Polarization: Activation (Tafel) and Concentration or Gas Diffusion Limits To determine actual cell performance, three losses must be deducted from the Nernst potential:

activation polarization, ohmic polarization, and concentration polarization. Definition of the ohmic polarization is simply the product of cell current and cell resistance. Both activation polarization and concentration polarization required additional description for basic understanding.

Activation Polarization: It is customary to express the voltage drop due to activation

polarization by a semi-empirical equation, called the Tafel equation (6). The equation for activation polarization is shown by Equation (2-1):

act o = RT n ln i i η α (2-1)

where α is the electron transfer coefficient of the reaction at the electrode being addressed, and io

is the exchange current density. Tafel plots provide a visual understanding of the activation polarization of a fuel cell. They are used to measure the exchange current density [given by the extrapolated intercept at ηact = 0 which is a measure of the maximum current that can be extracted

at negligible polarization (5)] and the transfer coefficient (from the slope).

The usual form of the Tafel equation that can be easily expressed by a Tafel Plot is

ηact = a + b log i (2-39)

where a = (-2.3RT/αn ) log io and b = 2.3RT/αn . The term b is called the Tafel slope, and is

obtained from the slope of a plot of ηact as a function of log i. The Tafel slope for an

electrochemical reaction is about 100 mV/decade (log current density) at room temperature. Thus, a ten-fold increase in current density causes a 100 mV increase in the activation polarization. Conversely, if the Tafel slope is only 50 mV/decade, then the same increase in current density produces a 50 mV increase in activation polarization. Clearly, there exists a strong incentive to develop electrocatalysts that yield a lower Tafel slope for electrochemical reactions.

5.0 4.0 3.0 2.0 1.0 0.0 0 100 200 300 (mV) Log i (mA/cm 2) η Exchange Current

Figure 2-8 Example of a Tafel Plot

The simplified description presented here did not consider the processes that give rise to activation polarization, except for attributing it to sluggish electrode kinetics. A detailed discussion of the subject is outside the scope of this presentation, but processes involving absorption of reactant species, transfer of electrons across the double layer, desorption of product species, and the nature of the electrode surface can all contribute to activation polarization.

Concentration Polarization: The rate of mass transport to an electrode surface in many cases

can be described by Fick's first law of diffusion:

i = n D (C C )B − S

δ (2-40)

where D is the diffusion coefficient of the reacting species, CB is its bulk concentration, CS is its

surface concentration, and δ is the thickness of the diffusion layer. The limiting current (iL) is a

measure of the maximum rate at which a reactant can be supplied to an electrode, and occurs when CS = 0, i.e.,

L

B

i = n DC

By appropriate manipulation of Equations (2-40) and (2-41), S B L C C = 1 i i − (2-42)

The Nernst equation for the reactant species at equilibrium conditions, or when no current is flowing, is

E = E + RT

n ln CB

i 0= ° (2-43)

When current is flowing, the surface concentration becomes less than the bulk concentration, and the Nernst equation becomes

E = E + RT n ln CS

° (2-44)

The potential difference (∆E) produced by a concentration change at the electrode is called the concentration polarization: ∆E = = RT n ln C C conc S B η (2-45)

Upon substituting Equations (2-42) in (2-45), the concentration polarization is given by the equation conc L = RT n ln 1 i i η _ − _ (2-46)

In this analysis of concentration polarization, the activation polarization is assumed to be negligible. The charge transfer reaction has such a high exchange current density that the activation polarization is negligible in comparison with the concentration polarization (most appropriate for the high temperature cells).

2.3 References

1. P.W. Atkins, “Physical Chemistry,” 3rd Edition, W.H. Freeman and Company, New York, NY, 1986.

2. S.N. Simons, R.B. King and P.R. Prokopius, in Symposium Proceedings Fuel Cells Technology Status and Applications, Figure 1, p. 46, Edited by E.H. Camara, Institute of Gas Technology, Chicago, IL, 45, 1982.

3. E.J. Cairns and H.A. Liebhafsky, Energy Conversion, p. 9, 63, 1969.

4. M.W. Chase, et al., “JANAF Thermochemical Tables,” Third Edition, American Chemical Society and the American Institute of Physics for the National Bureau of Standards (now National Institute of Standards and Technology), 1985.

5. A.J. Appleby and F.R. Foulkes, “Fuel Cell Handbook,” (Out of Print by Van Nostrand Reinhold, New York), contact Appleby at the Texas A&M University, 1989.

6. W. Stanley Angrist, “Direct Energy Conversion,” Third Edition, Allyn and Bacon, Inc. Boston, MA, date of publication unknown.

In discussions with the only U.S. PAFC manufacturer, it was determined that it is justifiable to directly use the PAFC performance information from the 1994 edition of the Fuel Cell Handbook. There have been only minor changes in cell performance, mostly due to changing the operating conditions of the cell. These are considered within the performance trends shown in this section. The manufacturer has concentrated on improving cell stability and life, and in improving the system components to improve reliability and lower cost. It should be noted that the performance shown in this section is based on information from contracts that the manufacturer had with the Department of Energy or outside institutions. Any new PAFC performance has been accomplished with company funding and is considered proprietary by the manufacturer (1).

The phosphoric acid fuel cell (PAFC) is the only fuel cell technology that is in commercialization. There are over 60 MW of demonstrators, worldwide, that have been tested, are being tested, or are being fabricated. Most of the plants are in the 50 to 200 kW capacity range, but large plants of 1 MW and 5 MW have been built. The largest plant operated to date achieved 11 MW of grid quality ac power (2, 3). Major efforts in the U.S. are concentrated on the improvement of PAFCs for stationary dispersed power plants and on-site cogeneration power plants. The major industrial participants are International Fuel Cells Corporation in the U.S. and Fuji Electric Corporation, Toshiba Corporation, and Mitsubishi Electric Corporation in Japan. In this section, the status of the cell components and the performance of PAFCs are discussed.

The electrochemical reactions occurring in PAFCs are

2

+ -

H → 2 H + 2 e (3-1)

at the anode, and

1/ 2 O + 2 H + 2 e 2 H O

+ -

2

at the cathode. The overall cell reaction is

1/ 2 O + H 2 2 → H O2 (3-3)

The electrochemical reactions occur on highly dispersed electrocatalyst particles supported on carbon black. Platinum (Pt) or Pt alloys are used as the catalyst at both electrodes.