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Modeling and Control of Crystallization

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A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Materials Processes".

Deadline for manuscript submissions: closed (30 June 2019) | Viewed by 53484

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Special Issue Editors

Dr. Christopher L. Burcham

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Guest Editor

Small Molecule Design and Development (SMDD), Eli Lilly and Company, Lilly Corporate Center, Indianapolis, IN 46285, USA

Dr. Meenesh R. Singh

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Guest Editor

Department of Chemical Engineering, University of Illinois at Chicago, Chicago, IL 60607, USA
Interests: integrated CO₂ capture and conversion; electrochemical conversion of N2 to nitrates and ammonia; decarbonization of cement manufacturing; efficient computational methods of studying crystal growth and nucleation
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Special Issue Information

Dear Colleagues,

Crystallization is an industrially important unit operation for the isolation, purification, and synthesis of a wide range of inorganic and organic materials, including pharmaceuticals, agrochemicals, semiconductors, catalysts, metal–organic frameworks, and other fine or specialty chemicals. Developing and subsequently controlling a crystallization process can be challenging and is often complicated by the solute coming from a multicomponent solution and the interactions of the solute with the solvents. Often, it is required that the solids be isolated consistently in a desired polymorphic form or as a specific solvate, while ensuring that high product purity is attained. The control of particle size and shape distribution may also be needed to avoid difficult filtrations, improve the activity of catalysts, modulate band gaps of semiconductors, or ensure product performance. Modeling and control of crystallization is one of the dominant research areas in materials science, with a rapidly growing number of publications at a current rate of ~2000 per year and a citation rate of ~ 17325 per year.

The objective of this Special Issue is to provide an opportunity for scientists and engineers all over the world to publish their latest and original findings on theoretical and practical approaches to the modeling and control of crystallization processes, during both development and routine commercial manufacture. Potential topics include, but are not limited to:

Process analytical technology (PAT) methods and tools that can lead to a more efficient development and control of robust crystallization processes
Case studies and examples of how commercial crystallization processes are developed.
Design and control of crystallization processes
Examples of integration of crystallization with other unit operations—distillation, liquid–liquid separation, membrane separation, solid–liquid separation and filtration, drying, wet milling, reactions
Population balance modeling for nucleation, growth, breakage, and aggregation processes
Computational schemes to simulate the crystallization process
Identification of parameters and kernels to predict size and shape distribution of crystals

Dr. Christopher L. Burcham
Dr. Meenesh R. Singh
Guest Editors

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Published Papers (10 papers)

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Research

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18 pages, 2522 KiB

Open AccessFeature PaperArticle

A Thermodynamic Approach for the Prediction of Oiling Out Boundaries from Solubility Data

by Venkateswarlu Bhamidi and Brendan P. Abolins

Processes 2019, 7(9), 577; https://doi.org/10.3390/pr7090577 - 1 Sep 2019

Cited by 6 | Viewed by 5273

Abstract

Many pharmaceutical molecules, fine chemicals, and proteins exhibit liquid–liquid phase separation (LLPS, also known as oiling out) during solution crystallization. LLPS is of significant concern in crystallization process development, as oiling out can compromise the effectiveness of a crystallization and can lead to operational problems. A comprehensive methodology that allows a process scientist/engineer to characterize the various phase boundaries relevant to oiling out is currently lacking. In this work, we present a modeling framework useful in predicting the binodal, spinodal, and gelation boundaries starting from the solubility data of a solute that is prone to oiling out. We collate the necessary theoretical concepts from the literature and describe a unified approach to model the phase equilibria of solute–solvent systems from first principles. The modeling effort is validated using experimental data reported in the literature for various solute–solvent systems. The predictive methods presented in this work can be easily implemented and help a process engineer establish the design space for a crystallization process that is affected by liquid–liquid phase separation. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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11 pages, 1965 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Modeling and Simulation of Crystallization of Metal–Organic Frameworks

by Anish V. Dighe, Roshan Y. Nemade and Meenesh R. Singh

Processes 2019, 7(8), 527; https://doi.org/10.3390/pr7080527 - 9 Aug 2019

Cited by 15 | Viewed by 8264

Abstract

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. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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17 pages, 9019 KiB

