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Automated and Material-Sparing Workflow for the Measurement of Crystal Nucleation and Growth Kinetics

  • Ryan J. Arruda
    Ryan J. Arruda
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
  • Paul A.J. Cally
    Paul A.J. Cally
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
  • Anthony Wylie
    Anthony Wylie
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
  • Nisha Shah
    Nisha Shah
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    More by Nisha Shah
  • Ibrahim Joel
    Ibrahim Joel
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    More by Ibrahim Joel
  • Zachary A. Leff
    Zachary A. Leff
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
  • Alexander Clark
    Alexander Clark
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
  • Griffin Fountain
    Griffin Fountain
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
  • Layane Neves
    Layane Neves
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    More by Layane Neves
  • Joseph Kratz
    Joseph Kratz
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    More by Joseph Kratz
  • Alpana A. Thorat
    Alpana A. Thorat
    Pfizer Worldwide Research and Development, Groton, Connecticut 06340, United States
  • Ivan Marziano
    Ivan Marziano
    Pfizer Worldwide Research and Development, Sandwich, Kent CT13 9NJ, U.K.
  • Peter R. Rose
    Peter R. Rose
    Pfizer Worldwide Research and Development, Groton, Connecticut 06340, United States
  • Kevin P. Girard
    Kevin P. Girard
    Pfizer Worldwide Research and Development, Groton, Connecticut 06340, United States
  • , and 
  • Gerard Capellades*
    Gerard Capellades
    Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    *Email: [email protected]
Cite this: Cryst. Growth Des. 2023, 23, 5, 3845–3861
Publication Date (Web):April 3, 2023
https://doi.org/10.1021/acs.cgd.3c00252

Copyright © 2023 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

The development of digital twins for model-based crystallization process development is often limited by the associated material-intensive and time-intensive experimental screenings. Methods for measuring primary nucleation rates are well established and common practices for academic studies; however, methods for the measurement of secondary nucleation and crystal growth rates are often inconsistent due to differing strategies in the selection of supersaturation models, particle size measurement techniques, and investigated scales. We hereby provide a workflow of automated methods for the experimental screening, data analysis, and parameter estimation for secondary nucleation and crystal growth kinetics in solution crystallization. The methods have been integrated with common experimental protocols in the determination of induction times for primary nucleation and with the use of commercially available tools that can be found in crystallization laboratories across academia and industry. These tools include a Technobis Crystalline as well as process simulation software, currently tailored to gPROMS FormulatedProducts. The methods have been demonstrated for two well-known model systems: antisolvent crystallization of acetaminophen from ethanol–water mixtures and cooling crystallization of a metastable polymorph of l-glutamic acid from water. The presented workflow will serve as a basis to standardize the analysis of crystallization kinetics for new systems, generating kinetic trends using similar methods that would aid in early process development as well as in academic studies.

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Synopsis

A methodology is presented for the rapid measurement of nucleation and growth kinetics using automated experiments in a Technobis Crystalline. This is done from image analysis data processed in Microsoft Excel and population balance models implemented in gPROMS FormulatedProducts.

Introduction

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Crystallization as a separation process plays a critical role in the manufacturing of bulk chemicals, food products, pharmaceuticals, and fine chemicals. Generally, crystallization process development serves one of two objectives: purification, or isolation of a solid with the desired crystal size, form, and structure. (1) These crystal quality attributes define the properties and behavior of the crystallized powder, including stability, processability, and dissolution behavior. (2,3) Ultimately, they depend on the history of the process and a delicate balance between nucleation and crystal growth kinetics.
Despite crystallization being one of the oldest separation processes, the mechanisms for nucleation and crystal growth are still poorly understood. Model-based process development suffers from major challenges, including poor scalability of nucleation rates and the lack of quantitative knowledge on the effects of system-specific solvents and process impurities on kinetics. (4−6) Consequently, process development is characterized by extensive experimental screenings over a narrow design space, where the solvent composition is selected based on solubility and then rarely varied, and the role of impurities is either neglected or investigated for a fixed composition. Mathematical models usually employ mass balances and population balances derived from first principles, but they are driven by empirical models for kinetics that are composition-dependent and subject to simplifications from limitations in our measurements of crystal growth. (7) These empirical models can be extremely useful in process development, but they are bound to a narrow space that is often suboptimal. For example, small variations in solvent composition can have a significant impact on crystallization kinetics. (5) Neglecting these solvent effects and designing antisolvent addition profiles based on solubility only will often lead to a significant limitation in the attainable crystal quality attributes. (8)
Many of the aforementioned challenges stem from the limited availability of representative crystallization feed in the early stages of process development and the typical length of experimental screening. A typical continuous crystallization experiment for screening nucleation and growth kinetics can take 1–2 work days to complete and analyze and utilizes feed material at the 1–5 L scale due to the time required to reach a steady state. (9−12) Manuscripts modeling crystallization kinetics will require a large number of experiments (usually 5–15 independent experiments), depending on whether they measure the effects of temperature and suspension density on kinetics. At the end of the screening, they will obtain crystallization kinetics for a very specific solvent composition and impurity profile. This is also assuming that experiments are not lost due to fouling, form transitions, or classification, and that the system does not exhibit behaviors like agglomeration, breakage, or size-dependent growth that would require more experiments to model. (13−15) Overall, it may take months and dozens of liters of feed material to calibrate a crystallization model, something that is intractable in early process development where the representative crude material (including synthesis impurities) is only available at the 10–100 mL scale and continues to vary as the synthesis steps are optimized. (16,17) This leads to a trade-off between the effects of scale and composition: one can study kinetics using representative crude, at a 1–10 mL scale for which kinetic parameters would not be scalable to industrial scales, or study kinetics using purified or recycled material at the 100–1000 mL scale, obtaining kinetics that are more representative of a larger scale, but ignoring solvent and impurity effects that may still appear during scale-up and implementation.
On the academic side, high-throughput methods that measure crystallization kinetics have played a central role in developing our understanding of the mechanisms behind nucleation and crystal growth. Nucleation studies are typically centered on primary nucleation using induction time experiments. These typically take place in small systems (volume < 5 mL) and consist of multiple dissolution and crystallization tests via heating and cooling cycles. Following a significant number of replicates, usually at the order of 100 for 1 mL scales, one can determine the rate of primary nucleation using induction time statistics. (18,19) These studies have become a central part of nucleation research, leading to the development of multiple setups to investigate induction times under stagnant, stirred, or flow conditions and at multiple scales. (20−24) More recently, Briuglia et al. presented a novel method to collect secondary nucleation kinetics from seeded experiments at the 5 mL scale, tracking the number of crystals per picture using in-line image analysis and assuming constant supersaturation during the early stages of crystallization. (25) The method allows for the investigation of seed size and fluid dynamics on secondary nucleation, opening the door to novel studies on the industrially dominant but rarely investigated secondary nucleation mechanisms. On crystal growth, most studies at the small scale are based on single crystals, often using flow cells and image analysis to investigate face-dependent growth. (26−28) Alternative studies utilize bulk powder, tracking desupersaturation profiles or crystal size distributions from batch and continuous crystallization data. (29,30) However, we do not yet have unified methods to simultaneously study primary nucleation, secondary nucleation, and crystal growth for the same system, and the available methods for secondary nucleation and crystal growth are often material- and labor-intensive.
In this work, we have developed a set of methods to standardize the collection of crystallization kinetic data using commercial tools that are commonly available in crystallization laboratories. The entire experimental screening for secondary nucleation and crystal growth can be completed in less than 48 h, using material at the 1–10 g scale and employing only the necessary amount of human intervention for quality control. The goal is not to replace existing methods of parameter estimation in more industrially relevant scales but instead to provide a feasible methodology for characterizing system behavior when materials are in short supply, for early screenings requiring multiple sets of conditions (e.g., solvent compositions or temperatures), and for fundamental studies where scalability is less of a concern. For industrial process development, these methods do not solve the issue of scalability, but they offer an efficient alternative to studying trends (including composition effects) that would inform the shortlisting of experimental conditions that need to be investigated at a more relevant scale. Their main advantage comes from saving critical materials and their mostly automated and reproducible data collection strategy. This paper includes a comprehensive description of the methods and the theory behind them, followed by applications in two case studies with well-known but distinct systems: (i) antisolvent crystallization of acetaminophen and (ii) cooling crystallization of a metastable polymorph for l-glutamic acid.

