Four-electrode cell

A four-electrode cell (also a Kelvin cell or four-terminal cell) is an electrochemical cell in which one pair of electrodes carries the current and a second pair, drawing almost none, senses the voltage. The sensing pair reads the potential between two points in the solution, so the voltage it reports leaves out the potential drop at the surfaces of the current-carrying electrodes and the resistance of the solution beyond the sensing points. Nearly all nanopore recordings use two electrodes instead, one in each chamber, because a pore's resistance is so much larger than the resistance the second pair would remove.

The arrangement comes from measurements of low resistance, where the leads and contacts matter. It is used in four-point probes for semiconductors, in tissue chambers in physiology, and, as a design on paper, in the MR1 Nanopore Reader.

In a two-electrode cell the voltage applied is divided between the pore and everything in series with it: the solution between pore and electrodes and the interface at each electrode, whose impedance includes a charge-transfer resistance and a double-layer capacitance. If that series resistance is R_s and the pore's is R_pore, the pore receives the fraction R_pore/(R_pore + R_s) of the applied voltage.

A review of ionic phenomena in nanoscale pores puts the resistance of the bulk solution in nanopore experiments below 5 kΩ.^[1] The table shows what a resistance of that size costs.

A pore 10 nm across in a membrane 20 nm thick has a resistance of about 33 MΩ in 1 M potassium chloride, which puts it between the second and third rows (see Pore conductance). A pore tens of micrometers wide, of the kind a Coulter counter uses, sits in the last three.

In a four-electrode cell the voltage is read by two further electrodes connected to a buffer with an input impedance so high that the current through them is negligible. With no current, there is no voltage drop at their surfaces, and the buffer reads the potential difference between the two points in solution where they sit. What stays in the measurement is the solution between those points, and that is why the sense electrodes are placed as near the pore as the cell allows.

Frank Wenner of the US Bureau of Standards described the arrangement for soil in 1915 and 1916: two outer electrodes pass current through the ground and two inner electrodes read the potential, which removes the contact resistance of the current electrodes from the result.^[2] In physiology the short-circuit technique that Hans Ussing and Klaus Zerahn described in 1951 for isolated frog skin uses a chamber with two electrodes that pass current and two that sense the voltage across the tissue. The current is adjusted until the voltage is zero, and the current needed is the "short-circuit current", a measure of net ion transport.^[3] Electrochemists use the cell to characterize electrolytes, and a 2017 paper described a method for concentrated binary electrolytes.^[4]

The standard nanopore cell is a pair of Ag/AgCl electrodes. For a pore of megohms to gigohms the voltage lost in the solution is a fraction of a percent, and the electrodes are placed where they are convenient. Their noise can matter more than their resistance: a study of pores 7 to 200 nm wide milled through silicon nitride found that the noise of the silver chloride electrodes can dominate when the pore is large or the salt concentration is high.^[5]

The four-electrode arrangement pays when the pore is a low-resistance one, such as a micropore, or when the electrodes drift slowly as current polarizes them.

The open design of the MR1 Nanopore Reader draws four pre-chloridized silver ribbons on its interposer: a drive electrode and a sense electrode on the cis side of the aperture, and a sense electrode and a current-return electrode on the trans side. The sense ribbons sit about 6.9 mm from the aperture, and the drive and return ribbons about 15.8 mm. The specification estimates that the solution resistance that stays in the measurement falls from 1.5 to 3 kΩ with remote electrodes to under 150 Ω, and says that the amplifier then measures "the pure transmembrane ionic current with zero drift".^[6] For micropores the repository's simulations give 25% to 40% of the applied voltage lost in two-electrode mode with a pore 10 µm wide, and 82% to 88% with one 100 µm wide.^[7] Nothing has been built; the repository's status line is "Designed. Simulated. Built and measured: not yet."^[8]

The documents differ with one another in a few places. The specification cites the method of the four-electrode cell as a 2017 paper in The Journal of Physical Chemistry C, volume 121, pages 4112 to 4119, with the DOI 10.1021/acs.jpcc.6b12543. That DOI belongs to a different paper, on making metal nanoparticles and patterns in polymer films with an electron nanobeam.^[9] The paper on the four-electrode cell runs from page 4112 to 4129 and has the DOI given earlier, 10.1021/acs.jpcc.6b11501. The specification's diagram puts the sense electrodes 3.5 mm from the pore and its text puts them at 6.85 to 6.90 mm. It gives the remaining solution resistance as under 150 Ω, and the micropore document gives under 10 Ω.^[6][7] The sense electrodes are themselves Ag/AgCl, so their own offset potentials, which follow the chloride concentration at each, stay in the reading.

• Ag/AgCl electrode
• Access resistance
• Transimpedance amplifier
• Patch clamp