One-dimensional random walk of a synthetic small molecule toward a thermodynamic sink

We report on the spontaneous intramolecular migration of α-methylene-4-nitrostyrene from amine group to amine group along oligoethyleneimine tracks up to eight repeat units in length (number of amine footholds, n = 3, 5, 9). Each track consists of n - 1 aliphatic secondary amine footholds plus a naphthylmethylamine group foothold situated at one end of the track. Under basic conditions the α-methylene-4-nitrostyrene unit undergoes a series of reversible intramolecular Michael-retro-Michael reactions between adjacent amine groups that move it up and down the track. For n = 3 and 5 it is possible to monitor the population of every positional isomer on the track by (1)H NMR spectroscopy. On the longest track (n = 9) the fraction of walkers on each end-foothold can be quantified with respect to those on the inner footholds. In all cases the naphthylmethylamine foothold acts as a thermodynamic sink with the steady-state distribution significantly biased in favor of the walker at that site. The dynamics of the walker migration is well described by the random walk of a Brownian particle in one dimension.