update'

Content/Theoretical Background.tex

@@ -1,27 +1,33 @@
+- electric vs. electrical ?
+- do not "require" (???) any external reformer
+-
+
+
 \chapter{Theoretical Background}
 \label{cap: Theorie}
 
 
-In this chapter, the fundamental concepts and components of fuel cells are explored to provide a comprehensive understanding of Proton Exchange Membrane Fuel Cells (PEMFCs). Section 2.1 covers the basic principles of fuel cells, followed by Section 2.2, which delves into the electrochemical fundamentals, including the thermodynamics of the cell (2.2.1). Section 2.3 focuses specifically on PEMFCs, discussing their operation (2.3.1), overpotential (2.3.2), and methods of characterization (2.3.4). Finally, Section 2.4 examines degradation mechanisms in PEMFCs, detailing the degradation of the platinum catalyst (2.4.1), membrane degradation (2.4.2), electrochemical carbon corrosion (2.4.3), and overall corrosion processes (2.4.4). This structure lays the groundwork for understanding the challenges and performance factors of PEMFCs in practical applications.
+In this chapter, the fundamental concepts and components of fuel cells are explored to provide a comprehensive understanding of Proton Exchange Membrane Fuel Cells (PEMFCs). Section 2.1 covers the basic principles of fuel cells, followed by Section 2.2, which explores electrochemical fundamentals, including the thermodynamics of the cell (2.2.1). Section 2.3 focuses specifically on PEMFCs, discussing their operation (2.3.1), overpotential (2.3.2), and methods of characterisation (2.3.4). Finally, Section 2.4 examines degradation mechanisms in PEMFCs, detailing the degradation of the platinum catalyst (2.4.1), membrane degradation (2.4.2), electrochemical carbon corrosion (2.4.3), and general corrosion processes (2.4.4). This structure lays the groundwork for understanding the challenges and performance factors of PEMFCs in practical applications.
 
 
 \section{Fundamentals of the Fuel Cell}
 \label{sec: Revox}
 
-As said in the introduction, the clear impact of the GHG emissions and specially of the CO$_2$ emissions on climate change and the environment is undeniable. Therefore, new technologies such as fuel cells with almost no emissions and also no noise pollution are becoming a promising alternative to conventional Internal combustion engines (ICEs). This engines continue to depend on fossil fuels to function, whereas fuel cells run on hydrogen and air which undergo an electrochemical reaction within the fuel cell to generate electrical power, this reaction results in water as a byproduct\citep{01_wilberforce_advances_2016,02_baroutaji2015materials}.
-Battery electric vehicles (BEVs) are another alternative to ICEs which could also lower GHG as well as CO$_2$ emissions but only if the electric energy is also produced by renewable sources. However, when comparing fuel cells with BEVs there are some advantages that are worth mentioning. Fuel cells can be recharged almost instantly like ICEs and unlike BEVs. Besides that fuel cells can also run on other fuels and not only on pure Hydrogen depending on the fuel cell type. Fuel cells do not need to be disposed like Batteries and have a much longer operation time. Last but not least fuel cells have a wider range of temperatures in which they can be operated \citep{01_wilberforce_advances_2016, 02_lucia2014overview}.
+As mentioned in the introduction, the clear impact of GHG and especially CO$_2$ emissions on climate change and the environment is undeniable. Therefore, new technologies such as fuel cells with practically zero emissions as well as no noise pollution are becoming a promising alternative to conventional internal combustion engines (ICEs). These engines continue to depend on fossil fuels to function, whereas fuel cells run on hydrogen and air undergoing electrochemical reactions within the fuel cell to generate electrical power. This reaction results in water as a byproduct \citep{01_wilberforce_advances_2016,02_baroutaji2015materials}.
+Battery electric vehicles (BEVs) are another alternative to ICEs that could lower GHG and CO$_2$ emissions, but only if the electric energy is also produced via renewable sources. However, when comparing fuel cells with BEVs there are some advantages worth mentioning. Fuel cells, like ICEs, can be
+recharged almost instantly; a feature that BEVs do not share. Besides this, fuel cells may also run on other fuels and not just on pure hydrogen. This does however depend on fuel cell type. Fuel cells do not need to be disposed of like batteries and have a much longer operation time. Finally, fuel cells have a wider range of temperatures in which they may be operated \citep{01_wilberforce_advances_2016, 02_lucia2014overview}.
 
