## Meeting Future Energy Demands **Energy Consumption** - The world uses 180 000 TWh of energy a year. - Energy is used for electricity generation, transport, space heating and agriculture. **Future Energy Challenges and Demands** - There are several reasons that drive the development of materials that help meet future energy demands. - **Portability** - An ever increasing number of portable electronics are becoming available and improvements in storage (and potentially conversion) technology will improve their functionality. - **Climate Change** - A rapid decarbonisation of the economy is required to mitigate the worst effects of climate change. Any technological development that will make it easier to achieve this is therefore useful. - **Fossil Fuel Availability** - Fossil fuels are non-renewable source and the cheap abundant oil of the past may not last long. - **Higher Prices** - Higher oil prices drive the use of more expensive extraction techniques such as *horizontal drilling*. - **Energy Independence** - The majority of oil production is completed by OPEC, which operates effectively as a cartel. This has contributed to large price volatility. - Renewables etc. should not have this volatility. - **Localised Pollution** - Current combustion techniques often give off $\ce{SO_x}$, $\ce{NO_x}$ gases and particulates that can have detrimental effects on human health and cause acid rain. **$\ce{CO2}$** **Emissions** - Since the industrial revolution, the level of $\ce{CO2}$ in the air has increased substantially. ![[NOAA_1.png#invert|cl]] %%https://www.noaa.gov/news-release/carbon-dioxide-now-more-than-50-higher-than-pre-industrial-levels %% - **Emission Sources** - There are many different sources of $\ce{CO2}$ emissions, with transportation, electricity production and industry emitting approximately a quarter each. - **Resulting Temperature** - The result of the increasing greenhouse gas emissions is rapidly warming climate. Almost every year ends up being the warmest in recorded history. - **Effects** - This warming will likely have very detrimental effects to climate, ecosystems and agriculture. **Decarbonisation of Energy Grids** - In order to combat this, it is imperative that a reduction in $\ce{CO2}$ emissions is achieved. - **Renewable Energy** - Massive progress has been made in renewables, which generate electricity in more climate friendly ways such as solar, wind, hydro, waves etc. - **Intermittency** - The largest issue with renewables is their intermittent nature and lack of control, meaning a considerable amount of energy will likely needed to be stored. - **Baseline Power** - It is still likely that a baseline of power will need to be generated, whether from nuclear, fuel cells or synthetic fuels. **Technologies in Development** - A number of technologies are in development to meet these challenges: - **Supercapacitors** - Electrical devices that can store a significant amount of electrical energy via the separation of charge and can discharge it in minutes. *Already used in F1 regenerative braking etc.* - **Batteries** - Electrical devices that can store energy via its conversion to chemical energy. *Already ubiquitous in everyday life.* - **Fuel Cells** - An electrochemical cell that converts chemical energy to electrical; often with greater efficiencies than traditional combustion. *Trial implementations widespread on vehicles like buses* - **Synthetic Fuels** - The creation of fuels from simple chemical components. If the carbon is sourced from the atmosphere, there should be net zero emissions. Achieves long term storage. - **Waste to Energy** - Incinerators have become a popular way of converting landfill waste to energy. Better than landfill due to reduced methane emissions but ideally not necessary. - **Photovoltaics** - Renewable energy that converts the sun rays to electrical energy. Already widespread but further efficiency gains improve economics. **Smoothing** - To solve the intermittency problem, technologies have been developed / are in development to store energy. - **Mechanical** - Store via kinetic energy in a flywheel, store via gravitational potential energy in pumped hydro. - **Electrochemical** - Solutions such as batteries or redox flow cells are in development. - **Fuel Cells** - Paired with electrolysis, should be able to smooth out energy demands. **Barriers to Change** - There are many barriers that prevent the immediate adoption of these technologies. - **Energy Density** - Compared to gasoline, batteries cannot store the same amount of energy in the same mass and volume. - **Power Density** - Additionally, batteries can be charged and discharged as rapidly as gasoline can. - **Long Term Stability** - Batteries and fuel cells still can have limited life spans. - **Mineral Availability -** Batteries, fuel cells and photovoltaics all contain elements that can be difficult to source (*e.g. conflict mining of Co for Li-ion batteries*). - **Public Opinion** - Substantial lobbying and advertising by the fossil fuel industry has managed to turn a large part of public opinion against the net zero effort and hence government policies are becoming worse. **Ragone Plot** - When comparing energy storage technologies, a Ragone plot plots specific power and specific energy. - **Conventional Fuels** - Conventional fuels are annoyingly good at being both power and energy dense, hence their ubiquity. - **Capacitors** - Many capacitors can rival the power density but don’t come close to the energy density of fuels. - **Batteries** - Somewhat lower energy density than fuels and substantially lower power density. ![[Dubal_1.gif#invert|cm]] %% 10.1039/C4CS00266K %% # Electrochemistry ## Impedance **Ohm’s Law** - For a DC circuit the voltage across a component is equal to its resistance multiplied by the current flowing through it. Additionally, the power can be calculated using the current and the voltage. $V=IR\qquad P=IV$ **Resistance,** $R$/Ω - The opposition to the flow of electrical current. It can also be expressed as: - **Resistivity,** ${\rho/}$Ωcm⁻¹ - The intrinsic equivalent of resistance, independent of the geometry. - **Conductance,** $G/$S A measure of the ease of flow of electrical current, *i.e.* the inverse of resistance. - **Conductivity,** $\sigma$/Scm⁻¹ - The intrinsic equivalent of conductance. $G=R^{-1}\qquad \rho = \frac{R\, l}{A}\qquad \sigma =\rho ^{-1}=\frac{l}{RA}$ **Impedance Spectroscopy** - Important technique used for the study of materials, from dielectrics to fuel cells. - **Advantage** - Allows the separation of different components with different time constants. - **Potential Components** - Effects of grain boundaries, electrode interfaces, defect gradients, space charge effects, charge transfer process and diffusion can be identified. - **Basic Idea** - A small sinusoidal voltage is applied to the system under consideration and the current response is measured. - **Addition** - This small sinusoidal voltage can be applied over a baseline DC voltage if desired. This is necessary if measuring an entire battery. **Reactance** - The opposition to a change in current or voltage. - In a DC circuit this is immaterial as there is no change in current; however becomes important in AC circuits. - **Phase Difference** - Reactance does not dissipate energy like a resistor, instead it stores the energy until a quarter of a cycle later. > [!core] Definition of Impedance > The opposition to alternating current presented from the combined resistance and reactance of a circuit. It is frequency dependent and described by a complex number. $Z(\omega)=\frac{V(\omega)}{I(\omega)} = Z' +iZ''$ > [!aside]- Fourier Transforms (Unexamined) > **Fourier Transform -** To convert between $V(\omega)$ and $V(t)$, a Fourier transform is used. Note that $\omega$ is the angular frequency. > $ \mathcal{F} \big[x(t)\big ] = \int ^{+\infty}_{-\infty} x(t)\cdot e^{-i\omega t}\, dt = \tilde x (\omega) $ > **Fourier Differentiation -** The Fourier transform of a derivative has a simple relationship with the Fourier transform of the original function. > $ \mathcal{ F} \big[x'(t)\big]=i\omega \cdot \tilde x(\omega) $ > > [!derivation]- Proof > > You can use integration by parts to prove this relationship. > > ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/Untitled.webp|cl]] > > **Extension to Further Derivatives -** This can be extended to both second derivatives and integration. > $\mathcal{F}\big[x''(t)\big]=-\omega^2\cdot \tilde x(\omega) \qquad \mathcal F\big[\!\smallint \!x(t)] =\frac{1}{i \omega}\cdot \tilde x(\omega)$ **Ideal Components** - Impedance responses can be analysed based on a number of idealised components. - **Resistor** - A resistor only has traditional resistance and hence has no phase shift. In a Nyquist plot, this shows as a frequency-invariant point on the real axis. - **Capacitor** - A capacitor results in current shifting 90° behind the voltage. In a Nyquist plot, this shows as a line going straight up the $-Z''$ axis. - **Inductor** - A inductor results in the current shifting 90° in front of the voltage. In a Nyquist plot, this shows as a line going down the $-Z''$ axis. ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-10.png]] **Equivalent Circuit** - Impedance spectra are frequently analysed via fitting to an equivalent circuit, where the features of the spectra are modelled by a combination of idealised components. **Parallel RC Circuit** - Many physical phenomenon can be modelled by a resistor and a capacitor. In a Nyquist plot, this appears as an arc or semicircle. - **Characteristic Frequency, $\omega_{max}$** - The frequency of the arc’s maxima can be used to find the capacitance and the resistance of the circuit. $\omega_{max}RC=1\qquad\qquad \omega_{max}=2\pi f_{max}$ ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-11.png|c]] **Brickwork Model** - A sample can often be modelled by the brickwork model, where the solid is interpreted as being composed of grain ‘bricks’ and grain boundary ‘mortar’. - **Thickness** - If you consider the total thickness contribution of the grain and grain boundary, it is seen that the grain boundary has a significantly higher capacitance. **Typical Capacitances** - The typical capacitance of a number of common phenomena are listed below. | **log Capacitance, log₁₀(C/F)** | **Phenomenon Responsible** | | ------------------------------- | -------------------------- | | -12 | Bulk | | -11 | Secondary Phases | | -11 → -8 | Grain Boundary | | -10 → -9 | Bulk Ferroelectric | | -9 → -7 | Surface Layer | | -7 → -5 | Sample-Electrode Interface | | -4 | Electrochemical Reaction | **Warburg Component** - Ionic diffusion at low frequencies can often show a 45° spike that is modelled by a theoretical Warburg component. - At these low frequencies, the ions are diffusing significant distances in the cycle. - **Electrode** - The exact shape can depend on whether it is at a non-blocking electrode or a blocking electrode. - **Temperature** - The spike will collapse at higher temperatures due to the finite thickness of the sample. It is also influenced by atmosphere. **Other Plots** - Resistive elements dominate the Nyquist plot (often grain boundaries), modulus plots instead show emphasise elements with the largest $C^{-1}$. > [!aside] See [[Impedance]] for more information **Arrhenius Plot** - Allows the determination of the activation energy by measuring the conductivity at a variety of different temperatures. $\sigma =\sigma _{0}\exp \left(\frac{-E_{a}}{RT}\right)\qquad \qquad \ln \sigma=- \frac{E_{a}}{RT} +\ln \sigma_{0}$ ## Interfaces **Electrode Interfaces** - The electrode interface is often where the electrochemistry happens. - **Non-Blocking Electrode** - In a non-blocking electrode the conducting ion can move through the interface and into the electrode. - *e.g.* An $\ce{Ag}$ metal electrode in contact with $\ce{Ag4RbI5}$ solid electrolyte allows the free motion of $\ce{Ag+}$ ions. - **Equilibrium** - An equilibrium is established across the interface preventing the build up of charge. - **Impedance Response** - Shows an arc as there is still some resistance provided by the interface and hence some capacitance. - **Blocking Electrode** - In a blocking electrode the conducting ion cannot move through the interface. - *e.g.