Dispersions in crystal nucleation and growth rates: Implications of fluctuation in supersaturation

Singh, Meenesh R.; Ramkrishna, Doraiswami

doi:10.1016/j.ces.2013.11.047

Cited by 21 publications

(20 citation statements)

References 13 publications

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“…Apart from addressing the fundamental question of what causes GRD and how to develop models to explain it, there are practical reasons to research GRD as it causes the particle size distribution (PSD) of seeds to broaden over time resulting in poor product quality 1. There is still significant research occurring on the general topic of GRD, including work on measuring the extent of GRD in particular systems [5−11], empirical modeling of GRD in real systems, and use of GRD models with the population balance framework 12–14 as well as further attempts to find physical reasons for GRD 15–17.…”

Section: Introductionmentioning

confidence: 99%

“…In one, experimental GRD data is used to parameterize a Monte Carlo model for GRD which is then used to control batch crystallization of ibuprofen more effectively than constant temperature or constant supersaturation control schemes 12. Another suggests that GRD is due to Brownian motion of solute molecules affecting local concentration and temperature and therefore supersaturation 15. A stochastic model of local supersaturation fluctuation was developed and shows qualitative agreement with potassium acid phthalate GRD data.…”

Section: Introductionmentioning

confidence: 99%

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Relationship between Surface Roughness, Internal Crystal Perfection, and Crystal Growth Rate

et al. 2016

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Potential mechanisms affecting growth rate dispersion (GRD) are investigated. Previous studies have identified surface roughness and internal lattice perfection as key mechanisms which are both evaluated with respect to GRD. Crystal growth of potassium dihydrogen phosphate was studied in two solvent mixtures, water and water‐ethanol. The surface roughness was analyzed by atomic force microscopy and the internal crystal perfection by X‐ray diffraction using a synchrotron source. The crystals grown at higher supersaturation have more pronounced and more frequent surface irregularities, supporting previous findings on a feedback mechanism between surface roughness and growth rate. No significant relationship was found between internal crystal perfection and growth rate, however, this is likely due to the size of the crystals analyzed herein and not the absence of any such mechanism in small crystals.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Relationship between Surface Roughness, Internal Crystal Perfection, and Crystal Growth Rate

et al. 2016

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“…The organic linker-BTC can also crystallize to form a needle-like (parallelepiped) crystals when the solution is supersaturated [21]. This size and morphology evolution of BTC crystals can be modeled using population balances [22][23][24][25][26] and measured using experimental tools [27,28]. The morphology of BTC can be described using h-vectors (see Supplementary Information)…”

Section: Concurrent Crystallization Of Btcmentioning

confidence: 99%

Modeling and Simulation of Crystallization of Metal–Organic Frameworks

2019

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Metal–organic frameworks (MOFs) are the porous, crystalline structures made of metal–ligands and organic linkers that have applications in gas storage, gas separation, and catalysis. Several experimental and computational tools have been developed over the past decade to investigate the performance of MOFs for such applications. However, the experimental synthesis of MOFs is still empirical and requires trial and error to produce desired structures, which is due to a limited understanding of the mechanism and factors affecting the crystallization of MOFs. Here, we show for the first time a comprehensive kinetic model coupled with population balance model to elucidate the mechanism of MOF synthesis and to estimate size distribution of MOFs growing in a solution of metal–ligand and organic linker. The oligomerization reactions involving metal–ligand and organic linker produce secondary building units (SBUs), which then aggregate slowly to yield MOFs. The formation of secondary building units (SBUs) and their evolution into MOFs are modeled using detailed kinetic rate equations and population balance equations, respectively. The effect of rate constants, aggregation frequency, the concentration of organic linkers, and concurrent crystallization of organic linkers are studied on the dynamics of SBU and MOF formation. The results qualitatively explain the longer timescales involved in the synthesis of MOF. The fundamental insights gained from modeling and simulation analysis can be used to optimize the operating conditions for a higher yield of MOF crystals.

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“…The widely used nucleation model is the empirical Nyvelt model and its modifications though there are advances in the investigations of crystal nucleation mechanisms using molecular modelling, quantum mechanics, and polythermal method [15]. A stochastic model was proposed to describe the dispersions in crystal nucleation and growth rates by implementing the fluctuations of density and temperature in crystallisation processes to obtain the size and shape dispersions of nuclei with the multi-dimensional maximisation of Gibbs free energy [16]. Clearly further research in this area is needed to accurately quantify the crystal nucleation mechanisms.…”

Section: Crystal Shape and Shape Distributionmentioning

confidence: 99%

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

2016

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Crystal morphology is known to be of great importance to the end-use properties of the crystal product and affect the down-stream processing such as in filtration and drying, but was previously regarded as too challenging to achieve automatic closed-loop control. As a consequence, previous work has focused on control the crystal size distribution (CSD) where the size of a crystal is often defined as the diameter of a sphere that has the same volume of the crystal. This paper reviews very promising new advances made in recent years in morphological population balance models for modelling and simulation of crystal shape distribution (CShD), measurement and estimation of crystal facet growth kinetics, as well as in 2D and 3D imaging for on-line characterisation of crystal morphology and CShD. A framework is presented integrating various components in order to achieve the ultimate objective of model-based closed-loop control of CShD. The knowledge gaps and challenges that require further research are also identified.

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Dispersions in crystal nucleation and growth rates: Implications of fluctuation in supersaturation

Cited by 21 publications

References 13 publications

Relationship between Surface Roughness, Internal Crystal Perfection, and Crystal Growth Rate

Relationship between Surface Roughness, Internal Crystal Perfection, and Crystal Growth Rate

Modeling and Simulation of Crystallization of Metal–Organic Frameworks

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

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