Secondary Nucleation Kinetics Research Articles

In-situ wet milling for particle size control in continuous crystallization: Expanding the attainable region

Continuous mixed-suspension mixed-product removal crystallizer cascades are robust and proven options for continuous manufacturing. However, when applied to a late-stage drug substance the desired particle size could not be achieved due to rapid crystal growth and slow secondary nucleation kinetics. This necessitated a batch terminal milling operation to achieve particle size control (Johnson et al., 2021). To overcome this and to intensify the process, an in-situ high-shear wet mill was integrated into the continuous equipment train to achieve the target physical properties of the drug substance that met the quality and manufacturability criteria needed for the drug product. This article describes the workflow used to optimize the equipment set and operational parameters. Incorporation of a high-shear wet mill operated intermittently in the continuous drug substance process greatly expanded the attainable particle size region, improved product quality, reduced cycle time, and simplified process development and scale-up compared to the process of batch milling after continuous crystallization. Small scale batch milling experiments were used to characterize milling performance at lab and production scales and inform operational space. Several lab-scale continuous runs were then used to define the process operating space and validate the process parameters necessary to meet the particle specifications of the product. Scale-up of the equipment set for in-situ milling was also demonstrated. This approach was tested at lab-scale on representative material operating for 70 h while changing the particle size of the product in real time. This illustrated the potential of intermittent milling for model-free particle size control.

Nucleation and Growth Kinetics of Sodium Chloride Crystallization from Water and Deuterium Oxide

Despite the ubiquity of the crystallization of sodium chloride (NaCl) throughout history, few detailed, well-controlled quantitative studies of the kinetics of NaCl crystallization have been published. Taking advantage of recent advances in technology such as image analysis for crystallite counting and ‘high-throughput’ techniques for characterizing the highly stochastic nucleation process, we report on a detailed examination of the primary and secondary nucleation kinetics of NaCl, crystallized from solution, in water (H2O) and in the isotopologue D2O. We show that crystallization conditions, especially sample agitation, have a very significant effect on crystallization kinetics. We also critically evaluate the workflow employed and the associated nucleation/growth models used to interpret its results, comparing outcomes from NaCl with those from organic crystal systems with which the workflow was originally developed and demonstrated. For primary nucleation, some key assumptions of the workflow and data interpretation are called into question for the NaCl system. Even so, it can still provide direct measurements of secondary nucleation and crystal growth from crystal counting and sizing, providing valuable characterization under consistent controlled conditions to enhance and ‘bring up to date’ the literature on the crystallization of this ubiquitous system.

Estimation of secondary nucleation kinetics of benzoic acid in batch crystallizer

The nucleation and growth kinetics of benzoic acid were determined in a population balance model, describing the seeded batch antisolvent crystallization process. The process analytical technologies (PATs) were utilized to record the evolution of chord length distributions (CLDs) in solid phase together with the concentration decay in liquid phase, which provided essential experimental information for parameter estimation. The model was solved using standard method of moments based on the moments calculated from CLDs and solute concentration. A developed model, incorporating the nucleation and crystal growth as functions of both supersaturation and solvent composition, has been constructed by fitting the zeroth moment of particles and concentration trends. The determined kinetic parameters were consequently validated against a new experiment with a different flow rate, indicating that the developed model predicted crystallization process reasonably well. This work illustrates the strategy in construct a population balance model for further simulation, model-based optimization and control studies of benzoic acid in antisolvent crystallization.

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.

Secondary Nucleation by Interparticle Energies. I. Thermodynamics

Secondary nucleation, in the absence of attrition, is known to be dependent on external fields, such as contact forces, shear, or interparticle forces. In this contribution, the thermodynamic effect of the presence of the seed crystal surface on secondary nucleation is derived in the context of the classical nucleation theory. The Gibbs free energy for the formation of a cluster close to a seed crystal is calculated with the addition of interparticle energies, namely, van der Waals attractive forces and Born repulsive forces. This results in the stabilization of a subcritical cluster close to the seed surface that can become a secondary nucleus more easily than under homogeneous nucleation conditions. Far from the seed surface, the developed model is reduced to the homogeneous nucleation described by the classical nucleation theory. The crystallization of paracetamol from an ethanol solution is taken as a case study, and the stabilization effect, given by the presence of interparticle energies, can be observed at different values of supersaturation. Three key indicators have been defined and calculated to describe the intensity of the stabilization effect, two of which, namely, the distance from the seed surface where the stabilization is active and the enhancement factor for supersaturation, are used in Part II of this series to describe the kinetics of secondary nucleation by interparticle energies.

