Crystal Size Distribution Research Articles

Uncertainty analysis of seed recipe for optimal control of crystal size distribution in batch cooling crystallization

Seed recipe is known to directly impact crystal growth behavior and product performance in crystallization processes. However, effectively evaluating and reducing the uncertain influence of seed recipe on product consistency in batch crystallization is challenging. This paper utilizes uncertainty analyses based on the population balance model to evaluate the impact of seed recipe destabilization. Monte Carlo simulation (MCS) was employed as a direct and efficient method to quantify the risk of failing to achieve the desired product crystal size distribution (CSD). Sensitivity analysis was conducted by integrating the modified Morris method with the PAWN method to analyze the effects of individual parameters and all parameters in the seed recipe from local and global perspectives. To achieve the targeted product CSD in the presence of seed recipe uncertainties, a novel linear weighted multi-objective function was developed to establish the optimal cooling profile, which was optimized by the enhanced particle swarm optimization (PSO) algorithm. The results demonstrated that even under seed recipe uncertainties, the targeted product CSD can be achieved with minimal error through cooling profile optimization alone, without dissolution.

Multivariate population balance modeling and simulation of ultrasound-assisted crystallization of a plate-type pharmaceutical: Nucleation, growth, and breakage

The application of ultrasound is recently gaining significant interest in crystallization because of its significant impact on nucleation and growth rates, particle breakage, crystal habit, polymorphism, and crystal size distribution. Pyrazinamide, an essential drug for the treatment of mycobacterium tuberculosis, has four different polymorphic forms. The metastable δ-polymorph exhibit plate-type habit which is desirable for downstream operations compared to commercially available needle-type α-polymorph. This contribution presents a detail experimental and computational study on the effect of ultrasound and its amplitude on nucleation, growth, and breakage of crystals for unseeded batch cooling sonocrystallization of δ-polymorph of pyrazinamide from its 1,4-dioxane solution. A series of sonocrystallization experiments are conducted with different cooling rates and ultrasonic amplitudes and a bivariate population balance model involving crystal nucleation, growth, and breakage is developed and fully validated. The model simulations give important insights on time evolution of mean crystal size and aspect ratio of plate-type crystals.

The Impact of Gravity Waves on the Evolution of Tropical Anvil Cirrus Microphysical Properties

AbstractAnvil cirrus generated by deep convection covers large fractions of the tropics and has important impacts on the Earth's radiation budget and climate. In situ measurements made with high‐altitude aircraft indicate a rapid transition in ice crystal size distributions and habits as anvil cirrus ages. We use numerical simulations to investigate the impact of high‐frequency gravity waves on the evolution of anvil cirrus microphysical properties. The impacts of both monochromatic gravity waves and ubiquitous stochastic mesoscale temperature fluctuations are simulated. In both cases, the interplay between wave‐driven temperature fluctuations, deposition growth/sublimation, and sedimentation causes accelerated removal of both small ice crystals (diameters less than about 10 μm) and large crystals (diameters larger than ≈30 μm). These changes are consistent with the observed evolution of anvil cirrus microphysical properties. The Kelvin effect (higher saturation vapor pressure over curved surfaces) is a critical factor in the anvil evolution, driving mass transfer from small to large ice crystals. The wave‐driven decrease in ice concentration is much faster for typical anvil cirrus detrained at ≃11.5–12.5 km than for less frequent anvils at 15.5–17.5 km because of the strong temperature dependence of deposition growth and sublimation rates. The simulations also show that waves, along with the Kelvin effect, drive growth of mid‐sized (5–20 μm) ice crystals, which is consistent with the observed transition to bullet rosette habits in aging anvil cirrus. We conclude that high‐frequency gravity waves, which are generally not resolved in large‐scale models, likely have important impacts on anvil cirrus microphysical properties and lifetimes.

