Deterministic Approach to Estimate Functionality of Chains Produced by Radical Copolymerization in the Presence of Secondary Reactions

Functional acrylic resins for the coatings and adhesives industry are often synthesized by radical solution copolymerization at high temperatures (>120 °C) using starved-feed semibatch operation. The kinetic Monte Carlo (KMC) stochastic modeling technique has emerged as a method to represent the placement of the functional comonomer units across the polymer distribution, thus providing the knowledge required to increase process efficiency and product quality. However, obtaining such information is computationally intensive, limiting the utilization of the method. To avoid this barrier, a series of mathematical expressions based on the Schulz–Flory probability distribution is derived to estimate the instantaneous mole and weight fractions of polymer chains containing a specific discrete number of comonomer units. A comparison of the results to those from a previously established KMC implementation demonstrates that the strategy can reasonably match the distribution of functionality obtained from the KMC simulator. This deterministic approach is then extended to the cumulative measures with satisfactory precision.

用于涂料与胶粘剂行业的功能性丙烯酸树脂，通常采用饥饿进料半间歇操作模式，在高于120℃的高温下通过自由基溶液共聚法合成。动力学蒙特卡洛（kinetic Monte Carlo, KMC）随机建模技术现已成为一种可表征功能性共聚单体单元在聚合物分布中排布方式的方法，可为提升工艺效率与产品质量提供必要的理论支撑。然而，获取此类信息的计算量十分庞大，限制了该方法的实际应用。为突破这一技术瓶颈，本文基于舒尔茨-弗洛里（Schulz–Flory）概率分布推导得到一系列数学表达式，用于估算含有特定离散数目共聚单体单元的聚合物链的瞬时摩尔分数与质量分数。将该策略所得结果与已有的KMC模拟结果进行对比后证实，本方法能够合理匹配KMC模拟器得到的官能团分布情况。随后，该确定性建模方法被拓展至累积分布的计算，且可获得令人满意的精度。