemical device based on solid oxide electrolysis cells can reach an electrical efficiency close to 100% lower heating value (LHV). Moreover, this system could be combined with different strategies of power to gas (e.g. methanation reactor) [16]. However, due to high operating temperatures of these cells, the material stability is affected which decreases the cell performance [17]. Commercial alkaline electrolysis has been used since the 20th century [18]. This alkaline electrolysis uses non-noble and less expensive catalysts. Which makes the quality of the utilized water insignificant since they are less sensitive to poisoning. Nonetheless, these technologies lead to a long-term corrosion problem [19]. The PEM technology is now compatible with fast start-up/shutdown, hence with intermittent operation [20] . Furthermore, the operation at ambient temperature makes it easier to real application. Among the electrolysis technologies, the Proton Electrolyte Membrane Water Electrolysis (PEMWE) is the best possible compromise in the current industrial process. PEMWE can electrolyze water with low energetic consumption and directly deliver pressurized hydrogen [21].
PEMWE energy conversion system converts electrical energy into chemical energy (Figure 1.3). The reactant involved is liquid water and the products are oxygen and hydrogen gas as represented in Equations (1.3) below:
Anodic reaction:→ 1 + 2 + + 2 − (1.1)
Cathodic reaction: 2 + + 2 − → (1.2)
Overall reaction:→ 1 + (1.3)
Figure 1.4 shows a schematic representation of a single cell of the Proton Electrolyte Membrane Water Electrolysis (PEMWE). The single cell consists of a proton electrolyte membrane, two electrodes, and flow field plates having flow channels machined in them, through which electrical energy is supplied to the electrodes. The flow channels are required to achieve circulation of the reactant (H2O at the anode side) and products (O2 at the anode side and H2 at the cathode side). The architecture of PEMWE is similar to proton electrolyte membrane fuel cells (PEMFC). The water flow at the inlet of the channels is distributed toward the anodic current collector. The protons pass through the membrane from the anode to the cathode and re-associating with the electrons to form gaseous hydrogen. The resulting hydrogen diffuses through the cathodic current collector and toward the outlet of the cathodic distribution channel. Simultaneously, oxygen bubbles are removed from the electrode into the anodic current collector and the water flow sweeps the bubbles away.

Polymer Electrolyte Membrane Fuel cells

Sir Humphry Davy introduced a simple fuel cell concept in 1802. However, the invention credit in 1839, based on reverse water electrolysis, went to Sir William Grove, also known as the father of the fuel cell. In 1889, the term “fuel cell” was first used by Charles Langer and Ludwig Mond [24]. Before the invention of the proton electrolyte membrane other fuel cell types existed such as solid-oxide fuel cells.
Due to their lightweight and their wide power ranges, PEMFCs are most suited for three broad areas [25], [26]:
• For transportations such as cars, buses, trains and trams, etc. [27], [28]
• For portable power, including military applications, small and large personal electronics, etc.
• For stationary power generation
The operating principle can be summarized in three chemical reactions:
Anodic reaction: → 2 + + 2 − (1.4)
Cathodic reaction: 1 + 2 + + 2 − → (1.5)
Overall reaction: 1 + → (1.6)
As shown in Figure 1.5, hydrogen fuel enters from the anode side. The protons are separated from the electrons on the surface of the catalyst. These protons will go through the membrane to the cathode side and the electrons pass in an external circuit generating electricity. On the cathode side, the hydrogen protons are combined with oxygen (from the air) to produce water.

Polymer Electrolyte Membrane compressor/concentration

Despite its name, EHC, also allows the purification of hydrogen. These devices are based on an assembly comprising anode and cathode gas-diffusion electrodes, and a solid (usually polymer-based) electrolyte situated between the electrodes. In an EHC system, electric energy is supplied to the cell to promote the transport of hydrogen (and only hydrogen) from the anodic to the cathodic compartment. To that goal, the operating principle of an electrochemical compressor (EHC) is simply to oxidize impure hydrogen at the positive electrode (anode) and to evolve hydrogen at the negative electrode; in the meantime, the protons produced at the positive electrode selectively migrate to the negative electrode through the proton-conductive membrane (Figure 1.6). This process can be summarized by the two electrochemical reactions (1.7) and (1.8):
Anodic reaction: H → 2H+ + 2e− (1.7)
Cathodic reaction: 2H+ + 2e− → H 2 (1.8)
The operating principle is simple. However, building a reliable efficient PEM device can be complicated due to many challenging technical details.1
Polymer Electrolyte Membrane cell basic concept

Single Cell Design

Every Polymer Electrolyte Membrane (PEM) device discussed in this thesis will be structured in the same architecture. The materials such as catalyst load or the reactants and the products are not similar, but the order of the structure remains the same, a multilayer assembly. As it is shown in Figure 1.7, on the edges Bipolar Plate (BP), which also support the feed flow channels (1), ensure electric connection between cells and the fluid distribution . The Gaskets (2) or the seals are generally inserted between the distribution channels and the Membrane Electrode Assembly (MEA).
MEA is mainly composed of two Gas Diffusion Layers (3) on both sides, two Catalyst Layers (4) with a Polymer Electrolyte membrane (PEM) (5) in the center.