Overview

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The presented methods can be divided into three steps (Figure 1): (i) experimental data collection, (ii) data processing, and (iii) parameter estimation. The first step involves a set of automated batch crystallization experiments conducted in a Technobis Crystalline. The system is programed to run dissolution–crystallization cycles via heating and cooling, in a similar way as it is done for induction time experiments, and to collect imaging data during crystallization events. The presented methods suggest 4 replicate runs at 4 different supersaturations, for a total of 16 experiments per studied temperature and solvent composition.

Figure 1

Figure 1. Methods overview including the required hardware and software for each step.

In step 2, the obtained data is processed using Microsoft Excel to obtain trends for the total number, length, area, and volume of crystals captured on camera during each crystallization event. A spreadsheet has been built to automatically find the start and end of the event, remove outliers from the data set based on user-defined metrics, and provide suggested initial conditions for parameter estimation.
In step 3, solubility curves as well as experimental trends at four different starting supersaturations are implemented to gPROMS FormulatedProducts (Siemens Process Systems Engineering) and used to determine the kinetic parameters for secondary nucleation and crystal growth.
At the expense of longer experimental screenings, these methods can also be combined with the established methodology for the determination of primary nucleation rates from induction times, which often uses the same hardware. (18) The only difference is that more replicates would be needed, extending the experimental screening from 1–2 days to approximately 1 week. If the methodology is expanded to include induction time studies, users should be aware of the limitations of those methods for systems with high nucleation rates or with significant variance in detecting the nucleation event, as discussed in recent literature. (31,32)
With sufficient planning and a modest amount of preliminary knowledge on the compound’s approximate solubility and kinetic behavior, the bulk of experimental data collection can be conducted largely unattended and within 1–2 days, obtaining solubility points as well as kinetic parameters from 16 crystallization experiments at 4 different starting supersaturations. These parameters will be bound to one studied temperature and solvent composition. Thus, larger screenings may be necessary to screen multiple temperatures or solvent compositions (e.g., for antisolvent crystallization with sequential additions).

Theory

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Data Collection

The bulk of experimental data is collected using a Technobis Crystalline. This equipment has eight parallel batch crystallizers as 8 mL vials, each with independent temperature control and overhead mixing capabilities. Each crystallizer can be operated independently and programed to follow a given heating/cooling profile. To monitor the crystallizing suspension, each crystallizer is equipped with a laser and detector that measures sample transmissivity (indicative of dissolution and crystallization events) and with microscope cameras paired with an image analysis program. These cameras can operate with a capture rate currently limited to up to 1 image/second. During a crystallization event, the equipment’s software processes each of the images, counting the number of crystals on camera and classifying them in size channels to generate a crystal size distribution. The instrument reports crystal size as the diameter of a circle with the same projected area as the captured crystal. As crystallization progresses, the total number and area of the crystals on camera increases following nucleation and crystal growth, and these metrics will be proportional to the total number and area of the crystals in suspension. This is true as long as the system is well mixed (imaging a representative suspension sample) and only for dilute systems (start of crystallization) until overlapping crystals start to be identified as a single entity by the image analysis program. When this happens, the total number of “crystals” detected will start decreasing instead (Figure 2). This limitation is one of the reasons why the experiments are not seeded as the camera quickly gets saturated even at low suspension densities (appr. 1% solids). Seeded experiments are possible, but they require very careful execution and are not suitable to be combined with automated dissolution–crystallization cycles. By starting from an unseeded system, several minutes of crystallization trends can be captured before the camera gets saturated. In addition, multiple replicates can be run unattended, providing further data points as needed for fast-crystallizing systems.

Figure 2

Figure 2. Example event for crystallization of l-glutamic acid from water, tracking the increase in the total number of crystals per picture and the subsequent drop due to crystal overlap. Only the highlighted area is considered acceptable for parameter estimation, covering an active crystallization event for a dilute system.

Several conditions can lead to a bias in the particle size analysis: the measurement of crystals out of focus, randomly overlapping crystals (even for dilute samples), and the inherently small sample size. Thus, the crystal size distributions must be studied not as an isolated metric but as trends that represent projections of nucleation and crystal growth. This is common practice for kinetic studies where similar biases are encountered (e.g., chord length distributions where a single crystal could present vastly different “sizes”), (33,34) where the estimated kinetics are not disconnected from the analytical technique used for estimating crystal size. Here, the proposed methods are based on moment trends where the number and area of crystals on camera change by orders of magnitude throughout an event, and kinetics are estimated from the rate of change rather than a specific size distribution.

