Growth Rate Estimation of β l-Glutamic Acid from Online Measurements of Multidimensional Particle Size Distributions and Concentration

Deconstructing 3D growth rates from transmission microscopy images of facetted crystals as captured in situ within supersaturated aqueous solutions

Here, a morphologically based approach is used for the in situ characterization of 3D growth rates of facetted crystals from the solution phase. Crystal images of single crystals of the β-form of l-glutamic acid are captured in situ during their growth at a relative supersaturation of 1.05 using transmission optical microscopy. The crystal growth rates estimated for both the {101} capping and {021} prismatic faces through image processing are consistent with those determined using reflection light mode [Jiang, Ma, Hazlehurst, Ilett, Jackson, Hogg & Roberts (2024 ▸). Cryst. Growth Des. 24, 3277-3288]. The growth rate in the {010} face is, for the first time, estimated from the shadow widths of the {021} prismatic faces and found to be typically about half that of the {021} prismatic faces. Analysis of the 3D shape during growth reveals that the initial needle-like crystal morphology develops during the growth process to become more tabular, associated with the Zingg factor evolving from 2.9 to 1.7 (>1). The change in relative solution supersaturation during the growth process is estimated from calculations of the crystal volume, offering an alternative approach to determine this dynamically from visual observations.

Automated Growth Rate Measurement of the Facet Surfaces of Single Crystals of the β-Form of l-Glutamic Acid Using Machine Learning Image Processing

Precision measurement of the growth rate of individual single crystal facets (hkl) represents an important component in the design of industrial crystallization processes. Current approaches for crystal growth measurement using optical microscopy are labor intensive and prone to error. An automated process using state-of-the-art computer vision and machine learning to segment and measure the crystal images is presented. The accuracies and efficiencies of the new crystal sizing approach are evaluated against existing manual and semi-automatic methods, demonstrating equivalent accuracy but over a much shorter time, thereby enabling a more complete kinematic analysis of the overall crystallization process. This is applied to measure in situ the crystal growth rates and through this determining the associated kinetic mechanisms for the crystallization of β-form l-glutamic acid from the solution phase. Growth on the {101} capping faces is consistent with a Birth and Spread mechanism, in agreement with the literature, while the growth rate of the {021} prismatic faces, previously not available in the literature, is consistent with a Burton-Cabrera-Frank screw dislocation mechanism. At a typical supersaturation of σ = 0.78, the growth rate of the {101} capping faces (3.2 × 10-8 m s-1) is found to be 17 times that of the {021} prismatic faces (1.9 × 10-9 m s-1). Both capping and prismatic faces are found to have dead zones in their growth kinetic profiles, with the capping faces (σc = 0.23) being about half that of the prismatic faces (σc = 0.46). The importance of this overall approach as an integral component of the digital design of industrial crystallization processes is highlighted.

Process Performance and Operational Challenges in Continuous Crystallization: A Study of the Polymorphs of L-Glutamic Acid

The crystallization of the two polymorphs of l-glutamic acid (LGA) is carried out in a continuous crystallization process, and its performance according to different criteria is evaluated. The study aims at identifying suitable operating conditions for producing either αLGA or βLGA with a high polymorphic purity. To this end, we investigate the process both from a theoretical perspective and through experiments using either a single stirred-tank crystallizer or a cascade of two stirred-tank crystallizers in series. In terms of theory, we extend the MSMPR-based steady-state stability analysis of Farmer et al. (Farmer, T. C. et al. AIChE J.2016, 62, 3505-3514) by accounting for the possibility of a nonrepresentative withdrawal of the solid phase from the crystallizer. Additionally, the process is simulated using population balance equations, thereby investigating the effect of operating conditions on polymorphic purity, yield, and productivity. Guided by the model-based conclusions, we identified suitable operating conditions and experimentally tested them. The experimental campaign has demonstrated that βLGA could be successfully and continuously produced in both process configurations according to the theory with performance as expected, whereas that was not possible for αLGA. The difference between the two stems from different operational challenges, whose consequence is that steady-state operation is attained in the case of βLGA but not in that of αLGA. In the former case, the needle-like βLGA crystals, which exhibit no agglomeration, tend to be only slightly oversampled; in the latter case, the prismatic αLGA crystals undergo major agglomeration and hence are very difficult to suspend and effectively withdraw from the crystallizer.