* A graphite electrode in contact with $\ce{Ag4RbI5}$ solid electrolyte will not allow $\ce{Ag^+}$ ions to transfer. - **Equilibrium** - No equilibrium is established and hence charge build up will occur (capacitance). - **Reaction** - If a sufficiently high potential is applied, the electrolyte will break down. This could lead to metal plating. - **Impedance Response** - The capacitance is sufficiently high that you almost get a purely capacitive response, but is just a giant arc. ![[irvine-1.png#invert|cs]] **Daniell Cell** - A classic electrochemical cell that produces electricity via a spontaneous reaction. $\begin{gather}\ce{Zn (s) + Cu^{2+} (aq) -> Zn^{2+} (aq) + Cu (s)} \\ \ce{Zn(s) | Zn^{2+} (aq) || Cu^{2+} (aq) | Cu (s)}\end{gather}$ ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/notion-1.webp|cs]] **Cell Potential, $E^\ominus_\text{cell}$ -** The potential difference between the anode and the cathode. - **Spontaneity -** For a reaction to be spontaneous, the reduction must have a greater potential than the oxidation. This makes $E^\ominus_\text{cell}$ positive. $ E^\ominus_\text{cell}=E^\ominus_\text{Cathode}-E^\ominus_\text{Anode} $ - **”ERROL”** - Reduction on right, oxidation on left. - **Standard Hydrogen Electrode** - The reduction potentials are measured against the standard hydrogen electrode, which is defined as $E^{\ominus}= 0.0 \rm\ V$. - **Gibbs Energy -** The Gibbs free energy can be related to the cell potential. $ \Delta G^\ominus =-nF E_\text{cell}^\ominus $ **Nernst Equation -** Relates the standard reduction potential of an electrode to different concentrations. $ \begin{gather*} \text{For } \ce{O + $n$ e- -> R}: \\ E_\text{cell} = E^\ominus_\text{cell} +\frac{kT}{\nu_e e}\ln \frac{[\ce{O}]}{[\ce{R}]} \end{gather*} $ **Overpotential**, $\eta$ - The deviation of the potential from its equilibrium value. $\eta = V - V_{eq}$ **Polarisation** - The departure of an electrode (or cell) potential from the reversible, equilibrium value upon application of Faradaic current. - **Electrode Types** - There are two ideal types of electrodes: - **Ideal Polarisable Electrode** - Application of a very small current leads to a large change in potential (in a certain voltage range). - In this scenario, no current passes through and it behaves as a capacitor. - **Ideal Non-Polarisable Electrode** - Application of current does not change the potential. - In this scenario, the current can pass through unimpeded. ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-8.png|cl]] - **Reduction Limit** - If the overpotential results in the Fermi level moving past the LUMO of a species in solution, that species will be reduced. - **Oxidation Limit** - If the overpotential results in the Fermi level lowering below the HOMO of a species in solution, that species will be oxidised. ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-9.png]] > [!core] Faradaic Processes > **Faradaic Process** - Charge is transferred across the interface as a result of an electrochemical reaction. > **Non-Faradaic Process** - Charge is **not** transferred across the interface and instead associated with the movement of ions, reorientation of solvent dipoles, adsorption and desorption at the interface. **Current Density** - A number of factors affect the current density at the electrode. - **Cathodic and Anodic** - The current density is defined as the sum of the cathodic current density (the reduction reaction) and the anodic current density (the oxidation reaction).[^1] $j = j_{a} + j_{c}$ - **Equilibrium Current Density** - If the reduction and oxidation reaction are in equilibrium, $j_{c} = - j_{a}$ and hence the net current is 0. - **Exchange Current Density, $j_0$** - The magnitude of both the cathodic and anodic current is equal to the exchange current density, the “background” current. **Electrode Kinetics** - The current density on an electrode can be affected by kinetic processes. - **Charge Transfer** - The current may be limited by the charge transfer process. - **Mass Transport** - For the electrode reaction to take place, the reactant species must be transported to the interface and product species away from the interface. - **Diffusion** - An ion or uncharged species can *diffuse* under the influence of a concentration gradient. - **Migration** - An ion can *migrate* under the influence of a potential gradient. - **Convection** - An ion or uncharged species can move towards the electrode when a mechanical force acts upon the solution. - **Limiting Step** - Mass transport becomes rate limiting at higher current densities. **Butler-Voltmer Equation** - If under charge-transfer control, the equation describes how the current depends on the overpotential of the electrode, $j=j_o\bigg[\exp\left(\frac{\alpha_{a} F\eta}{RT}\right)-\exp\left(-\frac{\alpha_{c}F\eta}{RT}\right)\bigg]$ where $\alpha_a$ and $\alpha_c$ are the charge transfer coefficients. **Tafel Equation** - For higher overpotentials (0.04 V - 0.1 V), the non-dominant current can be disregarded. $\begin{align*} \text{Anodic:}&&j&=j_{0}\exp\left(\frac{\alpha_{a} F\eta}{RT}\right) & \ln j &= \ln j_{0}+ \left(\frac{\alpha_{a} F\eta}{RT}\right)\\ \text{Cathodic:}&&j&=-j_{0}\exp\left(\frac{\alpha_{c} F\eta}{RT}\right) & \ln j &= \ln j_{0}- \left(\frac{\alpha_{c} F\eta}{RT}\right) \end{align*}$ - **Plot** - The logarithmic plot has a linear region from which $\alpha$ can be obtained. ^tafel ![[notion-1.png|cm]] **Electrical Double Layer** - The ionic environments around an electrode will be perturbed by the electric field. A number of models have been developed to describe this. - **Charge Balance** - Anions/cations from the electrolyte will diffuse close to the surface to create a charge of equal and opposite magnitude. - **Helmholtz Model** - Models the interface as a parallel-plate capacitor, where the counter-ions are attracted towards the surface. These ions are still solvated. - **Issues** - Does not account for absorption, solvent dipole moments, and inhomogeneities in the solution due to mixing and thermal motion. - **Gouy-Chapman Model** - Models the disrupting effect of thermal motion on the double layer that results in an non-uniform gradual decrease in charge density. - **Application** - Can model low concentration electrolyte solutions. - **Gouy-Chapman-Stern Model** - Attempts to combine the two models together where the ions closest to the electrode are constrained in a rigid plane while others are more dispersed. - **Bockris-Devantha-Muller Model** - Further improves the double layer models by incorporating specially adsorbed ions, solvent interactions and solvent dipole moments. ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-12.png]] ## Electrolytes **Electrolyte** - A medium that conducts ion but not electricity. - **Types** - There are various types of electrolytes, including salt solutions, salts in polymers, polyelectrolytes, inorganic solids and ionic liquids. ### Polymer Electrolytes **Polymer Electrolytes** - There are two primary types of polymer electrolytes. **Polymer-Salt Complex** - An inorganic salt dissolved into a polymer which allows the anions and/or cations to be mobile, *e.g.* $\ce{PEO.LiPF6}$. - **PEO** - Poly(ethylene oxide) is the most intensively studied polymer. - **Structure** - The structure of the polymer salt complexes varies with the polymer : salt ratio but shares a helical structure. - **Crystallinity** - The complex has a varying $T_g$ and hence can be amorphous or crystalline depending on the composition, the temperature and the method of preparation. - **Conductivity** - Amorphous complexes tend to have better conductivities. - **Segmental Motion** - Weak Li-O bonds can be formed and broken easily, allowing the $\ce{Li^+}$ to slowly move along the channels. - **NMR** - NMR can observed this motion and study the differences between amorphous and crystalline complexes. - **Conductivity** - The conductivity of the polymer-salt complex is given by the Vogel-Tamman-Fulcher equation, $\sigma =\sigma_{0}\exp\left(\frac{-B}{R(T-T_{0})}\right)$ where $B$ is a constant and $T_{0}$ is a characteristic temperature of the material (ideal glass transition temperature measured with infinite time). - **Viscosity** - The higher the temperature is above $T_0$, the less viscous it is. This results in faster polymer and ionic motion. - **Disorder** - The added disorder in the glassy state also aids ionic motion. - **Doping** - The doping of the counter ion can increase conductivity significantly by adjusting the energetics of defect creation. - *e.g.* Doping of $\ce{AsF6-}$ with $\ce{N(SO2CF3)2-}$ (TFSI) results in an increase in $\sigma$ of 1.5 orders of magnitude up to 5%, where a two-phase mixture is formed. - **Dissolution** - The dissolution of salts into the polymer is governed by Gibbs free energy. - **Enthalpic Contributions** - Enthalpic contributions dominate. Contributions include salt lattice energy (unfavourable), creation of polymer host sites (unfavourable), salt-polymer bonds (favourable) and electrostatic interactions (favourable). - **Counterion** - Preferably large and low charge such as *lithium triflate*, $\ce{LiCF3SO3}$. **Polyelectrolytes** - The polymer backbone itself has anionic groups which the $\ce{Li+}$ can bind to and diffuse. - **Improving Conductivity** - The conductivity can be improved via the addition of plasticiser *e.g. poly(ethylene glycol)*. - ***e.g. NAFION-117*** - Contains $\ce{SO3-}$ groups attached to the polymer backbone, the $\ce{Li+}$ can hop between the sites. ![[Nafion2.svg.png#invert|cm]] ### Solid State Electrolytes **Conductivity, $\sigma$** - The ionic or the electronic conductivity is given by $\sigma =ne\mu$ where $n$ is the number of mobile species, $e$ is the species’ charge and $\mu$ is the mobility. - **Total Conductivity,** $\sigma_{tot}$ - The total conductivity is the sum of the ionic and electronic conductivity. - **Ionic Transference Number, $t_{ion}$** - The fraction of total conductivity due to ionic conductivity. Should be as close to 1 as possible. $t_{ion}=\frac{\sigma_{ion}}{\sigma_{ion}+\sigma _{elec}}$ ^trans **Diversity** - There is a large diversity of inorganic ion conductors, including anionic conductors ($\ce{O^{2-}, F-, H-}$) and cationic conductors ($\ce{Li+, Na+, H+}$). **Structure Requirements** - To achieve a suitable conductivity (>10⁻³ S cm⁻¹) there are a number of structural requirements. - **Vacancies** - The structure has to have partially occupied sites in the structure of very stable interstitial sites. - **Hopping Pathways** - There has to be good pathways for the ion to conduct in as many dimensions as possible, with short hopping distances. - **Sites Equivalency** - Generally if the sites have equivalent symmetry and energies conduction can take place easier. **Conduction Pathways** - The ion often cannot take the most direct route through the structure and instead have to curve around other ions to minimise repulsion. > [!recap] Defect Recap **Defects** - Defect structures normally have improved conductivities due to a greater number of vacancies and hence a larger $n$. > - **Schottky Defect** - A pair of vacant sites resulting from the removal of both a cation and an anion. $\ce{Na^{x}_{Na} + Cl^{x}_{Cl} -> V'_{Na} + V^{.}_{Cl} + NaCl}$ >- **Frenkel Defect** - An ion is displaced from its site to an interstitial site. $\ce{Ag^{x}_{Ag} -> Ag^{.