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.

使用随机（蒙特卡罗）和确定性模拟和导出数学方程的解析解对在大量孤立（无质量交换）纳米级反应器（液滴）中进行的不可逆和可逆的活性聚合过程进行建模。用作引发剂的单体和活性单聚体在液滴中均匀地或根据泊松分布重新分布，从而产生含有少量生长链的纳米反应器。涉及少量分子的反应的随机性影响单个液滴中单体的浓度和链长分布，两者都不同于宏观系统中的反应。基于传播速率常数 ( k _p) 和去增殖 ( k _d ) 反应以及初始单体和活性单体浓度，以及数值模拟，允许预测过程的动力学和由此产生的产物的几个特征，例如链长分布。此外，它们还允许跟踪组成不同的液滴亚群的演变。此外，对于可逆过程，液滴中的平衡单体浓度s系统[M] _eq可以计算。由于活性离子和配位聚合以及纳米级分散体中的受控自由基聚合研究很少，因此这项工作中显示的理论预测可以促进它们的进一步发展。