-Before continuing into the way of operation and the electrochemistry behind the fuel cell, it is essential to briefly explain the different types of fuel cells. These can be categorized based on the type of electrolyte membrane they use into solid oxide fuel cells (SOFCs), molten carbonate fuel cells (MFCSs), alkaline fuel cells (AFCs) and the most important one for this Thesis: polymer electrolyte membrane fuel cells (PEMFCs)\citep{02_wang2020fundamentals}. Also depending on the fuel cell type, operating temperatures may vary between -40 to almost 1000°C which will be explained in the following\citep{02_Abderezzak2018}.
+Before continuing into the mode of operation and electrochemistry behind the fuel cell, it is essential to briefly explain the various types of fuel cells. These may be categorized based on the type of electrolyte membrane they use: solid oxide fuel cells (SOFCs), molten carbonate fuel cells (MFCSs), alkaline fuel cells (AFCs) and the most important for this thesis: polymer electrolyte membrane fuel cells (PEMFCs)\citep{02_wang2020fundamentals}. Also depending on the fuel cell type, operating temperatures may vary between -40 to almost 1000 °C. This phenomenon will be explained in the following\citep{02_Abderezzak2018}.
 
 \subsubsection{Solid Oxide Fuel Cells (SOFCs)}
 
-The operating temperatures of SOFCs is higher than in the other types of fuel cells ranging from 500 to 1000 °C \citep{SOFC_hauser2021effects}. This high operating temperature allows the fuel cell to run not only on pure hydrogen but with gases which also contain methane (CH$_4$), carbon dioxide (CO$_2$) as well as carbon monoxide (CO), water vapour (H$_2$O) and hydrogen H$_2$ \citep{SOFC_lin_analysis_2024}. If the anode fuel has CH$_4$ and water vapour in it, the methane (CH$_4$) can be reformed in the fuel cell by the process of steam reforming shown in the equation \ref{eq:Steam reforming} which will produce hydrogen (H$_2$)and carbon monoxide (CO) \citep{SOFC_Haberman2004}.
+The operating temperatures of SOFCs is higher than in the other types of fuel cells. They range from 500 to 1000 °C \citep{SOFC_hauser2021effects}. This high operating temperature allows the fuel cell to run not only on pure hydrogen but also with gases which also contain methane (CH$_4$), carbon dioxide (CO$_2$) as well as carbon monoxide (CO), water vapour (H$_2$O) and hydrogen H$_2$ \citep{SOFC_lin_analysis_2024}. If the anode fuel has CH$_4$ and water vapour in it, the methane (CH$_4$) may be reformed in the fuel cell by the process of steam reforming as shown in the equation \ref{eq:Steam reforming}, producing hydrogen (H$_2$)and carbon monoxide (CO) \citep{SOFC_Haberman2004}.
 \begin{equation}
 	\mathrm{CH}_4+\mathrm{H}_2 \mathrm{O} \leftrightarrow \mathrm{CO}+3 \mathrm{H}_2, \Delta H_{298}=2.06 \times 10^5 \mathrm{KJ} / \mathrm{Kmol}
 	\label{eq:Steam reforming}
 \end{equation}
 
-Another internal reaction is the water-gas-shift reaction which can turn carbon monoxide and water vapour into carbon dioxide and hydrogen in the SOFC as shown in the following equation \ref{eq:WGS} \citep{SOFC_lin_analysis_2024,SOFC_WGS_Buttler2016}.
+Another internal reaction is the water-gas-shift reaction, which can turn carbon monoxide and water vapour into carbon dioxide and hydrogen in the SOFC as shown in the following equation \ref{eq:WGS} \citep{SOFC_lin_analysis_2024,SOFC_WGS_Buttler2016}.
 
 \begin{equation}
 	\mathrm{CO}+\mathrm{H}_2 \mathrm{O} \leftrightarrow \mathrm{CO}_2+\mathrm{H}_2, \Delta H_{298}=-4.1 \times 10^4 \mathrm{KJ} / \mathrm{Kmol}
@@ -31,16 +37,16 @@ Another internal reaction is the water-gas-shift reaction which can turn carbon
 