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Two-Dimensional Population Balance Equations in Crystallization

The population balance equations (PBEs) serve as the primary governing equations for simulating the crystallization process. Two-dimensional (2D) PBEs pertain to crystals that exhibit anisotropic growth, which is characterized by changes in two internal coordinates. Because PBEs are the hyperbolic equations, it becomes imperative to establish a high-resolution scheme to reduce numerical diffusion and numerical dispersion, thereby ensuring accurate crystal size distribution. This paper uses Euler’s first-order explicit (EE) method–Peridynamic Differential Operator (PDDO) to solve 2D PBE, namely, the EE method for discretizing the time derivative and the PDDO for discretizing the internal crystal-size derivative. Five examples, including size-independent growth with smooth and non-smooth distributions, size-dependent growth, nucleation, and size-independent/dependent growth for batch crystallization are considered. The results show that the EE–PDDO method is more accurate than the HR method and that it is as good as the fifth-order Weighted Essential Non-Oscillatory (WENO) method in solving 2D PBE. This study extends the EE–PDDO method to the simulation of 2D PBE, and the advantages of the EE-PDDO method in dealing with discontinuous and sharp front problems are demonstrated.

Preliminary Result on Optimum Seed Generation Bandwidth for Object-Based Image Segmentation (OBIS) of Porphyritic Igneous Thin Sections

Crystal size distribution (CSD) analysis is one of many methods for studying the crystallization history of magma. It involves labor-intensive digitation of all crystals, which may prolong the processing of large data sets. This study presents a preliminary result of Object-Based Image Segmentation (OBIS) as a semi-automatic approach in crystal digitation. Five data sets containing 9 photomicrographs of porphyritic igneous rock thin sections were processed using SAGA GIS. The procedure produced an optimum bandwidth equation of y = 38.455 ln(x) + 114, where x is the average size of sampled crystal in mm. Segmentation tests on another sample using the formula returned good and consistent results with important notes on sensitivity to textures which may result in crystal segment separation, such as fractures, veins, and sieve, as well as the inability to separate all groundmass crystals. Even though it shows good results, this formula only applies where the pixel-to-length conversion factor of 562.2 pixel/mm. Keywords: OBIS, SAGA GIS, Optimum bandwidth, Photomicrograph, Porphyritic igneous rock thin section.

Exploring the separation properties of high-Si CHA membranes for the CO2 capturing technology: Impact of the selective layer thickness and growth mechanism

This study investigates the influence of the CHA selective layer's thickness, coated on a mono-channel alumina support using the secondary growth method, on the performance of CO2 separation from CH4. The membrane layer's thickness was explored by adjusting the concentration and duration of the seeding process, as well as the distribution of crystal size in the suspension. Single gas analysis results revealed that utilizing smaller crystal seeds, with an average crystallite size of approximately 600 nm, exhibited the highest performance. Furthermore, a membrane thickness of 2.1 μm demonstrated an ideal CO2/CH4 permselectivity of 205 with a CO2 permeance of 2.39 x 10-6 [mol/(m2sPa)]. For the equimolar CO2 - CH4 gas mixture, the high-Si membrane displayed a CO2/CH4 selectivity of 210 with a CO2 permeance of 8.06 x 10-7 [mol/(m2sPa)]. In both gas permeation measurement, CO2 permeance exhibited a slight linear decrease with increasing thickness, while CH4 permeance initially decreased and then increased non-linearly.

An open-source robust machine learning platform for real-time detection and classification of 2D material flakes

The most widely used method for obtaining high-quality two-dimensional (2D) materials is through mechanical exfoliation of bulk crystals. Manual identification of suitable flakes from the resulting random distribution of crystal thicknesses and sizes on a substrate is a time-consuming, tedious task. Here, we present a platform for fully automated scanning, detection, and classification of 2D materials, the source code of which we make openly available. Our platform is designed to be accurate, reliable, fast, and versatile in integrating new materials, making it suitable for everyday laboratory work. The implementation allows fully automated scanning and analysis of wafers with an average inference time of 100 ms for images of 2.3 Mpixels. The developed detection algorithm is based on a combination of the flakes’ optical contrast toward the substrate and their geometric shape. We demonstrate that it is able to detect the majority of exfoliated flakes of various materials, with an average recall (AR50) between 67% and 89%. We also show that the algorithm can be trained with as few as five flakes of a given material, which we demonstrate for the examples of few-layer graphene, WSe2, MoSe2, CrI3, 1T-TaS2 and hexagonal BN. Our platform has been tested over a two-year period, during which more than 106 images of multiple different materials were acquired by over 30 individual researchers.