Secondary nucleation in polymer crystallization: A kinetic view

Secondary nucleation on the surfaces of growing crystals plays a vital role in polymer crystallization, which determines the lamellar thickness at growth front and the radial growth rate. Though secondary nucleation has been intensively studied in the past decades, our understanding on the molecular mechanism and kinetics is not yet complete. In this perspective, we will briefly review the major advances in the secondary nucleation of flexible polymer chains in the past decade and discuss some remained questions from a viewpoint of kinetics. The main theories, thermodynamics and kinetics of secondary nucleation are first summarized. The difference of nucleation of polymer chains from that of small molecular crystals is revealed via analysis of kinetics. Then, the interplay of various microscopic processes leading to the final crystalline structures is discussed, such as lamellar thickening versus widening, intra-chain vs inter-chain nucleation, secondary nucleation versus lateral spreading, secondary vs primary nucleation, nucleation of polymorphisms, and so forth. Finally, some remained open questions are highlighted. Combining kinetic theory considering various microscopic processes and new experimental evidences at different length and time scales would greatly help deepen our understanding on the secondary nucleation during crystallization of flexible polymer chains.

Crystallization with Sinusoidal Modulation of Stirrer Speed: Frequency Response Analysis and Secondary Nucleation Kinetics

In crystallization, obtaining the proper nucleation and growth parameters is essential to the design of crystallization processes. This paper studies the response of crystal size distribution (CSD) to periodic oscillations in the stirrer speed within a mixed suspension mixed product removal (MSMPR) crystallizer. We start from a model in which all processes are coupled. Stirrer speed oscillations drive oscillations in the secondary nucleation kinetics. Oscillations in the nucleation rate drive damped waves in the population distribution of growing crystals. Changes in the population of crystals drive changes in the supersaturation. Supersaturation along with the total mass of crystals influences the nucleation rate. At low frequencies, including the pseudo-steady-state limit, effects of a change in stirring rate are attenuated by the coupling to other processes. At high frequencies, stirring rate oscillations lead to pronounced waves in the CSD that might facilitate studies of secondary nucleation.

Secondary Nucleation Kinetics of AIBN Crystallisation in Methanol: Online Imaging-Based Measurement and Modelling

The secondary nucleation process of 2,2-azobisisobutyronitrile (AIBN) seeded crystallisation in methanol in a stirred tank reactor was studied at varying initial supersaturation levels, temperatures, crystal seed numbers, and stirrer speeds. The average secondary nucleation rate, induction time, and agglomeration ratio were measured using on-line microscopic imaging. The initial supersaturation level, temperature, and stirrer speed were found to be positively correlated with the secondary nucleation rate. A small change in the crystal seed number, i.e., 1-20, did not substantially affect the secondary nucleation rate throughout the secondary nucleation process. An increase in the initial supersaturation level and crystal seed number decreased the induction time, and an increase in the strength of agitation promoted the initiation of secondary nucleation at a stirring rate greater than 250 revolutions per minute (rpm). Temperature exerted a complex effect on the induction time. Regarding the agglomeration ratio, the initial supersaturation level positively correlated with the agglomeration ratio, while the stirrer speed negatively correlated with this parameter. Finally, based on the measured data, the average secondary nucleation rate, induction time, and final crystal suspension density were correlated. This study provides guidance for the control of supersaturation, induction time, stirring, and other factors in the crystal seed addition process in AIBN crystallisation.

Experimental Estimation of Primary and Secondary Nucleation Kinetics of Antisolvent Crystallization As Measured by Induction Time

Methodologies for the estimation of nucleation rate parameters, which are rate constants and orders in antisolvent crystallization, are proposed with the aim of applying to the pharmaceutical indus...

