1.13 | Applications of Galvanic Cells - Energy Storage#
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For many of us, our first recognition of electrochemistry is that which is found within the batteries that power our portable devices. Earlier in this unit we have noted that energy can be extracted from simple galvanic reactions such as that found in the Cu-Zn cell. However the electrochemical reactions we use in modern batteries are all tailored to very specific use cases to optimize how much energy can be stored, what small or what shape the batter can be, how quickly energy can be released, as well as total cost, availability of materials, reliability, safety, and environmental impact. Many of these considerations can be determined based on our knowledge of the chemical reaction.
The Need for Energy Storage#
Beyond the opportunity to disconnect our portable electronics like computers, phones, and cars from a wall socket grid solutions for energy storage has also become a growing concern for larger scale installation of low cost energy sources like wind and solar. While these resources do allow for the economical generation of electricity from the scale of a single home to entire cities, the energy generated is not always available when it is needed.
Fig. 23 Time dependence of solar energy generation from a photovoltaic panel under different weather conditions and time scales.#
Fig. 23 shows the variation in electricity generated by a solar panel which can be quite substantial, not only due to the day-night cycle but also due to the weather and time of year. Nonetheless, people need reliable access to electricity independent of the time or current weather conditions. Thus there is a gowning need to storing and releasing energy across many time scales to even out the supply and demand of electricity from a matter of seconds when a cloud occludes the sun to seasonal variations in solar intensity over many months. While there are many ways to store energy, electrochemical cells have becoming an increasingly popular choice due to their ability to scale from very small to very large systems,[1] and the intrinsically high efficiency of converting chemical energy to electrical energy.[2]
Energy Density vs Specific Energy#
While the standard unit of energy is the Joule (J), within an engineering context as well as within our common experience with commercial batteries and the utility company is to express energy as the product of power and time. The standard unit of power is the Watt (W) where \(1\,W = 1\,J/s\), therefor a joul equivalent to a watt-second. In most common portable devices batteries will report how much energy they can store in Watt-hours and home energy usage is often reported in kilowatt-hours.
Fig. 24 Relationship between energy density and specific energy for common fuels in their oxidation reaction with molecular oxygen. (source)#
The density of a substance or materials is a measure of how much mass is present in a given volume. Likewise the energy density of a chemical reaction is how much energy is released per unit volume of reactants. The reciprocal of density is specific volume, volume occupied divided by mass. Likewise, specific energy is how much energy is released per unit mass of reactants. The relationship between energy density and specific energy for some common fuels is shown in Fig. 24.
The units of energy density are either joules per liter (J/L) or watt-hours per liter (Wh/L). The units of specific energy are either joules per kilogram (J/kg) or watt-hours per kilogram (Wh/kg). Qualitatively in Fig. 24 note that gases like hydrogen may have very high specific energy but their very low densities compared to solids and liquids means their energy densities are quite low which could require very large tanks to store the same amount of energy as a liquid like ethanol or a solid like coal (i.e. Anthracite).
Energy vs Power#
Another important consideration when storing electricity is how quickly you need to be able to store and release it. Power is a measure of how much energy can be exchanged in a given amount of time. As noted above the standard unit of power is the Watt (W) where \(1\,W = 1\,J/s\). Just like energy, we can measure the ratio between of how much power a battery can release and its volume (Power density) or mass (specific power).
Fig. 25 Relationship between energy density and specific energy for common fuels. (source)#
When energy and power can be compared across a variety of systems using a Ragone plot, as shown in Fig. 25. Generally for batteries, the more quickly energy is released the less total energy can be extracted. This is experienced when perhaps your making heaving use of your phone and it heats up and the battery drains more quickly. This is because when operating at higher power more energy is expended as heat rather than as the useful work of operating electronic circuits in your device. Other types of systems are specifically designs to operate as a particular power level. For example there is a minimum amount of fuel that needs to be burned to keep a car’s internal combustion engine running or in the case of solid rocket boosters the fuel at a fixed set rate.
Compared to burning fuels, electrochemical cells typically have much lower power and energy densities and there for are generally more expensive to build and install per kWh stored. However, they do have other advantages in certain applications. For example they do not generate gas, in rechargeable batteries the electrochemical reaction can be reversed by putting energy into the cell (no refueling), they do not generate large amounts of heat, their are silent, and can be made much smaller than fuel burning engines.
