# The Development of Current Collection in Micro-Tubular Solid Oxide Fuel Cells--A Review
## 4 Current Collector Performance  
Fundamentally, an SOFC interconnect must have a low ohmic resistance to minimise ohmic polarisation and thus must have a high electrical conductivity (bulk) and a low contact resistance. The resistance to electron flow or ion flow is governed by [PERSON]'s law, from which we observe the proportional nature of voltage drop with current and resistance. The Area-Specific Resistance (ASR) is the key metric used to determine the ohmic resistance of a cell. This normalised metric allows for comparison of different sized cells on an equivalent basis. The ASR of a cell can be derived from experimental data as an average over a potential range within the linear ohmic region from the gradient of the polarisation curve (Equation (1)):  
\[ASR\ \Big{[}\Omega\cdot\text{cm}^{2}\Big{]}=\frac{\eta_{ ohmic}[\text{V}]}{\Delta i\ [\text{A}\cdot\text{cm}^{-2}]} \tag{1}\]  
where the potential range should be the ohmic overpotential \(\eta_{ ohmic}[\text{V}]\), taken over the linear ohmic loss dominated region of the i-V curve and \(\Delta i\) is the current density difference over that range. The ASR can also be measured locally at a given potential or current by electrochemical impedance spectroscopy (EIS), where the total resistance \(R_{T}\) is measured and then adjusted by the active area (Equation (2)) [57]:  
\[ASR\ \Big{[}\Omega\cdot\text{cm}^{2}\Big{]}=\ A_{cell}\Big{[}\text{cm}^{2} \Big{]}*R_{T}[\Omega] \tag{2}\]  
It should be noted that the ASR calculated in Equations (1) and (2) are for the entire cell, and so the contribution from activation and mass transport polarisation is present, even though the data acquisition conditions are set so that the ohmic effects dominate the results. However, the ohmic polarisation, \(R_{\Sigma\Omega}\) [\(\Omega\)], which is cell-specific, can be directly acquired from EIS data, yet still contains a contribution from ionic flow resistance in the electrolyte and electron flow in the electrodes and interconnect. However, adjusting this value by the cell area does not give the ASR. The ASR of a virgin or tested material can be calculated ex situ by measuring the resistivity, \(\rho\), of known material thickness, Equation (3) [6]:  
\[ASR\ \Big{[}\Omega\cdot\text{cm}^{2}\Big{]}=x\ [\text{m}]*\ \rho\ [\Omega\cdot\text{cm}] \tag{3}\]  
ASR targets for interconnect materials of the past (pre-2000s) were \(<\)100 m\(\Omega\cdot\text{cm}^{2}\). With the more recent advancements in R&D, this target has been lowered by an order of magnitude within the last five years to \(<\)10 m\(\Omega\cdot\text{cm}^{2}\)[58, 59; 22]. The target for overall cell resistance is \(<\)500 m\(\Omega\) with \(<\)1 \(\Omega\) deemed to be acceptable. The typical contribution of an SOFC interconnect to the ohmic polarisation is around 20 to 25%. The ohmic resistance of the interconnect itself can be broken down into contributions from the bulk material conductivity (which is the inverse of the resistivity), Equation (4), and the contact resistance. Targets for values of the contact resistance are between 0.01 and 0.05 \(\Omega\cdot\text{cm}^{2}\)[60].  
\[\sigma\ \Big{[}\text{S}\cdot\text{m}^{-1}\Big{]}=\ \frac{l}{RA} \tag{4}\]The three major factors related to interconnect contact resistance are (a) dimension tolerance and flatness of the interconnect, (b) nonuniform compression from the interconnect on to the electrode and (c) the state of the contact surface (roughness, spallation, defects). While optimising the cell materials for low resistance is important, it is common to test the performance of the material within a cell, which will better account for the real-world tolerances in contacting, hence the use of the cell ASR as a common metric in comparisons.