Secondary nucleation and growth kinetics of aluminum hydroxide crystallization from potassium aluminate solution

Aluminate hydroxide crystallization is a significant process in the recovery of aluminum from aluminum-containing ore with an alkaline method. In this work, two kinetics models for secondary nucleation and growth of aluminum hydroxide crystallization from potassium aluminate solution were developed theoretically. The numerical model based on the population balance equation in conjunction with the supersaturation measured by inductively coupled plasma optical emission spectrometry (ICP-OES) was applied to estimate the kinetic parameters of the crystallization. On the other hand, the kinetics were also evaluated by a semi-empirical power model based on the supersaturation of solution and the chord length distribution (CLD) generated by the focused beam reflectance measurement (FBRM). The activation energies for secondary nucleation and growth in the numerical model were estimated as 55.0 kJ mol−1 and 80.0 kJ mol−1, compared to values of 53.3 kJ mol−1 and 131 kJ mol−1 obtained by the FBRM-based semi-empirical power model. The kinetics of secondary nucleation and growth in both models showed around 4.5 and 2 order of dependence on Al(OH)3 (relative) supersaturation, respectively. Furthermore, the comparisons of results of two methods were discussed.

Application of Wet Milling-Based Automated Direct Nucleation Control in Continuous Cooling Crystallization Processes

A novel wet milling-based automated direct nucleation control (WMADNC) concept is proposed and implemented in two continuous cooling crystallization processes in this work. In process 1, WMADNC is implemented upstream to provide closed-loop controlled primary nucleation kinetics and produce seed crystals in situ for continuous mixed suspension mixed product removal crystallizer (MSMPRC). In process 2, WMADNC is applied downstream to achieve closed-loop controlled secondary nucleation kinetics and reduce particle size for crystals in the MSMPRC through recycling. For both processes, a focused beam reflectance measurement (FBRM)-based closed-loop control approach is successfully implemented to control the nucleation kinetics inside the wet mill therefore to control the final chord length distribution (CLD). In the proposed WMADNC approach, the process critical quality attributes (CQA) (e.g., particle number or size) can be directly controlled by the automated closed-loop control framework, which on one hand...

The effects of supersaturation, temperature, agitation and seed surface area on the secondary nucleation of paracetamol in ethanol solutions

This work details the estimation of the secondary nucleation kinetics of paracetamol in ethanol solutions for cooling crystallisation processes, by means of isothermal under-seeded batch experiments. A numerical model, incorporating the population balance equation and the method of moments has been developed to describe the seeding process for a typical cooling crystallisation process, accounting for the primary and secondary nucleation and subsequent crystal growth. Primary nucleation and growth kinetics have been previously evaluated from induction time experiments and isothermal seeded batch experiments, respectively, allowing the secondary nucleation rate to be evaluated for a wide range of experimental conditions. The experimental technique involved the utilisation of two in-situ Process Analytical Techniques (PAT), a Focused Beam Reflectance Measurement (FBRM®) utilised to qualitatively indicate the occurrence of secondary nucleation and an Attenuated Total Reflectance — Fourier Transform Infrared (ATR-FTIR) probe employed for the online monitoring of solute concentration. Initial Particle Size Distributions (PSD) were used in conjunction with desupersaturation profiles to determine the secondary nucleation rate as a function of supersaturation, temperature and crystal surface area. Furthermore, the effects of agitation rate on the secondary nucleation rate were also investigated. Experimental data were compared to the model simulation, with the accuracy of the estimated secondary nucleation kinetics validated by means of the final product PSD and solute concentration.

Crystallization of Pentaerythritol II. Model Experiments

Kinetics of crystallization of the pentaerythritol has been determined in laboratory experiments: MSMPR (Mixed Suspension Mixed Product Removal) crystallizer experiments served for determination of the kinetics of secondary nucleation and of the kinetics of crystal growth.

Iterative parameter estimation for extraction of crystallization kinetics of potassium chloride from batch experiments

AbstractExtraction of crystallization kinetics, the fundamental information which governs the performance of a crystallization process, is characterized by experimental difficulties in MSMPR and mathematical difficulties in batch crystallization. Here, a rigorous approach is taken to estimate kinetic parameters from a batch crystallizer. The two step LaxWendorff technique is adapted for the solution of the population balance in a batch crystallizer and an iterative self‐correcting least squares algorithm is implemented for the estimation of the kinetic parameters. The need for multi‐response estimation as opposed to single‐response from terminal CSD is demonstrated. The kinetics extracted are average ones, representing primary and secondary nucleation kinetics. It is found that the kinetic parameters estimated by multi‐response technique have a superior predictive capability as opposed to those obtained using the terminal CSD only. An advantage of the proposed algorithm is that the measurement of course of supersaturation, which is difficult to perform, is not required.