Processing Imaging Data

The Crystalline exports imaging data as a particle size distribution for each captured image. For a given crystallization event, one can calculate the total number of crystals in a picture as the sum of counts for the equivalent size distribution. A 15-point moving average for this metric (equivalent to a modest 15 s crystallization period) can be used to find a baseline for the experiment as well as the start of crystallization. Starting points for the moving average, at event times where crystallization rates are negligible (e.g., first 2 min in Figure 2), will define the baseline of “crystal” measurements/picture detected before crystallization started. These may come from suspended dust or background noise. In Figure 2, this background was Nmin = 4 crystals/picture. The maximum value for the moving average will define the critical point where a change in slope is observed owing to the saturation of the camera due to crystal overlap. For Figure 2, this happens for a moving average of Nmax = 190 crystals/picture at t = 14.1 min. Equation 1 calculates the maximum range of values between the baseline and the saturation point for the camera
ΔN=NmaxNmin
(1)
Using the total change from background to saturation (ΔN), experimental trends can be cropped for parameter estimation following standardized metrics and a conservative range. In this work, the data was cropped from the time when the moving average reached 10% of ΔN above the baseline (eq 2) and until the moving average reached 80% of ΔN above the baseline (eq 3). This is to ensure that kinetics are estimated for a sufficient crystal population where secondary nucleation is not limited by a low crystal count and that measurements are stopped far before the camera gets saturated.
Nstart=Nmin+0.1ΔN
(2)
Nend=Nmin+0.8ΔN
(3)
For the cropped time range, the total number (Ntot), length (Ltot), area (Atot), and volume (Vtot) of crystals captured on each picture can be determined from eqs 47, respectively.
Ntot=ichannelsNi
(4)
Ltot=ichannelsNiLi
(5)
Atot=ichannelskaNiLi2
(6)
Vtot=ichannelskvNiLi3
(7)
Here, Ni is the number of crystals seen in the picture, for the size channel i and Li is the size of the channel, expressed as the diameter of the equivalent circle with the same projected 2D area as the detected crystals. ka and kv are area and volume factors that depend not just on crystal shape but also on the orientation of the crystals on camera and on what is obtained as the characteristic crystal dimension (Li). For randomly oriented cubic crystals presenting a squared 2D projection, and a characteristic length that is not the side of the cube but a projected circle diameter instead, these values were estimated in eqs 8 and 9.
ka=32π
(8)
kv=(π4)3/2
(9)
A full derivation for these shape factors and for the model can be found in the Supporting Information. Ultimately, the total number, length, area, and volume of the crystals on camera are projections of how the suspended crystals nucleate and grow. With the appropriate models, these projected metrics can be used to estimate the nucleation and growth kinetics of the captured system.
Here, note that the Crystalline only captures two independent metrics: the number of crystals in a picture (projection of nucleation) and the area of those crystals (projection of crystal growth that is also affected by nucleation). Four metrics can be calculated, but Ltot, Atot, and Vtot are not independent. For parameter estimation, only the total number and area of the crystals will be used. The others will only play a role in determining the initial conditions for the experiment.

Batch Crystallization Model

For a batch crystallizer with negligible agglomeration or breakage, the moments of the crystal population evolve according to a set of differential equations as described in eq 10. (30,35)
dμjdt=0jB+jGμj1
(10)
where μj(μmj/g) represents the j’th moment, B(g1s1) is the rate of crystal nucleation, and Gm/s) is the unidimensional crystal growth rate, projected as the change in the observed dimension over time. For the experiments in this work, crystal growth is seen as a projection of a changing crystal area, expressed in a single dimension (Li) as the equivalent diameter of a circle with the same projected area as the growing crystal.
The zeroth moment of the distribution (μ0, g–1) represents the total crystal concentration in the sample (number of crystals/g suspension), and the first moment (μ1, μm/g) represents the total length of the crystals (if they were to be placed side by side) per gram of suspension. With the appropriate shape factors (ka and kv), the second (μ2, μm2/g) and third (μ3, μm3/g) moments of the distribution become projections of the total crystal area and the total crystal volume in 1 g of suspension, respectively. Equation 10 can be solved with initial conditions for the crystal moments, and with experimental trends in how those moments change over time, the kinetics can be calibrated. The kinetic expressions for secondary nucleation (B, g–1 s–1) and crystal growth (G, μm/s) can be expressed as a function of the evolving supersaturation (σ) and solids concentration (MT, g/g) as in eqs 11 and 12. The choice of a secondary nucleation model is based on the fact that, during the exported kinetic trends (Figure 2), the system is seeded with negligible primary nucleation rates (as evidenced by the induction times in the order of several minutes or hours).
B=kbσbMTj
(11)
G=kgσg
(12)
Here, kb(g1s1),b,j,kg(μm/s) and g are kinetic parameters, unique for the specific conditions of solute (including form), solvent, temperature, and mixing. Due to the inherent noise in imaging data, the methods hereby described recommend at least four experiments to estimate values for kb and kg. Because these parameters depend on mixing, temperature, and solvent composition, all the experiments should be conducted at constant conditions, varying only the total solute concentration (starting supersaturation) between runs. The values for b and g are typically assumed to be 2 and 1, respectively. (7,36) Similarly, j usually takes values between two-thirds and 2. For secondary nucleation driven by crystal-impeller and crystal-wall collisions, values of j closer to 1 are expected. If secondary nucleation is driven by crystal–crystal collisions, a second-order dependence is expected instead. (37) This work is based on modeling kinetics in dilute systems with limited crystal–crystal collisions. Thus, j is assumed to have a value of 1.
The expression for supersaturation is also an important choice for the nucleation and growth models. Multiple simplifications of the thermodynamic measure of supersaturation can be found in the literature. Some of these simplifications were made to circumvent the difficulty in measuring activity coefficients, while others were mathematical simplifications that dropped a logarithm under the assumption that the system is near equilibrium. Aside from the fact that using different expressions to calculate supersaturation leads to inconsistencies between parameters estimated by different groups, some of those simplifications can lead to errors of over 500% in the estimation of kb and kg, even for near-equilibrium systems. (29,38) In this work, where significant variations in supersaturation are expected within the batch experiments, we have used the thermodynamic expression for supersaturation (Equation 13) and the methods described by Schall, Capellades, and Myerson for the estimation of activity coefficients. (38)
σ=ln(γxγsatxsat)
(13)
where x (mol/mol solution) and xsat(mol/mol solution) are the mole fraction mother liquor concentration and solubility, respectively. γ and γsat are dimensionless activity coefficients for the supersaturated solution and for the saturated state.

