Page 255 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

2 32 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

polarisation, (b) concentration polarisation, and (c) activation polarisation;
these are discussed belo147.

9.2 Ohmic Polarisation’
All matters (except superconductors, of course) offer a resistance to the motion of
electrical charge, and this behavior, in the sitnplest case, can be described by
Ohm’s law. The assumed linear behavior between voltage drop and current
density can be described by resistivity, a material property. Transport of oxide
ions through the electrolyte is thus governed by the ionic resistivity of the
electrolyte. Similarly, transport of electrons (or electron holes) through the
electrodes (the cathode and the anode) is governed by their respective electronic
resistivities (corrected for porosity and the possible existence of secondary,
insulating phases). Because of these ohmic resistances, at a given current
density, there is a voltage loss, qohm, given by

where p,, pc, and pa, are respectively electrolyte, cathode, and anode resistivities,
and Z,, Zc, and la, are respectively electrolyte, cathode, and anode thicknesses, and
Rcontact is any possible contact resistance. The ohmic polarisation can be
described using an equivalent circuit comprising a simple resistor with a zero
capacitance in parallel. For this reason, its response time is essentially zero, i.e.
it’s instantaneous. In reality, however, the response time is not zero but very,
very small. Fast response allows its determination using current interruption.
In most SOFCs, the main contribution to qohm is from the electrolyte, since its
(e.g. yttria-stabilised zirconia, YSZ) ionic resistivity is much greater than
electronic resistivities of the cathode (e.g. Sr-doped LaMn03, LSM), and the
anode (e.g. Ni + YSZ cermet). For example, the ionic resistivity of YSZ at 800°C
is -50 Qcm. By contrast, electronic resistivity of LSM is Qcm and that of
the Ni + YSZ cermet is on the order of Qcm. Thus, the electrolyte
contribution to ohmic polarisation can be large, especially in thick electrolyte-
supported cells. The recent move towards electrode-supported cells, in which
electrolyte is a thin film of 5 to 30 microns, reduces the ohmic polarisation. Also,
the use of higher conductivity electrolyte materials such as doped ceria and
lanthanum gallate lowers the ohmic polarisation.
Most of the discussion in this chapter is centered on cells made with traditional
materials such as YSZ electrolyte, Ni + YSZ anode, and LSM + YSZ cathode:
although its extension to other materials is essentially straightforward. The
relative contributions of various polarisations vary widely among the different
cell designs; anode-supported, cathode-supported, and electrolyte-supported.
Ohmic contribution is the smallest in electrode-supported cells due to the thin

The term ‘ohmic polarisation’ is often referred to as the ‘ohmic loss’, and is part of the overall loss,
q(i). As such, here it is referred to as ohmic polarisation, although both terminologies are in general use.