Conceptual Validation of Stochastic and Deterministic Methods To Estimate Crystal Nucleation Rates
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Date
2023-02-01
Publication Type
Journal Article
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yes
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Abstract
This work presents a generalized framework to assess the accuracy of methods to estimate primary and secondary nucleation rates from experimental data. The crystallization process of a well-studied model compound was simulated by means of a novel stochastic modeling methodology. Nucleation rates were estimated from the simulated data through multiple methods and were compared with the true values. For primary nucleation, no method considered in this work was able to estimate the rates accurately under general conditions. Two deterministic methods that are widely used in the literature were shown to overpredict rates in the presence of secondary nucleation. This behavior is shared by all methods that extract rates from deterministic process attributes, as they are insensitive to primary nucleation if secondary nucleation is sufficiently fast. Two stochastic methods were found to be accurate independent of whether secondary nucleation is present, but they underestimated rates in the case where a large number of primary nuclei are formed. We hence proposed a criterion to probe the accuracy of stochastic methods for arbitrary data sets, thus providing the theoretical foundations required for their rational use. Finally, we showed how both primary and secondary nucleation rates can be inferred from the same set of detection time data by combining deterministic and stochastic considerations.
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published
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Book title
Journal / series
Volume
23 (2)
Pages / Article No.
899 - 914
Publisher
American Chemical Society
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Edition / version
Methods
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Date collected
Date created
Subject
Crystallization; Crystals; Mathematical methods; Nucleation; Supersaturation
Organisational unit
03484 - Mazzotti, Marco (emeritus) / Mazzotti, Marco (emeritus)
Notes
Funding
788607 - Studying Secondary Nucleation for the Intensification of Continuous Crystallization (EC)