The basic principles of potentiometric measurement of ion concentration using the ion-selective electrode chain are discussed in greater detail elsewhere. Similarly, the marvellous properties of ion-selective electrode membranes are interesting enough to merit their own chapter. Additionally, as a main reference for this topic, I refer the readers to Nallanna Lakshminarayanaiah's Membrane Electrodes (2012), as well as Martin Frant's two articles.
Structure of the potassium-sensitive electrode
One cannot speak too broadly, having experience of only one blood gas analyser. The locally available unit features a potassium-sensitive electrode with a ionophore-impregnated PVC membrane.
The protective cellophane membrane is semipermeable, and its purpose seems to be keeping the larger molecules from befouling the delicate PVC inside. Water and ions get through.
Inside, the PVC membrane awaits, loaded with valinomycin. This is an interesting development.
Prior to impregnated plastics, ion-selective electrode membranes were composed of a porous wick which was soaked with some sort of hydrophobic ion carrier, typically in the form of a thick oily organic solvent. The wick was usually clay (which was experimentally convenient), and the solvent could be any sort of organic liquid. This historical aside is of little relevance (but was the topic of a digression anyway). Suffice to say, the potassium-selective electrode features a PVC membrane doped with a potassium-selective ionophore. Radiometer do not specify which, but valinomycin is historically a popular choice. It is a macrolide antibiotic with a ring-shaped molecule (the image below, Figure 4 from Chapter 8 in Lakshminarayanaiah's Membrane electrodes, is used repeatedly in these chapters precisely because valinomycin is the prototypical model ionophore).
The potassium ion measures about 1.33 angstrom across, and just about fits the cavity as depicted, which is between 2.7 and 3.3 angstrom across. An electrode with a valinomycin-impregnated PVC membrane can be up to 5000 times more selective for potassium when compared to sodium.
For the potassium electrode in the local blood gas analyser, the detection limits are between 0.5 and 25mmol/L. History has afforded the author exposure to blood gas results which approach this limit.