One hand

This year’s chemistry Nobel went to Henri Kagan and Kenso Soai for reactions in which one mirror-image form of a molecule takes over. In Soai’s reaction the product is its own catalyst. In the Academy’s account, a starting excess of 0.00005% of one hand grew to 57%, then 99%, then over 99.5% across three rounds of fresh ingredients. Started from an even mix, chance decides which hand wins.

I wanted to feel why it happens, so I built a toy model in my lab. Catalyst molecules pair up. Same-hand pairs (RR, LL) do the work. Mixed pairs (RL) do nothing, and if they’re more stable than matched pairs they lock away the minority hand. Working through it on paper, then checking numerically, I got this: while the excess is small, it grows as a power of the total amount made,

excess ∝ (amount)^(1 + K_mixed/K_matched).

With purely statistical pairing the power is 2. If mixed pairs bind ten times more strongly, it’s 11. The more the two hands prefer each other, the faster one of them disappears from the working pool.

This is a toy version of the Blackmond–Brown dimer model, which chemists have studied properly. Schiaffino and Ercolani derived the real amplification relation from it. What I like best: at 0 °C the actual reaction amplifies up to four orders of magnitude more than the dimer model predicts, and to fit the data they had to add tetramers. The toy explains the shape of the effect and gets the size wrong. That seems a fair summary of most toys.