Projected Experimental Moments

Even if the system is dilute (negligible crystal overlap on camera) and well mixed (representative sampling), the Crystalline does not measure distribution moments directly. Instead, only a projection of those is provided on camera. The crystals captured in an image will indeed have a specific size, area, and volume, but what is seen is only a projection of the total number and area on a small sample mass that is being captured and processed by the image analysis algorithm. We can define this mass using a proportionality constant, θ (g/picture), with its value representing the total mass of suspension seen in a single picture. This constant will depend on the camera’s magnification, with varying capture areas and imaging depth depending on the chosen hardware. It is also expected to vary slightly between systems owing to a varying imaging depth (autofocus), solution density, and optical properties of the system (including refractive index for the solvent and crystals).
For systems presenting a constant solvent composition and a similar size range, approximate values of θ can be estimated for a given magnification and later refined during parameter estimation. This work uses a 4 μm/pixel magnification, covering a maximum picture area of 4.9 mm2 and a capture depth that could fall anywhere from 500 μm to 3 mm. These broad boundaries are approximated based on the appearance of the different types of impellers on camera. Assuming an approximate solvent density of 1 mg/μL, lower and upper bounds for θ were set within the broad range of 1 mg/picture to 15 mg/picture, with 7 mg/picture as the initial guess. Parameter estimation converged at θ values of 5.45 ± 0.09 mg/picture and 5.65 ± 0.06 mg/picture for acetaminophen and glutamic acid, respectively. Here, it is important to note that this value is different from the total mass of the system that is in focus: (i) crystals slightly out of focus are still measured by the algorithm and (ii) because crystals hitting the image bounds are neglected from image analysis, the effective image area that is analyzed is smaller than the total image area (see Figure 2 for examples of both). These make the estimation of a universal θ a complicated endeavor and reinforce the fact that the exact value is, within reasonable boundaries, system-dependent (e.g., particle size range, or habit). The moments projected on camera depend on θ, following 14.
Ntot=μ0θ
(14)
Ltot=μ1θ
(15)
Atot=kaμ2θ
(16)
Vtot=kvμ3θ
(17)
Combining eq 10 with 14, the total number, length, area, and volume of the crystals projected on camera can be expressed as a function of crystallization kinetics and the proportionality constant θ, following eqs 1821.
dNtotdt=Bθ
(18)
dLtotdt=GNtot
(19)
dAtotdt=2GkaLtot
(20)
dVtotdt=3GkvkaAtot
(21)
Provided with initial conditions where the suspension density is not negligible (eq 11 requires MT > 0), which can be obtained from a moving average at Nstart (Figure 2), experimental data for Ntot and Atot over time and for ≥4 crystallization events at different starting points can be used to estimate the nucleation and growth parameters kb and kg. A full model description including gPROMS nomenclature and the code structure can be found in the Supporting Information. The necessary experimental data and their placement in model calibration are summarized in Figure 3.

Figure 3

Figure 3. Block diagram of the data flow for estimation of kinetic parameters in the gPROMS model, including necessary experimental data and its potential sources.

Methodology

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Hardware

The presented methods are tailored for a Technobis Crystalline using 4 μm/pixel cameras. Samples with the desired solute concentration are loaded into 8 mL vials with overhead stirring. The typical sample size includes 5.5 g of the solvent. Volumes may be adjusted for different systems, but large samples are preferred to mitigate evaporation at the headspace and to minimize induction times. (39) A hook-shaped stirrer was used in this work, but the methods are not bound to a specific choice of stirrer.

Selection of Crystallization Conditions

The first step is to select a range of reasonable crystallization conditions for the system that needs to be studied. Here, preliminary knowledge of solubility values or crystallization behavior (e.g., tendency to aggregate or polymorphism) is an advantage that is often available from early crystallization screening. The end goal of this step is to select a reasonable temperature, solvent composition, and four reasonable starting supersaturations for data collection. The selection of temperature and solvent composition depends on the overall plans for the process (batch vs continuous, cooling vs antisolvent, one vs multiple stages...), so they need to be evaluated in context with process development plans. The methods hereby described estimate values for kb and kg and both are solvent-dependent and temperature-dependent. If testing those factors is part of the screening, the methods can be repeated for each potential combination.
Once a desired crystallization temperature and solvent composition have been selected, four starting solute concentrations can be used for the kinetic screening. We recommend selecting a broad range of solute concentrations that meet the following criteria:
  • Concentrations 5 mg/g above the solubility value at the chosen temperature and solvent composition. This is to ensure a minimum suspension density (MT > 0.5 wt % at equilibrium) that meets a reasonable signal-to-noise ratio during image analysis. Low suspension densities can lead to trends that are difficult to differentiate from the baseline (NNmin).

  • Average induction times between 5 min and 3 h. Currently, the Crystalline has a limit in the file size for data collection of approximately 1 gigabyte, which is filled with approximately 4 h of image collection at 1 image/second. The induction time should be predictable within a 1 hour window so that four events can be captured on camera at 1 image/second, without incurring storage space limitations for the imaging data. Because four replicate runs are conducted on average at each concentration, it is not necessary that every event is captured on camera. If no knowledge of induction time behavior is available but the solute is a small molecule, it is recommended to start a run with concentrations approximately 1.5 times the solubility value and extend the capturing range to 5 h to get ballpark values of the induction time. The other 2–3 concentrations can be adjusted based on the results of this run.

  • Batch crystallization times longer than 1 min, to ensure a sufficient amount of data in a given event. Again, if no knowledge of crystallization kinetics for the solute is available, it is recommended to run a first experiment with concentrations 1.5 times the solubility (for small-molecule systems) and adjust future concentration values accordingly. Larger molecules may require higher supersaturations to reach a reasonable induction time. Systems presenting crystallization times under 1 min will require a higher number of replicated events to get accurate trends.

  • Concentrations for which the saturation temperature is not higher than 10 °C below the boiling point of the solvent so that the solute can be dissolved by the Crystalline using heating (crystallization event must start from a clear solution). If this is not possible (e.g., systems with a flat solubility curve), crystallization can be triggered using antisolvent addition at the expense of more random error due to manual intervention.

Within those constraints, concentration values can be adjusted to be evenly spread across a reasonable range for the process. Here, it is also important to ensure that differences in supersaturation are large enough between concentrations so that clear trends can be provided for parameter estimation. If the range is too narrow, there will be a significant overlap between the measured imaging trends at different supersaturations. In these cases, it may be impossible to break the correlation between the kinetic parameters and θ without expanding the range of experimental conditions. This, again, can be rapidly seen during the first test and adjusted accordingly.
The models in this work are adjusted assuming that concentrations will be taken as mg solute/g solvent. Mass-based metrics are considered more robust with varying temperatures and solvent compositions (not sensitive to a changing density), and recipes are easy to program and follow when the fractions are provided on a solvent basis instead of a total solution basis.

