Accurate prediction of the particle size distribution (PSD) evolution of growing nanometer scale particles is important in designing gas-phase synthesis reactors for the production of nanomaterials. Towards improved predictions of growth, we model the evolution of the PSD of 1-4 nm TiO particles from the decomposition of titanium tetraisoproxide (TTIP) using a two-dimensional (2D) sectional method, uniquely with coagulation rates derived from molecular dynamics (MD) trajectory calculations which account for detailed particle–particle interactions. The PSDs predicted by the 2D sectional method are compared to recent experimental measurements of PSDs in the 1-3 nm range in a flow tube reactor. The nucleation of particles is modeled based on prior mobility measurements of ions attributed to TTIP and their decomposition, with the specific nucleation rate here fitted as a fraction of base nucleation rate () derived from these prior measurements. In the 2D sectional model, we examine the influence of the initial (nucleated) particle charge distribution on the PSD, with different coagulation rate coefficients for neutral-charged and charged-charged particle collisions. With the MD-derived coagulation rate coefficients, we find that using nucleation rate coefficients between 0.005 and 0.03 leads to strong agreement between modeled PSD and measured PSD for a wide variety of experimental residence times, initial TTIP concentrations and temperatures. Increasing the charge fraction from 0% (uncharged) to 80% (bipolar) does not result in a significant change in the PSD, because the particles rapidly self-neutralize through coagulation based on the simulation results. The results with MD-derived coagulation rate coefficients are compared to those of the sectional method with classical kinetic theory of gases (KTG) rates with a constant enhancement factor to account for potential interactions. Through comparison, we find that the predictions from the classical KTG model consistently exhibit weaker coagulation rates than the MD-derived model during the PSD evolution.

中文翻译：

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使用二维截面方法和分子动力学 (MD) 确定的凝结速率对二氧化钛 (TiO2) 纳米团簇进行建模

准确预测生长的纳米级颗粒的粒度分布 (PSD) 演变对于设计用于纳米材料生产的气相合成反应器非常重要。为了改进生长预测，我们使用二维 (2D) 截面方法模拟四异丙醇钛 (TTIP) 分解中 1-4 nm TiO2 颗粒的 PSD 演变，并采用独特的来自分子动力学 (MD) 的凝固速率）轨迹计算，考虑了详细的粒子-粒子相互作用。将二维截面方法预测的 PSD 与最近在流管反应器中 1-3 nm 范围内的 PSD 实验测量结果进行了比较。粒子的成核是基于 TTIP 及其分解所产生的离子的先前迁移率测量进行建模的，此处的特定成核速率被拟合为从这些先前测量得出的基本成核速率 () 的一部分。在二维截面模型中，我们研究了初始（有核）粒子电荷分布对 PSD 的影响，其中中性电荷和带电粒子碰撞具有不同的凝固速率系数。通过 MD 导出的凝结速率系数，我们发现使用 0.005 至 0.03 之间的成核速率系数可以在各种实验停留时间、初始 TTIP 浓度和温度下使建模 PSD 与测量 PSD 之间具有很强的一致性。将电荷分数从 0%（不带电）增加到 80%（双极）不会导致 PSD 发生显着变化，因为根据模拟结果，颗粒通过凝结快速自中和。将 MD 导出的凝结速率系数的结果与采用经典气体动力学理论 (KTG) 速率的截面方法的结果进行比较，并使用恒定的增强因子来解释潜在的相互作用。通过比较，我们发现在 PSD 演化过程中，经典 KTG 模型的预测始终表现出比 MD 衍生模型更弱的凝血率。