}_{i} + V'_{Ag}}$ >- **Intrinsic Defects** - At all temperatures the crystal structure will contain Schottky and Frenkel defects. >- **Extrinsic Defects** - Doping the structure with other elements will increase the defect concentration substantially at room temperature. **Ionic Hopping Model** - The diffusion of ions can be modelled as hoping between the sites. - **Barrier** - All the ions will be vibrating in their site but a certain proportion of them will have sufficient thermal energy to escape the site. - **Application of Field** - If a field is applied to the material, the jumps become biased downwards. - **Hopping Enthalpy, $\Delta H_{m}$** - A low barrier height is required for high ionic conductivity. - **Arrhenius Behaviour** - The prefactor for a hopping conductor has a $T^{-1}$ dependence in the prefactor and hence $\sigma T$ is often plotted, $\begin{align*}\sigma T &= \frac{Nq^{2}a_{0}^{2}\nu}{gk_{B}}\cdot\exp\left(\frac{\Delta S}{k_{B}}\right)\cdot\exp\frac{-\Delta H_{m}}{k_{B}T}\\\sigma T &= A \cdot \exp \left(- \frac{\Delta H_{m}}{k_{B}T}\right)\end{align*}$ where $N$ is the number mobile ions, $q$ is the charge, $a_{0}$ is the jump distance, $\nu$ is the attempt frequency, $g$ is a geometrical factor. - **Choice** - Both this model and the Arrhenius model tend to give similar results, this one slightly more theoretically grounded. ^arrhenius **Determining Migration Pathways** - There are a number of techniques for determining migration pathways. - **NMR** - The peak shape can be strongly influenced by diffusion, can result in both broadening and narrowing. - $\ce{^7Li}$ is NMR active. - **Crystallography** - Diffraction methods can indicate ionic motion with large anisotropic thermal displacement parameters. - **[[Perovskites#^18e8fa|Neutrons]]** - This tends to require neutrons as light elements are the ones diffusing. - **Total Scattering** - Total scattering techniques that produce pair distribution functions also give information on local disorder (*this was my placement*). - **DFT-MD** - [[Chemical Applications of Electronic Structure Calculations#^6ff4eb|Computational methods]] can estimate migration pathways in the solid. Limiting factor is the computational method. # Photovoltaics **Photovoltaics, PV** - Devices that convert light into electrical energy. - **Excitation** - In all materials, the absorption of photons will result in the excitation of electrons to a higher energy level. - **Separation** - Photovoltaic devices depend on the subsequent separation of this charge before recombination, allowing the energy to be used for useful work. **Semiconductor PVs** - A semiconductor PV is composed of two regions of p- and n-doped semiconductor. - The band structure is engineered in such as way that the excited electron moves in the opposite direction to the created hole. ![[Standard_Solar_Cell-1.png#invert|cm]] %% https://en.wikipedia.org/wiki/Schottky_junction_solar_cell#/media/File:Standard_Solar_Cell.png %% **Dye-sensitized PVs** - An alternate PV technology where an electron is excited from the HOMO to the LUMO of a dye molecule, which then separated. **Solar Cell Efficiency** - The sun emits more light at certain wavelengths and hence a solar cell should be designed so the band gap matches this wavelength. - **Wrong Band Gap** - If the band gap is too large, not enough excitations will take place; if the band gap is too small, the excitation won’t have that high a voltage. - **Stacking** - Multiple types of solar cells can be stacked to increase their efficiency. **Solar Cell Parameters** - A solar cell can be characterised by a number of parameters. - **Short Circuit Current (Density), $j_{SC}$** - The current generated in a short circuit, where no load is placed on the cell. - **Open Circuit Voltage**, $V_{OC}$ - The voltage across the cell when not connected together. - **Ideal** - In the ideal case, the short circuit current could be generated for all voltages up to and including $V_{OC}$. - **Inefficiencies** - The roundness of the corner (in both current and power) indicate the inefficiencies of the cell. ![[Own3.png#invertW|cl]] - **Fill Factor, $FF$** - A way to numerically quantify the inefficiency, calculated by $FF = \frac{I_{mp}V_{mp}}{I_{SC}V_{OC}}$ where $I_{mp}$ and $V_{mp}$ are the current and voltage at maximum power respectively. - **Photon Conversion Efficiency, $\eta$** - Rather than comparing against the ideal power of the cell, compare against the power of the sun. $\eta = \frac{I_{mp}V_{mp}}{P_{sun}}$ # Batteries **Basic Components** - All batteries have the following common components. - **Electrodes** - Each battery contains two electrodes, which are the site of oxidation and reduction reactions. - **Electrolyte** - Separating the two electrodes is an electrolyte that is ionically conductive but is not electrically conductive. >[!core] Electrode Terminology >**Anode and Cathode** - Whether the electrode is the anode or the cathode switches during charge and discharge. Despite this, some people refer to their behaviour when discharging. > > > **“An Ox, Red Cat”** - Anode is site of oxidation, cathode is site of reduction. > >**Positive and Negative Electrode** - A less ambiguous terminology that does not switch depending on whether the battery is charging or discharging. > >**Discharge** - The positive electrode is the site of reduction during discharge (therefore the cathode); the negative electrode is the site of oxidation during discharge (therefore the anode). > > **Charge** - The positive electrode is the site of oxidation; the negative electrode is the site reduction. > > **Justifying the Name** - The negative electrode is negative during discharge as it is generating electrons and pushing them away; it is negative during charging as an external power source pushes the electrons to that electrode. > > ***e.g. Li-ion*** > $\begin{align*} \textbf{Discharge:} \\ \oplus \text{ Electrode:}&& \ce{Li_{1-x}CoO2 + x Li^{+} + $x$ e- &->[Reduction][Co^4+->Co^3+]LiCoO2 } \\ \ominus \text{ Electrode:} &&\ce{xLiC6 &->[Oxidation][C_{6}^{-} -> C] xLi^{+} + 6x C + $x$e-}\\ \textbf{Charge:} \\ \oplus \text{ Electrode:}&& \ce{LiCoO2 &->[Oxidation][Co^3+->Co^4+] Li_{1-x}CoO2 + x Li^{+} + $x$ e-} \\ \ominus \text{ Electrode:} &&\ce{xLi^{+} + 6x C + $x$e- &->[Reduction][C->C_{6}^{-}]xLiC6} \end{align*}$ > In these notes, all equilbrium equations are written with discharge going right. **Electrode Types** - On the broadest level, electrodes can be classified as: - **Intercalation Electrodes** - The redox process is completed via intercalation of an ion in the structure. - Intercalation is a process where a guest atom or ion is reversibly inserted between the layers of a solid host without causing major structural disruption. - **Insertion Electrodes** - The redox process is completed via insertion of ions into a non-layered host structure (*e.g. 1D channels*). - **Conversion Electrode** - The redox process is completed via major structural disruption, creating two distinct phases. - **Types of Behaviour** - The potential-capacity curves differ substantially depending on the type of behaviour. - **Single Phase** - If the Li is added to the structure in a solid solution, one phase is present through the whole process. The potential tends to change as you go through the solid solution. - **Two Phase** - If only the two-end members are observed and only the proportion of each changes, the potential is much flatter. ![[ara-notes-1.png#invert|cl]] ### Important Metrics **Cell Potential** - The equilibrium potential difference between the two electrodes. $E = -\frac{\Delta G}{nF}=E_{red}-E_{cat}$ **Capacity** - The batteries capacity defines how much charge it can store in one complete charge or discharge. It is typically expressed in mAh. - **Specific Capacity, $Q_s$** - The capacity per unit mass of electrode material, typically expressed in mAh g⁻¹.$Q_{s} = I \frac{t}{m}$ - **Volumetric Capacity, $Q_V$** - The capacity per unit volume of electrode material, typically expressed in mAh cm⁻³. $Q_{V}=I \frac{t}{V}$ **Faraday’s Law** - The amount of charge transferred in an electrochemical reaction. $Q = zF \frac{m}{M_{w}}$ where $Q$ is the charge, $m$ is the mass of material, $M_w$ is the molar mass, $F$ is the Faraday constant and $z$ is the valence number. - **Implication** - Low molar mass allows more charge to be transferred for the same mass. - **Theoretical Specific Capacity** - We can use Faraday’s law to express the theoretical capacity for an electrode. $Q_{ts} = \frac{nF}{M_{w}}$ - Important to get $n$ right in this equation, it is not always 1. - **Practical Capacity** - The practical capacity may be significantly smaller than the theoretical capacity if the full discharge/charge is not possible. >[!example] Theoretical Capacity of $\ce{LiFePO4}$ >Calculate the theoretical capacity of the positive electrode $\ce{LiFePO4}$. > > ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-1.png|cl]] **Specific Energy** - The amount of energy stored per unit mass, expressed in Wh kg⁻¹.$W^{th}_{e}=\frac{\Delta G}{\sum_i n_iM_i}$ - **Integration** - The energy is the area underneath the potential-capacity curve, *i.e.* $W_{e}=\int^{Q}_{0}V(Q)\,dQ$. - **Simple Process** - For a simple two-phase redox process at a constant potential, $W_{e}=Q_{s}V$. - **Practical Value** - Much lower due to the mass of all other cell components. - **Volumetric Energy Density** - Similarly, the volumetric energy density may be calculated by using the density of the material. **Coulombic Efficiency, $\%CE$** - Describes the reversibility of the material, *i.e.* the ratio of the discharge capacity and the charge capacity. $\%CE = \frac{Q_{dis}}{Q_{ch}}\times 100\%$ - **Desired Value** - It should be very close to 1; low CE may indicate the presence of side reactions. **Capacity Retention** - Describes the loss of capacity upon cycling. $\%CR=\frac{Q_{\text{nth dis}}}{Q_{\text{1st dis}}}\times 100 \%$ - **Usability** - Cells are typically said to be usable until the capacity is below 80%. **Rate Capability** - The cell performance as a function of cycling rate. - **Cycling Rate** - Can be expressed as mA g⁻¹, however commonly expressed using **C rate**. In this form, C/$n$ is the number of hours, $n$, for a full charge or discharge. **Other Metrics** - As well as the electrochemical metrics, other factors must be considered. - **Cost** - The cheaper the better. - **Toxicity** - Avoidance of toxic elements is better environmentally and likely cheaper. - **Safety** - Want batteries that have a low risk of exploding etc. - **Natural Abundance** - Batteries that use elements that are more naturally abundant will likely be cheaper and easier to source. ## Pre-Lithium Ion **Voltaic Pile** - The first prototype of a battery invented by Alessandro Volta. - **Chemistry** - A pile of cells with zinc and copper metal separated by electrolyte-soaked felt. $\ce{Zn|Zn^{2+}||2H+|H2|Cu}$ ![[Voltaic_pile.svg.png#invert|cm]] **Lead-Acid Batteries** - The first commonly-available rechargeable battery. Very heavy batteries, poor safety. - **Negative Electrode** - Upon discharge, $\ce{Pb}$ oxidises to $\ce{PbSO4}$. - **Positive Electrode** - Upon discharge, $\ce{PbO2}$ reduces to $\ce{PbSO4}$. - **Electrolyte** - The electrolyte is $\ce{H2SO4}$. **Ni-Cd Batteries** - Former popular battery technology for power tools etc., phased out due to Cd toxicity. - **Discharging** - On positive electrode, the oxygen is reduced from $\ce{H2O}$ and $\ce{OOH-}$ to $\ce{3 OH-}$ while the nickel oxidises from $\ce{Ni+}$ to $\ce{Ni^2+}$. On the negative electrode, the Cd is oxidised from $\ce{Cd}$ to $\ce{Cd^2+}$ $\begin{align*} \oplus \text{ Electrode:}&& \ce{NiOOH + H2O + e- &<=>Ni(OH)2 + OH-}\\ \ominus \text{ Electrode:}&& \ce{Cd + 2OH- &<=>Cd(OH)2 + 2e-} \end{align*}$ - **Memory Effect** - The battery loses capacity when repeatedly recharged from partial discharge. **Ni-MH Batteries** - Slight improvement on Ni-Cd cells, were used in the first electric cars. Some problems with self-discharge. - **Discharging** - Same positive electrode as Ni-Cd; on the negative electrode $\ce{H-}$ oxidises to $\ce{H^{+}}$ while the metal reduces from $\ce{M^{+x}}$ to $\ce{M^{+x-1}}$. $\begin{align*} \oplus \text{ Electrode:}&& \ce{NiOOH + H2O + e- &<=>Ni(OH)2 + OH-}\\ \ominus \text{ Electrode:}&& \ce{MH_x + OH- &<=>MH_{x-1} + H2O + e-} \end{align*}$ - **Negative Electrodes** - Examples include $\ce{LaNi5H6}$ or $\ce{TiH2}$. ## Lithium-Ion **Lithium-Ion Batteries** - In the present day, lithium-ion batteries are the dominant chemistry due to their reliability, high cell voltage, high energy density etc. - **Development** - The development of Li-ion was credited to John Goodenough, Stanley Whittingham and Akira Yoshino in the 2019 Nobel prize. - **Original Chemistry** - The original chemistry involved the reduction of $\ce{Co^4+}$ to $\ce{Co^3+}$ on the positive electrode while $\ce{C6^-}$ is oxidised to graphite on the negative electrode. - Li is “happier” as $\ce{Li+}$ in the negative electrode than being basically $\ce{Li}$ metal in the graphite. $\begin{align*} \oplus \text{ Electrode:}&& \ce{Li_{1-x}CoO2 + x Li^{+} + $x$ e- &<=> LiCoO2} \\ \ominus \text{ Electrode:} &&\ce{xLiC6 &<=> xLi^{+} + 6x C + $x$e- }\\ \end{align*}$ ![[Akhmetov-1.jpg#invert|cm]] %% https://doi.org/10.3390/electronics12051152 %% **Packaging** - There is more to a Li-ion battery than the simple cell above. ![[Hou-1.png#invert]] %% https://doi.org/10.1002/aenm.201904152 %% - **Separator** - If using a liquid electrolyte, a glass fibre or porous polymer membrane must be placed between the electrodes to ensure separation. - **Additives** - Numerous additives will be added to the electrodes for better performance - conducting additive for better electron transport (*e.g. amorphous C*), binder to ensure good cohesion and grain contact (*e.g. polymer*). - **Current Collector** - Provides rigid support for the electrode and the electrical contact. Al for positive electrode, Cu for graphitic negative electrodes. - **Importance** - Much of the increases in energy densities etc. are from constant improvements in packaging and formulation; rather than a great shift in chemistry. ### Positive Electrodes **Positive Electrodes** - The