The Effect of Three Factors Interaction on the Size Distribution of White Sugar Crystals in the Batch Vacuum Pan

Crystal size disribution is a parameter used to indicate the quality of sugar crystals obtained from the crystallization process. The better the crystal size distribution, the better the quality of the sugar crystals produced. The good quality of sugar crystals has an impact on the easier separation process that will occur in the centrifugal machine and can reduce sugar loss both in the centrifugal machine and in the sugar grader. The purpose of this study is to determine the effect of the number of sugar seeds, the quality of the mother liquor and the length of time used in the crystallization process on the quality of white sugar crystals produced in the Batch Vacuum Pan and to obtain the best interaction from several levels used for each factor, which can be used as a reference for producing sugar products that have crystal size distribution values according to the desired standard. Each treatment was carried out twice. Observations were made on material characteristics (brix, pol, and purity) and product sugar characteristics (average crystal size and coefficient of variation of crystal size). Measurement of the characteristics of sugar using a sieving (granulometer) which is then calculated using the ICUMSA GS2-37 method. The influence of factor’s main effect and interaction were analyzed using analysis of variance at the level of p value ≤ 0.05. Further tests for each factor’s main effect and interaction with p values ≤ 0.05 were carried out using the Duncan Multiple Range Test (DMRT). The best distribution of sugar crystal size was obtained from the interaction of sugar seed factors with levels of 3 m3, 5 m3, or 10 m3 which interacted with the quality factor of mother liquor (fine liquor + 0 m3 molasses), and 2 hours of cooking time, Where the results of the interaction of this factor produce a percentage of sugar with a size larger than 0.8 mm as much as 80%.

Prediction of temperature-dependent nucleation and growth rates from crystallization-related heat release.

We propose a method for determining the time and, therefore, temperature-dependent relative nucleation and growth rates during crystallization. We do so by linking the partial differential equationgoverning the time dynamics of the crystal size distribution to kinetic (Avrami) parameters describing heat release. This approach is tested in silico by nucleating and growing diffusion limited aggregates with time-varying morphology and growth rates unhindered by impingement. The associated heat release is analyzed, showing that nucleation and growth rates could be extracted with high fidelity.

PEGDA hydrogel microspheres with encapsulated salt for versatile control of protein crystallization

Due to their biocompatibility and adjustable chemical structure and morphology, hydrogels have great potential in many applications, and can be used to enhance protein crystal quality and crystallization efficiency, contributing to biomedicine manufacturing. Monodispersed PEGDA hydrogel microspheres (HMSs) were synthesized using a Lego-inspired microfluidic device. The generated droplets were then UV polymerized, partially hydrolyzed with 0.1 M NaOH solution to improve their absorption capacity, and soaked in a buffer solution containing 0, 0.5, 1, 2, and 4 M NaCl. Salt-loaded HMSs were used as the medium for the enhanced crystallization of hen egg white lysozyme from aqueous solutions. Different supersaturations were achieved in the protein solutions by releasing NaCl of different concentrations from HMSs, as confirmed by electrical conductivity measurements. HMSs with or without NaCl can both provide heterogeneous nucleation sites due to their nano-porous structure and wrinkled surface. The addition of NaCl-loaded HMSs to the protein solution can also increase or decrease the supersaturation in the whole solution or locally near the HMS, leading to controllable nucleation time and crystal size distribution dependent on the NaCl concentration loaded into HMSs.