Open AccessFeature PaperArticle

Direct Observation of Growth Rate Dispersion in the Enzymatic Reactive Crystallization of Ampicillin

by Matthew A. McDonald, Andreas S. Bommarius, Martha A. Grover and Ronald W. Rousseau

Processes 2019, 7(6), 390; https://doi.org/10.3390/pr7060390 - 22 Jun 2019

Cited by 9 | Viewed by 4496

Abstract

Prediction and control of crystal size distributions, a prerequisite for production of consistent crystalline material in the pharmaceutical industry, requires knowledge of potential non-idealities of crystal growth. Ampicillin is one such medicine consumed in crystal form (ampicillin trihydrate). Typically it is assumed that all crystals of the same chemical and geometric type grow at the same rate, however a distribution of growth rates is often observed experimentally. In this study, ampicillin produced enzymatically is crystallized and a distribution of growth rates is observed as individual crystals are monitored by microscopy. Most studies of growth rate dispersion use complex flow apparatuses to maintain a constant supersaturation or imprecise measurements of size distributions to reconstruct growth rate dispersions. In this study, the controllable enzyme reaction enables the same information to be gathered from fewer, less complicated experiments. The growth rates of individual ampicillin trihydrate crystals were found to be normally distributed, with each crystal having an intrinsic growth rate that is constant in time. Differences in the individual crystals, such as different number and arrangement of dislocations and surface morphology, best explain the observed growth rates. There is a critical supersaturation below which growth is not observed, thought to be caused by reactants adsorbing to the crystal surface and pinning advancing growth steps. The distribution of critical supersaturation also suggests that individual crystals’ surface morphologies cause a distribution of growth rates. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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11 pages, 2504 KiB

Open AccessFeature PaperArticle

Advantages of Utilizing Population Balance Modeling of Crystallization Processes for Particle Size Distribution Prediction of an Active Pharmaceutical Ingredient

by Tamar Rosenbaum, Li Tan and Joshua Engstrom

Processes 2019, 7(6), 355; https://doi.org/10.3390/pr7060355 - 10 Jun 2019

Cited by 7 | Viewed by 4327

Abstract

Active pharmaceutical ingredient (API) particle size distribution is important for both downstream processing operations and in vivo performance. Crystallization process parameters and reactor configuration are important in controlling API particle size distribution (PSD). Given the large number of parameters and the scale-dependence of many parameters, it can be difficult to design a scalable crystallization process that delivers a target PSD. Population balance modeling is a useful tool for understanding crystallization kinetics, which are primarily scale-independent, predicting PSD, and studying the impact of process parameters on PSD. Although population balance modeling (PBM) does have certain limitations, such as scale dependency of secondary nucleation, and is currently limited in commercial software packages to one particle dimension, which has difficulty in predicting PSD for high aspect ratio morphologies, there is still much to be gained from applying PBM in API crystallization processes. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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15 pages, 8318 KiB

Open AccessArticle

On Molecular Descriptors of Face-Centered Cubic Lattice

by Hong Yang, Muhammad Aamer Rashid, Sarfraz Ahmad, Saima Sami Khan and Muhammad Kamran Siddiqui

Processes 2019, 7(5), 280; https://doi.org/10.3390/pr7050280 - 13 May 2019

Cited by 14 | Viewed by 3819

Abstract

Face-centered cubic lattice

F C C (n)

Face-centered cubic lattice

F C C (n)

has received extensive consideration as of late, inferable from its recognized properties and non-poisonous nature, minimal effort, plenitude, and basic creation process. The graph of a face-centered cubic cross-section contains cube points and face centres. A topological index of a molecular graph G is a numeric amount identified with G, which depicts its topological properties. In this paper, using graph theory tools, we computed the molecular descriptors (topological indices)—to be specific, Zagreb-type indices, a forgotten index, a Balaban index, the fourth version of an atom–bond connectivity index, and the fifth version of a geometric arithmetic index for face-centered cubic lattice