positive electrodes of a cell tends to be the most-expensive rate-limiting component. #### Layered Metal Oxides **Layered Metal Oxides** - The most common type of positive electrode material. $\ce{Li_{1-x}MO2 + x Li^{+} + $x$ e- <=> LiMO2}$ $\ce{LiCoO2}$ - The original positive electrode material, first commercialised by Sony. - **O3 Structure** - Adopts a layered structure denoted O3, indicating octahedral Li coordination with 3 transition metal layers per unit cell. - **Capacity** - Despite a high theoretical capacity (273 mAh g⁻¹), it only has a limited practical capacity (130 mAh g⁻¹) due to a poorly reversible monoclinic phase transition at $x \approx 0.5$. ![[Lithium-cobalt-oxide-3D-polyhedra.png]]![[ara-notes-2.png#invert]] - **Downsides** - Expensive, Co toxic, conflict mining of Co in DRC. $\ce{LiNiO2}$ - An alternative material that uses Ni. Ni is cheaper but still toxic. - **Li/Ni Disorder** - The smaller Ni ions can now fit better in the Li sites, resulting in unwanted disorder. Need careful synthesis to prevent. - **Ni Issues** - Ni is not that much better than Co as it is also toxic and supply has been disrupted due to Russia. $\ce{Li(Ni, Co)O2}$ - Mix Ni and Co to create a more stable, higher capacity electrode than $\ce{LiCoO2}$ as monoclinic phase transition supressed (170 mAh g⁻¹). - **Commercialisation** - Has been commercialised with a small amount of Al dopant to give NCA. $\ce{Li(Ni,Mn,Co)O2}$, **NMC** - Addition of electrochemically inactive $\ce{Mn^4+}$ maintain structural stability, while allowing $\ce{Ni^2+}$ and $\ce{Co^3+}$ to oxidise to $\ce{Ni^4+}$ and $\ce{Co^4+}$ during charging. - **Ni Rich NMC** - Originally focus was on 3:3:3 ratio, extensive focus now on 6:2:2 and 8:1:1 to reduce Co content. - **Issues** - NMC has higher capacity (>180 mAh g⁻¹) but lower capacity retention, lower thermal stability and bigger volume changes. #### Spinels **Spinel Structures** - An alternative positive electrode that works using insertion rather than intercalation. $\ce{Li_{1-x}M2O4 + x Li+ +$x$ e- <=> LiM2O4}$ $\ce{LiMn2O4}$ - Significant research effort into this spinel but has lower capacities of around 110 mAh g⁻¹. - **Advantages** - Cheaper, safer, less toxic, good rate capability due to fast $\ce{Li+}$ diffusion. - **Disproportionation Problems** - The $\ce{Mn^3+}$ produced at the end of discharge may disproportionate into $\ce{Mn^{2+}}$ and $\ce{Mn^4+}$. The resulting $\ce{Mn^2+}$ may dissolve into the electrolyte. Worse at high temps. - **Further Insertion** - Further insertion of $\ce{Li+}$ is possible but less reversible due $\ce{Mn^3+}$ Jahn-Teller distortion. ![[ara-notes-3.png#invert]] ![[ara-notes-4.png#invert]] $\ce{Li_{1+x}Mn_{2-x}O4}$ - A more stable structure that reduces likelihood of disproportionation but has lower capacity. Substitution of Mn for Al etc. can improve performance. $\ce{LiMn_{1.5}Ni_{0.5}O4}$ - $\ce{Mn^4+}$ becomes electrochemically inactive and instead $\ce{Ni^4+}$ reduces to $\ce{Ni^2+}$ on discharge. Very high operating voltages (4.7 V). - **Advantages** - High energy densities, good rate capability. - **Issues** - Hard to find a stable electrolyte hence low Coulombic efficiencies. - **Order/Disorder** - Can have order or disorder between the Mn/Ni sites, ordered structure is better. #### Polyanionic Frameworks **Polyanionic Frameworks** - Another important class of materials in materials containing polyanions. - **Inductive Effect** - The polyanions increase the reduction potential of the metal and hence increases the energy stored in the battery. - The polyanions withdraw electron density from metal ions and hence weakens the covalent M-O bond. - In the reduction step, the electron moves from ‘vacuum’ into an antibonding orbital and hence the weakening of the covalent M-O bon will increase this energy. - **Effect Strength** - The strength of the inductive effect depends on both the structure type and the identity of the polyanion. - $\ce{SO4}$ - The strongest polyanion but not usable as the positive electrode needs to be the source of Li and $\ce{Fe2SO4}$ has no lithium. ![[ara-notes-5.png#invert|cl]] ![[ara-notes-6.png#invert|cl]] - **Drawbacks of Polyanion Batteries** - The extra mass of the polyanion results in lower capacities; tend to have low electronic and ionic conductivity. - **Improvements** - The conductivity can be improved by decreasing particle size and carbon coating. $\ce{LiFePO4}$, **LFP** - The most common polyanionic framework material. Relatively low voltage of 3.3 V against Li⁺/Li. ![[ara-notes-7.png#invert|cl]] - **Properties** - High rate performance and relatively cheap - dominant battery chemistry for power tools. $\ce{LiMnPO4}$ - Increases the reduction potential (4.1 V) but has very poor conductivity and large volume change ($\ce{Mn^3+}$ is Jahn-Teller active). $\ce{LiCoPO4}$ - Even higher voltage (4.8 V) but challenging to work with as it unstable towards the electrolyte. - **Fixes** - Various strategies including doping, surface modification and electrolyte additives have been developed to combat this. $\ce{Li(Fe,Mn)PO4}$ - Attempts to combine the performance of LFP batteries with the high voltage of LMP. - **Advantages** - Discharge capacity relatively similar but increases energy density compared to LFP. Commercial development underway. - **Issues** - Problems with tap density (doesn’t pack well) which limits volumetric densities. $\ce{Li2FeSiO4}$ - An alternative polyanion choice with very cheap raw materials and an operating voltage of 3 V. - **Multiple Li Extraction** - There is a possibility of extracting more than one lithium but this is not realised due a voltage drop and structural transformation. #### New Directions **New Directions** - A number of more experimental structure are being developed. **Fluorosulphates** - The use of sulphates gives highest potential of any polyanion. - So far has shown higher voltages than other polyanion frameworks but lower capacities. **Li-rich Layered Phases** - Intentional site disorder to put $\ce{Li+}$ in the transition metal site too. - $\ce{Li[Mn_{0.6}Ni_{0.2}Li_{0.2}]O3}$ - Traditional layered metal oxide materials, Ni redox. - $\ce{Li_{1.33}Mn_{0.67}O3}$- Despite $\ce{Mn^4+}$ being redox inactive, can still charge up due to oxygen redox. - **Oxygen Redox** - Both materials can do oxygen redox, whereby after metals are fully oxidised the oxygen can form superoxides etc. - **Properties** - This gives voltage plateau at 4.5 V and moderate rate performance but has voltage decay upon cycling and significant voltage hysteresis. **Other Oxygen Redox Materials** - Other materials have been explored for O redox such as disordered rock salts. - **Hysteresis** - Often very large voltage hysteresis that it substantially improved at higher temperatures (*ca.* 60°C). $\ce{Cu_{2.33}V_{4}O_{11}}$ - Shows reversible Li insertion via the growth of Cu nanorods. ### Negative Electrodes **Li Metal** - From a capacity and potential point of view, Li metal would be the ideal negative electrode (3600 mAh g⁻¹ capacity). - **Issues** - Li metal will react with the solvent and can grow dendrites. - **Dendrites** - A dendrite is a thin wire of metal that grows into the electrolyte. If it grows enough to bridge the electrodes, it causes a short circuit. - **Plating** - Rather than doing this, ideally the deposited Li would plate the electrode evenly. - **Solid State Batteries** - Li metal electrodes may have a place in solid state batteries, where the solid electrolyte blocks dendrite growth. - **New Electrolytes** - Some research has found that alternative liquid electrolytes may retard dendrite growth and allow Li metal use. **Carbon Electrodes** - Graphite and coke are the most widely used materials for negative electrodes (theoretical capacity 372 mAh g⁻¹ / 790 mAh cm⁻³). $\ce{LiC6 <=> C6 + Li+ +e-}$ - **Advantages** - Non-toxic, low cost, redox potential close to Li⁺/Li, no major structural changes. - **Solid Electrolyte Interphase, SEI** - The first charge of the cell has a lower Coulombic efficiency due to a side reaction with electrolyte. - **Layer** - This forms a barrier on the surface of the negative electrode which can prevent further electrolyte decomposition. - As this only happens on the first charge, this is tolerable. - **Factors** - The choice of electrolyte salt and solvent have a large impact on the morphology, composition and stability of the SEI. - **Extra Li** - To make up for the lost Li, more positive electrode is added. ![[admi202101891-fig-0001-m.jpg#invert|cs]] - **Issues** - Despite its widespread use, there are number of reasons to look for alternatives. - **Unstable** - The carbon can be unstable to exfoliation. - **SEI** - Although the SEI is tolerable, ideally it wouldn’t happen as it would enable greater energy densities. - **Unsafe** - The potential is close to Li⁺/Li and hence is quite reactive. Fast charging may resulting in dangerous Li plating. - **Current Collector** - As Al alloys with Li, must use more expensive and heavy Cu collector. **Insertion Oxide Electrodes** - A much safer negative electrode at the expense of reduced cell voltages and low capacities. - $\ce{Li4Ti5O12}$ - Spinel structure with higher reduction potential of 1.5 V vs Li⁺/Li, lower capacity of 170 mAh g⁻¹. Good capacity retention and no volume change on cycling. $\ce{Li7Ti5O12 <=> Li4Ti5O12 + 3 Li+ + 3e-}$ - $\ce{TiO2}$ **Bronze** - The bronze polymorph of $\ce{TiO2}$ is the most open polymorph of $\ce{TiO2}$ and can be prepared as a nanomaterial, enabling great rate performance. - **Pairing** - The high reduction potential can be offset by using a positive electrode with a higher reduction potential. - $\ce{TiNb2O7}$ - Another open framework structure. - $\ce{Nb16W5O55}$ and $\ce{Nb18W16O93}$ - Tungsten bronze derivates have also been reported with excellent rate performance. - $\ce{Li_{1+x}V_{1-x}O2}$ - Has a much lower reduction potential (*ca.* 0.1 V vs Li⁺/Li) with high theoretical volumetric capacity of 1360 mAh cm⁻³. - **Stoichiometry** - Requires excess Li to work, the stochiometric material is basically inactive. - **Geometry** - Li⁺ is intercalated into the tetrahedral site. If stochiometric, this is face sharing with V³⁺. If there is an excess of Li⁺, some Li is in the V site and the face-sharing is significantly less unfavourable. ![[ara-notes-8.png#invert|cl]] **Nano-Structuring** - Nano-structuring is good for high rate performance. - **Advantages** - Results in short Li⁺ and e⁻ diffusion paths and increases contact area with the electrolyte. - **Disadvantages** - The high surface area can result in problems with electrolyte decomposition, typically low packing densities. **Conversion Metal Oxides** - Binary metal oxides cannot accommodate lithium but can react with $\ce{Li+}$ to form amorphous $\ce{Li2O}$ and metallic nanoparticles. - **Advantages** - Large capacities and good capacity retention. - **Disadvantages** - Can show large voltage hysteresis, resulting in poor Coulombic efficiencies. Also has poor rate capabilities. - **Compounds** - Many different metal oxides can be used such as $\ce{Fe2O3}$ or $\ce{CoO}$. Additionally fluorides, sulfides etc. can be used too. - **Nano-structuring** - Making the particles smaller helps the hysteresis. - ***e.g. $\ce{Fe2O3}$ Nanoparticles*** - Shows much better performance (still not great) when nanostructured. $\ce{2Fe + 3Li2O <=> Fe2O3 + 3Li+ + 3e^-}$ ![[ara-notes-9.png#invert|cl]] **Alloys** - The reversible alloying of Li has the possibilities for large capacities but can have issues with large volume changes (up to 300%). - **Examples** - Can alloy to $\ce{Li_{4.4}Sn}$ (capacity 993 mAh g⁻¹) or $\ce{Li_{4.4}Si}$ (capacity 4200 mAh g⁻¹). - **Volume Change** - The 300% volume change of $\ce{Li_{4.4}Si}$ can cause cracking and loss of electrical contact, resulting in large capacity fading. - **Nano-Structuring** - Has the potential to combat the issues of volume expansion. It reduces cracking and makes phase transitions more facile. - Still has problems with long term cycling. - **Flexible Binders** - Could also add more flexibility to the binders, *e.g. carboxymethyl cellulose* - **Limit Capacity** - With such a higher capacity, we could artificially limit it to improve cell lifetimes. - **Disadvantages** - Can no longer tell the battery health and may result in an unstable SEI. **Siloxene** - A potential layered Si intercalation anode. **Organic Electrodes** - Use of organic salts as a negative electrode has been reported. - **Possibilities** - Gives ideal reduction potential of 1 V Li⁺/Li (good safety characteristics, use Al current collector, cell voltage not reduced too much). - **Disadvantages** - The poor electrical conductivity tends to limit rate capability. - ***Example*** - Lithium terephthalic acid salts have been tested. ### Electrolytes **Liquid Electrolytes** - Most commercial batteries use liquid electrolytes, where a lithium salt is dissolved in a non-aqueous solvent. - **Requirements** - There are numerous requirements for a liquid electrolyte: - High dielectric constant enhances salt solubility. - High ionic conductivity (> 1 mS cm⁻¹) and low electronic conductivity. - Low viscosity to allow ions to move through solvent. - Wide electrochemical stability window (ideally 0 to 5 V vs Li⁺/Li) - Good thermal and chemical stability; compatible with other components. - Low cost, low toxicity and low flammability. - **Typical Example** - A typical example of an electrolyte is 1 M $\ce{LiPF6}$ dissolved in a mixture of linear and cyclic organic carbonates *e.g.