Calculating Energy Stored in a Galvanic Cell#
Consider an experiment where we measure the potential of a galvanic cell as a function of the amount of charge passed. Using the Nerst equation the potential of the cell at any point over the course of the reaction going from 100 % reactants to 100 % products can be calculated.
As a first example, the reaction of lithium with iodine has some unique properties that make it an interesting candidate for a practical battery.
Because all of the products and reactants are solids the Nernst equation simplifies to predict the voltage of the cell to be constant regardless of how much the reaction has progressed, Fig. 26. But how can this be? How does an electrochemical reaction proceed without the electrolyte solution? The answer is that in this particular case LiI is a solid that is capable of conducting lithium ions.
Fig. 26 The discharge profile of a Li-I cell as a function of the amount of charge passed. The potential of the cell remains constant as the reaction proceeds. The total amount of useful work released (\(\Delta G_{rxn}\)) is equal to the area under the curve.#
The plot shown in Fig. 26 shows the potential of the Li-\(I_2\) cell (in units of volts) as a function of the amount of charge passed in units of coloumbs. The area under the curve will have units of \(C \cdot V = C \cdot \frac{J}{C} = J\) and is equal to the total amount of useful work that that was released. Theoretically the total amount of work measured should be equal to \(\Delta G_{rxn}\). If the total amount of two reactants (Li and \(I_2\)) are known then the free energy of formation for LiI could be experimentally determined with units of J/mol.
Batteries#
Experimental determination of charge and energy stored#
The specific charge capacity of an electrochemical cell (or battery) is the amount of charge that can be passed for every gram of reactants. While the standard units for charge are Coulombs, you will most often find the capacity or amount ot charge stored by a battery written (on the side of the actual battery) in units of mAh (milliamp-hours) or Ah (amp-hours). Speicic capacity will therefore have units of milliamp-hours per gram (mAh/g) or amp-hours per gram (Ah/g) or coulombs per gram (C/g). Also on the side of a commercial battery you will find the voltage of the battery in units of V, and perhaps the total energy stored in units of Wh (watt-hours). The amount of energy stored can also be approximated by multiplying the specific capacity by the nominal (assumed constant) voltage of the battery. An example of a the descriptoin on the side of a commercial battery (one or more electrochemical cells packed together) is shown in Fig. 27.
Fig. 27 Description of a battery with a total charge capacity of 10,000 mAh, a nominal voltage of 3.7 V, and a total energy stored of 37 Wh.#
Specific Capacity and Reaction Progress#
When comparing different battery chemistries, say a lithium-iodine cell versus a Zn-Cu cell vs a Li-ion battery, the voltage versus charge profile can instead be plotted as a function of specific capacity where the amount of charge passed is divided by the total initial mass of the reactants for each reaction, Fig. 28. This plot will then show how much energy is stored and at what voltage for the least amount of weight. A similar plot using charge density may likewise also be useful consider when comparing different battery reactions.
Fig. 28 The discharge profile of a Li-I cell as a function of the amount of specific capacity (left) and progress of reaction x (right).#
Alternatively, we can also show the same voltage-capacity profiles in terms of the stoichiometry of the reaction in which case it is called a voltage-composition profile, Fig. 28. In the case of the lithium-iodine reaction the progress of the reaction can be expressed a the variable \(x\) which is equal to the mole equivalents of LiI formed for any point between the start (only reactants present) and the end (only products present) of the reaction:
When the reaction is at 10% completion \(x = 0.1\) and 0.1 moles of Li have reacted with 0.05 moles of \(I_2\) to form 0.1 moles of LiI. When the reaction is at 90% completion \(x = 0.9\) and 0.9 moles of Li have reacted with 0.45 moles of \(I_2\) to form 0.9 moles of LiI.
Characteristics of a Battery#
As an energy storage device there are a few unique properties of batteries that can either be advantageous or disadvantageous depending on the application.
The electrodes a fixed in place and not easily replaced. It is usually more practical to replace the entire battery than to replace the electrodes.
The reaction is almost always Faradaic. That is, the voltage of the cell is primarily determined by the free energy of associated with a stoichiometric chemical reaction.
