Brian Burrows
Macquorie University North Ryde, N.S.W. 21 13, Australia
Principles of Electrochemical Energy Conversion
Electrochemical energy conversion is one of the most interesting and relevant ways in which to illustrate the fundamentals of electrode kinetics. A number of articles have recently appeared in THIS JOURNAL which pertain to electrode kinetics (1-5). A descriptive article on fuel cells has also appeared (4). The purpose nf this paper is to discuss the major principles involved in electrochemical energy conversion and to relate these to the kinetics of electrode processes. The conversion of chemical energy to electrical energy is one of the energy conversion methods collectively described as direct energy conversion (5). Since electrical energy is easy to transport, easy to use, and easy to control, it is favored as the terminal form of energy for transmission and distribution. Thus any device which can cleanly, efficiently,and directly convert some inconvenient form of energy to electrical energy is of considerable interest. Among the methods of direct energy conversion are the following (5)
- --
-
electrochemical (chemical energy electrical energy) photovoltaic (solar energy electrical energy) magnetohydrodynamic (kinetio energy of plasma electrical energy) thermionic (heat energy electrical energy) thermoelectric (heat energy electrical energy)
electrochemical energy converter or electrochemical electricity producer, i.e., fuel cells and primary ceUs electrochemical electricity store", i.e., secondary cells
This classification is rather cumbersome hut is designed to draw attention to the operational fact that primary cells and fuel cells differ only in the way in which the reactants are stored, and are straightout energy converters. Secondary cells are also energy converters, but have the unique property of being able to accept and store electricity (as chemical energy) and deliver it on demand. An electrochemical system can he represented as the sum of an anode and a cathode reaction in an overall cell reaction. I n common with ot.her chemical reactions an electrochemical reaction can be characterized by an equilibrium constant (or AGO of reaction) and by a reaction mechanism (including the rate of the slowest step). In comparing the capabilities of different cells from an energy conversion point of view some convenient parameter is desirable. It is relatively easy to compare cell systems thermodynamically, but under operating conditions, as when current is being drawn from a cell, no single parameter is adequate because of the complexity of the electrochemical system.. A convenient starting point, however, is the specific energy. Speciflc Energy
The electrochemical method is the only one which is commercial and has been for many years. The other methods are as yet in various stages of research and development. Batteries of course are the most common manifestation of electrochemical energy converters and have traditionally fulfilled the need for a small portable electric power supply of a few watts to a few hundred watts. However, under the twin stimuli of space flight (where clean, reliable power sources of high energy to weight and volume ratios are needed) and the need for pollution-free automobiles, there has been a rebirth of interest in electrochemicalenergy conversion. Recent developments have been in two related areas: the construction of multi-kilowatt fuel batteries (or fuel cells) which have an external supply of fuel and oxidant (6,7), and the development of nonaqueous batteries having more energy and power per unit weight and longer shelf-life than conventional aqueous batteries (8). Electrochemical devices are usually classified as follows
The specific energy, or energy per unit weight associated with the reactants in a cell, is used as a measure of the theoretical capability of an electrochemical reaction. We can define the specific energy (So) as follows
primary (i.e., non-rechargeable) cells secondary (i.e.,rechargeable) cells fuel cells (i.e., primary cells with external storage of reactants)
So can be considered as the amount of chemical energy converted to electrical energy per kg of reactants when the cell is operating a t maximum electrochemical efficiency, i.e., the operating voltage is the equilibrium
An alternative classification (7,9) is as follows 732
/
Journal of Chemical Education
Et-dV) X Q(C) kg-, So = w(kg of reactants)
where E,=ois the thermodynamic (or zero current) cell potential and Q is the maximum amount of charge in coulombs capable of being delivered by the cell reaction. In the technical literature the specific energy is more widely quoted in terms of W-hr/kg where
Now Q is related to w by Faraday's Law, viz.
