Modelling and Data Analysis of Stochastic Nucleation in Crystallisation
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Date
2018-03-06
Publication Type
Doctoral Thesis
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Abstract
Nucleation is an important and challenging scientific problem in its own right, which can be investigated from different perspectives and looking at very different scales, from the level of molecular interactions to that of macroscopic, industrial units.
In particular, crystal nucleation is a crucial step in several technologies constituting the backbone of important industries, e.g. pharmaceutical purifications or semi-conductor material production, as well as in several biological processes, e.g insulin metabolism or hemozoin crystallisation in malaria treatments or amyloid proteins aggregation.
The models and the methods of data analysis developed in this thesis to rationalise and describe the random behaviour of crystallisation processes are based on the three foundations: the results of nucleation theories, the approach of population balance equations, and the mathematics of stochastic processes.
This work focuses first on the physical premises and on the mathematical construction of the models, elucidating the difference between nucleation time and detection time and discussing the mathematical and practical consequences of this difference.
The models are validated against the experimental data collected in several systems at different operating conditions.
The statistical premises necessary to perform a meaningful analysis of the data and the numerical methods used to estimate the model parameters are then illustrated.
To examine the quality of the agreement between the models and the data, the possible limitations due to the design of the experiments and to the detection techniques selected for the measurements are discussed.
Since a meaningful characterisation of stochastic processes requires a large amount of data of high quality, the third part of the work focuses on this problem.
This part shows the experimental protocol and the criteria adopted to guarantee well controlled and reproducible operating conditions, to which detection time experiments are known to be very sensitive.
A careful analysis of the statistical assumptions allows to determine when one can combine different series of experiments carried out at nominally identical conditions.
Furthermore, this analysis also yields a parameter-free method to compute the confidence intervals of nucleation rates estimated from empirical distributions.
The method is developed assuming that nucleation follows an exponential distribution, but it can be generalised to other statistics.
Finally, given the importance of polymorphs in a lot of different applications, the competitive nucleation of several polymorphs is investigated, based on the crystallisation experiments of isonicotinamide from ethanol.
The stochastic nucleation model previously developed is extended to account for the formation of an arbitrary number of polymorphs, highlighting the main advantages and limitations of the model.
The behaviour of the system predicted by the model is then compared with the experiments, commenting on the similarities and differences between them.
The results of this thesis show that a deep understanding of nucleation, and therefore a correct description of this phenomenon, requires data of increasing quantity and quality as well as an accurate analysis of such data, which is based on the mathematical and statistical tools illustrated and developed in this work.
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Examiner : Mazzotti, M.
Examiner : Arosio, Paolo
Examiner : Braatz, Richard D.
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ETH Zurich
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Subject
Crystallisation; Stochastic processes; Nucleation; Modelling; Statistical analysis; Polymorphism
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03484 - Mazzotti, Marco (emeritus) / Mazzotti, Marco (emeritus)