Crystalline Program

The Crystalline program for kinetic screening is provided in Table 1. Following this program, samples are subjected to four heating/cooling cycles where they are first fully dissolved and then crystallized, mimicking typical induction time experiments. Typical stirring speeds are set at 1000 rpm to minimize induction times, but they can be adjusted for each system to ensure that solids are fully suspended and to prevent crystal deposition on the vial cap. Note that nucleation kinetics depend on mixing speed; thus, the chosen value must be consistent between runs. The four replicates serve multiple purposes: (1) to quantify the reproducibility of the kinetic trends, (2) to detect outliers from a different crystallizing polymorph, and (3) to buffer the fact that some events may not happen or be captured on camera, owing to the stochasticity of induction times.
Table 1. Recommended Crystalline Program Containing Four Crystallization Cycles and a Polythermal Solubility Test. For the Measured Sample, This Program Should Give up to Four Crystallization Events (See Repetitions on the Last Column) and One Accurate Solubility Value (Last, Slow Heating Ramp)
a

Crystallization temperature (Tc) and maximum temperature (Tmax) need to be adjusted for each compound, based on desired crystallization conditions and expected sample solubility. For safety reasons, Tmax should not exceed the boiling point of the solvent.

b

This value is there to minimize storage space limitations, and it needs to be adjusted to be the minimum induction time expected for the sample. It defines at which point the camera will start recording at 1 picture/second.

At the end of the fourth crystallization cycle, the sample is slowly heated at a rate of 0.05 °C/min, obtaining a polythermal solubility value at a slow heating rate. (40) This is to minimize the effect that dissolution kinetics may have on the obtained value, using slower heating rates than those already demonstrated in prior work. (41) Estimating solubilities near the saturation temperature of the samples is important in order to calculate activity coefficients and supersaturation. This step will also help in identifying potential polymorphs due to their extended duration and the broad range of investigated temperatures. The last step of the program involves cooling the system down to room temperature. This does not provide any data, and it does not have to be completed; it is a quality-of-life step to ensure that if the system is left unattended at the end of the program, the sample would have recrystallized as a stirred suspension. Stopping a program with a hot, supersaturated system would stop the impellers and let the solute crystallize unagitated, often leading to encrustation that is difficult to clean from the impeller.

Exporting Data

At the end of the program, users need to carefully inspect the resulting data before exporting it for analysis. Temperature and transmissivity should follow the trends illustrated in Figure 4, presenting up to four crystallization events (drops in transmissivity) and full dissolution between events. Users should place particular focus on the following.
1.

Navigate the images to check that all crystallization events started from a clear solution, that the first crystals formed at the desired crystallization temperature (Tc), and that the entire crystallization event happens at this constant temperature. In addition, check that the crystal habit is consistent for each of the events. Significant differences in crystal habit may be indicative of polymorphism.

2.

Check the dissolution temperatures for each of the crystallized suspensions (use images if necessary). At these high heating rates, saturation temperatures will not be accurate, but they should be reasonably precise. A significant shift in dissolution temperature (e.g., 5–10 °C) may also be indicative of polymorphism. If a shift is found, use the images (change in habit) and the transmissivity trends to investigate whether a transition could have occurred during crystallization, after crystallization, or during the heating step. An alternative scenario that could cause a gradual shift in dissolution temperatures would come from solvent evaporation (e.g., loose cap or a damaged o-ring) or from crystallization on the vial cap. Users are advised to look for those trends and to check the status of the vial (solvent level, lack of crystals above the solution) toward the end of the experiment. This is to ensure that all replicated kinetic events occurred at the same intended supersaturation.

3.

Observe the transmissivity trends for each of the events and the time required to move from 100% transmissivity to a constant low transmissivity (equilibrium value or zero). A sudden change in kinetics for one of the events could also be indicative of polymorphism or caused by a loose or stuck impeller. Similarly, observe the images throughout the event to ensure that crystal habit is consistent, that crystal number and size constantly increase (no issues with settling, floating, or dissolving crystals), and that samples present negligible aggregation or fouling (crystals stuck on camera).

Figure 4

Figure 4. Example of the program results for crystallization of l-glutamic acid in water, with a sample concentration of 35 mg/g solvent, Tc = 10 °C, and Tmax = 80 °C. Highlighted areas represent a typical induction time measurement in green (optional for this work, if primary nucleation kinetics are desired), and a typical crystallization event (purple) as it would be cropped by the user. The latter is the same 20 min event included in Figure 2.

During user evaluation, polymorphism should be investigated holistically. Samples without a clear change in habit or behavior should just be treated as suspicious events, and clear instances of polymorphism should be recorded and isolated from the data sets. With sufficient events at different concentrations, it would be possible to determine kinetics for the different crystallizing polymorphs, but this falls out of the scope of this work.
Once the number of valid events has been determined, the particle size distributions for these events should be exported for a representative range where the crystallization event is fully captured at a constant temperature. The exported files will be further cropped based on eqs 2 and 3, so it is best to err on the side of exporting a time period that is too broad. The first exported value should include a completely clear solution, and the last exported value should have a saturated camera with significant crystal overlap. The highlighted range in Figure 4 (purple) is the exported range for the sample event that led to Figure 2.

Data Processing

Each of the exported events is treated as a separate crystallization experiment. The data provided by the system includes a set of particle size distributions, one for each image taken during the event. The total number, length, area, and volume of the crystals in those distributions are first calculated (eqs 47). Then, moving averages are taken for the number of crystals per picture and used to determine a cropping range (times for Nstart and Nend, eqs 13). The data is cropped following that range, and the initial conditions for parameter estimation are determined from the first few values. The number of values depends on sample kinetics, but the default is a moving average over the first 10 points of the event.
At this point, there is also the option to remove outliers. This is important if a hook-shaped mixer is used. Because the mixer rotates close to the vial wall, it is often captured on camera. For those samples, it will cover part of the image and thus lead to a sudden decrease in the total number of crystals seen on camera. This decrease in crystal count may also occur if an image randomly presents overlapping large crystals. These outliers would erroneously skew the data toward slower nucleation rates. For the systems studied in this work, images presenting a number of crystals of less than 70% of the moving average were removed from the data sets. Figure 5 is an example of the trends before and after outlier removal.

Figure 5

Figure 5. Removal of outliers for an acetaminophen crystallization event (40 mg/g solvent, 25% ethanol in water, 10 °C) that used an overhead hook for stirring. (a) Raw data for the number of crystals per picture during the event. (b) Data for the same event after outlier removal. Outliers were removed if they were found below 70% of the moving average’s value.

