Inherent stochastic distribution of nucleation of HMBTAD in different solution volume.

• Developing a mathematical model to investigate the influence of solution volume on stochastic distribution of induction time. • Calculating transition volume of HMBTAD-acetonitrile system, at which the induction time becomes reproducible. • Measuring the induction time of HMBTAD in acetonitrile in different solution volumes to validate the mathematical model. 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. [ABSTRACT FROM AUTHOR]