A multiscale modeling description of free-radical polymerization processes is presented. The polymerization process is described at the macroscale by coupling the Fokker-Planck Equation (FPE) for the particle size distribution (PSD) prediction at the mesoscale with a kinetic Monte Carlo (kMC) simulation at the microscale. The finite element method is adopted to solve the mesoscopic scale to capture the nonlinear evolution of the PSD, successfully facing challenges related to accuracy and computational cost in the FPE numerical solution. Additionally, the proposed model captures the evolution of the average number of free-radicals and secondary nucleation rate at the microscopic level. The control of the secondary nucleation rate is in fact critical to satisfactorily obtain high quality structured polymer particles. Finally, a closed-form model is developed at the microscopic scale to handle the curse of dimensionality. Simulations to evaluate the capabilities of the proposed numerical scheme and sensitivity analyses with respect to the system inputs and uncertainties in the initial condition of the PSD are performed.

提出了自由基聚合过程的多尺度建模描述。通过将中尺度的粒度分布（PSD）预测的Fokker-Planck方程（FPE）与微观尺度的动力学Monte Carlo（kMC）模拟耦合，可以在宏观尺度上描述聚合过程。采用有限元方法求解介观尺度，以捕获PSD的非线性演化，成功地解决了FPE数值解中与精度和计算成本有关的挑战。另外，提出的模型在微观水平上捕获了平均自由基数目和二次成核率的演变。实际上，次级成核速率的控制对于令人满意地获得高质量的结构化聚合物颗粒至关重要。最后，在微观尺度上开发了一个封闭形式的模型，以处理维数的诅咒。进行了仿真，以评估所提出的数值方案的能力以及针对PSD初始条件下的系统输入和不确定性进行灵敏度分析。