Stochastic Nature of Heterogeneous Nucleation

However, for some properties, the probability of observation is distributed over a range of values, so that observation of a certain value (at the peak of the 

Haymet and coworkers used an automated lag-time apparatus (ALTA) to obtain statistical data on the supercooling point (SCP, also known as freezing temperature) of water freezing to ice (Wilson et al., 2003) and water/tetrahydrofuran (THF) freezing to hydrate/ice (Wilson et al., 2005). The SCP is the temperature of spontaneous freezing of a solution (Zachariassen, 1982). A small sample (300 rL) was cooled linearly (at 4.5 K/min) until the sample froze. The frozen sample was melted, and then refrozen. This freezing-melting cycle was repeated over 300 times on the same sample. 

Wilson et al. (2003, 2005) demonstrate the stochastic nature of the SCP, and that many measurements should be performed on a single sample in order to obtain statistically valid measurements of the SCP. However, a particularly 

FIGURE 3.16 Survival curves for four back-to-back series of 300 runs each on the same THF/water (10 wt% THF) sample in the same tube. The nucleation temperature is not changed significantly between each data series. (Reproduced from Wilson, P.W., Lester, D., Haymet, A.D J., Chem. Eng. Sci., 60, 2937 (2005). With permission from Elsevier.) 

Each survival curve clearly shows that at smaller supercooling temperatures (i.e., higher experimental temperatures) all runs remained unfrozen, while at larger supercooling temperatures (i.e., lower experimental temperatures) all runs were frozen. From these survival curves, Wilson et al. (2003, 2005) defined the nucleation temperature for a given sample, also called the SCP, or kinetic freezing point, as the temperature at which half the runs of the same sample have frozen (T50). The inherent width of each survival curve was considered as an indication of the stochastic nature of nucleation, with the 10-90 width (i.e., the range of temperature from 10% samples unfrozen to 90% samples frozen) to be an indicator of the error bars for the SCP. 

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