Controlling Crystal Growth of a Rare Earth Element Scandium Salt in Antisolvent Crystallization

Recovering scandium from hydrometallurgical residue bears the potential of a better supply of an industry depending on imports from countries with more mineral resources than Europe. To recover scandium from unused metal production residue, strip liquors from a solvent extraction process are treated with an antisolvent to crystallize the ammonium scandium fluoride salt (NH4)3ScF6 with high product yields. However, high local supersaturation leads to strong nucleation, resulting in small crystals, which are difficult to handle in the subsequent solid-liquid separation. Reducing local supersaturation makes it possible to reduce nucleation and control crystal growth. Key operation parameters are the concentration of ethanol in the feed and its addition rate. The concentration of the antisolvent in the feed causes a shorter mixing time in the proximity of the antisolvent inlet, which leads to a smaller local supersaturation and therefore less nucleation and more crystal growth. Lowering the antisolvent addition rate enhances this effect. The crystal size distribution during and at the end of the fed-batch process is analyzed by SEM imagery of sampled and dried crystals. To produce reproducible crystal size distribution from SEM images the neural network Mask R-CNN has been trained for the automated crystal detection and size analysis.

Controlled Growth of Highly Defected Zirconium-Metal-Organic Frameworks via a Reaction-Diffusion System for Water Remediation.

The relentless growth of metal-organic framework (MOF) chemistry is paralleled by the persistent urge to control the MOFs physical and chemical properties. While this control is mostly achieved by solvothermal syntheses, room temperature procedures stand out as more convenient and sustainable pathways for the production of MOF materials. Herein, a novel approach to control the crystal size and defect numbers of a dihydroxy-functionalized zirconium-based metal-organic framework (UiO-66(OH)2) at room temperature is reported. Through a reaction-diffusion method in a 1D system, zirconium salt was diffused into an agar gel matrix containing the organic linker to form nanocrystals of UiO-66(OH)2 with tailored structural features that include crystal size distribution, surface area, and defect number. By variation of the synthesis parameters of the system, hierarchical MOF nanocrystals with an average size ranging from 30 nm up to 270 nm and surface areas between 201 and 500 m2 g-1 were obtained in a one-pot synthetic route. To stress the importance of crystal size, morphology, and structural defects on the adsorption properties of UiO-66(OH)2, the adsorption capacity of the MOF toward methylene blue dye was tested with the largest and most defected crystals achieving the best performance of 202 mg/g. The distinctive structural characteristics including the hierarchical micromesoporous frameworks, the nanosized particles, and the highly defective crystals obtained by our synthesis procedure are deemed challenging through the conventional synthesis methods. This work paves the way for engineering MOF crystals with tunable physical and chemical properties, using a green synthesis procedure, for their advantageous use in many desirable applications.

The regulation of organic molecules to the morphology and corrosion protection ability of CaCO3 coating on biomedical MgZnCa alloy

A controllable corrosion rate is an ideal condition for magnesium (Mg) alloy as biodegradable metallic materials. Calcium carbonate (CaCO3) coating has been proven to possess a robust anti-corrosion property for Mg alloy. To further regulate the morphology and corrosion protection ability of the CaCO3 coating, in current study, different organic molecules, including amino acids (Tyr and Glu), amine (DOPA), proteins (COL and BSA) and peptide (CPP), were added into the coating formation electrolyte, affecting the morphology, polymorph composition, and the crystal size distribution of precipitated CaCO3. The results revealed that Tyr exhibited little effect on the polymorph composition of the CaCO3-based coating, while Glu, DOPA, COL and BSA generally promoted the formation of vaterite but inhibited the formation of rod-like aragonite precipitates and calcite in the coatings. In contrast, CPP suppressed the precipitation of CaCO3 crystals because of its high affinity to Ca2+ ions. The addition of those organics reduced the size of calcite crystals. Consequently, the organic molecules mediated CaCO3-based coatings showed better compactness and homogeneity, which maintained the strong adhesion strength of the coatings to the substrate and further enhanced the corrosion protection abilities of the coating for the substrate. The results of the study pave the way for the development of CaCO3-based coatings with advanced properties for Mg alloys as biomedical materials.