Data processing should yield cropped trends for the number, length, area, and volume of crystals on camera as illustrated in Figure 6. From these trends, only the number and area of crystals per picture are used for parameter estimation, but the total length and volume are used as initial conditions for the respective moments.

Figure 6

Figure 6. Processed trends for an acetaminophen crystallization event (40 mg/g solvent, 25 vol % ethanol in water, 10 °C) after outlier removal, showing the evolution of the total number, length, area, and volume of crystals on camera. The fraction of points removed as outliers is illustrated from the counts at 0 crystals/picture.

In addition to the kinetic data, the parameter estimation models will require an accurate solubility curve for the system. In this work, solubility was expressed following an empirical model (eq 22).
xsat=α·exp(βT)
(22)
where xsat is the mole fraction solubility, T is the temperature expressed in Kelvin, and α and β are constants calibrated from experimental solubility values. These values can be obtained from the previously described polythermal solubility tests, from the literature, or from prior data (e.g., isothermal solubility).

Parameter Estimation

A population balance model was implemented in gPROMS FormulatedProducts and used to estimate the values for kb and kg from four crystallization events. A summary of the equations and nomenclature is available in the Supporting Information. For a given experiment, input parameters are the total concentrations of solute, solvent, and antisolvent (if any) as mass fractions, the crystallization temperature (in Kelvin), and the initial conditions for the total number, length, area, and volume of crystals on camera. In addition to those conditions, properties of the solute and solvent system must be provided. These include the solubility constants from eq 22, the crystal shape factors (eqs 8 and 9), and the densities and molar masses of the solute and solvents. The model also accounts for solvate formation, and solvation terms can be implemented (stoichiometry in mol solvent/mol solute). Finally, the estimation of activities requires the melting point and the enthalpy of fusion for the solute. (38,42) These can be obtained from a single test using differential scanning calorimetry using the isolated crystal form.
Reasonable initial guesses for the crystallization parameters can be obtained from the literature or from the results of this work. However, note that literature values may be based on a different supersaturation expression, and thus, their values will be affected by the change in methods. (38) For θ, reasonable values can be estimated for each magnification, knowing the total capture area for the image and using an approximated value for the measurement depth (expected between 0.5 and 3 mm). For the 4 μm/pixel camera and the systems presented in this work, the initial guess was set at 7 mg/picture (measurement depth of appr. 1.5 mm) with lower and upper bounds at 1 mg/picture and 15 mg/picture, respectively.
To facilitate the comparison between multiple systems, and because of the inherent noise in imaging data, the estimation of kinetic parameters was limited to values for kb and kg, and the values of b, j, and g were assumed to be 2, 1, and 1, respectively. To estimate confidence intervals and guide parameter estimation, a constant-variance model was implemented where the variance in experimental values for Ntot and Atot was determined from the experimental background at the start of the event (e.g., first 2 min in Figure 2). If the spread of the data increases significantly during a run, the model would have to be adapted to a relative variance instead. Results from parameter estimation are evaluated based on the goodness of fit to both Ntot and Atot and ensuring a lack of correlation between the estimated parameter values for kb, kg, and θ. The latter is especially important to break the relationship between kb and θ that would stem from the combined eqs 11 and 18. Four studied conditions were enough for the systems in this work, but it is recommended to expand the number of conditions if a significant correlation is found between the two. At the same time and within this context, systems should be compared following similar and realistic values for θ, especially if there is a risk for correlations with kinetic parameters. Large changes in θ are not expected for systems using the same camera, so keeping consistent values when comparing systems minimizes the risk of erroneous conclusions from parameter estimation resolving a local minimum with a non-negligible correlation between θ and a kinetic parameter.

Case Study 1: Antisolvent Crystallization of Acetaminophen from Ethanol–Water

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The first investigated system involved the antisolvent crystallization of acetaminophen, using ethanol as the solvent and water as the antisolvent. The chosen temperature and solvent fractions are 10 °C and 1:3 ethanol/water, by volume.

Materials

Acetaminophen powder (98.0%) was purchased from TCI America. Ethanol (99.5%) was purchased from Millipore Sigma. Deionized water was generated in-house.

Selection of Crystallization Conditions

Crystallization conditions for kinetic screening were chosen based on an approximate solubility of 40 mg/g at 20 °C, (43) with the expectation that the solubility at the crystallization temperature of 10 °C would be lower. Concentration values were initially selected as 50, 60, 70, and 80 mg/g for kinetic screening. The latter presented very short induction times and crystallized during sample cooling, so it was not used for parameter estimation. However, its solubility value was still utilized to build a solubility curve. To obtain a fourth concentration value for kinetic screening, an additional experiment was conducted with a concentration of 40 mg/g. Finally, polythermal solubility samples at 25, 30, 35, 120, and 160 mg/g were taken to capture a higher range of the solubility curve.

Solubility and Kinetic Trends

Polythermal solubility screening for the studied concentrations yielded the solubility curve in Figure 7. These values were obtained without replicates and from an automated spreadsheet that searches for the dissolution point in transmissivity data; thus, they are a worst-case scenario for accuracy but the most time-effective scenario. If time and materials are available, it is recommended to run isothermal screenings instead to reach higher accuracy. We proceeded with this solubility curve to test the models in a scenario where the entire screening is automated and only the minimum amount of time and materials is available. The solubility constant values for eq 22 (α = 1.835 mol/mol; β = 0.04308 K–1) were obtained from these results and used for parameter estimation in gPROMS.

Figure 7

Figure 7. Solubility curve for acetaminophen in 25 vol % ethanol and 75 vol % water. Data was obtained from polythermal solubility screening that was integrated with the Crystalline program.

For the kinetic screening, three replicate events were obtained for each of the low concentrations (40, 50, and 60 mg/g) and all four replicate events were successful for the 70 mg/g concentration. The unsuccessful experiments were due to either lack of crystallization or crystallization outside the capturing rate of 1 picture/second. The trends for the successful runs were found to be reproducible enough to warrant a visible increase in kinetics as the concentration increases (Figure 8). Polymorphic behavior was not observed for this solvent composition and crystallization conditions.

Figure 8

Figure 8. Overlay of the raw data (before outlier removal) for all 13 successful crystallization events for acetaminophen, with starting times adjusted at the equivalent initial signal. Concentrations are organized by color and individual crystallization events are organized by marker shape.

Parameter Estimation

After event cropping and outlier removal, events from Figure 8 were implemented into the gPROMS model for parameter estimation. The model fit to the experimental data provided in Figure 9.

Figure 9

Figure 9. Best fits for acetaminophen parameter estimation. (a) Total number of crystals per picture (Ntot); (b) total crystal area per picture (Atot).