Polymer Electrolyte Membrane

All the devices in this present work have a PEM. The membrane is the central element of the single cell. This electrolyte prevents the reactants present at the anode side to mix with the products present at the cathode side. It also allows the migration of protons from the anode to the cathode [31]. One of the most used membranes is the Nafion® membrane. In the 1960’s, Nafion® was introduced by DuPont [32]. The thickness of the commercialized membranes varies between 20 and 254 µm. It is a fluoropolymer made by sulfonated tetrafluorethylene [33]. Structurally (Figure 1.8), PEM membranes is a perfluorosulfonic acid (PFSA) polymer consisting of two elements: the sulfonate acid and a polymer matrix of Teflon® [34]. These membranes have the chemical and thermal stability of Teflon® [35] and the hydrophilic property of sulfonate acid sites [36].
The most important characteristics sought in a membrane are the proton conductivity, the water permeability, the chemical resistance and the mechanical resistance [33]. One of the disadvantages of Nafion® membranes is that they are known to lose water at temperatures exceeding 100°C therefore the ionic conductivity sharply declines [38].
The Nafion® membrane is mainly characterized by (λm) the water content of the Nafion®, ( + ) the proton conductivity (S / m), (m) the membrane thickness (m) and ( ) the diffusion coefficient in the membrane (m2 / s) [31].
The membrane conductivity formula differs in the literature. The ones commonly used are:
For Neubrand [39][40]: + = (0.0013 3 + 0.0298 2 + 0.2658 ) exp ( ( 1 − 1 )) (1.9) with (T) the temperature in K.
For Springer et al. [41] used for Nafion® 117 in PEMFC: + = (0.005139 − 0.00326) exp (1268( 1 − 1 )) (1.10)
The effective proton conductivity is [31]: + = . + (1.11) ε is the porosity of the Nafion® membrane.

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Catalyst Layer

The catalytic layer (or active layer / reaction layer) is where the electrochemical half-reactions occur. Therefore, a thin coating layer is needed to speed up the reactions. As shown in Figure 1.9, this acts as a porous active layer on both sides of the membrane [42].
In this PEMFC, the electro catalyst is often a noble metal such as platinum or its alloys/composites like carbon-supported Pt-based particles loaded on a Nafion® ionomer. This catalyst is chosen for its high kinetics towards the hydrogen oxidation reaction and hydrogen evolution reaction (ORR, HORHER). However, due to the high cost of the raw materials used, most of the efforts research is currently based on optimizing electro-catalysis. Thus, to lower the cost, the use of Pt-based electro-catalysts must be reduced. To do so, enlarging its electrochemically active surface area (ECSA) using nanoparticles can be one of the solutions [44]. Accordingly, the best compromise for platinum nanoparticles between the mass activity and the stability was a diameter of 4 nm [45].
The different materials need to be chosen depending on the system operating conditions (targeted performances), and the nature of the impurities in the hydrogen feed. For example, in the case of the PEMWE, at the anode, since it is an oxygen evolution reaction (OER), the electro catalyst is commonly the iridium (Ir, IrO2). However, at the cathode side it is a HER, so it is a platinum-based electro catalyst.
In Hydrogen pumping devices, specially the EHC for compression and purification, currently, platinum is considered the leading electro catalyst for the hydrogen oxidation reaction (HOR) and the hydrogen evolution reaction (HER) [29].
The parameters needed for modeling the catalytic layers (CL) will be (i0,a,c) the current density (A / m²), (αa,c) the electrochemical exchange coefficient, (σa,c) the proton conductivity (S / m), δcc the catalytic layer thickness (m), (εcc) the porosity and (γa,c) roughness coefficient [31].

Gas Diffusion Layer (GDL)

The GDL provides a structural backing of the CL by allowing a good electrical conductivity and a transport of the reactants through its hydrophobic porous structure. They also play a crucial role in heat discharge and water management [46].
On the Hydrogen side, the most common Gas Diffusion Layers (GDL) are carbon paper and carbon cloth, such as the figure shows for a PEMFC [48] (Figure 1.10). Same GDL is used for the EHC. As for the oxygen side, porous titanium GDLs are mostly used in the PEM electrolysis [49][50] (Figure 1.11).
The porosity of GDL differs between 30% and 90% with pore size between 12m to 95m. This difference affects its characteristics such as electrical conductivity, thermal conductivity, and permeability. Therefore, the porosity is important for the cell efficiency [48]. Hwang et al. [51] have claimed that Ti-felt GDLs in Fuel cell mode, reduced porosity enhances the efficiency in wet conditions by lowering the resistance of mass transport. Grigoriev et al. [52] have stated that the porosity of GDL in PEM electrolysis should lie between 30% and 50%. Because a higher porosity GDLs simplify gas removal however it boosts the ohmic losses.
The GDL thickness can affect the water management and the thermal and electrical resistance. The thickness of titanium GDL in PEMWE varies between 250 µm and 1000 µm [48] while the carbon GDL in PEMFC varies between 200 μm and 300 μm [46].
The GDLs are characterized by the following variables: ( ) the electrical conductivity (S / m), (GDL) the diffusion layer thickness (m) and ( ) the porosity [31].

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

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