On the kinetics of body versus end evaporation and addition of supramolecular polymers

Abstract.: The kinetics of the self-assembly of supramolecular polymers is dictated by how monomers, dimers, trimers etc., attach to and detach from each other. It is for this reasons that researchers have proposed a plethora of pathways to explain the kinetics of various self-assembling supramolecules, including sulfur, linear micelles, living polymers and protein fibrils. Recent observations hint at the importance of a hitherto ignored molecular aggregation pathway that we refer to as “body evaporation and addition”. In this pathway, monomers can enter at or dissociate from any point along the backbone of the polymer. In this paper, we compare predictions for the well-established end evaporation and addition pathway with those that we obtained for the newly proposed body evaporation and addition model. We quantify the lag time, characteristic of nucleated reversible polymerisation, in terms of the time it takes to obtain half of the steady-state polymerised fraction and the apparent growth rate at that point, and obtain power laws for both as a function of the total monomer concentration. We find, perhaps not entirely unexpectedly, that the body evaporation and addition pathway speeds up the relaxation of the polymerised monomeric mass relative to that of the end evaporation and addition. However, the presence of the body evaporation and addition pathway does not affect the dependence of the lag time on the total monomer concentration and it remains the same as that for the case of end evaporation and addition. The scaling of the lag time with the forward rate is different for the two models, suggesting that they may be distinguished experimentally.