Secondary Nucleation by Interparticle Energies. III. Nucleation Rate Model

A nucleation rate model for describing the kinetics of secondary nucleation caused by interparticle energies (SNIPEs) is derived theoretically, verified numerically, and validated experimentally. The theoretical derivation reveals that the SNIPE mechanism can be viewed as enhanced primary nucleation, i.e., primary nucleation with a lower thermodynamic energy barrier (for nucleation) and a smaller critical nucleus size, both caused by the interparticle interactions and the associated energy between the surface of a seed crystal and a molecular cluster in solution, as shown in part I of this series. In the case of a sufficiently agitated suspension, the model depends on four parameters: two reflecting primary nucleation kinetics and the other two accounting for the intensity and effective spatial range of the interparticle interactions. As a numerical verification of the model, we show that the nucleation kinetics described by the SNIPE rate model is in quantitative agreement with those given by the kinetic rate equation model developed in part II of this series. A sensitivity analysis of the SNIPE rate model is conducted to present the effect of key model parameters on the nucleation kinetics. Moreover, the SNIPE rate model is validated by fitting the model to the time-resolved data of secondary nucleation experiments as well as to two other, well-known secondary nucleation rate models. Importantly, all of the estimated parameter values for the SNIPE model were consistent with the theoretical estimates, while some of the estimated parameter values for one of the well-known secondary nucleation models deviated from the corresponding theoretical values significantly.

Size measurement and prediction for L-glutamic acid crystal growth during stirred crystallization based on imaging analysis

In this paper, a crystal image analysis method is presented to measure and predict crystal sizes, based on cooling crystallization of β-form L-glutamic acid (LGA) by using an in-situ non-invasive imaging system. The proposed method consists of image restoration, image segmentation, crystal size measurement, and size prediction. To cope with the effects of noise pollution, uneven illumination and movement blurring, the image processing method is conducted for segmenting crystal images captured from the stirring reactor. Thus, the crystal size distribution for crystal population is obtained by using a probability density function. In addition, a short-term prediction method is given for crystal sizes. An experimental study on the cooling crystallization process of β-form LGA is shown to demonstrate the effectiveness of the proposed method.

Growth and Aggregation Regulate Clusters Structural Properties and Gel Time

When particles undergo aggregation, very often they form structures that can be described with fractal geometry concepts. The spatial organization of the particles embedded in these aggregates, quantified by means of their fractal dimension, plays a key role in the clusters' diffusion and aggregation process. Fractal dimensions are typically known for some specific, ideal aggregation scenarios, such as for diluted diffusion limited cluster aggregation (DLCA) or reaction limited cluster aggregation (RLCA). The situation becomes significantly more complicated as soon as the initial particle concentration increases and fractal-dimension changing phenomena, such as particle growth, occur. In this frame, the aim of the present work is twofold: (i) to investigate the clusters' spatial organization in a scenario where growth and aggregation occur simultaneously and (ii) to assess the corresponding aggregation kinetics. To this end, an ad hoc Monte Carlo model has been developed. Both DLCA and RLCA regimes have been explored at several initial primary particle concentrations and for different growth rates. The results were discussed in terms of the characteristic times of growth (τ_G) and aggregation (τ_A), as well as the rate at which the structural properties change, v_R. It was then possible to propose empirical correlations in the form d_m = d_m (v_R) and t_gel = t_gel (τ_A, τ_G) to relate the evolution of the mass mobility exponent d_m and the gel times to the simultaneously occurring processes of growth and aggregation.

Modeling of strontium chloride hexahydrate growth during unseeded batch cooling crystallization by two-dimensional population balance equation

The growth of strontium chloride hexahydrate during unseeded batch cooling crystallization was modeled by the two-dimensional population balance equation.