This fit was done while fixing the values for b, j, and g to 2, 1, and 1, respectively. Better fits can be obtained if the values for b and g are released. However, this also leads to a high correlation between kb and b (0.93) and between kg and g (0.87), which makes a comparison between systems a difficult endeavor and compromises the accuracy of the estimates. If these parameters need to be accurately estimated, more experiments would be recommended at new starting concentrations. The current fit (Figure 9) led to the parameters summarized in Table 2, with a negligible correlation between kb and kg (−0.07) and a low correlation between θ and the kinetic parameters (−0.32 for kg and −0.74 for kb).
Table 2. Parameter Estimates for Acetaminophen in 25 Vol % Ethanol and 75 Vol % Water at a Crystallization Temperature of 10 °C. The Estimates Include 95% Confidence Intervals
parametervalueUnits
kb(2.08 ± 0.03)·105g–1 s–1
B2 
J1 
kg2.31 ± 0.02μm/s
G1 
θ5.45 ± 0.09mg/picture

Accuracy and Repeatability of Parameter Estimates

A common method to validate the accuracy of the obtained estimates is by comparison with similar published studies. Multiple kinetic studies are available in the literature, studying the crystallization of acetaminophen at various supersaturations, temperatures, and solvents. However, a direct comparison between kinetic parameters is difficult as secondary nucleation kinetics are highly sensitive to variations in scale and mixing, growth kinetics depend on how the technique used to track crystal growth sees crystal size, and expressions for kinetics and supersaturation often differ significantly between studies. In addition, some parameter estimates in the literature present high correlations between the pre-exponential factors, activation energies, and supersaturation orders, making a direct comparison a difficult task. To the best of our knowledge, there are no studies working with acetaminophen in 1:3 ethanol/water and using the Crystalline (or imaging) for particle size analysis. Following Maldonado et al.’s data mining of crystallization kinetic parameters, kb values for acetaminophen have been found to be anywhere between 3 g–1 s–1 and 1018 g–1 s–1 in varying mixtures of ethanol, water, and methanol. For growth rates, constants present less variability and usually fall at the order of 1–100 μm/s, but those depend on how the analytical technique sees crystal size, the value of g, the choice of supersaturation expression, and the operating solvent and temperature. The obtained values are realistic within those very broad ranges, but this is difficult to assess from the literature alone.
The accuracy, robustness, and scalability of these methods were investigated using several approaches. First, this study was replicated in two different sites (Rowan University and Pfizer) using separate raw materials, scientists, and Crystalline machines. In the latter, the Crystalline setup also had a higher camera magnification (2.8 μm/pixel instead of 4 μm/pixel). The estimated parameters were tested for prediction of the new experimental data, allowing the gPROMS program to change only the value of θ to account for the different magnifications. One of the limitations of using a higher magnification is the capture of a representative crystal number and the added noise in the larger moments of the distribution due to error propagation. This is discussed in detail in the “Method Limitations” Section. By changing the magnification from 4 to 2.8 μm/pixel, the capture area decreases from 4.9 to 2.4 mm2. Once we account for the fact that crystals at the edge of a picture are not counted, the effective area is decreased even further, and the capture depth is also expected to decrease. The estimation of θ for the system at this new magnification converged at 2.26 ± 0.02 mg/picture (from the 5.45 ± 0.09 mg/picture in the 4 μm/pixel magnification, Table 2). This new value is reasonable considering the change in capture area and depth. Results for the prediction of crystallization trends using the parameters in Table 2 on data obtained at Pfizer are provided in Figure 10. Here, the total length rather than the total crystal area is being used as it provided a greater precision to compensate for the added random error at the higher magnifications.

Figure 10

Figure 10. Reproducibility of the methods: using parameters estimated from experiments at Rowan University to predict kinetic trends obtained from experiments at Pfizer, with a corrected θ of 2.26 mg/picture due to the higher magnification in the Crystalline. (a) total number of crystals per picture (Ntot); (b) total crystal length per picture (Ltot).

Scalability

The determination of scalable parameters is not the primary goal of these methods as it is already known that different scales and mixing environments will trigger significant changes in secondary nucleation kinetics. (7) Crystallization models based on semiempirical expressions are bound to work only within the narrow range of conditions in which they were calibrated. However, how scalable those parameters are, to be used as early indicators of system behavior, is still an interesting question, especially for industrial practitioners. A worst-case scenario was investigated, where the system was changed not just in scale but also in the mode of operation. Here, two continuous Mixed Suspension Mixed Product Removal (MSMPR) experiments were conducted at the 150 mL scale (scale-up factor of 30), varying both feed concentration and residence time between runs. A complete description of these experiments and results is provided in the Supporting Information. The model overestimated the steady-state crystal size and underestimated the yield, presumably due to an underestimation of the nucleation rate at the larger scale.
This study further supports that these methods are not intended to replace parameter estimation at relevant scales but rather to guide early process development as well as academic studies operating at smaller scales. The proposed methods can be used to investigate temperature, solvent, and impurity effects on kinetics in early process development, narrowing the design space so that kinetics only need to be polished with 1–2 experiments at the right scale. This is done while providing valuable solubility data as well as with an indication of how process conditions may affect polymorphism, aggregation behavior, or fouling. As internal or public databases are built following consistent methods, new systems will be quickly classified by comparison with similar solutes (e.g., fast nucleating or slow growing), providing early guidance for the selection of crystallization processes (e.g., batch vs continuous) on a system-by-system basis.

Case Study 2: Cooling Crystallization of l-Glutamic Acid from Water

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The second model system was chosen based on its well-known polymorphic behavior, to test the methods for the determination of crystallization kinetics on a metastable polymorph (α form of l-glutamic acid), and their ability to identify form transitions by changes in solubility, kinetics, or habit. Here, cooling crystallization was considered using water as the solvent and using a final crystallization temperature of 10 °C.

Materials

l-Glutamic acid powder (99.0%) was purchased from TCI America. Deionized water was generated in-house.

Selection of Crystallization Conditions

Conditions for kinetic screening were selected based on solubility values published by Ni et al. (44) l-Glutamic acid presents an approximate solubility of 8 g/L for the α form at 10 °C and a rapidly increasing slope, reaching solubility values around 70 g/L at 65 °C. The early kinetic screening was conducted at concentrations of 20, 30, and 40 mg/g on a solvent basis. However, 40 mg/g failed to produce acceptable trends: events produced either the needle-shaped β form or a highly aggregated form that was suspected to be α-l-glutamic acid but was too small to clearly distinguish crystal habit (Figure 11) and difficult to isolate due to rapid form transitions to the needle-shaped β polymorph.

