Treating nitrogen with respect is one of the things I have learned to appreciate over the years. No other element has so much going for it, especially under seemingly trivial conditions and in mundane settings. When Iain Watson was doing his PhD in my lab, he stumbled upon an effect that helped shape our thinking for many years. At that point of time, we had just started looking at the properties of amines in constrained environments. Iain discovered that aziridines displayed some aberrant behaviour in palladium-catalyzed allylic amination reactions. The kinetic branched product never isomerized into the linear one, which was odd considering what had been known prior to our work. We spent several years trying to understand this effect; several generations of my students took those results further and developed some rather nice methods. The irony is that we still have arguments about the origins of allyl aziridine stability against isomerization. But then again, at least the experimentally observed aberration was at the very “start” of the cyclic amine series, allowing us to end any argument with “Oh well, these rings are seriously strained after all… Let’s just go have a beer or something”. You probably know how circular arguments develop and propagate.
http://pubs.acs.org/doi/abs/10.1021/ja049242f
http://www.nature.com/nmeth/journal/v12/n3/full/nmeth.3256.html
Now hold on to your seats. Professor Igor Alabugin of Florida State University sent me a really nice book chapter he has been writing. In it, he elaborates on the s-character trends in the secondary amine series and cites a paper that made me scratch my head. This 2014 Nature Methods piece prescribes the use of azetidines (four-membered heterocycles with one nitrogen) in order to dramatically boost the quantum yield of certain fluorescent dyes. The three- and five-membered congeners are both inferior in this application, whereas the four-membered one hits the sweet spot.
Planting outliers in a series where one might naively expect some cute little trend is where organic chemistry is at its finest. The rationale behind the azetidine effect is most likely rather complicated. That’s ok: incorporating azetidines into dyes is now billed as a general method to improve fluorophores for live-cell microscopy. Way to go, azetidines…
amphoteros 
sorting out quantum yields is especially problematic, QYs come from how the excited and ground state surfaces interact – in fluorescent dyes you need to keep the surfaces far apart in energy to avoid alternative ways of releasing the energy – as a super super no-nothing guess, perhaps the high QY’s are because 4 membered rings have some kind of fixed conformation, while the 3 and 5 membered rings are more flexible and allow conical intersections do develop as ring flips, etc. occur…?
Well, this is a good point but they do say that the aziridine variant gave “a colorless solution with no discernible fluorescence, a result suggesting that the ring strain in the aziridine substituents forces the rhodamine molecule to adopt a colorless, nonfluorescent lactone form”. So I think the answer is complex here. There are likely some interesting push/pull subtleties. This should be interesting to understand.
as a naive non-expert in the field, my guess would be that enhancing the interaction of nitrogen lone pair with aryl is important for fluorescence, and aziridine kills it perhaps because aziridine has a similar effect as putting an electron-withdrawing substituent on N. Azetidine does not have this effect (as can be seen readily from the pKA comparison)
Julolidine is another example of aniline whose introduction sometimes dramatically improves performance of fluorescent dyes – and I wonder if there is anything in common electronically in julolidine with the effect that the aziridine introduction makes.
the last sentence should have been …with the effect that the azetidine introduction …
Thanks a lot for bringing up that cool juolidine molecule! You make an interesting point. In terms of the electron-withdrawing effect, this is one of the arguments we have considered in the past. It is also important to recall the unusually low pKa of an aziridinium ion. One of the annoying things is that aziridine is not on Mayr’s nucleophilicity scale (Herbert and I communicated several times and I planned to send a student but it has not panned out…). This makes me wonder if azetidine is there… Just looked (http://www.cup.lmu.de/oc/mayr/reaktionsdatenbank/fe/showclass/41) and it is not there either… These metrics are useful.