 \subsubsection{Molten Carbonate Fuel Cells (MCFCs)}
 
-MCFCs are also high temperature cells with an operating temperature of about 600 to 700 °C and a Electrolyte made out of molten carbonate (CO$_3$$^{2-}$). Like SOFCs they can also be operated not only with pure hydrogen (H$_2$) but also with biogas which could also contain CH$_4$ as well as CO$_2$ and CO \citep{02_lucia2014overview, 02_wang2020fundamentals}.
-Therefore, SOFCs and MCFCs do not any external reformer to convert other fuel types into H$_2$ as they use the same reforming reactions from the equations \ref{eq:Steam reforming} and \ref{eq:WGS}
+MCFCs are also high temperature cells with an operating temperature of about 600 to 700 °C and a electrolyte made out of molten carbonate (CO$_3$$^{2-}$). Like SOFCs, they can also be operated with both pure hydrogen (H$_2$) and biogas, which could also contain CH$_4$ as well as CO$_2$ and CO \citep{02_lucia2014overview, 02_wang2020fundamentals}.
+As such, SOFCs and MCFCs do not require any external reformer to convert other fuel types into H$_2$ as they use the same reforming reactions from the equations \ref{eq:Steam reforming} and \ref{eq:WGS}
 \citep{MCFScontreras2021molten}.
-It is also possible to combine SOFC and MCFC with working temperatures of 550-700°C which are slighlty higher than a normal MCFC at 650
-\citep{MCFS_cui2021review}. Furthermor, the electrical efficiency of the MCFCs can reach up to 60\% \citep{wang_preparation_2018}.
+It is also possible to combine SOFC and MCFC with working temperatures of 550-700 °C which are slighlty higher than a normal MCFC at 650 °C
+\citep{MCFS_cui2021review}. Furthermore, the electrical efficiency of the MCFCs can reach up to 60\% \citep{wang_preparation_2018}.
 
 
 \subsubsection{Alkaline Fuel Cells (AFCs)}
 
-For AFCs the operating temperature is about 50-200 °C which is much lower than those of the SOFC and MCFC but a lot closer to the temperature in which PEMFCs are operated \citep{02_wang2020fundamentals}. Another main difference between AFCs and SOFCs is, that the electrolyte in a AFC is liquid unlike the solid state of the ceramics used in SOFCs. AFCs uses a potassium hydroxide solution (KOH) as an electrolyte which is embedded in the matrix \citep{02_Abderezzak2018,02_wang2020fundamentals}. Unlike SOFCs and MCFC and due to the lower temperature, AFCs can be poisoned by carbon dioxide (CO$_2$). In that case, the alkaline electrolyte could  react directly with the CO$_2$ which could lead to the the following reaction equations \ref{eq:AFC_Poisoning} \citep{AFC_mclean2002assessment}:
+For AFCs, the operating temperature is about 50-200 °C, much lower than that of the SOFC and MCFC, but much closer to the temperature in which PEMFCs are operated \citep{02_wang2020fundamentals}. Another important difference between AFCs and SOFCs is that the electrolyte in a AFC is liquid, unlike the solid state of the ceramics used in SOFCs. AFCs use a potassium hydroxide solution (KOH) as an electrolyte embedded in the matrix \citep{02_Abderezzak2018,02_wang2020fundamentals}. Unlike SOFCs and MCFC and due to the lower temperature, AFCs can be poisoned by carbon dioxide (CO$_2$). In this case, the alkaline electrolyte could react directly with the CO$_2$ leading to the following reaction equations \ref{eq:AFC_Poisoning} \citep{AFC_mclean2002assessment}:
 
 \begin{equation}
 	\begin{aligned}
@@ -50,22 +56,22 @@ For AFCs the operating temperature is about 50-200 °C which is much lower than
 \label{eq:AFC_Poisoning}
 \end{equation}
 
-This reaction could reduce the ionic conductivity of the electrolyte as well as block the pores in the electrode. The carbonate shown in the equation \ref{eq:AFC_Poisoning} could also block the pores of the catalyst resulting in the aforementioned reduction of ionic conductivity in the electrolyte
+This reaction could reduce the ionic conductivity of the electrolyte and block the pores in the electrode. The carbonate shown in the equation \ref{eq:AFC_Poisoning} could also block the pores of the catalyst, resulting in the aforementioned reduction of ionic conductivity in the electrolyte
 \citep{AFC_mclean2002assessment, AFC_AlSaleh1994_CO2, AFC_AlSaleh1994_Ni}.
 
