# What is happening in this video of solvated electrons donated from sodium in ammonia?

I just saw the Periodic Video Liquid Electrons - Periodic Table of Videos where sodium is added to liquid ammonia. The demonstration shows that even if electrons are solvated, if you have a high enough electron density, the substance will turn shiny and reflective and metallic. Sodium is dissolved in liquid ammonia and donates the electrons to the solution.

There are a number of things happening in the demonstration that I don't understand.

There is supposed to be a separation - once a high enough electron density is reached, the solution is supposed to separate into a high electron density and low electron density layer. Why the separation instead of a uniform concentration? And why would the high electron concentration layer float on top?

Also, at concentrations below the metallic appearance, the sodium in ammonia solution starts out very strongly blue colored. Why? What is it about adding sodium to liquid ammonia that instantly produces such a deep blue, almost black color?

It seems that the demonstration did not go quite as planned, so isopropyl alcohol was added, producing sodium isopropoxide. Why?

• The isopropanol is added to quench the highly reactive solution and would be required whatever the result of the reaction was. This is a common way to (gently) destroy sodium metal that you don't want to have to throw down the sink. – matt_black Apr 10 '17 at 0:22
• @matt_black perhaps "destroy sodium metal" is not the best way to describe what is happening? Watching the video, it seems to have been added early on in the demonstration, and the reason is explained. I just don't understand their explanation. – uhoh Apr 10 '17 at 0:28
• They say in the video they add the isopropanol to "quench" the reaction: this means to destroy any remnants of unreacted sodium metal as you can't dispose of the metal easily (unlike sodium isopropoxide). This has the beneficial effect of destroying the dark blue low-concentration sodium/ammonia solution making it easier to see the metallic sheen of the high concentration solution. It wasn't that the experiment didn't work just that it was hard to see the result on video. – matt_black Apr 10 '17 at 7:55
• @matt_black ok I see, to consume the remaining unreacted sodium metal so it can be disposed of later more safely, and to help viewers focus on the metallic color and not the strikingly blue layer. Thanks! – uhoh Apr 10 '17 at 8:45

I'll try an answer to this question because I watched this video a while back and did a bit of reading on it at the time and I think I understand the big picture. The problem is that these solvated electrons are very complicated things, and do not lend themselves to the traditional ways that chemists would like to think about things. For that reason, there is quite a lot of literature coming from physicists which is very complicated but nonetheless valuable. Additionally, solvated electrons show up in more than just this rather unusual metal-liquid ammonia solution. For instance, a recent paper in Nature chemistry by Sieferman et. al. [1] showed that there are transient solvated electrons at the surface of water which can have major implications for natural electron transfer reactions. So, understanding these systems is truly quite important.

## The Blue Color:

In order to get at the deep blue color which is seen in this sodium-ammonia solution, we must understand what it is that is absorbing (reddish) visible light and hence leading to the transmission of a lot of blue light.

As it happens, at low concentrations of sodium (I'll address this in a bit), the solvated electrons exist in a bound state. This is not too dissimilar to ordinary electronic energy levels, except that there is not really a molecule to be found. Rather, the electron exists in a bound state which it creates for itself. That is, the electron polarizes the surrounding solvent such that it is contained in a bound state. Sometimes people refer to this electron as being a "polaron". One important difference between this and energy levels in a molecule is that electronic excitations generally take place from one bound state to another bound state. In the case of a solvated electron, however, the transitions are from a bound state to a continuum state.

Obviously one question that would be nice to answer is why is it such a deep blue solution? Well, this sort of question is always hard to address because the color of things is more or less an accident. The fact that it is blue just tells you that the electron is relatively weakly bound because it is excited by reddish light.

For more details on the bound-continuum transition, see Aulich's paper [2] which uses photo-electron emission to study solvated electrons as a function of concentration and photon energy. For a theoretical treatment of the bound states at dilute concentrations of metals, see Jortner's paper [3].

## The Transition to a Bronze Color:

One reason that people have been very interested in this system is because of this transition that takes place as the concentration of metal increases. Let me first try to give some intuition as to why this transition takes place at all. First, going off of our model that the electrons polarize the solvent and exist in a low-energy, bound state, we should expect that as more electrons are added to the solution (i.e. as more sodium is added), these cavities which the electrons occupy will become closer and closer to each other. This means that electron-electron interactions become quite important. This means two things: first, we have to begin worrying about satisfying Pauli exclusion, and second, we have to be concerned that at some point the electrostatic repulsions will become larger than the binding energy of this electron.

These two points have been studied by some physicists. Alavi and Frenkel's paper [4] develops a model and then performs simulations on ideal fermions (I honestly don't know what makes a fermion ideal and don't understand this paper), demonstrates that the low-concentration bound states are very unstable as the concentration of electrons increases. Thus, some transition must take place.