Phase composition and luminescent properties of cesium lead bromide perovskite nanopowders

Halide perovskite nanopowders were synthesized by ligand-assisted re-precipitation technique with different volume ratios of mixture solution to antisolvent (toluene). It was found that with an increase in the proportion of toluene, the phase formed as a result of recrystallization changes predominantly from Cs4PbBr6 to the CsPbBr3, while less stable CsPb2Br5 phase was also discovered. The change in the phase composition of powders obtained with different volume ratios of mixture solution to toluene is explained by the salting out effect of slightly soluble compounds. The phase composition had a correlation with the crystal size distribution, as well as with the photoluminescence quantum yield. Optical properties, including absorption spectra, photoluminescence excitation and luminescence spectra were investigated. Nanopowders obtained with a ratio of the mixture of solution to toluene of about 1:0.9 had the maximum quantum efficiency. The following was associated with the formation of low-dimensional CsPbBr3 “slabbed” crystals sticked on rhombohedral Cs4PbBr6 crystals. The composite film based on nanocrystals and thermoplastic polyurethane was made by hot pressing, the potential of its use as a phosphor coating for an ultraviolet LED was shown.

Tuning membrane properties to control supersaturation of antisolvent crystallization

The crystal morphology influences the properties of organic compounds, especially in pharmaceutics such as the dissolution and absorption of drugs in the human cells. In antisolvent crystallization, the crystal size and shape are tied to the degree of mixing and dosage of antisolvent, which could be controlled using membranes with specific morphology/surface properties. Little is known though on the relationship between membrane characteristics, antisolvent mass transfer and crystal properties. Flat sheet polyvinylidene fluoride (PVDF) membranes were prepared using non-solvent induced phase separation, to illustrate the impact of membrane characteristics on the resulting crystal size distribution (CSD) obtained using membrane-assisted antisolvent crystallization (MAAC). The crystallization of glycine was taken as case study. We showed the antisolvent transmembrane flux increased when the membrane thickness decreased, or when the hydrophobicity or the porosity increased. After MAAC operation, membranes had no significant change in surface functional groups, hydrophobicity nor structure. The best-performing membrane was found to have 119° hydrophobicity, 89.4 % porosity and 140 μm thickness, reaching high reproducibility of CSD corresponding to stable transmembrane fluxes throughout 180 min of operation. The capacity of MAAC to consistently produce a narrow CSD at optimum membrane characteristics makes this technology very competitive with conventional crystallization processes.

DISSOLUTION OF A POLYDISPERSE SYSTEM OF PARTICLES IN A NO-FLOW APPARATUS

The processes of dissolution and crystallization are mass transfer phenomena that have a number of complex physicochemical features, and which are very difficult to theoretically describe in various mathematical models. During the dissolution process, the crystals may undergo various changes, such as grinding, combining and crystal growth. As a result of the process of mass dissolution of crystals, different speeds of movement of individual faces can be observed, which can lead to their disappearance. These phenomena are the result of complex dynamics of the dissolution process, which includes inter-actions between solvent molecules and the crystal surface. In this work, the process of mass dissolution was studied using the crystal size distribution density function. The task was set to obtain an analytical solution of the equation. The main object of the study was the diffusion law of movement of the radius of spherical crystals during a periodic process. As part of this study, analytical solutions were obtained for some interesting practical cases related to the process of mass dissolution of spherical crystals and the density function of crystal size distribution. These solutions were described in the article in the form of mathematical formulas and supplemented with graphical data characterizing the main parameters of the process. The use of these analytical solutions can be useful for a more accurate description and improvement of the mass dissolution process itself. Optimizing this process will improve its efficiency, provide more precise control and efficient use of reagents.

Microstructure tuned Na3V2(PO4)3@C electrodes toward ultra-long-life sodium-ion batteries.

Sodium-ion batteries (SIBs) are emerging as the best replacement for Li-ion batteries. In this regard, research on developing a reliable cathode material for SIBs is burgeoning. Rhombohedral Na3V2(PO4)3 (NVP), is a typical sodium super ionic conductor (NASICON) type material having prominent usage as a cathode material for SIBs. In this study, we prepared an NVP@C composite using a one-step hydrothermal method (at 180 °C) and consecutively calcined at different temperatures (750, 800, 850, and 900 °C). All the samples were thoroughly characterized and the changes in the crystal structure and particle size distribution were investigated using a Rietveld refinement method. NVP calcined at 850 °C exhibits the best battery performance with a discharge capacity of 94 mA h g-1 and retention up to 90% after 250 cycles at 2C. It also exhibits remarkable cycling stability with 94% (63 mA h g-1) retention after 2000 cycles at high-rate endurance (10C). The observed electrochemical performances of the samples were correlated with improved electrical conductivity due to the conductive carbon mixing with Na3V2(PO4)3 and enhancement in the crystallinity.