 \subsubsection{Polymer Electrolyte Membrane Fuel Cells (PEMFCs)}
 
-For Polymer electrolyte membrane fuel cells the operating temperature can be lower than those from the other fuel cell types including the AFCs, PEMFCs can be operated at 40 to 80 °C \citep{02_lucia2014overview}. For high temperature PEMFCs the operating temperature can even go as high as 150-180 °C \citep{02_wang2020fundamentals}. Because of its low operating temperature and its high output power density it is highly suited for mobile applications like the automotive industry. PEMFCs run on pure hydrogen as fuel and cannot use Biogas containing methane (CH$_4$), carbon dioxide (CO$_2$) or carbon monoxide CO as they cannot reform it internally to pure hydrogen H$_2$ \citep{PEM_Atuomotive_arrigoni2022greenhouse}. 
+For polymer electrolyte membrane fuel cells, the operating temperature may be lower than that of the other fuel cell types including the AFCs. PEMFCs can be operated at 40 to 80 °C \citep{02_lucia2014overview}. For high temperature PEMFCs, the operating temperature may even reach up top 150-180 °C \citep{02_wang2020fundamentals}. Because of its low operating temperature and high output power density, it is highly suited to mobile applications like the automotive industry. PEMFCs run on pure hydrogen as fuel and cannot use biogas containing methane (CH$_4$), carbon dioxide (CO$_2$) or carbon monoxide (CO) as they cannot reform it internally to pure hydrogen H$_2$ \citep{PEM_Atuomotive_arrigoni2022greenhouse}. 
 
-Its mobile applications have turned the PEMFCs into one of the biggest research fields in the search for greener alternatives to conventional ICEs. It typically features a solid polymer electrolyte membrane and porous carbon electrodes with platinum functioning as catalyst \citep{01_wilberforce_developments_2017}.
+Its mobile applications have turned the PEMFCs into one of the biggest research fields in the search for greener alternatives to conventional ICEs. They typically features a solid polymer electrolyte membrane and porous carbon electrodes with platinum functioning as catalyst \citep{01_wilberforce_developments_2017}.
 
-Since this thesis focuses its attention on automobile applications, the following sections will provide a detailed explanation of the relevant fuel cell. However, before looking into the way of function the subsequent section will first cover the electrochemical fundamentals. 
+Since this thesis focuses its attention on automobile applications, the following sections will provide a detailed explanation of the relevant fuel cell. However, before looking into their mode of operation, the subsequent section will first cover the relevant electrochemical fundamentals. 
 
 
 
-\section{Electrochemical  Fundamentals}
+\section{Electrochemical Fundamentals}
 
-The function of a fuel cell is to transform the chemical energy stored in the fuel (hydrogen H$_2$) in electrical energy. During this electrochemical reaction the fuel is transformed but the fuel cell is not consumed by the energy production unlike in a battery. In a fuel cell the electrochemical redox reaction is split in two between the cathode and the anode which are separated by an electrolyte \citep{Fundamentals_o2016fuel}.
+The function of a fuel cell is to transform the chemical energy stored in the fuel (hydrogen H$_2$) into electrical energy. During this electrochemical reaction, the fuel is transformed, but the fuel cell is not consumed by the energy production as in a battery. In a fuel cell, the electrochemical redox reaction is split in two between the cathode and the anode separated by an electrolyte \citep{Fundamentals_o2016fuel}.
 
 \begin{align}
 	\text{Anode:} \quad & \text{H}_2 \rightarrow 2\text{H}^+ + 2e^- \\
@@ -74,17 +80,17 @@ The function of a fuel cell is to transform the chemical energy stored in the fu
 	\label{eq:PEM}
 \end{align}
 
