The reaction is straightforward:
Simply melt the sulfur, add the limonene and wait. The sulfur rings upon heating break apart and form thiyl groups which react with the unsaturated bonds in the limonene. This is remarkably similar another sulfur/organic copolymer ($) that I blogged about 2 years ago (1, 2), which took the same approach of heat and dump. In both cases, the unsaturated organic compound needs to be low enough in volatility that the hot sulfur (> 170 oC) doesn't evaporate too much of it off.
As is shown above, there are stretches of sulfur-sulfur (sulfide) bonds between the organic segments, and these are what capture the mercury (hence the old name for thiols of "mercaptans"). I did find it somewhat surprising that the amounts of sulfur:liminone were 50:50 on a mass basis.
"An equal mass of sulfur and limonene was chosen to maximize the content of both industrial by-products in the final material."The authors themselves note that sulfur is produced at nearly 1000x the rate of liminone, so maybe trying to incorporate a little more sulfur would be a good idea. Additionally, the formula weight for liminone is 136 g/mol while that of sulfur (S8) is 256 g/mol, which further skews the ratio of the comonomers towards the limonene.
I also wonder how long researchers are going to keep running these reactions in open flasks. The engineer in me is makes it really difficult to not scream at the monitor about running the reaction under pressure so that the volatility would no longer be a concern. Or maybe in a twin-screw extruder, for continuous production of the polymers. That would make for a great patent, wouldn't it. Or maybe I should say "would have"...