pH probe bulb - what is happening within the glass?

I am trying to understand how the glass bulb of a pH electrode of a pH meter works - the glass bulb itself. Not the reference electrode or the rest of the electrode (HCl, Ag/AgCl wire, etc...), the math, or the equilibrium yet. For this question just the glass bulb of the pH electrode.

Here is what I have learned so far. This is my current understanding. I'm not saying it is right - but it's where I am right now.

The thin-walled glass bulb has a conductive solution inside, and the outside should be kept in liquid at all times as well. This hydrates a thin layer of the glass on the outside and the inside. I assume these layers are manufactured differently, otherwise, the glass should be uniformly hydrated after a long enough time. It is important that the middle layer of the glass remains very low conductivity so that a potential difference can be maintained; there are likely other reasons as well.

The glass is amorphous and in this case, the exterior layers are somewhat porous, so there is a large volume of Si-O groups exposed to the solution. Protons will stick to these groups and establish a negative charge on the outside of the glass. The number is related to the pH or hydronium concentration of the solution on the outside of the electrode.

edit: I have just started to read this early discussion, where the idea that the glass itself may behave as a sort of buffer:

Hughes (3) has pointed out that the hydrogen ion concentration in the glass phase may be held relatively constant by the buffer action of the glass which is a mixture of the salt of a weak acid $(\ce{Na2SiO3})$ with the anhydride of that acid (excess $\ce{SiO2})$.

Note: The hydrated layer is also called a "gel layer", but it is not clear if this is formed naturally as the glass hydrates, or if there is a special gel-enabling material applied to each surface during manufacture.

1. Do these have to be specially prepared layers of more porous, hydratable glass on the inside and outside of the glass bulb? If so, roughly speaking how is this done? If not, what does limit the depth of the hydrated layer?
2. When inserted into an acid/base solution, is it just protons diffusing into the hydrated layer of the pH probe bulb by jumping between Si-O sites, or is it the hydronium ions in solution that is diffusing into the glass?
3. Why is it this often called an ion exchange process? (e.g. not in the Mettler link but in the other two links below, and several random textbooks pulled from a library shelf). Are there Li or Na ions in the glass that are moving? What is being "exchanged"?

below: From Theory and Practice of pH Measurement.

below: From The Glass pH Electrode by Petr Vany´sek.

• This question is a little complex, but I believe that understanding one or two underlying processes within the glass is all that I need here.
– uhoh
Apr 8, 2017 at 23:56
• electrochem.org/dl/interface/sum/sum04/IF6-04-Pages19-20.pdf This short article gives some useful information for you. In particular, I believe it addresses the third part of your original question. 1st page, right around equation 2: "The exchange of hydronium (or written as proton, H+) between the solid membrane and the surrounding solution, and the equilibrium nature of this exchange, is the key principle of H3O+ sensing. " Equation 2 shows that the ion exchange is with the silicon of the glass membrane. Apr 21, 2017 at 4:27
• @Tyberius Yep, that's the pdf I've linked to in the question and the source of the figure of the bulb labeled Figure 1, and it is one of the statements there that are bothering me and brought me here to get expert help. I think it is somewhat vague. I am not sure it actually clears up beyond all doubt that hydronium ions do all of the diffusing, and not just the protons, and 3. asks about exchange, and the metal ions within the glass (Li, Na) itself. After all The Chalkboard magazine column is not intended to be a scholarly reference source.
– uhoh
Apr 21, 2017 at 5:15
• Have you looked at the Wikipedia page for "glass electrode"? References 8 through 12 cited in the "Metallic function..." section might be worth tracking down. en.wikipedia.org/wiki/Glass_electrode Apr 27, 2017 at 17:52
• I remember having read that no H+ ions are crossing the glass membrane, because if Tritium chloride is inserted in the inner solution instead of usual HCl, the radioactivity stays inside the bulb, and never gets out, even after many weeks. Unfortunately I don't remember the reference of this experiment. Nov 5, 2020 at 10:34

My reference for all information and pictures is Harris' Quantitative Chemical Analysis, 9th ed., pp 347-9. I think it'll be worth your while to consult those pages, but I'll try to summarize the important points here.

An ion-selective electrode is characterized by a thin membrane that, well, selectively binds ions. The glass electrode is an ion-selective electrode for $\ce{H+}$ made of amorphous silicate glass, which consists of connected $\ce{SiO4}$ tetrahedra.

Presumably, no special preparative techniques are required for the glass, and the depth of the hydrated gel layer is mediated by the strength and range of the intermolecular interactions between water and the glass.

Protons are the main ions that bind to the layer, leading to the selectivity of the electrode. They diffuse between the solution and the hydrated gel layer and displace the metal ions originally present on the surface of the glass, which describes an ion-exchange process. Note that they cannot, however, diffuse through the inner glass layer.

A few side remarks.

• Equilibrium is reached when the favorable binding of protons to the glass surface is balanced by the unfavorable electrostatic repulsion and chemical potential gradient that result from diffusion into the hydrated gel layer. This provides an equation relating the potential difference to the pH of the solution and allows for $\ce{pH}$ measurement.
• Something has to be able to move through the inner layer of the glass membrane to conduct a current and hence allow for a measurement of the potential difference. It turns out that sodium ions can move through this inner layer, but only sluggishly---the resistance of the glass membrane is about $10^8\,\Omega$.
• As you've mentioned, the electrical resistance of the glass is of the order of 100 MΩ or more, and is very sensitive to temperature, thus the need for a very high input impedance amplifier. However it does deliver a small current (nA). I had thought that the conductivity of the glass is due to electron (or hole) carriers, not the movement of sodium ions. My thinking was that ionic conductivity might "use up" sodium since its not necessarily replenished by the solutions on the outside or AgCl inside. Perhaps for Na sensitive ionic probes the situation is different.
– uhoh
Aug 7, 2017 at 1:30
• I'm glad to help. (1) Yes, they are; I've updated my post. (2) I don't know enough about this to comment, but Harris does state that sodium ions are responsible for current: "The $\ce{H+}$-sensitive membrane may be thought of as two surfaces electrically connected by $\ce{Na+}$ transport." Aug 7, 2017 at 2:50
• Oops, sorry, forgot to write @uhoh. Aug 7, 2017 at 3:02
• Looks great, thank you for all this work! Below my meta question Does anybody here know how a pH probe's glass bulb electrode works? @Martin-マーチン commented "Sometimes it just takes more time. Don't give up just yet." :) +n!
– uhoh
Aug 7, 2017 at 5:59

I guess H+ ions are able to diffuse through the glass layer. After all, if the glass would soften at 900 K, then the probability of reaching or exceeding the activation energy for diffusion of an ion (H+, Na+) at 300 K is about exp(-900/300) = 0.05 which is quite high.