The solutions available for the well‐known Smith–Ewart recurrence equation (assuming size monodispersity) for calculating the average number of radicals per particle ( $\overline{n}$) do not consider the contribution of nucleation and coagulation of active particles. Notwithstanding this limitation, they are often used to calculate $\overline{n}$ in simplified mathematical models for commercial simulation software of industrial processes or for process control purposes. In this work, algebraic equations to calculate $\overline{n}$ for 0–1 systems that consider such contributions are developed. It is found that in the nucleation stage under typical conditions of emulsion polymerization, if nucleation and coagulation of particles are not considered in the calculation of $\overline{n}$, it could lead to large errors although its effect still needs to be evaluated in other relevant process parameters as well. However, such significant error could be present for a case of study where secondary nucleation and limited coagulation is experimentally detected.

中文翻译：

---

乳液聚合中每个颗粒平均自由基数的简化计算：颗粒成核和混凝速率的影响

可用于著名的Smith-Ewart递归方程（假定尺寸为单分散性）的解决方案，用于计算每个粒子的平均自由基数（ $\overline{ñ}$）不要考虑活性颗粒的成核和凝聚作用。尽管有此限制，但它们通常用于计算$\overline{ñ}$用于工业过程的商业模拟软件或过程控制目的的简化数学模型。在这项工作中，要计算代数方程$\overline{ñ}$针对0–1的系统，考虑了这种贡献。发现在乳液聚合的典型条件下的成核阶段，如果不考虑颗粒的成核和凝结，$\overline{ñ}$，这可能会导致较大的错误，尽管其效果仍然需要在其他相关过程参数中进行评估。但是，对于通过实验检测到二次成核和有限凝结的研究案例，可能会出现这种重大错误。