Living polymerization in nano-scale volumes. Impact of process conditions on polymerization kinetics and product characteristics

Living polymerization processes, irreversible and reversible, proceeding in a large number of isolated (no mass exchange) nano-scale reactors (droplets) were modeled using stochastic (Monte Carlo) and deterministic simulations and analytical solutions of derived mathematical equations. Monomer and living unimer used as initiator were redistributed in droplets uniformly or accordingly to the Poisson distribution, resulting in nanoreactors containing a small number of growing chains. Stochasticity of reactions involving low number of molecules affects the concentration of monomer and chain length distributions in individual droplets, both differing from ones accounted in macroscopic system. The developed mathematical description, based on values of rate constants of propagation (k(p)) and depropagation (k(d)) reactions and on initial monomer and living unimer concentrations, as well as numerical simulations, allow predicting kinetics of the process and of several characteristics of the products resulting therefrom, e.g. chain length distribution. Moreover, they allow also following evolution of droplet subpopulations that differ in composition. Moreover, for the reversible process the equilibrium monomer concentration in a droplets system [M](eq) can be calculated. As living ionic and coordination polymerization and the controlled radical polymerization in nano-scale dispersions are rather little explored the theoretical predictions shown in this work could facilitate their further development.