The reaction can be either reversible or irreversible. In the case of a rechargeable (secondary) battery the reaction can be reversed by applying a voltage to the cell. In the case of a primary battery the reaction is irreversible and the battery cannot be recharged.
Batteries usually have a fixed volume.
A battery contains a fixed amount of reactants and products. To increase storage either additional cells need to be added or the battery needs to be replaced with a larger one. However, because of this (and their fixed volumes) batteries are also completely self-contained and more easily miniaturized than other energy storage devices.
Redox Flow Cells#
In most commercial batteries the two electrodes are composed of solids. However, as we have seen there are many redox half reactions that involve the conversion of a liquid to ions dissolved in solution such as \(Hg\,(l) \rightarrow Hg^{2+}\,(aq) + 2e^-\) or \(Fe^{2+}\,(aq) \rightarrow Fe^{2+}\,(aq) + e^-\). When all of the reactants and products in an electrochemical cell exist as fluids it is possible to reorganize the construction of the electrochemical cell to pump the reagents from a large reservoir into a smaller cell where they solutions can pass over the electrodes to participate in the electrochemical reaction. An example of a rudimentary redox flow cell is shown in Fig. 29
Fig. 29 The anatomy of a redox flow battery where soluble or liquid reductants and oxidants are stored in separate tanks and pumped past the electrodes where the electrochemical reaction occurs. A semipermeable membrane or ion selective solid electrolyte separate the two redox active solutions to prevent their direct mixing and forcing electron to pass through the external circuit for the reaction to proceed (left). The voltage dependence of a charged redox flow battery as electrons are passed through the circuit (discharged) to do work (right).#
Within a redox flow cell, because all of the reagents are in the liquid state, care must be taken to prevent the mixing of the reductant’s solution (anolyte) and the oxidant’s solution (catholyte) all the while allowing ions of the electrolyte salt to diffuse across the cell for charge balance (as in any electrochemical cell). This can be accomplished using materials that selectively conduct only specific ions. Sodium \(\beta\)-alumina for example is an inorganic oxide that only allows \(Na^+\) to conduct through its crystal structure and can be used to make high temperature sodium-sulfur cells that employ molten sodium and molten sulfur electrodes. Similarly cationic polymers can be synthesize that can selectively conduct only anions like \(Cl^-\) or \(Br^-\).
A key advantage of a redox flow cell of this design is that it become much easier to increase the amount of charge that can be stored by simply increasing the size of the tanks filled with anolyte and catholyte or keep separate takes available to stored charged anolyte and catholyte separate from the electrodes and other electrical components of the cell.
When both the reactants and products of an electrochemical reaction are solutions, necessarily the relative concentrations of reactants and products must change over the course of the reaction. This is not necessarily the case in batteries where only a single ion participate in both the anode and cathode reaction. For example, in the Li-ion battery reaction \(LiC_6 + FePO_4 -> C_6 + LiFePO_4 \), the oxidative half-reaction of \(LiC_6\) yields one equivalent of \(Li^+\) while the reductive half-reaction consumes one equivalent of \(Li^+\). Thus the concentration of ions is constant and dissolved \(Li^+\) does not appear in the net reaction. The Nernst equation would therefore predict the voltage of this Li-ion battery to be constant as the amount of charge passed through the circuit increases. That is, since all reactants and products are solids \(Q=1\) and \(E_{cell} = E_{cell}^{\circ}\). But consider the redox reaction of a hypothetical redox flow cell:
Here the Nernst equation would predict \(E_{cell}\) to change as charge passes and the reaction proceeds in teh forward direction, because
Ultimately this may result in a less than ideal scenarion where the voltage of the battery changes significantly depending if it is 90% charged or 10% charged. This could make engineering compatible electronic equipment much more difficult if the voltage of the power supply is constantly changing.
Characteristics of a Redox Flow Cell#
Redox flow cells are batteries constructed to handle redox reactions where all the reactants and products are either liquids or solutions.
Redox flow cells are most often developed with reversible redox reactions. That is they are usually rechargeable (aka secondary) batteries
Redox flow cells are Faradaic
Redox flow cell have semi-fixed volumes (amounts of reactants). Reactant reservoirs can be exchanges in principle but may be challenging to refuel during operation.