Numerical study of the fluid fracturing mechanism of granite at the mineral grain scale

Hydraulic fracturing is an essential technique for reservoir stimulation in the process of deep energy exploitation. Granite is composed of different rock-forming minerals and exhibits obvious heterogeneity at the mesoscale, which affects the strength and deformation characteristics of rocks and controls the damage and failure processes. Therefore, in this paper, based on the discrete element fluid-solid coupling algorithm and multiple parallel bond-grain based model (Multi Pb-GBM), a numerical model of a granite hydraulic fracturing test is established to study the evolution of hydraulic fractures in crystalline granite under different ground stress conditions. The main conclusions are as follows. The crack propagation of hydraulic fractures in granite is determined by the in situ stress state, crystal size, and mineral distribution, and the ground stress is the main controlling factor. The final fracture mode affects the maximum principal stress and shear stress, and the generation of cracks changes the distribution of the stress field. The hydraulic fracturing initiation pressure decreases with decreasing crystal size. The influence of the crystal size on the crack inclination angle is mainly reflected in local areas, and the general trend of the fissure dip angle distribution is along the direction of the maximum in situ stress. This study not only has important theoretical significance for clarifying the propagation mechanism of hydraulic fractures but also provides a theoretical basis for deep reservoir reconstruction and energy extraction.

Antisolvent Crystallization of Papain

Protein crystallization plays a crucial role in the food and pharmaceutical industries, enhancing product quality and efficiency by improving purity and controlled particle characteristics. This study focused on the crystallization of the versatile protein papain, extracted from papaya. Antisolvent crystallization was performed. This method is cost-effective and is a simple and energy-efficient approach. Beyond protein crystal production, the antisolvent crystallization process serves as a method for encapsulating active pharmaceutical ingredients (APIs). The study investigated organic solvents like ethanol, acetone, and acetonitrile as potential antisolvents. Additionally, the impact of variables such as the solvent-to-antisolvent (S:AS) volume ratio and papain concentration on particle size, particle size distribution, zeta potential, crystallization yield, and residual activity of papain crystals were examined. Ethanol emerged as the optimal antisolvent, reducing the solubility of papain and preserving papain’s crystalline structure with minimal activity loss. Optimal conditions were identified at a 1:4 S:AS volume ratio and a papain concentration of 30 mg/mL, resulting in nanosized spherical crystals with a high yield and preserved activity. This research underscored the crucial role of thoughtful parameter selection in antisolvent crystallization to achieve specific particle characteristics while maintaining the functionality of the crystallized substance.

Performance of membrane distillation assisted crystallization and crystal characteristics for resource recovery from desalination brine

Membrane distillation crystallization (MDC) has been widely studied in recent year for its potential for resource recovery from desalination brine with high concentrations. In this study, crystal samples produced from a bench-scale MDC system have been analysed for crystal morphology, crystal purity and crystal size distribution (CSD). In addition, orthogonal fractional factorial (OFF) experimental design has been introduced to evaluate the influence of various operating conditions on the crystal size and CSD. Feed temperature (40 to 60 °C), crystallization time (60 to 180 min) and the feed composition have been used as the control factors. The results show that the MD in the MDC system maintains a consistent flux of 1.32 to 4.2 kg/m2·h across various feed compositions; higher feed temperatures led to the formation of larger crystal clusters, while longer crystallization time yielded more cubic-shaped crystals; an overall NaCl purity exceeding 99.08 % has been achieved throughout all the experiments; and the increased feed temperature and prolonged crystallization time results in a narrower CSD. The result of OFF experimental design identifies feed temperature as the dominant factor affecting crystal size and CSD. However, the presence of impurities in the feed water could pose challenge to the thermal stability and longevity of the membrane.