Substituting for Q in eqn. (1) and since AG we can writ,e So
=
-AG(J mole-') M(kg mole-') X 3600
=
nFE,=,
hr kg-L
cell potential and the reactants are completely converted into products. Of course no cell from which current is being drawn actually behaves in this way and in general we can write for the realized specific energy (SE)(8) Sn = SoKwtKec
(5)
where K,, is the weight efficiency and K., is the electrochemical efficiency. The weight efficiency,K,,, is equal to the weight of the active electrode material divided by the weight of the total cell including electrolyte, cell container, etc. Thus L,will always be less than unity and its optimization is primarily an engineering concern. The electrochemical efficiency, K,,, is given by the product of the voltage efficiency (e,) and the coulombic efficiency (e,), viz. K.,
=
ewe.
(6)
The voltage efficiencyis equal to 1 - (Z?/E',=,) where 2 7 is the sum of the potential losses or overpotentials (an older term for overpotential is polarization). The e, term takes into account the fact that as soon as a current is drawn from a cell the cell voltage decreases from its reversible value by 27. The coulombic (or faradaic) efficiency is the charge recovered from the cell (Qrcmuarcd) divided by the theoretical maximum coulombic capacity (Q,.,,) of the electrodes, viz.
geneous reaction can be considered as consisting of the following individual steps (1) transport of readant(8) to the electrode-electrolyte interface by migration, diffusion, or convection (2) adsorption of reactant(8)on electrode surface (3) electron-transfer between reactant(s) (in the interfacial region or in the adsorbed state) and electrode substrate. (4) deaorption of product(8) fromelectrodesurface (5) transport of products away from the interface
When an electrochemical reaction is taking place (or when current is being drawn from a cell) the potential of each electrode will deviate from its thermodynamic (or zero current value) to an extent depending upon which of the above steps is rate-determining. In other words, the performance of a cell is determined by the kinetics of the heterogeneous charge-transfer process, and the rate of mass transport through the electrolyte solution. The above two performance limitations correspond to the charge-transfer overpotential (?,-,) and to the mass-transfer overpotential (q,,-,), respectively. A third source of potential loss, the ohmic overpotential (qn), is a result of the resistance of the electrolyte between the electrodes. When, as is often the case in practical cells, the electrodes are porous and/or the active electrode material is a poor conductor then the resistance in the electrodes can also contribute significantly to the ohmic overpotential. Charge-Transfer Overpotential
For a simple electrode process Q,, is calculated from Faraday's Law (eqn. (3)). As a result of the incomplete conversion of reactants into products (due to side reactions, film formation on electrodes, etc.) Q,,, will generally be less than Q,., For an electrochemical reaction under the chosen conditions of temperature, pressure, and concentration of reactants, the maximum possible value of S, is So. However, under conditions of current drain both e, and e, will be less than unity and an important goal in electrochemical energy conversion is to maximize both of these factors. Most of the recent physico-chemical research on both old and new electrochemical devices has concentrated on improving K,,. An alternative way of expressing the operating characteristics of a battery is in terms of specific power in W kg-'. Since the product of voltage and current gives the power in watts the discharge performance of a battery system is simply specified in terms of the specific power a t the particular voltage or current of interest. A disadvantage of this approach is, however, that the power cannot be related to a theoretical maximum in the way that the specificenergy can. It is the specific power which is of prime importance from a motive power point of view. An electrochemical energy convertor which has a large specific energy hut which can only release this energy at a slow rate u~ould be a low power device and thus of little use for electric automobile applications. Electrochemical Efficiency
All electrochemical devices rely on the same fundamental process to produce electricity, namely, the transfer of electrons across electrolyte-electrode phase boundaries. This electron-transfer process is preceded and followed by other steps and the overall hetero-
Oxidant
+ n e e Reductant
