I'd like to share something I just learned, and run by what I'm trying to figure out.
Supersaturation is the driving force of all crystallization processes. That's why the solubility curves are so crucial to know, because then you can calculate your supersaturation ratio and try and design a crystallization scheme which maintains that ratio within the metastable zone width (MSZW).
There is a widely expressed way of correlating supersaturation with nucleation rate and crystal growth, and it is probably the only graph one is likely to find when researching the relationship. However, there is a more accurate way of describing this relationship that I found in Mullin's "Crystallization, 4th ed." (THE Source) which shows that the conventional ways of expressing this relationship do not apply for DMT crystallization.
The 1st picture are the two methods of describing this correlation with supersaturation and nucleation rate / crystal growth. The graph on the left is Mullin's (source material reproduced as well below), the right something you will find anywhere on the internet, here from a white paper from Mettler Toledo.
Conventional theory will tell you that nucleation rate increases exponentially with increasing supersaturation. It would mean: the higher you supersaturate your solution, the more your end product will be a bunch of tiny crystals rather than. Lower supersaturation ratios will favor crystal growth and lead to larger crystals.
Yet, looking at the graph Mullin has, we see that this is just the theoretical vision, and not what happens in reality. In practice, there is a maximum and then a sharp decrease. To quote:
"Melts frequently demonstrate abnormal nucleation characteristics [...]. The rate of nucleation usually follows an exponential curve (solid line in Figure 5.2) as the supercooling is increased, but reaches a maximum and subsequently decreases (broken curve in Figure 5.2). Tamman (1925) suggested that this behavior was caused by the sharp increase in viscosity with supercooling which restricted molecular movement and inhibited the formation of ordered crystal structures."
I attached pictures of the Pull 1 sample extracted at 97.5C (give or take) so the supersaturation ratio at RT was huge. Nucleation should have been exponential, but the crystals were actually fairly well developed, and several but not by any large amount. The next picture is the pull at 85C, which also should have yielded a high number of little crystals but actually formed just into a single crystal.
The most interesting formations occurred with the ones at 75C, 65C, and 40C, and they are shown at the end. Mullin points out that this reversal of the nucleation rate has been confined to melts, but also has been noted in extremely viscous solutions.
We are always working with melts with DMT (unless you stick to below 46C), so this is directly applicable.
Two of the samples demonstrating this strange crystal formation came from melted samples, although not the third.
The first page of the source material discusses three main variables which govern the rate of nucleation: temperature, degree of supersaturation, and interfacial tension. I think the latter played a huge part in the formation of this crystal, as well as the lowered degree of supersaturation.
It's, well, crystallization is complicated, I'm not quite sure exactly yet how to describe these processes completely, but I do think it's good to bear in mind this other relationship between some of these values which you probably won't find elsewhere.
Samvidbuho attached the following image(s):
Two Differing Models on the Effects of Supersaturation on the Rate of Nucleation.PNG
(102kb) downloaded 135 time(s). Pull 1, 97.5C, Extract.jpg
(1,305kb) downloaded 135 time(s). Pull 1, 85.0C, Extract.jpg
(628kb) downloaded 132 time(s). Pull 1, 75.0C, Extract_time 1.JPG
(217kb) downloaded 131 time(s). Pull 1, 75.0C, Extract_time 2(b).jpg
(1,291kb) downloaded 132 time(s). Pull 1, 40.0C (lbottom) & 65.0C (top), Extracts.JPG
(306kb) downloaded 132 time(s). Pull 1, 65.0C, Extract (1).JPG
(160kb) downloaded 131 time(s). Chapter 5 - Nucleation, pp. 184-185 ('Crystallization', 4th ed., Mullin).PNG
(229kb) downloaded 131 time(s). Chapter 5 - Nucleation, pp. 186-187 ('Crystallization', 4th ed., Mullin).PNG
(285kb) downloaded 131 time(s).