* 1:1 mixture ethylene carbonate (EC) and dimethyl carbonate (DMC). - **Additives** - Additives such as vinylene carbonate (VC) help form a stable SEI layer on the first cycle. (Sacrificial, not well understood) - **Advantages** - Tend to be cheap, easy to prepare, high ionic conductivity. - **Issues** - Reaction of $\ce{LiPF6}$ with water to produce HF, volatile, flammable, some salts corrode Al. There is regulatory pressure to reduce F usage. ![[ara-notes-10.png#invert|cl]] **Gel Electrolytes** - Alternatively, a liquid organic electrolyte may encapsulated in a polymer mesh to allow for flexible solid state batteries. - Attempts to access the best of both worlds, with the high ionic conductivity of liquid electrolytes but with additional stability. **Solid Electrolytes** - Both crystalline and polymer solid electrolytes are being developed. - **Advantages**: - **Safety** - The non-flammable and non-volatile nature of crystalline material improves safety and stability. The batteries will also be more shock and temperature resistant. - **Simplicity** - Should allow simpler device design and fabrication without the need for liquid containment, easier to miniaturise. - **Energy Densities** - A simple switch to all SSB will not improve energy densities that much but may enable different electrodes (Li metal 👀). - **Requirements**: - **Competitive with Liquid Electrolytes** - Must have a similar ionic conductivity, negligible electrical conductivity, high thermal and electrochemical stability etc. - **Interface Stability** - Additionally, the electrolyte-electrode interfaces must be stable - no interface reactions, similar thermal expansion to prevent delamination. - **Interface Issues** - Unfortunately, there are many issues at the interface. - **Imperfect Solid-Solid Contact** - Much harder to ensure good contact between the surfaces than with liquid. - **Dendrites** - Dendrite growth is still a problem, tends to occur along grain boundaries. - **Mechanical Pressures** - Tensile or compressive strains due to thermal expansion or cycling can result in cracking and delamination. - **Li Depletion** - The electrolyte can be Li depleted at the interfaces. - **Design** - To get the required ionic conductivity, a number of structures (*for instance perovskites or garnets*) have been trailed. The presence of vacancies for the Li⁺ ions to hop to is key. - ***e.g. Thio-LISICON*** - $\ce{Li10GeP2S12}$ is one of the more promising candidates, exhibits great ionic conductivity at room temperature. - **Drawback** - Has poor electrode compatibility with Li giving low Coulombic efficiencies. This has been corrected by $\ce{Li_{9.6}P3S12}$ **Ionic Liquids** - A liquid that is made up of entirely ionic species without solvent. - **Properties** - Very high ionic conductivity, high thermal and electrochemical stability. - **Advantages** - Very low flammability, negligible vapour pressure, relatively environmentally friendly. - **Disadvantages** - High viscosity limits high rate cycling, expensive and difficult to prepare. - **Molten Salt** - The high temperature equivalent of this, often uses eutectic compositions. ### Battery Recycling **Lithium Availability** - Although lithium is relatively abundant, it still has some availability problems. - **Geographical Distribution** - Chile, Bolivia, Argentina and Australia hold the majority of the known reserves, while China has over 60% of global refining capacity. - **Dependence** - This therefore means the supply chain is not particularly resilient and has unfavourable geopolitics. - **Price Volatility** - The price of Li is quite volatile, which is not ideal for manufacturers. - **Quantity** - If lithium is to be used in both grid storage and electric vehicles, there may not be enough out there. **Recycling** - The price of Li is not particularly far off what is needed to be make recycling worthwhile, as well as being more environmentally friendly. - **Cell Content** - The cells contain many different components that need to be separated before reuse. This includes metals (from current collector), plastics (binder, separator), metal oxides (cathodes) and carbonaceous materials (anodes). - **Methods** - There are multiple different methods for recycling. - **Pyrometallurgical** - The battery is effectively melted down. This is the simplest and most technologically ready method but results in less, poorer quality recovered material. - Under 50% of material recovered. - **Hydrometallurgical** - The battery is treated with strong acid or base. This somewhat more complex but gives better higher quality recovered material with lower energy usage. - Around 70% of material recovered. - **Direct Recycling** - Physical separation of the components is the complex method but allows the most material to be successfully recovered. - Potentially recover over 90% of material. - **Issues** - There are a number of barriers to efficient recycling. - **Lack of Standardisation** - Each manufacturer makes cells in a different way, making it very hard to automate the process. - **Design** - A battery pack designed for recycling will likely come at the cost of some performance (energy density etc.). - *For instance, Tesla’s cylindrical cell design is harder to recycle then flat designs.* - **Blade Design** - An interlocking design of anodes and cathodes can allow much simpler disassembly. ![[ara-notes-11.png#invert|cl]] - **Shredding** - Right now batteries tend to be shred and not delaminated, making material separation harder and increasing waste. **Reuse** - The reuse of batteries would be even more sustainable. - **Ex-Automotive Batteries** - Automotive batteries have high performance thresholds and hence reach their end of life relatively quickly. - **’Easier’ Applications** - Other battery applications, *e.g. grid storage*, care less about these performance characteristics and hence can reuse the battery. - *For instance, a reduction of gravimetric energy density is likely to matter a lot less for fixed storage, where the selection is primarily based on price.* ## Post-Lithium Ion ### Supercapacitors **Supercapacitor** - A capacitor that can store significantly more charge than a standard capacitor. - **Capacitor** - A traditional capacitor stores the energy in an electric field, it does not undertake any electrochemical processes. The capacitance can be defined as $C=\frac{Q}{V}$ where $C$ is the capacitance, $Q$ is the charge and $V$ is the voltage. - **Ideal Parallel Plate Capacitor** - The capacitance for an ideal parallel plate capacitor is given by $C=\varepsilon_0\varepsilon_r\frac{A}{d}$ where $\varepsilon_0$ is the permittivity of free space, $\varepsilon_r$ is the relative permittivity, $A$ is the plate area and $d$ is the separation. ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-2.png]] **Traditional Capacitors** - A traditional capacitor made of two conductive plates and high $\varepsilon_r$ separator. **Double Layer Capacitor** - An electrolyte is placed between the plates (referred to as electrodes) and the separator. - **Charge Storage** - The charge is no longer stored across the separator but instead in the electrical double layer that forms in the electrolyte. - **Separation** - As the separation is now a few atomic lengths, this has very high capacitance. - **Surface Area Maximisation** - The surface area of the electrode-electrolyte interface should be maximised which can be achieved using activated carbon or carbon nanotubes. - **Non-Faradaic** - This process is still non-Faradaic, *i.e* no charge-transfer through the interface. - **Advantages** - Very rapid response times, long life (no electrochemical processes), high power. **Psuedocapacitors** - Store charge via charge transfer between the electrode and electrolyte. - **Faradaic** - The process is now Faradaic as charge is transferred. - **Mechanism** - A redox reaction occurs at the interface, allowing the storage of more charge than a conventional capacitor. This can be adsorption or intercalation. - ***e.g. $\ce{RuO2}$*** - A ruthenium oxide pseudocapacitor stores charge via the surface level redox of $\ce{Ru^4+/Ru^3+}$. - **Pseudo Designation** - These aren’t really capacitors, however their kinetics mean they act like them. - **Advantages** - Although they have a lower power density, they have higher energy densities and bridge the gap between capacitors and batteries. **Psuedocapacitor Continuum** - There is a smooth continuum between non-Faradaic capacitors and Faradaic batteries, with pseudocapacitors in between. - **Limiting Behaviour** - The limiting behaviour defines the type of material, in batteries the process is diffusion limited. - **Distinguishing the Two** - The peak in CV will shift in potential with batteries, won’t shift with pesudo-capacitors (kinetics fast enough). - **Slope** - The logarithmic ratio between the max current and the sweep rate, $\log j_{max}/\log (v/t)$, indicates the type of behaviour. If greater than 1, capacitive, if less than 0.5, diffusion-limited. ![[ara-notes-12.png#invert|cl]] **Advantages of Supercapacitors**: - **High Power Density** - The removal of ionic diffusion limits allows much faster redox reactions and results in greater power. - **Long-Life Expectancy** - The smaller (or no) amount of redox results in less potential for irreversible phase changes. This allows almost unlimited cyclability. - **Others** - Long shelf life, high efficiency, wide operating temperature window, environmentally benign and safe. **Disadvantages of Supercapacitors**: - **Lower Energy Density** - By not utilising diffusion, there is a significant limit to the energy density. - **High Cost** - The current materials (*e.g. RuO₂ or nanostructured carbon*) are expensive. - **Self-Discharge** - They have high self-discharge rates of up to 40% a day. **Applications** - Despite this, there are a number of possible applications. - **Short Duration Power** - Allows more energy to be absorbed in regenerative breaking. - **Fast Response Times** - Can quickly kick in in uninterruptable power supplies, allowing seamless transition. ### Lithium-Sulfur **Lithium-Sulfur Batteries** - Lithium-sulfur batteries are a promising technology for increasing energy densities. - **Electrodes** - Use Li negative electrode and elemental sulfur positive electrode, which has an order of magnitude more capacity (1672 mAh g⁻¹). - **Electrolyte** - Utilise an organic electrolyte to conduct Li⁺ ions. ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/wikipedia-1.png#invert|cm]] **Sulfur Positive Electrode** - When fully charged, the sulfur is an elemental $\ce{S8}$ state. Through the discharge, go through a variety of Li-sulfur compounds to arrive at $\ce{Li2S}$. - **Potential** - The potential is 2.15 V vs Li⁺/Li. - **Overall Reaction** - Assuming it goes to completion, the overall reversible reaction is $\ce{S8 + 16 Li+ +16 e- <=> 8 Li2S}$ ![[ara-notes-13.png#invert|cm]] **Challenges** - There are number of remaining challenges to surmount. - **Insulating** - Both $\ce{S_8}$ and $\ce{Li2S}$ are electrical insulators and poor Li-ion conductors and hence require additives, reducing the specific capacity. - **Volume Expansion** - The conversion reaction has large volume changes of about 80%. - **Polysulfide Shuttle** - Some of the intermediate polysulfide molecules ($\ce{Li2S8}$ to $\ce{Li2S4}$) are soluble in the liquid electrolyte. - **Passivating Layer** - As well as simply shuttling around, it can be further reduced to $\ce{Li2S2}$ or $\ce{Li2S}$ which are insoluble, forming a passivating layer on the anode. - Results in sluggish redox kinetics and capacity fade. - **Lithium Corrosion** - Lithium suffers from uneven plating resulting in dendrites. - **Dead Li** - Some Li becomes ‘dead’ or not active due to voids etc. **Potential Fixes**: - **Encapsulation** - The polysulfides may be trapped in the positive electrode by encapsulation with carbon or metal oxides. - **Potential Carbons** - Many carbons have been trailed, including mesoporous carbons, carbon nanotubes and graphene oxides. - **Solid State Electrolyte** - A poly(ethylene oxide) electrolyte containing zirconia nanoparticles can allow the Li shuttle without the polyanion shuttle. - **High Temperatures** - The ionic conductivity is not high enough to be used at room temperatures yet. - **$\ce{MnO2}$ Nanosheets** - Addition of $\ce{MnO2}$ nanosheets will act as a redox mediator. They oxidise soluble polysulfides at the surface to prevent the shuttle. **Applications** - Still quite a lot of development required for widespread use, right now only likely to be used in specialised applications. ### Multivalent Systems **Premise** - Multivalent systems are attractive as every ion transfers more charge which should lead to higher capacities. **$\ce{Mg^2+}$ Batteries** - The most developed multivalent battery. - **Advantages** - Higher capacities, higher energy density, low cost. - **Disadvantages** - Low ionic mobility, hard to desolvate $\ce{Mg^2+}$, low voltages. - **Negative Electrodes** - Mg metal is a suitable negative electrode, it can be handled in air and does not form dendrites. - **Positive Electrode** - Harder to find a suitable positive electrodes. Oxides tend to bind to the higher charge $\ce{Mg^2+}$ too strongly, can look to sulphides instead. - ***e.g. $\ce{Mg_xMo6S8}$*** - The Chevrel phase was the first positive electrode demonstrated. - Good reversibility, low capacity and low voltage (sulfur for oxygen not helping). - ***e.g. $\ce{Mg_xTiS2}$*** - An intercalation host for $\ce{Mg^2+}$. Only operates at high temperatures, very poor rate performance. - ***e.g. $\ce{Mg_xTi2S4}$ Thiospinel*** - An insertion host based on a spinel. Improved rate performance, still requires elevated temperatures. - **$\ce{[Mg-Cl]^+}$ Shuttle** - Can make a good positive electrode with good rate performance in expanded $\ce{TiS2}$ (already intercalated with organic molecule) but addition chloride ion results in lower charged density. - Uses ionic liquid, accompanied by large volume changes. **$\ce{Ca^{2+}}$ Batteries** - Very similar to $\ce{Mg^{2+}}$ but less development. - **Comparison with $\ce{Mg^2+}$** - On the positive side, it is higher voltage and less polarising (more mobile); one the negative side it is heavier. - **Awaiting Components** - No suitable positive electrode or electrolyte has been found. - **Prussian Blues** - Prussian blues are being developed as a positive electrode with a capacity of 120 mAh g⁻¹. - **Layered $\ce{TiS2}$** - Although it has higher voltages and capacity, really bad rate performance. - **Organic Electrodes** - Recent development in the use of organic positive electrodes with a CaSn alloy for a negative electrode. $\ce{Al^3+}$ **Batteries** - The aluminium ion by itself will not move, hence need to use $\ce{AlCl4-}$. ### Sodium Ion **Sodium-Ion Batteries** - The most developed alternative to lithium ion. - **Advantages** - Abundance of sodium leads to lower costs, similar chemistry to Li⁺, can use Al for both current collectors. - **Disadvantages** - Sodium is wee bit chunky therefore poorer energy densities and good rate performance more difficult. **Positive Electrodes** - Sodium compounds have a stronger tendency to adopt layer structures due to its larger ionic radius. - **Coordination** - Sodium primarily adopts a trigonal prismatic (P) coordination, as opposed to lithium’s octahedral coordination. - **Electrochemical Activity** - Some Na compounds are electrochemically active while their Li counterparts. - *e.g. can’t reduce $\ce{Fe^{4+}}$ in lithium-ion cathodes, can for sodium-ion cathodes.* - **Polyanionic Frameworks** - Just as with lithium-ion, can utilise the inductive effect. - $\ce{NaFePO4}$ - The required olivine structure is only metastable and must be prepared using *chimie douce* deintercalation of $\ce{LiFePO4}$. - $\ce{Na4Fe3(PO4)2(P2O7)}$ - Offers capacities of 110 mAh g⁻¹, under development by BYD. - **Vanadium Phosphates** - There has been quite a lot of work on vanadium phosphates which can access multiple oxidation states. - **Advantages** - High voltages and good rate capability. - **Disadvantages** - $\ce{V^5+}$ is very toxic, carcinogenic. - **Sulfates** - Sulfates such as $\ce{Na2Fe2(SO4)3}$ can give high voltages (inductive effect) with reasonable rate performance. - **Layered Structures** - There are three dominant types of layered structures. ![[ara-notes-14.png#invert]] - **O3** - Have higher initial Na content (0.8 - 1) resulting in higher initial capacities. Poorer water stability. - **Poor Rate Capability** - Greater energy barrier for $\ce{Na+}$ as it passes through triangular face of octahedra. - **Poor Cycling Stability** - If enough $\ce{Na+}$ is taken out, it often transitions to P3. - **P2** - Lower Na content (<0.7) but has better rate capability (rectangular face) and better cycling stability. - **P3**- Higher voltages possible, prismatic site gives good rate capability. Sodium content normally lacking. - $\ce{Na_x[Fe_{0.5}Mn_{0.5}]O3}$ - Normally seen as the benchmark material, adopts P2 structure. - Fe and Mn cheap and safe, high capacity. Wide voltage range and significant capacity fade. - $\ce{Na_xMnO2}$ - Shows many phase transitions through cycling due to Jahn-Teller distortions and charge ordering. - Only takes one transition to be poorly reversible to cause problem. - $\ce{Na_xMn_{1-y}Mg_yO2}$ - Substitution of Mn for Mg removes many of the transitions. - $\ce{\beta-NaMnO2}$ - High temperature phase has corrugated layers. Cycles well but has poor rate performance. - **Anion Redox** - As with lithium, anion redox is widely observed in layered sodium transition metal oxides. - Often more reversible, strongly dependent on structure. - **Structures** - Both the P2 and P3 structures support anion redox. - **Cycle Life** - Although promising, the cycle life needs to be improved. - **Prussian Blues** - Very open cubic structures which allow sodium ion diffusion at the expense of volumetric capacity. - **Commercial Electrodes** - Currently two main structures: - $\ce{NaMn_{0.33}Fe_{0.33}Ni_{0.33}O2}$ - O3 structure with 130 mAh g⁻¹ capacity and 3V potential. Compromise candidate widely used by Chinese firms. - **Faradion** - Use a material that is a composite of P2 and O3 structures with a capacity of greater than 140 mAh g⁻¹ and 3.3 V. **Negative Electrodes** - Can no longer use graphite as a negative electrode (doesn’t intercalate). - **Al Current Collector** - Na does not alloy with Al, allowing the use of an Al current collector. - **Hard Carbon** - The primary alternative is amorphous hard carbon. It is a mix of graphitic sheets with open pores. - **Cycling** - The sodium ions first insert between the graphene layers or absorb onto the surface. They are then absorbed into the microporosity. This gives two/three regions on the potential-capacity graph. - **First Cycle Irreversible Capacity** - There is significant capacity loss on the first cycle as it is impossible to get all the sodium ions out. - **Synthesis** - Hard carbon is created by pyrolysis of biomass, the temperature of pyrolysis affects its behaviour. - The pyrolysis temperature affects the amount of each type of insertion/absorption, must be carefully controlled. - **Templating** - Templating of the hard carbon to tune the pore structure has the ability to improve the capacity significantly. ![[yu-1.png#invert|cm]] %% https://link-springer-com.ezproxy.st-andrews.ac.uk/article/10.1007/s12598-020-01443-z/figures/7 %% - **$\ce{Na2Ti3O7}$** - Has a potential remarkably close to Na⁺/Na but has poor capacities. - Both poor initial gravimetric capacity and poor capacity retention. - **Alloys** - Despite a large volume change (up to 420%), SnNa alloys seem to cycle better than their lithium counterparts. - **Pb Alloys** - Also works well but toxicity means unlikely to be used. - **Organic Electrodes** - Works quite well with conjugated dicarboxylates. Reasonable rate performance, requires a lot of conductive additives. - **Electrolytes** - The electrolytes used in sodium ion batteries tend to be pretty similar to lithium, somewhat underdeveloped area. - **Liquid Electrolytes** - Tend to use similar salts such as $\ce{NaPF6}$ and $\ce{NaClO4}$ in organic carbonates. - **SEI** - The solid electrolyte interphase tends to be less stable and thinner. - **Polymer Electrolytes** - Polymer electrolytes have been demonstrated - **Solid State Electrolytes** - All solid-state sodium ion batteries are being developed. **Commercialisation** - Sodium batteries are beginning to be commercialised for both grid storage applications and EVs. ### Potassium Ion **Potassium Ion** - Another alternative with similar*ish* chemistries to lithium and sodium. ![[ara-notes-15.png#invert|cl]] - **Positive Electrodes** - Most commonly use Prussian blue analogues. - **Layered Oxides** - Large volume changes make them unstable towards long-term cycling. - **Prussian Blue Analogues** - The open 3D framework allows for good reversibility for $\ce{K+}$ extraction and reinsertion. **Negative Electrodes** - Graphite works relatively well as negative electrode, although there is a significant amount of first cycle capacity loss. # Fuel Cells **Fuel Cells** - An electrochemical device that converts chemical energy to potential energy. - **Fuel** - A fuel must be continuously supplied to the fuel cell, this can be hydrogen or hydrocarbons. - **Oxidant** - The fuel cell also requires an oxidant, which tends to be oxygen from the atmosphere. - **Potential Advantages**: - **Efficiency** - Compared to combustion engines, fuel cells promise much higher efficiencies as less energy is wasted as heat. - **Low Emissions** - $\ce{H2}$ fuel cells only emit $\ce{H2O}$, hydrocarbon fuel cells still better as they only emit $\ce{CO2}$ and emit lower amounts due to higher efficiency. - **Noise** - Fuel cells are quiet, unlike engines. **Technologies** - There are numerous common types of fuel cells. They primarily differ on their electrolyte. - **Polymer Electrolyte/Membrane, PEM** - Contains a solid organic polymer soaked in water to allow $\ce{H^+}$ conduction. - **Operating Conditions** - Lowest operating temperature of 60°C to 100°C. - **Phosphoric Acid, PAFC** - Uses a phosphoric acid-soaked ceramic matrix with interconnected pores as the electrolyte. - **Operating Conditions** - Requires raised temperatures of 175°C to 200°C to keep the acid a liquid. - **Alkaline, AFC** - Uses an aqueous solution of potassium hydroxide soaked in a matrix for the electrolyte. - **Operating Conditions** - Relatively low temperatures of 90°C to 100°C. - **Molten Carbonate, MCFC** - A more unusual fuel cell technology with molten alkali metal carbonates soaked into a matrix for the electrolyte. - **Eutectic** - A mix of carbonates are used to lower the melting point. - **Operating Conditions** - Requires high temperatures of 600°C to 1000°C to melt the carbonates. - **$\ce{CO2}$** - The reaction consumes $\ce{CO2}$ at the cathode and produces it at the anode. - **Solid Oxide, SOFC** - The electrolyte is a $\ce{O^2-}$ conducting ceramic material. - **Operating Conditions** - Requires high temperatures of 600°C to 1000°C to have enough ionic conductivity. **Chemistries** - If using hydrogen, all have the same overall cell reaction that produces water from hydrogen and oxygen. Only differ in ion that is transported. ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-3.png]] **Fuels** - All fuel cell types can use ultrapure $\ce{H2}$, but other fuels only work with some of them. - **Poisoning** - Both PEM and AFC fuel cells can have their Pt electrodes poisoned by impurity gases. The rest of the fuel cells can use normal $\ce{H2}$. - **Reformed Hydrocarbons** - Only MCFC and SOFC can use reformed hydrocarbons as fuel. - **Mechanism** - SOFCs can either use direct oxidation or reform the fuel *in-situ.