The basic principles of potentiometric measurement of ion concentration using the ion-selective electrode chain are discussed in greater detail elsewhere. 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.
The basic structure of the ion-selective electrode calls for a membrane which excludes all ions except for the ion of interest. In this fashion, the potential generated across the membrane is generated only because that specific ion species is migrating across it.
The ion species migrates across the membrane along a concentration gradient, assuming there is substantially less (or more) of that specific ion in the reference solution when compared to the sample.
Obviously, if the concentration of that ion in both solutions is exactly the same, there is no ion migration, and no potential difference is generated. Because the ion concentration in the reference solution is known, the magnitude of the potential difference can be related directly to the concentration of the ion in the sample, and on this concept rests the whole premise of potentiometric measurement. Thus, the selectivity of the membrane is central to the function of these electrodes.
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.
Clearly this was cumbersome to maintain. PVC was introduced in 1967 and rapidly became a popular durable alternative. The PVC is structurally identical to this porous wick, with the exception of the fact that the solvent - instead of being soaked into the wick - is a plasticiser, and bonded by solvation forces to the PVC.
In the old wick model, the solvent was constantly being washed out in the process of routine use. Even though it is usually an oily hydrophobic substance, the rate of loss was such that demanded a constant replacement, to the point where electrode design would incorporate a reservoir of solvent in contact with the membrane, to service its replenisment.
In contrast, and contrary to the somewhat misleading diagram above, the PVC-solvent polymer does not form any "pores" or channels of any sort. It is a homogenous medium in which the solvent is evenly distributed. The trapped solvent in the PVC cannot go anywhere, and no additional solvent must ever be added - this "wick" will practically never dry out or degrade in exposure to normal physiological fluids.
Sure, some loss still occurs, but it is miniscule; an old 1980 paper offers a solvent-sample partition coefficient of around 105 as a target for manufacturers to ensure "a continuous-use lifetime of at least 1 year". Obviously, one can still destroy this membrane rapidly if one tortures an ABG machine by funneling raw turpentine into it, or doing something insane to that effect, but normal blood at 37°C should be quite benign.
In the abovementioned manner, membranes consisting of only 30% PVC can be manufactured - the rest consisting of plasticiser and ionophore. The plasticiser can still be considered a liquid, just as in the soaked wick - the solvation forces holding it still permit the movement of molecules.
One can discuss this in terms of diffusion coefficients. For medically relevant ions, the diffusion coefficient of the plasticiser in a 30% PVC membrane may be in the order of 10-7 or 10-8 cm2 s-1, which resembles that of a viscous liquid. As one decreases the amount of plasticiser, the diffusion coefficient also degrades, and with membranes consisting of more than 80% PVC there is so little plasticiser that the diffusion coefficient resembles that of a solid (in the order of 10-11 cm2 s-1). In other words, doubling the amount of plasticiser seems to increase the ion permeability of PVC by up to ten thousand-fold.
High permeability is only one step in the design of a good ISE membrane. So far nothing has been said here about selectivity, which is actually the most important feature (whereas permeability is purely an issue of convenience; if one were patient one could merely wait longer for diffusion to occur). If one were to be concerned purely with permeability, one might settle on mere cellophane, which is highly permeable to water and ions, but not to the larger organic molecules of the bloodstream (which makes it a convenient sneeze-shield for the delicate PVC membranes of the Radiometer electrodes in the local unit).
The selectivity of the ion-sensing electrode membranes is conferred by ionophore molecules, which enjoy a vigorous and entertaining discussion in this recent article. Essentially, ionophores are molecules which act as ion-binding receptors, which are selective for specific ions. One can use a handful of such molecules as an impurity admixture, to "dope" an otherwise ion-impermeable plasticiser solvent. The result is a solvent which contains selective ion carriers, and is therefore selectively permeable.
The ionophore collects an ion at the sample-membrane boundary; the concentration of ion-bound ionophores at the boundary increases, and they diffuse around the membrane until their concentration is the same in all parts of the membrane. As they diffuse to the opposite membrane boundary, the ionophores encounter a reference solution with a much lower concentration of the selected ion; the ions diffuse from the ionophores into the reference solution, "freeing" ionophores to collect more ions. Thus, the concentration gradient between the sample and the reference solution drives the ionophore-facilitated transport of ions.
The first commercially exploited ionophore mechanism was discovered by Moore and Pressman in 1964, when they observed the effect of the macrolide antibiotic valinomycin on the transport of K+ ions across a mitochondrial membrane. Valinomycin has a ring structure, and the ring happens to have a gap in it which fits the potassium ion very precisely. The diagram below is Figure 4 from Chapter 8 in Lakshminarayanaiah's Membrane electrodes (1976); one can find it on page 227.
The potassium ion measures about 1.33 angrom across, and just about fits the cavity as depicted, which is between 2.7 and 3.3 angstrom across. Apparently, an electrode with a valinomycin-impregnated PVC membrane can be up to 5000 times more selective for potassium when compared to sodium.
Since valinomycin, countless swarms of ionophores have been developed and have reached commercial availability. Of these, many are based on crown ethers - ring-shaped molecules with cation selectivity; others are something else entirely (eg. nystatin the polyene antifungal drug, which is sodium-selective). To illustrate, a quick Google search has revealed several scientific supply catalogues bristling with vast arrays of ion-selective substances and electrodes based on them (here is one representative example). For each of the the many atoms in their many sizes and valencies, there are dozens of ionophores with suitably size/charge matched receptor sites. If one were that way inclined, one could commission a blood gas analyser which reports on the entire periodic table. The author recoils in horror from the inventive cruelty of any clinical case scenario which might require the serial measurements of serum thorium with the thorium-sensitive electrode.