F C C (n)

. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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12 pages, 1363 KiB

Open AccessFeature PaperArticle

Thermodynamic vs. Kinetic Basis for Polymorph Selection

by Benjamin K. Hodnett and Vivek Verma

Processes 2019, 7(5), 272; https://doi.org/10.3390/pr7050272 - 9 May 2019

Cited by 4 | Viewed by 4587

Abstract

Ratios of equilibrium solubilities rarely exceed two-fold for polymorph pairs. A model has been developed based on two intrinsic properties of polymorph pairs, namely the ratio of equilibrium solubilities of the individual pairs (C^*_me/C^*_st) and the ratio of interfacial energies (γ_st/γ_me) and one applied experimental condition, namely the supersaturation identifies which one of a pair of polymorphs nucleates first. A domain diagram has been developed, which identifies the point where the critical free energy of nucleation for the polymorph pair are identical. Essentially, for a system supersaturated with respect to both polymorphs, the model identifies that low supersaturation with respect to the stable polymorph (S_st) leads to an extremely small supersaturation with respect to the metastable polymorph (S_me), radically driving up the critical free energy with respect to the metastable polymorph. Generally, high supersaturations sometimes much higher than the upper limit of the metastable zone, are required to kinetically favour the metastable polymorph. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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13 pages, 1231 KiB

Open AccessFeature PaperArticle

Exploring New Crystal Structures of Glycine via Electric Field-Induced Structural Transformations with Molecular Dynamics Simulations

by Pelin Su Bulutoglu, Conor Parks, Nandkishor K. Nere, Shailendra Bordawekar and Doraiswami Ramkrishna

Processes 2019, 7(5), 268; https://doi.org/10.3390/pr7050268 - 8 May 2019

Cited by 8 | Viewed by 4272

Abstract

Being able to control polymorphism of a crystal is of great importance to many industries, including the pharmaceutical industry, since the crystal’s structure determines significant physical properties of a material. While there are many conventional methods used to control the final crystal structure that comes out of a crystallization unit, these methods fail to go beyond a few known structures that are kinetically accessible. Recent studies have shown that externally applied fields have the potential to effectively control polymorphism and to extend the set of observable polymorphs that are not accessible through conventional methods. This computational study focuses on the application of high-intensity dc electric fields (e-fields) to induce solid-state transformation of glycine crystals to obtain new polymorphs that have not been observed via experiments. Through molecular dynamics simulations of solid-state

α

β

-, and

γ

-glycine crystals, it has been shown that the new polymorphs sustain their structures within 125 ns after the electric field has been turned off. It was also demonstrated that strength and direction of the electric field and the initial structure of the crystal are parameters that affect the resulting polymorph. Our results showed that application of high-intensity dc electric fields on solid-state crystals can be an effective crystal structure control method for the exploration of new crystal structures of known materials and to extend the range of physical properties a material can have. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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16 pages, 3078 KiB

Open AccessFeature PaperArticle

Mechanism and Modelling of Reactive Crystallization Process of Lithium Carbonate

by Shaolei Zhao, Jie Gao, Siyang Ma, Chao Li, Yiming Ma, Yang He, Junbo Gong, Fu Zhou, Bingyuan Zhang and Weiwei Tang