* - **Processing** - The more processing that is need to be done beforehand, the less coinvent the fuel cell is and the more losses in processing. - **Conversion to $\ce{H2 + CO}$** - Via the reaction $\ce{CH4 + H2O -> CO + 3H2}$. - **Water-Gas Shift Reaction** - Via the reaction $\ce{CO + H2O -> CO2 + H2}$. ![[rtb-notes-8.png#invert|c]] **Pathways** - A number of pathways have to be maintained to allow operation. - **Ionic Conduction** - The ion must be able to conduct across the electrolyte to the reaction site on the electrodes. - **Electronic Conduction** - Electrons must be able to conduct through the electrodes and not conduct through the electrolyte. - **Gas Exchange** - The electrodes must be porous to allow gases to reach the reaction site. However, the electrolyte must be dense to prevent gas diffusion. ## Electrochemistry **Reversible Potential/Open Circuit Voltage (OCV)** - The reversible potential of a fuel cell is calculated using the Nernst equation. $E = E^{\ominus}-\frac{RT}{nF}\ln Q$ - **Concentration Cell** - A potential of 10 mV is generated between pure oxygen ($p_{O_{2}}=1 \rm\ atm$) and air ($p_{O_{2}}=0.21 \rm\ atm$). Here $E^\ominus$ is 0 V as the same reaction is taking place at both sides. $E=\frac{RT}{nF}\, \ln\frac{p_{O_{2},2}}{p_{O_{2},1}}$ > [!derivation]- > ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-4.png]] - **Fuel Cell Approximation** - A fuel cell can be approximated to a concentration cell $(E^{\ominus}=0 \rm\ V)$ by calculating the partial pressure of oxygen using the hydrogen-oxygen-water equilibrium constant. >[!example] Calculating Fuel Cell OCV >Calculate the open circuit voltage of a fuel cell operating at 800°C with 1 atm of $\ce{H2}$ on one side and 1 atm of $\ce{O2}$ on the other. > >![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-5.png]] **Overpotential, $\eta$** - The difference between the potential the open circuit voltage and the measured voltage. $\eta =E_{OCV}-E$ **Characteristic Curve** - A voltage-current characteristic curve is commonly used to describe the behaviour of a fuel cell. - This shows the changing overpotential that is found with increasing current density. ![[rtb-notes-1.png#invert|cl]] **Overpotential Contributions** - There are three primary contributions to the overpotential that give three regions on the characteristic curve. - **Activation Overpotential** - Polarisation losses due to sluggish electrode kinetics. - **Contributions** - Absorption of reactants, electron transfer across double layer, desorption of the product species and the electrode surface. - Given by the [[#^tafel|Tafel equation]], see previously. $\eta_{act}=\frac{RT}{\alpha nF}\, \ln \frac{j}{j_{0}}$ - **Ohmic Overpotential** - Current losses due to electronic, ionic and contact resistances. Given by a simple Ohm’s law dependence. $\eta_{ohm}=I(R_{e}+R_{i}+R_{c})$ - **Ionic Conductivity of Electrolyte** - The ionic conductivity of the electrolyte has a significant contribution to this. - **Concentration Overpotential** - The losses that arise due to slow diffusion of the reactants to the reaction site. - **Concentration Gradient** - As the reactant is consumed, a concentration gradient is formed and must diffuse to the site. - **Limiting Current Density, $j_{L}$** - The maximum current density at which point the concentration of the reactant is zero at the reaction site. - **Fick’s First Law of Diffusion** - The current density controlled by diffusion is given by $j= \frac{nFD(C_{B}-C_{S})}{\delta}$ where $D$ is the diffusion coefficient, $C_{B}$ is the bulk concentration, $C_{S}$ is the surface concentration and $\delta$ is the thickness of the diffusion layer. - **Limiting Current Density** - Given by when $C_S$ equals 0. $j_{L}= \frac{nFDC_{B}}{\delta}$ - **Overpotential Equation** - The overpotential equation can be derived as $\eta_{conc}=\frac{RT}{nF}\ln \left(1-\frac{j}{j_{L}}\right)$ ![[St Andrews/02 Public Notes/02.02 University Notes/CH5715 Energy Materials/attachments/ipad-6.png|cs]] ## Polymer Electrolyte Membrane Cells **Electrolyte** - A PEM fuel cell generally has a perfluorinated polymer electrolyte such as Nafion. ![[Nafion2.svg.png#invert|cm]] - **Moist** - The polymer must be kept wet to allow $\ce{H^+}$ conduction while not flooding the electrodes. - **Perfluorination** - A perfluroinated polymer is used to give good chemical and thermal stability. - **Sulfate Groups** - The polymer chains contain sulfate-end groups that allow the protons to diffuse through the polymer membrane. - **Clustering** - The fluorinated chain is hydrophobic and hence the hydrophilic end groups cluster together to give a conduction route through the material. **Electrodes** - The electrodes are made of conductive carbon particles coated with platinum catalyst nanoparticles. - **Porosity** - The electrodes must be porous to allow gas exchange. **Cell Design** - The cell is designed in such a way that the hydrogen and oxygen flow perpendicular to each other. - **Current Collector** - The current collectors are milled in a striped pattern to allow gas flow and electrical conduction. ![[f05-f02.png#invert|cm]] **Reformates** - PEM fuel cells cannot directly use hydrocarbons but can be operated using a reformer. - **Reformer** - The reformer reacts methane and water together to produce reformate. $\ce{CH4 + H2O -> H2 + CO2 (+CO)}$ - **CO Poisoning** - Small amounts of CO can have a large detrimental impact on the characteristic curve. **Direct Methanol PEM Fuel Cells** - An alternative chemistry of cell that uses similar components to traditional PEM cells. $\begin{matrix} \text{Anode} & \ce{CH3OH + H2O -> CO2 + 6 H+ + 6e-} \\ \text{Cathode} & \ce{\frac{3}{2}O2 + 6H+ + 6e- -> 3H2O} \\\hline &\ce{CH3OH + \frac{3}{2} O2 -> CO2 + 2 H2O}\end{matrix}$ - **Catalysts** - Requires very effective anode catalysts, better than Pt. Ir or transition metal oxides can potentially be used. ## Solid Oxide Fuel Cells **Fuel Cell Design** - There are three possible designs for a solid oxide fuel cell. ![[fig_02.jpg#invert|c]] - **Planar (b)** - The fuel cell consists of a sandwich of plates. The interconnect has channels machined into it for gas flow. - **Direction** - The different gases flow perpendicularly to each other. - **Manufacture** - Much easier to make flat ceramics but harder to engineer in the gas flow. - **Volumetric Density** - Good volumetric density as cells can pack very well. - **Tubular (a)** - The fuel cell stack is wrapped into a cylinder. The fuel mix is passed over the outside of the cylinder, air is passed through the middle. - **Manufacture** - Although harder to make the ceramics, the engineering for the gas flow is much easier. - **Rolls Royce Design (c)** - An alternate design that allows fuels on a flat surface. - **Scalability** - The fuel cell is designed with greater scalability in mind. ![[rtb-notes-2.png|cl]] - **Support** - Both planar and tubular cells need one layer that is capable of supporting the structure. This can be one of the electrodes or the metal interconnect. - **Thickness** - A cathode may be *ca.* 1 mm thick compared to the 40 μm it would be otherwise. - **Electrolyte** - This enables the electrolyte to be very thin, keeping the resistance down. - **Material Choice** - Due to the high operating temperatures, refractory materials that can withstand the temperature for a sustained period must be used. - **Manufacture** - In general, the manufacture of the ceramics is difficult as the ceramics need to be large and thin. It is of upmost importance that the electrolyte is crack-free. ### Electrolyte Materials **Electrolyte** - The electrolyte is a dense ceramic that can conduct $\ce{O^2-}$ ions. - **Requirements** - It must be dense so gases cannot diffuse and have negligible electrical conductivity. Additionally it must have chemical and mechanical stability and be easy enough to manufacture. **Anion Mobility** - There are two forces that can induce anion mobility. - **Activity Gradient** - A potential is generated by a spontaneous process following the Nernst equation. - **Applied Electric Field** - The application of electric field can force a non-spontaneous process to occur, *e.g. electrolyser*. **Enabling Conductivity** - One of the easiest ways to increase conductivity is to introduce defects into the lattice. - **Vacancies** - The addition of vacancies allows ions to jump from site to site, enabling conduction. - **Aliovalent Doping** - Vacancies are added via doping the structure with cations of alternate charge. Use [[Kröger-Vink Notation]]. - *e.g.* **Yttria-Stabilised Zirconia** - The most commonly used electrolyte is a created by the doping of yttria into zirconia. $\ce{Y2O3 +2Zr^x_{Zr} + 4O_^x_O -> 2Y'_{Zr} + V^{..}_{O} + 3O^x_O + 2 ZrO2}$ **Semiconductivity** - Variable oxidation state ions can become semiconductors via partial reduction and oxidation. - **p-Type** - Oxidation of a cation results in hole conduction. - *e.g.* **NiO** - The $\ce{Ni^2+}$ ion can be oxidised to $\ce{Ni^3+}$. Electrons can then jump from $\ce{Ni^2+}$ ions to $\ce{Ni^3+}$ ions, allowing electronic charge to be transferred. $\ce{Ni^{x}_{Ni} + \frac{1}{2}O2 -> V^{''}_{Ni} + 2 h^{.} + NiO}$ - **n-Type** - Reduction of cation results in electron conduction. - *e.g.* **CeO₂** - The $\ce{Ce^4+}$ ion can be reduced to $\ce{Ce^3+}$. The extra electron on $\ce{Ce^3+}$ can then jump to $\ce{Ce^4+}$ ions. $\ce{O^{x}_{O} -> V^{..}_{O} + 2e^{'} +1/2 O2}$ - **Small Polaron Mechanism** - These mechanisms are referred to as the small polaron mechanism. - **Simple Conductivity Relationships** - For the simplest defect equilibrium, the conductivity and $p_{O_{2}}$ have the following relationship. - **p-Type** - For the equilibrium $\ce{2 O^{x}_{O} + 4h^{.} <=> 2 V^{..}_O +O2}$, $\sigma \propto p_{O_2}^{1/4}$. - **n-Type** - For the equilibrium $\ce{2 O^{x}_{O} <=> 2V^{..}_{O} + 4e' + O2 }$, $\sigma \propto p_{O_2}^{-1/4}$. - **Derivation** - Use the equilibrium to find $\ce{[h^.]}$. Compared to the variation in oxygen partial pressure, $\ce{[V^{..}_{O}]}$ and $\ce{[O_O^x]}$ is effectively constant. - **Mobilities** - Both electrons and holes have higher mobilities than ions and will dominate conduction. Hence semiconductivity is undesirable for electrolytes. - **Atmospheres** - The electrolytes are subjected to very different oxygen partial pressures on each side and there should not be major semiconductivity in either case. - **Ionic Transference Number, $t_{ion}$** - [[#^trans|See previously]] ![[ipad-13.png|cl]] **Ionic Conductivity** - The ionic conductivity can be calculated by the following equation $\sigma_{i}=\frac{\nu_{0}F^{2}l^{2}z_{i}^{2}}{RT}[\ce{V^{..}_O}](C_{O}-[\ce{V^{..}_O}])\exp\left(- \frac{\Delta H_{m}}{RT}\right)$ where $\nu_{0}$ is the ionic vibration frequency, $l$ is the jump length, $z_{i}$ is the charge on the ion, $[\ce{V^{..}_O}]$ is vacancy concentration, $C_O$ is the oxygen site concentration and $\Delta H_{m}$ is the migration enthalpy. - **Migration Enthalpy, $\Delta H_{m}$** - Describes the activation barrier to movement through the lattice. - **[[#^arrhenius|Arrhenius Plot]]** - An Arrhenius plot is convenient for comparing electrolytes and determining their migration enthalpy. ![[rtb-notes-4.png#invert|cl]] **Fluorite Materials** - A simple cubic structure with the formula $\ce{MO2}$. - **Description** - A primitive lattice of oxygen ions with cations occupying alternate cube centres. ![[rtb-notes-3.png#invert|cm]] - **YSZ, $\ce{Zr_{1-x}Y_{x}O_{2-\delta}}$** - A very common electrolyte material. - **Stabilisation** - $\ce{ZrO2}$ does not adopt the fluorite structure at room temperature, this only occurs if doped with 15% $\ce{YO_{1.5}}$. - **Other Dopants** - Other dopants results in differing conductivities. $\ce{Yb2O3}$ has better conductivity but is too expensive. - **Defect Clustering** - If too much dopant is added, the $\ce{V^{..