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Electrochemical Theory and Physics

Geraint Minton

OXIS Energy, E1 Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB, UK

1.1 Overview of a LiS cell

On discharge, the overall process occurring in a lithium-sulfur (LiS) cell is the reaction of lithium and sulfur to form lithium sulfide, Li2S, according to the reaction shown in Eq. (1.1).

Although both reactants are present in the cell, its design, shown in Figure 1.1, prevents the reaction from taking place directly. The cell comprises a lithium metal electrode and a mixed carbon/sulfur (C/S) electrode. The latter is composed of a mix of highly porous carbon, which provides both electronic conductivity and an electrochemically active surface; sulfur, which is the active material in this electrode; and binder, which holds the structure together. The two electrodes are divided by a separator material, which stops the active materials from making direct contact and also prevents electrons passing internally between the electrodes. Contact between the active materials in each electrode is made indirectly, via an electrolyte, which is in contact with the lithium electrode and permeates the separator and C/S electrode. The electrolyte is composed of a solvent in which a lithium salt, plus any additives, has been dissolved. Adjacent to the C/S electrode is a current collector material to facilitate the flow of electrons to and from and external circuit, a task which is performed by the lithium metal on the other side of the cell.

Figure 1.1 Structure of a LiS cell, indicating the two electrodes, separator, and C/S electrode current collector. Also indicated are the reactions at each electrode and the electron pathway on discharge.

By preventing the direct contact of lithium and sulfur, the design of the cell means that the reaction in Eq. ( 1.1) takes place indirectly: one or both species have to enter the electrolyte in order to react, a process which consumes electrons from (or releases them to) the electrode surfaces. These electrochemical reactions are the fundamental process which must occur in any electrochemical cell, since without them charge would not be replenished on the electrodes when an external current flows, causing the voltage to rapidly decrease to zero. Considering the electrochemical steps occurring in a LiS cell, the overall cell reaction in Eq. ( 1.1) can be split into the following overall half-reactions occurring at each electrode:

where the equations are written in the standard form Ox+ne-?Re, in which Ox is the oxidized (more positively charged) form of the species, Re is the reduced (more negatively charged) form, and e- is an electron. In order for the overall cell reaction to be satisfied, on discharge the lithium reaction must run to the left (electrochemical oxidation), with ions and electrons being formed from the lithium metal, while the C/S reaction must run to the right (electrochemical reduction), with electrons being consumed and ions being formed by the reaction of solid-phase sulfur. In separating out the reactions in this manner, it is possible to see how the reactions generate the electronic charge in the electrodes which flows as the external current when the electrodes are connected.

The cell half-reactions might indicate that only electrochemical reactions occur in the cell, but this is not the case. The initial state of the cell includes solid-phase sulfur, so a dissolution step is required; and to form the precipitated Li2S, a chemical reaction is required to combine the lithium and sulfur ions:

Furthermore, as with the phase change processes at either end of the reaction mechanism, the reactions occurring at the C/S electrode do not appear to take place in a single step, as Eq. (1.2b) may suggest. Instead, a host of intermediate species are produced through both chemical and electrochemical elementary steps [1]. These intermediate species consist of sulfur anions of varying chain lengths, collectively known as polysulfides. They are commonly split into two groups: "high-order" species are those with chain lengths of five to eight atoms, and "low-order" species are those with chain lengths of one to four atoms.

Since the exact reaction mechanism is currently unknown, and may even vary under different operational conditions [2-5] or electrolyte compositions, this chapter does not attempt to describe how each individual process affects a LiS cell. Instead, the focus is on how different types of reaction processes contribute to (or detract from) the electrochemical performance of a cell, using a LiS as a reference point.

Before continuing, it will be useful to define how the electrodes are referred to throughout this chapter. The lithium reaction has to generate electrons on discharge, while the polysulfide species have to accept them. Since current flow is in the direction opposite to the flow of electrons, electronic current will flow from the C/S electrode to the lithium electrode, making the lithium electrode the anode on discharge. However, the direction of the current is reversed on charge, which would make the C/S electrode the anode; and if the cell is at rest, then there is no anode. In order to simplify the terminology, and because it is commonly the discharge which is of more interest, the lithium electrode will herein be referred to as the anode, regardless of the direction (or presence) of a current, and the C/S electrode will be referred to as the cathode.

1.2 The Development of the Cell Voltage

The purpose of an electrochemical cell is to drive an electric current through a circuit which is connected across the terminals of the cell. This flow of current occurs spontaneously: naively electrons move from the electrode with the lower electric potential to the one with the higher electric potential, causing the difference between the two electrode potentials to decrease. Thus, maintaining a current requires electrons to be spontaneously generated at the lower potential electrode and consumed at the higher potential electrode; otherwise, the electrode potentials would equilibrate and the flow of electrons would stop.

Thermodynamically, a process will occur spontaneously if it lowers the free energy of a system, where the free energy is the internal energy of the system minus that part of the internal energy which can do no useful work. In the case of an electrochemical cell, the system is the electrochemical cell and the external circuit, and a process is anything occurring within the system, for example the conversion of one species to another via a reaction, or the trend for a species to move in one direction or another. A useful aspect to remember when discussing processes is that we are always considering the net outcome of a very large number of individual random events, some of which increase the free energy and some of which lower it. The "direction" represents how this stochastic process is biased, and this bias is always in the direction which minimizes the free energy, because it is more likely that a particle in a higher energy state will move to a lower energy state than the reverse occurring.

Coupled with the notion of the events occurring at random is the fact that the processes do not stop when equilibrium is reached - for example, individual particles in a gas do not stop moving just because there is no concentration gradient. Instead, equilibrium implies that the bias to the process has been removed - the number of particles in the gas moving to the left is now equal to the number moving to the right, so there is no net change in the concentration.

There are two forms of the free energy commonly used to describe processes in an electrochemical system: the Gibbs free energy G , typically used when discussing the reaction processes, and the Helmholtz free energy F , commonly used when discussing the electrolyte composition [6-9] and species transport. How they are related and defined is beyond the scope of this chapter and, since we will not consider volume or pressure changes in the cell, the two are essentially equivalent. Related to the free energy is the electrochemical potential µ i of the species in the system, which is also often more convenient to work with [10,11]. This term represents the change that occurs in the free energy of a system when a particle of type i is added to a point in the system from a point outside of it, and can be used to derive expressions for the system behavior. Under the assumption that there are a large number of particles in the system [12], the electrochemical potential is determined by the following relationships:

where N i is the number of molecules of type i and the subscripts indicate the properties held constant during the differentiation: p is the pressure, T is the temperature, V is the volume, and N j?i is the quantity of all species except species i . The notion of how the...