in which the electron-transfer step is rate limiting a general relation between current and potential can be derived (6,9-11) and is as follows i
=
iO[exp[-a(nF/RT)nl - exp[(l
- a)(nF/RT)vll
(8)
where i is the current density in A cm-=, a is the transfer coefficient which lies between 0 and 1, n, F, R , and T have their usual meaning, il is the charge-transfer overpotential or the difference between the working potential of the electrode and its equilibrium (or zero current) potential, i.e. Finally, i O is the exchange current density and is a measure of the rate of the electrode process since it is related to the standard rate constant, k,, through the equation i O = nFk,Coxl-PEED
(9)
There is no simple way of expressing 7 in eqn. (8) in terms of other uarameters exceut in s~ecialcases. One such case which is pertinent ti elect6ochemical devices RT RT is that when 7 is large i.e., 171 >> -or /q(>> -anF (1 - d n F . This occurs when more current, i, is being &awn from or forced through the electrode than the intrinsic rate, in, of the electron-transfer reaction can comfortably sustain. The result is a departure of the electrode potential from its equilibrium value by some amount 7. In such cases the general i - 7 relation simplifies to the Tafel relation (10) which for the cathodic reaction is
Volume 48, Number 1 1, November 1971
/ 733
and for the reverse (anodic) reaction is
Note that the usual convention is that i 2 0 for 7 5 0, that is, the overvoltage is negative for a net cathodic process and positive for a net anodic process. Another special case which is convenient for graphical purposes is when u = 0.5. Equation (8) can then be simplified to
A plot of 7 (in units of RT/nF) versus i (in multiples of iO)is shown in the figure, curve (a) for cathodic (i.e., positive) currents. The anodic curve is symmetrical with the cathodic in the diagonally opposite quadrant. The plot of eqn. (12) reveals that the rate of loss of potential is greatest a t lower currents. Or, in other words, the rate of increase in is greatest a t the lower multiples of iO. At higher multiples of i O the overpotential increases relatively slowly. Furthermore it can be seen that the larger the exchange current density the smaller the potential loss at a given current drain (discharge) or applied current (charge). As an example we might consider an electrode reaction with an i0of lo-= A cm+ (invalues generally lie in the range 10-la to 10' A cm-% (12)). This electrode couple would, if discharged a t a practical current density of say lo-% A cm-% (i.e., 1 0 9 ) have an overpotential of almost 0.5 V for a = 0.5. Larger values of a give smaller q values and vice versa (see eqn. (10)). For the same discharge condition an electrode couple with an iO of A c m P would have a potential loss of only 0.24 V. Thus for an electrode couple to have a high specific energy under practical conditions of current drain the magnitude of iois of considerable importance. Mass-Transfer Overpotential
Equation (8) is derived on the assumption that the rate determining step in the electrode process is the rate of charge transfer. This assumption implies that the rate of mass transport (generally by diffusion) is fast enough to maintain the concentrations (or activities, to be exact) of reactants in the vicinity of the electrode the same as the concentrations in the bulk of the solution phase. When, however, the mass-transport step is the slowest, a difference will arise between the interfacial concentrations CoS and CRSand the bulk concentrations Cob and CRb. This concentration difference in turn causes a decrease in the equilibrium (or zero current) potential which is called the mass-transfer overpotential. Concentration (7, 9) and diffusion overpotential (11) are also widely used in place of masst,ransfer (10) overpotential. The latter is a more general term covering contributions from convection and migration as well as from diffusion. In the present context only diffusive mass-transport is being coosidered. An expression for 7 , - , can be derived from the Nernst equation (10) and is
Relationship beteen ovorvoltoge and the current parameters i/iO1,I*, and i'. Curve ( a ) shows o n,_t venur i relation for P/L' 1 according to oqn. 11 21. Curve Ib) shorn a 7,-rvenus i/L' plot for P/i.l>> 1 according to eqn. 121). Curve lc) shows o plot of qt,t,~ versus i/L1 for = 0.1. Curve (dl shows o plot of 7t.t.1 versus i / i L for P / L Z = 1. Both curves lc) and Id) were obtoinod by the summation of curves (a) and Id) in the appropriate current range.
lo-' A em-*.
(20)
If in
