Abstract Influence of solution volume on the inherent stochastic distribution of induction time during nucleation process was investigated by developing a mathematical model based on Single Nucleus Mechanism and the Poisson’s distribution. The results show that the distribution of induction time turns narrower with the increase of solution volume, indicating that the stochastic nature of nucleation become weaker. Based on the mathematical model, the stochastic distribution of crystal nucleation at different solution volume can be determined. The induction time of HMBTAD in acetonitrile were measured at different volumes to validate the mathematical model. Transition volume at which the induction time becomes reproducible was also calculated from the mathematical model. The theoretically calculated value of transition volume is consistent with experimental result obtained from induction time measurement, which also verify the correctness of mathematical model.

中文翻译：

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HMBTAD 成核在不同溶液体积中的固有随机分布

摘要 通过建立基于单核机制和泊松分布的数学模型，研究了溶液体积对成核过程中诱导时间固有随机分布的影响。结果表明，随着溶液体积的增加，诱导时间的分布变窄，表明成核的随机性变弱。基于数学模型，可以确定不同溶液体积下晶体成核的随机分布。测量不同体积的 HMBTAD 在乙腈中的诱导时间以验证数学模型。诱导时间变得可再现的转变体积也从数学模型计算。