Redox flow cells have been deployed for large “grid” scale energy storage
The voltage of a redox flow cell changes as the battery is discharged since the concentrations of reactants and products are changes with reaction extent (\(Q\)).
Fuel Cells#
Fuel cells are like redox flow batteries but the electrochemical reaction is not reversible and the product generates (typically water vapor and carbon dioxide gas) are emitted a waste products. Fuels cells have an advantage of using common chemical compounds that are readily available including dihydrogen, hydrocarbons and alcohols as fuel and dioxygen or air as the oxidant. In many cases refueling is faster than recharging.
Fig. 30 The anatomy of a fuel cell where a fuel and oxidant are stored in separate tanks and pumped past the electrodes where the electrochemical reaction occurs Fig. 30. A semipermeable membrane or ion selective solid electrolyte separate the oxidants from the reductant to to prevent their direct mixing and forcing electron to pass through the circuit for the reaction to proceed (left). The voltage dependence of a charged fuel cell as electrons are passed through the circuit (discharged) to do work (right).#
In a fuel cell the cathode the anode are typically placed very close together with a thin solid electrolyte separating cathode from anode. Only ions are allowed to conduct through the electronically insulating solid electrolyte.
In the case of the \(H_2\)-\(O_2\) fuel cell at the cathode \(O_2\) is reduced to oxide (\(O^{–2}\)), Since the only produce is an ion that cannot possible diffuse into the gaseous environment of the \(O_2\) side of the cell not waste products are generated of the cathode side and all of the \(O^{–2}\) must conduct through the solid electrolyte to the anode side of the cell. At the anode \(H_2\) is oxidized to \(H^+\). Also an ion H+ cannot diffuse through the gaseous state of the \(H_2\) side of the cell and instead undergoes an acid-base reaction with \(O^{–2}\) at the interface of the solid electrolyte and the anode to form water. At the high temperatures at which this particular fuel cell this water is then vented as a gas from the cell.
Over the life cycle of a fuel cell the effective concentration of \(H_2\) and \(O_2\) at the anode and cathode respectively remains relatively constant and the concentration of the produce \(H_2O\) is ideal kept low as it is vented from the cell. In this scenario the reaction quotient, \(Q\), is close zero and the \(E_{cell} \approx E_{cell}^{\circ}\). The cell potential is however temperature dependant where
for the redox reaction \(H_2 + O_2 \rightarrow H_2O\), \(\Delta S < 0\), and the cell voltage will decrease as temperature increases. However—as we’ll see in the next unit—as temperature increases the rate of reaction increases resulting in a balancing act between getting more current from a cell at higher temperatures but at the cost of operating at a lower thermodynamic potential.
Characteristics of a Fuel Cell#
Similar construction to a redox flow cell but the products of the electrochemical reaction are released as waste.
Fuel cells are primary cells (not rechargeable)
A fuel (i.e. a reductant) needs to be added to operate. If the oxidant is air then that’s all that is needed from the user to operate the cell.
Widely variable capacity depends only on how much fuel the user adds to the cell.
Cell voltages are typically low (< 2 V), often limited by the small \(E_{rxn}\) for common combustion reactions fuel cells employ.
Significant engineering challenge to fabricate efficient and rugged material stacks of the different anode, solid electrolyte, and cathode materials.
Fuels are most similar to the how the mitochondria convert glucose fuel to electrical potential via the proton pump and other integral proteins.
Capacitors#
Capacitors are not electrochemical cells since not electrochemical reaction takes place when they are charge and discharge. Nonetheless their construction, and ability to store electrical energy between two electrodes merits consideration in comparison to the batteries and fuel cells discussed so far. Indeed the particular properties of capacitors are often complementary to electrochemical reactions and solve many energy storage problems that other electrochemical cells are not well suited for.
Fig. 31 The anatomy of an electrolytic capacitor composed of an electrolyte solution and two redox inert electrodes. By applying a voltage ions of opposite charges will accumulate at the electrodes forming a concentration gradient in the solution, screening electrode charge and allowing more charge to be stored (left). The voltage dependence of a charged capacitor as electrons are passed through the circuit (discharged) to do work (right)#
There are two major types of capacitors: dry and electrolytic. Dry cells are composed of two electrodes and a dielectric material (electronic insulator) between them. The amount charge that can be stored is limited by the dielectric constant and the areas of the two electrodes. Despite the name, no electrochemical reaction takes place within an electrolytic capacitor. An electrolytic capacitor is composed of two electrodes separated by an electrolyte solution, Fig. 31.