Processes 2019, 7(5), 248; https://doi.org/10.3390/pr7050248 - 28 Apr 2019

Cited by 17 | Viewed by 7999

Abstract

The reactive crystallization of lithium carbonate (Li₂CO₃) from lithium sulfate (Li₂SO₄) and sodium carbonate (Na₂CO₃) solutions is a key process in harvesting solid lithium, whether from ores, brines, or clays. However, the process kinetics and mechanism remain poorly understood and the modelling of the reactive crystallization of Li₂CO₃ is not available. Hence, this work aims to determine the kinetics and mechanisms of the nucleation and growth of Li₂CO₃ reactive crystallization by induction time measurements and to model and optimize the crystallization process using response surface methodology. Induction time measurements were carried out as functions of initial supersaturation and temperature using a laser method. It was found that the primary nucleation mechanism of Li₂CO₃ varies with solution supersaturations, in which, expectedly, the heterogenous nucleation mechanism dominates at low supersaturations while the homogeneous nucleation mode governs at high supersaturations. The transition point between heterogenous and homogenous nucleation was found to vary with temperatures. Growth modes of Li₂CO₃ crystals were investigated by relating induction time data with various growth mechanisms, revealing a two-dimensional nucleation-mediated growth mechanism. The modelling and optimization of a complex reactive crystallization were performed by response surface methodology (RSM), and the effects of various crystallization parameters on product and process performances were examined. Solution concentration was found to be the critical factor determining the yield of crystallization, while stirring speed was found to play a dominant role in the particle size of Li₂CO₃ crystals. Our findings may provide a better understanding of the reactive crystallization process of Li₂CO₃ and are critical in relation to the crystallization design and control of Li₂CO₃ production from lithium sulfate sources. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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12 pages, 5015 KiB

Open AccessArticle

Microstructure and Resistivity Analysis of Silver Nanoparticle-Based Crystalline Conductive Films Synthesized using PEG Surfactant

by Faisal Mustafa, Muhammad Razwan and Saima Shabbir

Processes 2019, 7(5), 245; https://doi.org/10.3390/pr7050245 - 27 Apr 2019

Cited by 14 | Viewed by 4540

Abstract

Silver nanoparticle-based crystalline conductive films were synthesized using a simple and environmentally friendly method centered on chemical reduction. A stoichiometric balance of three different molecular weights of polyethylene glycol (PEG) was used as a capping agent. Resistivity, and its correlation with temperature and the particle size of nanoparticle films, was probed. The silver nanoparticles were characterized using thermogravimetric analysis (TGA) and field emission scanning electron microscopy (FESEM). Further silver films deposited on a glass substrate were characterized by FESEM, Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) and resistivity measurements. Particle size distribution and room temperature electrical conductivity were also investigated. The high conductivity of sintered films suggested applications for the ink-jet printing of electronic circuitry on thermally sensitive substrates. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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Review

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24 pages, 2962 KiB

Open AccessFeature PaperReview

Review and Modeling of Crystal Growth of Atropisomers from Solutions

by Lotfi Derdour, Eric J. Chan and Dimitri Skliar

Processes 2019, 7(9), 611; https://doi.org/10.3390/pr7090611 - 10 Sep 2019

Cited by 5 | Viewed by 4467

Abstract

In this paper, theories on anisotropic crystal growth and crystallization of atropisomers are reviewed and a model for anisotropic crystal growth from solution containing slow inter-converting conformers is presented. The model applies to systems with growth-dominated crystallization from solutions and assumes that only one conformation participates in the solute integration step and is present in the crystal lattice. Other conformers, defined as the wrong conformers, must convert to the right conformer before they can assemble to the crystal lattice. The model presents a simple implicit method for evaluating the growth inhibition effect by the wrong conformers. The crystal growth model applies to anisotropic growth in two main directions, namely a slow-growing face and a fast-growing face and requires the knowledge of solute crystal face integration coefficients in both directions. A parameter estimation algorithm was derived to extract those coefficients from data about temporal concentration and crystal size during crystallization and was designed to have a short run time, while providing a high-resolution estimation. The model predicts a size-dependent growth rate and simulations indicated that for a given seed size and solvent system and for an isothermal anti-solvent addition crystallization, the seed loading and the supersaturation at seeding are the main factors impacting the final aspect ratio. The model predicts a decrease of the growth inhibition effect by the wrong conformer with increasing temperature, likely due to faster equilibration between conformers and/or a decrease of the population of the wrong conformer, if of low energy, at elevated temperatures. Finally, the model predicts that solute surface integration becomes the rate-limiting mechanism for high solute integration activation energies, resulting in no impact of the WC on the overall crystal growth process. Full article

(This article belongs to the Special Issue Modeling and Control of Crystallization)

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