Modulation of the cooperativity in the assembly of multistranded supramolecular polymers

It is highly desirable that supramolecular polymers self-assemble following small changes in the environment. The degree of responsiveness depends on the degree of cooperativity at play during the assembly. Understanding how to modulate and quantify cooperativity is therefore highly desirable for the study and design of responsive polymers. Here we show that the cooperative assembly of a porphyrin-based, double-stranded polymer is triggered by changes in building blocks and in salt concentration. We develop a model that accounts for this responsiveness by assuming the binding of the salt countercations to the double-stranded polymer. Using our assembly model we generate plots that show the increase in concentration of polymer versus the normalized concentration of monomer. These plots are ideally suited to appreciate changes in cooperativity, and show that, for our system, these changes are consistent with the increase in polymer length observed experimentally. Unexpectedly, we find that polymer stability increases when cooperativity decreases. We attribute this behaviour to the fact that increasing salt concentration stabilizes the overall polymer more than the nucleus. In other words, the cooperativity factor α, defined as the ratio between the growth constant K_g and the nucleation constant K_n decreases as the overall stability of the polymer increases. Using our model to simulate the data, we generate cooperativity plots to explore changes in cooperativity for multistranded polymers. We find that, for the same pairwise association constants, the cooperativity sharply increases with the number of strands in the polymer. We attribute this dependence to the fact that the larger the number of strands, the larger is the nucleus necessary to trigger polymer growth. We show therefore that the cooperativity factor α does not properly account for the cooperativity behaviour of multistranded polymers, or any supramolecular polymer with a nucleus composed of more than 2 building blocks, and propose the use of the corrected cooperativity factor α_m. Finally, we show that multistranded polymers display highly cooperative polymerisation with pairwise association constants as low as 10 M^-1 between the building blocks, which should simplify the design of responsive supramolecular polymers.