}_O}$ and $\ce{Y^{'}_{Zr}}$ will cluster together and reduce ion mobility. - Therefore there is an optimum amount of doping before this occurs. - **CGO, $\ce{Ce_{1-x}Gd_{x}O_{2-\delta}}$** - An alternative electrolyte material with higher conductivity by with more issues. - **Other Dopants** - Again a variety of other dopants can be used, Gd and Sm offer the best performance. - **Chemical Stability** - CGO is less chemically stable as the $\ce{Ce^4+}$ can be reduced in strongly reducing atmospheres. - **Loss** - In the fuel environment, $n$-type conduction becomes dominant above 570°C, which results in losses. - This makes the biggest difference at low power (charge can choose to go via electronic means); once at typical cell voltages it makes less of an impact. - **Max Operating Temperatures** - Due to this temperatures need to be kept under 600°C. - **Mechanical Stability** - CGO also has substantial thermal expansions which can lead to mechanical issues. **Perovskite Electrolytes** - Alternatively, perovskite electrolytes have been investigated. - **LSGM, $\ce{La_{1-x}Sr_{x}Ga_{1-y}Mg_{y}O_{3-\delta}}$** - A potential candidate where divalent cations are doped into the structure to introduce vacancies. - **Advantages** - Similar conductivity to CGO without the electronic conductivity problem. - **Disadvantages** - Difficult to process. **Grain Boundaries** - Grain boundaries in the solid electrolyte will present an extra barrier to the movement of ions and increase resistance. - **Impurities** - Impurity phases can also accumulate at the grain boundary, making the problem even worse. Quite often $\ce{SiO2}$ impurities. - **Grain Sizes** - Large grains are beneficial as they reduce the number of grain boundaries. **Impedance Characterisation** - Impedance spectroscopy can be completed on the entire fuel cell, which can separate out four sources of resistance. - **Electrolyte** - The electrolyte contributes both bulk and grain boundary resistance. - **Electrode** - The electrode contributes charge transfer and electrode reaction resistances. ![[rtb-notes-5.png#invert|cm]] ### Electrode Materials **Requirements** - There are a number of requirements for the electrode. - **Mixed Conductor** - The electrode ideally should be able to conduct both ions and electrons. It is possible for it to only be an electronic conductor. - **Porosity** - The electrode must be made porous to allow gas transfer to the reaction site. - **Catalyst** - The electrode should be able to catalyse the redox processes that are occurring at the electrode. - **Compatibility** - The electrode must be compatible with the electrolyte so there is no interfacial reaction. They should also have similar thermal expansion properties to prevent delamination. - **Structural Support** - Depending on the cell design, it may also need to act as a structural support. #### Cathodes **Cathode** - The cathode is responsible for the reduction of molecular oxygen. $\ce{O2 (g) +4e- -> 2O^{2-}(s)}$ - **Limiting Process** - It is often the limiting electrochemical process in working SOFCs and a major source of inefficiency loss in intermediate and lower temperatures $\ce{H2}$ SOFCs. **Process** - A number of processes occur at the cathode. - Absorption and/or partial reduction of oxygen at the electrode surface. - Surface transport of $\ce{O^2-}$ - Charge transfer of $\ce{O^2-}$ across the electrode/electrolyte interface. - **Mixed Conductors** - Additionally, mixed conductors also have absorption of oxygen into the bulk electrode and bulk conduction of $\ce{O^2-}$. **Perovskites** - The main cathode materials are perovskites. - **LSM, $\ce{La_{1-x}Sr_{x}MnO_{3-\delta}}$** - The most popular cathode material. The charge compensation of $\ce{Sr^2+}$ is completed via two mechanisms. - **Oxygen Vacancies** - The reduced charge on the strontium is compensated for by oxygen vacancies to give ionic conduction.$\ce{2 SrO + 2 La^{x}_{La} + O^{x}_{O}-> 2 Sr^{'}_{La} +V^{..}_{O} + La2O3}$ - **Oxidation** - The reduced charge on the strontium is compensated for by oxidation to $\ce{Mn^4+}$. This can be interpreted as an increase in hole concentration and results in $p$-type semiconductivity. $\ce{2SrO + \frac{1}{2} O2 + 2 La^{x}_{La} -> 2Sr'_{La} + 2h^{.} + La2O3 }$ - **Equilibrium** - These two types of defects are in an equilibrium. $\ce{2 O^{x}_{O} + 4h^{.} <=> 2 V^{..}_{O} + O2 (g)}$ - **Neutrality Condition** - To ensure the neutrality of the structure $\ce{2[V^{..}_{O}] + [h^{.}] = [Sr'_{La}]}$ - **Control** - The equilibrium shows that a change in the partial pressure of oxygen will control the ratio of oxygen vacancies to holes and the oxygen stoichiometry. - **Negative $\delta$** - The oxygen stoichiometry can be increased past 3 by the oxidation to $\ce{Mn^4+}$. $\ce{\frac{1}{2}O2 -> 2h^{.} + O^''_{i}}$ - **Transition Metal Choice** - By changing the transition metal, the reduction potential of $\ce{M^{4+} + e^{-}<=> M^{3+}}$ is changed and hence $p_{O_{2}}$ for a specific $\delta$ changes. ![[rtb-notes-6.png#invert|cl]] - **High $p_{O_{2}}$ Conductivity** - At the cathode, $p_{O_{2}}$ will be high. This favours the hole side of the equation. Additionally the holes have higher mobility. - The resulting conductivity is essentially electronic. The conductivity is given by $\sigma =n_{h}e\mu_h$. - **Activation Energy** - The small polaron mechanism has small activation energies of 0.5 - 5 kJ mol⁻¹. - **LSC, $\ce{La_{1-x}Sr_{x}CoO_{3-\delta}}$** - A similar perovskite structure with divergent properties. - **Metallic Conductor** - LSC shows metallic conductivity unlike LSM. - **Metallic Conductivity** - Characterised by very high electrical conductivity (> 1000 S cm⁻¹) that decreases with increasing temperature. Result of delocalised electrons. - **Overlap** - LSC has better overlap between the orbitals. This results in the O-2p and Co-3d bands overlapping, resulting in metallic behaviour. *See* [Mineshge et. al, *J. Solid State Chem.*](https://doi.org/10.1006/jssc.1998.8051) - **Metal-Insulator Transition** - The material exhibits a metal-insulator transition at low temperatures and low $p_{O_{2}}$. ![[mineshige-1.png#invert|cl]] - **Oxygen Conductor** - LSC is significantly improved oxygen conductor. - **Reasoning** - $\ce{Mn^4+}$ is more stable than $\ce{Co^4+}$ and therefore, examining the equilibrium, for the same amount of Sr dopant there is more oxygen vacancies in LSC (right side favoured). - **Mixed Conductor** - LSC is true mixed conductor, which is desirable for the electrolyte. **Stability** - If the stability of the two materials is compared, it is found the LSM is preferable. - **LSM** - $\ce{LaMnO3}$ is stable up to $\log p_{O_{2}} = -15$ whereby it decomposes into its elemental oxides. This is sufficient for fuel cell operation. - **LSC** - $\ce{LaCoO3}$ is only stable up to $\log p_{O_{2}} = -8$ whereby it decomposes to $\ce{La2CoO4}$ and $\ce{CoO}$. This is less ideal. **Electrolyte Compatibility** - The materials must be compatible with the electrolyte at high temperature. Unfortunately, perovskites can react with fluorites to form pyrochlores in the following reaction. $\ce{2x ABO3 + 2 MO2 -> x A2M2O7 +2 M_{1-x}B_{x}O2}$ - **Pyrochlore** - An ordered fluorite structure with lower ionic conductivity. Undesirable. - **Reaction Rate** - For the B ion, Cu > Ni > Co > Fe > Mn; for the M ion Zr >> Ce. - **YSZ Compatibility** - As Zr is quite reactive, LSC reacts too much and only LSM can be used. - **CGO Compatibility** - The lower reactivity of Zr means a wider range of cathodes can be used. - **A-Site Deficiency** - This can somewhat be mitigated by introducing A-site deficiency to reduce the activity of A, *i.e.* $\ce{(La, Sr)_{1-y}MnO3}$. **Cathode Choice** - LSM is generally chosen. - **LSM** - Due to being primarily an electronic conductor, its performance is very dependent on the microstructure and processing (including composites). - **LSC** - As it is a mixed conductor, it is less dependent upon microstructure and processing. However, due to the poor stability and electrolyte compatibility, it is disfavoured. **Thermal Expansion** - Ideally the thermal expansion of the electrolyte and electrode should be matched. - **Composition** - The composition can be tweaked to change the thermal expansion but LSM is always greater than YSZ. - **Composite** - Instead an intermediate YSZ/LSM composite can be used to bridge the materials and smear out the thermal expansion different. **Three Phase Boundary** - The three-phase boundary is where the electrode, electrolyte and gas are in contact. - **Pure Electronic Conducting Electrode** If the electrode is a pure electrical conductor (no ionic conduction) the electrochemistry must take place with nanometres of the three-phase boundary for the $\ce{O^{2-}}$ to get there. - In this respect, LSM does not have sufficient ionic conductivity and falls into this class. - **Composite** - Composite electrolyte/electrode boundary can be useful as it expands the three phase boundary. This increases the kinetics. ![[rtb-notes-7.png#invert|cm]] #### Anode **Operation with Hydrocarbons** - Requires a catalyst that can either directly oxidise the hydrocarbon or can reform *in-situ.* A number of possible reactions can take place. - **Direct Oxidation** - A catalyst that can do direct oxidation will give the highest theoretical efficiency. This an electrochemical equivalent to combustion. $\ce{CH4 + 4 O^{2-} -> CO2 + 2H2O + 8e-}$ - **Internal Reforming** - Rather than direct oxidation of the methane, it can be reformed *in-situ*. $\ce{CH4 + H2O -> CO + 3H2 \qquad \text{then} \qquad H2 + O^{2-} -> H2O + 2e-}$ - **Side Reactions** - A number of alternate reactions can take place in the same environment. $\begin{gather*}\ce{CO + H2O -> CO2 +H2 \\ CH4 + CO2 -> 2CO + 2H2}\end{gather*}$ - **Partial Oxidation** - Some authors have proposed adding a little bit oxygen to give of heat in a very exothermic reaction. $\ce{CH4 + O2 -> CO2 + H2}$ - **Methane Cracking** - One significant issue is the unwanted cracking of methane to produce carbon at the reaction site. $\ce{CH4 -> C + 2H2}$ **Anode Materials** - There are two main types: - **Single Phase** - Tend to have better stability and easier processing. - **Composite/Cermet** - A combination of electrolyte material, electronic conductor and catalyst. Normally more tuneable and have multifunctionality. - **$\ce{Ni/ZrO2}$ Cermet** - This catalyst does can complete direct oxidation or internal reforming above 500°C. - **Cracking** - It unfortunately produces solid carbon at temperatures above 650°C that can cover the active site or push the catalyst off the YSZ base. - **Sulfur/Oxygen Reaction** - Can react with sulfur or oxygen impurities to give nickel oxide or nickel sulfide. - Upon cooling this may then reverse due a more oxidising atmosphere and repeated cycling may result in failure. - **$\ce{Ru/La(Sr)CrO3}$** - Ru is a steam-reforming catalyst with a $\ce{La(Sr)CrO3}$ electronic conducting support. The water is regenerated after the electrochemical reaction. - **$\ce{Cu/CeO2}$** - Convert hydrocarbons directly (butane) using $\ce{Cu, CeO2}$ and YSZ skeleton. $\ce{CeO2}$ is the direct oxidation catalyst. - **C Deposition** - There was some limited carbon deposition but this beneficial as it improved electrical contact between the Cu particles. - **Disadvantages** - Worked better for higher hydrocarbons (not methane), needs high temperatures and showed Cu sintering. - $\ce{La_{0.75}Sr_{0.25}Cr_{0.5}Mn_{0.5}}$ - Showed good selectivity at 900°C for direct oxidation. ## System Considerations **Power System Efficiencies** - SOFCs (and to a lesser extent PAFCs) promise better efficiencies than both combustion engines and gas power plants. - **Carnot Limitation** - The maximum efficiency, $\eta_{max}$, that can be derived from an ideal, reversible heat engine between two temperature limits $T_h$ and $T_l$. $\eta _{max}= \frac{T_{h}- T_{l}} {T_{h}}$ - **Electrochemical Maximum Efficiency** - The efficiency can be represented as the Gibbs energy divided by the enthalpy change. $\eta _{max} = \frac{\Delta G}{\Delta H}\times 100\% = - \frac{T\Delta S}{\Delta H}\times 100\% $ - **Higher Heating Values** - Include the full energy content as defined by bring all products of reaction to 25°C. - **Lower Heating Values** - Neglects the extra energy in the water vapour due to the the temperature given off. This gives a lower energy. ![[rtb-notes-9.png#invert|cl]] **Emission Performance** - Compared to combustion process, there is significant emission gains. - **$\ce{CO2}$** - Due to normally having higher efficiencies, less $\ce{CO2}$ needs to be emitted to give the same amount of energy. - **Other Pollutants** - Drastically less $\ce{NO_x}$, $\ce{SO2}$ and particulates. **Applications** - There are numerous applications of fuel cells. - **Transportation** - Fuel cells have been successfully put into vehicles, generally as trail runs. - **Honda Clarity** - The first commercially available PEMFC car that is has been sold in California by appointment. - **Buses** - Hydrogen fuel cells have been trailed in many buses including Aberdeen. - **Portable Electronic Devices** - In your dreams Richard. - **Auxiliary Power Unit** - Rather than driving an alternator to generate electrical power in a vehicle, use a fuel cell to generate electricity on the side with greater efficiencies. - **Generator Replacements** - Could replace generators for events etc. - **Combined Heating + Power** - Replacement of a household boiler with a natural gas unit that uses the heat and electricity produced. - **Remote Community Node** - Could use fuel cells and electrolysis to smooth out renewable energies variable output and allow matching of supply with demand. # References + Footnotes [^1]: This is assuming one of the currents is defined negative (normally the cathodic one). Can also be defined as the difference if both are positive values