-In the anode the oxidation part of the reaction takes place. Electrons are removed from the Hydrogen H$_2$ as shown in the equation (2.4). In the Cathode those liberated electrons are consumed by the reduction reaction and oxygen (O$_2$) and 2H$^+$ form water (H$_2$O) as a product. This is summed up in the overall reaction from te equation (2.6) \citep*{Fundamentals_o2016fuel}. Moreover, the anodic reaction can also be called hydrogen oxidation reaction (HOR) and the cathodic reaction is called oxygen reduction reaction (ORR) \citep{Fundamentals_scherer2012fuel}.
+In the anode, the oxidation part of the reaction takes place. Electrons are removed from the hydrogen H$_2$ as shown in the equation (2.4). In the cathode, these liberated electrons are consumed by the reduction reaction, and oxygen (O$_2$) and 2H$^+$ form water (H$_2$O) as a product. This is summarised in the overall reaction from the equation (2.6) \citep*{Fundamentals_o2016fuel}. The anodic reaction may be called a hydrogen oxidation reaction (HOR) and the cathodic reaction a oxygen reduction reaction (ORR) \citep{Fundamentals_scherer2012fuel}.
 
 \subsection{Thermodynamics of the Cell}
 
-In addition, the reaction produces heat (or enthalpy H) since there is a difference $\Delta$H between the enthalpy of the products and the enthalpy of the reactants \citep{Fund_barbir2008fuel}.
+In addition, the reaction produces heat (or enthalpy H), since there is a difference $\Delta$H between the enthalpy of the products and the enthalpy of the reactants \citep{Fund_barbir2008fuel}.
 \begin{equation}
 	\Delta H=\Delta H_{product}- \Delta H_{reactant}
 	\label{eq:Enthalpy}
 \end{equation}
 
-The Gibbs free energy corresponds to the enthalpy in the reaction that can be converted to electricity. It is defined by the following equation (\ref{eq:Gibbs}). $\Delta$H is the difference of the enthalpy and T$\Delta$S expresses the losses of entropy ($\Delta$S) which are dependent on the temperature
+The Gibbs free energy corresponds to the enthalpy in the reaction that can be converted to electricity. It is defined by the following equation (\ref{eq:Gibbs}). $\Delta$H is the difference of the enthalpy and T$\Delta$S expresses the losses in entropy ($\Delta$S) which are dependent on temperature
 \citep{Fund_barbir2008fuel}.
 
 \begin{equation}
@@ -92,7 +98,7 @@ The Gibbs free energy corresponds to the enthalpy in the reaction that can be co
 	\label{eq:Gibbs}
 \end{equation}
 
-Furthermore, with the help of the Faraday constant F (96,487 C/mol) and n for the number of electrons transferred in the reaction as well as a value for $\Delta$G for the Gibbs free energy the reversible theoretical potential E$_{rev}$ of a cell and in standard conditions can be calculated with the following equation
+Furthermore, using the Faraday constant F (96,487 C/mol) and n for the number of electrons transferred in the reaction as well as a value for $\Delta$G for the Gibbs free energy, the reversible theoretical potential E$_{rev}$ of a cell and in standard conditions may be calculated via following equation
 \citep{Fundamentals_scherer2012fuel}:
 
 \begin{equation}
@@ -100,7 +106,7 @@ Furthermore, with the help of the Faraday constant F (96,487 C/mol) and n for th
 	\label{eq:E}
 \end{equation}
 
-E$_{rev}$ can also be referred to as E$^0$ which is the open circuit voltage (OCV) in standard conditions (1 atm and 25°C or 298K)\citep{Fundamentals_scherer2012fuel, F_omran2021mathematical}. Since this equation (\ref{eq:E}) can be used only in standard conditions the reversible potential of a cell in non-standard conditions cannot by calculated by it. In a non-standard case where the temperature or the pressure is another, the Nernst equation can be used
+E$_{rev}$ can also be referred to as E$^0$, the open circuit voltage (OCV) in standard conditions (1 atm and 25°C or 298K)\citep{Fundamentals_scherer2012fuel, F_omran2021mathematical}. Since this equation (\ref{eq:E}) can be used only in standard conditions, it cannot be used to calculate the reversible potential of a cell in non-standard conditions. In a non-standard case where the temperature or the pressure is different, the Nernst equation can be used
 \citep*{Fundamentals_o2016fuel,Nernst_sahu2014performance}.
 
 \begin{equation}
@@ -108,36 +114,36 @@ E$_{rev}$ can also be referred to as E$^0$ which is the open circuit voltage (OC
 	\label{eq:nernst}
 \end{equation}
 