Upon charging the dissolved ions in the electrolyte solution are attracted to electrodes of opposite charge where they can effectively screen the charge in the electrodes surface allow more charge to be stored on the polarized electrodes than would be possible in an equivalent dry cell. The build of of ions of opposite charge at the electrodes is call the electrical double layer and the charge that it stores is call the double layer capacitance.
The voltage of a capacitor is proportional to the amount excess charge on the electrode or \(V_{cell} = C \cdot q\) where \(C\) is the capacitance of the cell with unit \(\frac{V}{C}\), and \(q\) is the amount of excess positive or negative charge on the electrodes in units of Coulombs.
Characteristics of an Electrolytic Capacitor#
No redox reaction takes place
Not Faradaic but capacitive
Charge capacity based on teh dielectric constant between electrodes (dry cell)
or
A liquid electrolytes double layer capacitanceExtremely fast charge and discharge since operation is only limited by the diffusion of electrons and ions and not the intrinsic rate of a chemical reaction.
Excellent for use when high power is needed for a short period of time. Capacitors can discharge over minutes to milliseconds; rates generally not accessible to batteries
Capacitors are extremely stable since no electrochemical reaction takes place can can operate for decades continuously charging and discharging without breaking down.
Capacitors cannot output a constant voltage making them less ideal as a power source.
Capacitors generally store much less energy than batteries of the same size (much lower charge capacities).
Kinetics Preview: Rates of Reaction in Batteries#
The rate of an electrochemical reactions is easily measured using an ammeter to determine how much charge is passed through the circuit per unit time. Using an external circuit the rate at which electrons are allowed to pass from anode to cathode can be controlled. Depending on how fast electrons pass through the circuit both the observed voltage of the cell and the total amount of charge that can be extracted within a certain range of voltages will also change. Typically as the rate of the electrochemical reaction in a galvanic cell increases the observed voltage will decrease, Fig. 32. Just as we saw in applications of electrolytic cells here this decrease in voltage at faster rates results from kinetic overpotential. Ohmic drop is a type of overpotential which describes the phenomena that as more current passes through the the internal resistance for the electrochemical will decrease the cell’s output voltage by an amount \(V_{ohm} = IR\). There is also an overpotential associated with the two electrochemical half reactions that can be quite large and is dependant upon the intrinsic rate at which a reaction takes place.
Fig. 32 The voltage dependence of a charged battery as electrons are passed through the circuit (discharged) to do work. As the rate of discharge increases the voltage of the battery will decrease due to ohmic losses (V = IR) and the overpotential \(\eta\) of the reaction. Most devices require a minimum output voltage to operate and will shut off if the battery voltage drops below this threshold.#
In the case of a rechargeable battery this electrochemical cell is galvanic during discharge when energy is extracted to do work and electrolytic during charging when energy is transferred into the the electrochemical cell to reverse the current and drive the reaction backwards. Kinetic overpotenial will decrease the voltage during discharge and increase the applied voltage during charge, Fig. 33. The thermodynamic potential will lay somewhere in between the charge and the discharge curves.
Fig. 33 The voltage dependence of a rechargeable battery upon discharge (to the right) and charge (to the left). When charging, the battery behaves as an electrolytic cell with an overpotential, \(\eta\), which in addition to ohmic losses (V = IR) will result in charging the battery requiring a higher voltage (more energy input) than was possible during discharge at the same rate.#
As charge and discharge rates increase a battery the actual amount of charge that can be transferred within The range of operating voltages of a rechargeable batter are either based on limits from other decomposition reactions taking place outside this range (e.g. decomposition of water in the electrolyte to \(O_2\) and \(H_2\)) or the limited range of voltage from which useful work can be practically extracted. Due to kinetic overpotential increasing with the discharge rate the cell is run at, this means that less charge will pass through the cell before these voltage limits are reached, Fig. 32.