The best paper on the theory of this transition can be found here [5]. The reason this transition is so interesting is that it is a "metal to non-metal" transition. Remember when you were first introduced to metals and the characteristic description is that they are a "sea of electrons"? That is, the electrons are free to move around, and this leads to high conductivity and other observable properties, one of which is that they absorb and reflect nearly all wavelengths of light, which leads to the silvery color of most metals.

Well, the exact same phenomenon is being observed here, but it's very peculiar because this is all happening in a liquid. For instance, Schroeder et. al. wrote a paper [6] which measures the conductivity of several metal-ammonia solutions as a function of concentration of the metal. I unfortunately couldn't add the relevant figure, but the conductivity basically increases linearly with concentration of the metal until it hits a plateau and does not increase any further.

This gradual increase explains what is going on when we see a separation into two phases. The explanation goes like this. There is only so much space which allows for the existence of the bound states we described above because these bound states occupy a cavity of relatively large volume in the solvent. As more metal is added, more electrons are free in the solution, but the solution is already saturated with these bound electrons. Thus, the electrostatic and exclusion effects become such that any additional electrons added can only exist in a metallic state. This is peculiar because this metallic state is in the liquid phase and is actually fairly dense (I read this somewhere but can't remember the reference... Will update later). If one continues adding electrons, they always become incorporated into the metallic state because the bound states are saturated. Eventually, enough electrons are present that the destabilizing effects due the presence of other electrons is large enough that no possible bound state can exist and the whole system becomes metallic. Hence the plateau in the conductivity plot I described above. At this point, I believe the sodium ceases to dissolve and just stays as plain old metal sodium.

I do not have a good explanation for why the metallic phase is specifically bronze colored as opposed to silvery. I suspect this is a very subtle feature and would certainly be temperature dependent. I haven't described the temperature dependence of all of this, but there quite a few papers that address only this point and it seems to be quite complicated.

I also don't know why the metallic phase forms on the top. I suspect this may just be an artefact of the experiment in that video. That is, it is entirely feasible that solid would sink to the bottom if it didn't just freeze to the side of the test tube. I could be wrong about that though.

## References:

1. Siefermann, K. R., Liu, Y., Lugovoy, E., Link, O., Faubel, M., Buck, U., ... & Abel, B. (2010). Binding energies, lifetimes and implications of bulk and interface solvated electrons in water. Nature chemistry, 2(4), 274-279. DOI
2. Aulich, H., Baron, B., Delahay, P., & Lugo, R. (1973). Photoelectron emission by solvated electrons in liquid ammonia. The Journal of Chemical Physics, 58(10), 4439-4443. DOI
3. Jortner, J. (1959). Energy levels of bound electrons in liquid ammonia. The Journal of Chemical Physics, 30(3), 839-846. DOI
4. Alavi, A., & Frenkel, D. (1992). Grand‐canonical simulations of solvated ideal fermions. Evidence for phase separation. The Journal of chemical physics, 97(12), 9249-9257. DOI
5. Jortner, J., Cohen, M. H. (1976). Metal-nonmetal transition in metal-ammonia solution. Physical Review B, 13 (4), 1548-1568.
6. Schroeder, R. L., Thompson, J. C., & Oertel, P. L. (1969). Conduction in Concentrated Solutions of Several Metals in Liquid Ammonia. Physical Review, 178(1), 298. DOI
7. Thompson, J. C. (1968). Metal-nonmetal transition in metal-ammonia solutions. Reviews of modern physics, 40(4), 704.
8. Schroeder, R. L., Thompson, J. C., & Oertel, P. L. (1969). Conduction in Concentrated Solutions of Several Metals in Liquid Ammonia. Physical Review, 178(1), 298.
• This is stackexchange at it's finest - thank you so much for the substantial, thorough, and thoughtful answer! You've sent me to the library today which is always a very good thing. I'm marking this as accepted because you've addressed the optical properties with my main focus here. I will break out the question of the separation of layers as a linked but separate, stand-alone question in a few hours, since it is probably not strongly related. – uhoh Apr 10 '17 at 0:42
• First off, awesome +1 answer. I do still have one point of confusion regarding the phase of the bronze colored material. At one point you said "this is all happening in a liquid" and shortly thereafter "a solid is formed (I believe) and the electrons move more or less freely around". I'm probably mixing up just what you are referring to, but my question about this is simply, is this bronze colored sea of solvated electrons precipitating out as a solid or is it a liquid (as it appears to be), or is it something more complex and kind of in between the two? – airhuff Apr 10 '17 at 1:35
• Good point @airhuff . This is a detail which was unclear to me but I updated that sentence because indeed it is still a liquid from what I can tell. This would definitely be relevant to why it stays on top. – jheindel Apr 10 '17 at 6:23
• I'm not sure a full answer is 100% ironed out here, but I'm going to click accept because there is enough insight and linked material to help me on my way to understand what's happening. Once I'm finished reading I'll ask some additional follow-up questions. Thanks for the very helpful answer! – uhoh Apr 17 '17 at 1:16
• Just to let you know, I've just asked the follow-up question How to think of solvated electrons? – uhoh Jul 26 '17 at 8:54