Estimation of nucleation kinetics from crystal size distribution transients of a continuous crystallizer

Four techniques which can be used for the estimation of nucleation kinetics under unsteadystate conditions are applied to transients of a 20-1 evaporative ammonium sulfate crystallizer. A moment and a Laplace transformation technique appear not to be feasible because they rely heavily on the measurement of the number of small crystals. The present crystal size distribution (CSD) measurement technique is inaccurate in this size range and therefore both methods suffer severely from measurement noise. The third technique, using the method of characteristics, indicates the appearance of so-called secondary nucleation kinetics. The technique is unsuitable for estimating the kinetic parameters quantitatively, again as a result of the measurement noise. Therefore a fourth technique, which uses a non-linear parameter estimation routine, has been developed. This technique is very successful in estimating the parameters in a secondary nucleation model. With the estimated parameters the second and third moments of the CSD can be predicted. If additional moments are to be predicted it is shown that other phenomena which affect the crystal size distribution, such as crystal attrition, must be included in the dynamic model of the process.

Crystallization kinetics of potassium sulfate in an MSMPR agitated vessel

AbstractNew data are reported on the crystallization kinetics of potassium sulfate solutions in a laboratory‐scale continuous MSMPR cooling crystallizer. Population density distributions determined down to 1 μm by laser light scattering and sieve analysis are corrected for the effects of crystal agglomeration and shape variation and are used to determine accurate growth and nucleation rates. The crystal growth rate is strongly size‐dependent, second order with respect to supersaturation, with a high overall activation energy. The surface reaction contribution to the growth process is comparatively large, with a diffusion dependency that increases with crystal size and temperature. While largely consistent with most previous studies, a marked deviation is detected in growth rates at small sizes at which very strong curvature is exhibited in the population density distributions. Secondary nucleation rates vary linearly with suspension density, and the zero size order and activation energy are similar to those of growth but significantly are both much lower at a larger effective size. These observations support the view that growth rate dispersion may be responsible in large part for the substantial variation in reported secondary nucleation kinetics.

Kinetics of secondary nucleation with attrition and the mean size of product crystals from the continuous stirred crystalliser

A form of kinetic equation of nucleation has been proposed expressing also the mechanism of attrition of crystals. In limiting cases this equation expresses the secondary nucleation due to attrition or caused by other mechanisms while both limit expressions are quite different. The resulting relation enables correlation of experimental data also in the case when it is not possible to neglect any of the mentioned phenomena. Relation has been derived for the mean size of product crystals from the MSMPR (mixed suspension, mixed product removal) crystalliser showing that in cases with the prevailing attrition of crystals it might be advantageous to operate at a larger crystalliser output i.e. with a shorter residence time of crystals in the unit.

Measurement and scale‐up of secondary nucleation kinetics for the potash alum‐water system

AbstractSecondary nucleation kinetics for potash alum in draft‐tube baffled crystallizers have been determined from steady state crystal size distributions measured down to about 5 μm. Differences in nucleation rates were found for crystallizers of similar geometry but different capacity. Models relating the frequency of crystal/propeller collisions to crystallizer geometry and operating parameters were compared. In general, these successfully accounted for the observed differences in nucleation rates.

Growth and dissolution of potash alum crystals in the subsieve size range

AbstractOverall growth and dissolution rates of potash alum crystals have been measured over the size range 3 to 70 μm. The derived surface integration growth kinetics, which are found to be linear with respect to supersaturation and strongly size dependent, are evaluated in terms of the step model of crystal growth. The results emphasize the importance of independently measuring growth kinetics before secondary nucleation kinetics can be calculated from MSMPR experiments.

Determination of the kinetics of secondary nucleation in batch crystallizers

AbstractThe kinetics of secondary nucleation have been determined from measurement of the supersaturation as a function of time following the addition of seed nuclei to a supercooled solution in a well‐stirred batch crystallizer. Population balance mathematics have been used to show that the secondary nucleation kinetics may be inferred from the supersaturation‐time curve. The method has been applied to the determination of the kinetics of the secondary nucleation of ice and found to give results in excellent agreement with those obtained from tedious particle counts. In addition, it has been shown that the moment of the particle size distribution that best correlates the nucleation rate data can be inferred from the initial transient of the supersaturation‐time history.