-To be able to understand the Nernst equation first the concept of chemical potential $\mu$ has to be explained \citep{Nernst_mardle2021examination}. The chemical potential describes how the number of molecules or atoms $n_i$ of a species $i$ afects the thermodynamic potentials. In this case $a$ is the activity of the species. which for an ideal gas is $a_i$ = $p_i$/$p^0$. If the gas is non ideal it has to be multiplied with $\gamma$ wich describes how far away the gas is from an ideal one $(0<\gamma<1)$ with $\gamma=1$ as an ideal gas \citep{Fundamentals_o2016fuel}. In the Nernst equation $v_i$ refers to the stoichiometric coefficient of the products or of the reactants. R is the gas constant (R = 8,314 J/molK)
+To be able to understand the Nernst equation, the concept of chemical potential $\mu$ must first be explained \citep{Nernst_mardle2021examination}. The chemical potential describes how the number of molecules or atoms $n_i$ of a species $i$ affects thermodynamic potentials. In this case, $a$ is the activity of the species, which for an ideal gas is $a_i$ = $p_i$/$p^0$. If the gas is non-ideal, it must be multiplied with $\gamma$, which describes how far away the gas is from an ideal one $(0<\gamma<1)$ with $\gamma=1$ as an ideal gas \citep{Fundamentals_o2016fuel}. In the Nernst equation, $v_i$ refers to the stoichiometric coefficient of the products or of the reactants. R is the gas constant (R = 8,314 J/molK).
 
 \begin{equation}
 	\mu=\mu^0+R \operatorname{Tln}(a)
 	\label{eq:mu}
 \end{equation}
 
-The following equation can also be rewritten to describe how the chemical potential relates to the Gibbs free energy.
+The following equation may also be rewritten to describe how the chemical potential relates to the Gibbs free energy.
 
 \begin{equation}
 	\mu_i^\alpha=\left(\frac{\partial G}{\partial n_i}\right)_{T, p, n_{j \neq i}}
 	\label{eq:chem1}
 \end{equation}
 
-Using the equations (\ref{eq:chem1}) and (\ref{eq:mu}) it is possible to calculate how the Gibbs free energy changes with the $i$ different chemical species resulting in the following equation (\ref{eq:gibbs_2}):
+Using the equations (\ref{eq:chem1}) and (\ref{eq:mu}), it is possible to calculate how the Gibbs free energy changes with the $i$ different chemical species, resulting in the following equation (\ref{eq:gibbs_2}):
 
 \begin{equation}
 	d G=\sum_i \mu_i d n_i=\sum_i\left(\mu_i^0+R T \ln a_i\right) d n_i
 	\label{eq:gibbs_2}
 \end{equation}
 
-Finally this equation (\ref{eq:gibbs_2}) can be inserted into the equation (\ref{eq:E}) to form the Nernst equation (\ref{eq:nernst}) in its general form\citep{Fundamentals_o2016fuel}.
+Finally, this equation (\ref{eq:gibbs_2}) can be inserted into the equation (\ref{eq:E}) to form the Nernst equation (\ref{eq:nernst}) in its general form\citep{Fundamentals_o2016fuel}.
 
 \newpage
 
 \section{PEMFC}
 \label{sec: PEMFC}
 
-Since this Thesis focuses on the automotive applications of fuel cells the focus of the following sections will shift to the Polymer Electrolyte Membrane Fuel Cell (PEMFC) which are the most widely used in automotive contexts due to their low operating temperature as well as its high output power density \citep{PEM_Atuomotive_arrigoni2022greenhouse}.
-In the following section \ref{subsec:2_wayoffunct} the PEMFC will be described in more detailed way starting with its main components and its way of function.
+Since this thesis focuses on the automotive applications of fuel cells, the focus of the following sections will shift to the Polymer Electrolyte Membrane Fuel Cell (PEMFC), which is the most widely used in automotive contexts due to its low operating temperature as well as its high output power density \citep{PEM_Atuomotive_arrigoni2022greenhouse}.
+In the following section \ref{subsec:2_wayoffunct}, the PEMFC will be described in more detail, starting with its main components and its way of function.
 
 \subsection{Way of Function PEMFCs}
 \label{subsec:2_wayoffunct}