Figure 11

Figure 11. Comparison of crystal habits obtained during crystallization of l-glutamic acid from water at 35 and 40 mg/g (solvent basis).

In this context, and because significant differences in kinetics could be observed between 20 and 30 mg/g, two more concentrations were investigated using 25 and 35 mg/g. For solubility screening, multiple concentrations were tested between 8 and 40 mg/g using the polythermal method, but every test led to the transition from the metastable α form to the stable β form (Figure 12), making the determination of the saturation temperature for the crystallized α form a difficult task.

Figure 12

Figure 12. Form transition from α-l-glutamic acid to β-l-glutamic acid during polythermal solubility screening and subsequent dissolution of the β form at a higher saturation temperature.

Determination of solubilities for metastable polymorphs fell out of the scope of this work, but similar methods have been described in recent literature. (45) Here, literature values for solubility (Ni et al.) (44) were used to estimate the solubility constant values for eq 22 (α = 2.22 mol/mol; β = 0.03683 K–1). The kinetic trends at the four studied concentrations are compared in Figure 13. All four events at 35 mg/g were successful and produced the α form. The lower concentrations also produced the α form, but due to inconsistency of induction times, runs at 25, 30, and 35 mg/g only had 3, 2, and 1 valid event, respectively. In contrast with the acetaminophen system, glutamic acid presents slower kinetics and thus a broader range of valid data points before the camera gets saturated (350–800 pictures/event, in contrast with the 75–300 pictures/event for acetaminophen, comparing Figures 8 and 13). Collecting more events was not deemed necessary due to the already demonstrated reproducibility and the higher number of data points per crystallization experiment.

Figure 13

Figure 13. Overlay of the raw data for all 10 successful crystallization events for α-l-glutamic acid, with starting times adjusted at the equivalent initial signal. Concentrations are organized by color (labeled), and individual crystallization events are organized by marker shape.

Parameter Estimation

The best fit to the experimental data is provided in Figure 14, which is a closer fit to that obtained for acetaminophen in Figure 9. Note that values for the supersaturation dependence in kinetics (b and g) have been assumed for both systems. Thus, the quality of the fit also depends on whether the assumed values are accurate for the studied solute.

Figure 14

Figure 14. Best fits for parameter estimation for crystallization kinetics of the α form of l-glutamic acid. (a) Total number of crystals per picture (Ntot); (b) total crystal area per picture (Atot).

The estimated kinetic parameters are summarized in Table 3 and compared to those for acetaminophen. As expected from the raw data, kinetics for glutamic acid are significantly slower than those for acetaminophen. The estimated values for θ are considerably close and would overlap if the different solvent densities are considered in calculating θ on a volume basis instead of a mass basis. The proximity of θ values allows for a direct comparison between the kinetic parameters for both systems. On secondary nucleation, the glutamic acid system presented nucleation rates approximately 12 times slower than acetaminophen at equivalent supersaturations and suspension densities. The crystal growth rate was 6 times smaller at the same supersaturations. The slower kinetics explain how it took approximately 8 times longer for the system to saturate the camera during kinetic screening (Figures 8 and 13).
Table 3. Parameter Estimates for α-l-Glutamic Acid in Water at a Crystallization Temperature of 10 °C. The Estimates Include 95% Confidence Intervals and Are Compared with the Values for Acetaminophen
parameterα-l-glutamic acid (water)acetaminophen (1:3 ethanol/water)units
kb(1.67 ± 0.01)·104(2.08 ± 0.03)·105g–1 s–1
b22 
j11 
kg0.375 ± 0.0022.31 ± 0.02μm/s
g11 
θ5.65 ± 0.065.45 ± 0.09mg/picture

Method Limitations

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Beyond the two presented case studies, these methods have already been tested for four additional systems, including inorganic salts. Results for these systems will be covered in a future publication, but they have helped in obtaining a holistic understanding of the method’s capabilities and limitations. This section provides a comprehensive list of the main method limitations that should be considered by practitioners intending to apply the described methodology to their research.

Camera Magnification

Multiple versions of the Crystalline are commercially available, with different and built-in camera magnifications. While high magnifications are often chosen by practitioners to detect the onset of nucleation and for crystallization studies dealing with small particles, obtaining representative kinetic trends with a capture rate limited to up to 1 picture/second requires each picture to capture a sufficiently large number of crystals for size analysis. Furthermore, large crystals that are not fully captured on camera (hitting the edge of the image) are not counted in image analysis, skewing the average crystal size toward smaller values. This bias error is maximized for the higher magnifications, where the image area gets progressively smaller and a particle is more likely to hit the edge of the picture. For these reasons, lower magnifications are recommended for these methods. The experiments in this work were conducted using a 4 μm/pixel camera, covering a 1.9 × 2.6 mm window with a total area of 4.9 mm2. Higher magnifications were tested (1.9 μm/pixel), but moving from a capture area of 4.9 mm2 to approximately 0.9 × 1.3 mm (1.2 mm2) significantly decreased the signal/noise ratio and severely limited the number of crystals that could be captured on camera before the image became saturated (Figure 15). A magnification of 2.8 μm/pixel, as used for Figure 10, is likely the highest viable magnification. If the 2.8 μm/pixel magnification is used, it is recommended to fit the kinetic parameters based on number and length data, instead of using number and area. Overall and for typical crystal sizes in small-molecule organic systems, it is recommended to use small magnifications (4 μm/pixel) whenever possible in order to maximize the signal/noise ratio in image analysis.

Figure 15

Figure 15. Comparison of the performance of the 4 μm/pixel camera against the 1.9 μm/pixel camera for two separate crystallization events of 35 mg/g of l-glutamic acid in water at 10 °C. At the higher magnification, the camera gets saturated sooner and with approximately 1/4 of the number of crystals per picture, limiting both the duration and the amount of valid imaging data obtained from a crystallization event.

Low Solubilities

The solubility of the solute also plays an important role in determining the feasibility of these methods. Ideally, tests should be conducted at supersaturation ratios that provide reasonable induction times, long enough to prevent crystallization during crash cooling (variable temperature) but short enough to be easily predicted and captured on camera (ideally under 3 h). These highly depend on the kinetics of the system, but they are rarely above 100% supersaturation. Together with a reasonable supersaturation, the amount of crystallized material needs to be sufficient to give a high signal-to-noise ratio and get at least 100 crystals/picture before the system reaches equilibrium. If the system’s solubility is too low (e.g., 1 g/L), very small concentrations (e.g., 2 g/L) will already yield very high supersaturations, but they will not suffice in getting a reasonable suspension density, even at equilibrium (e.g., 1 g/L or 0.1 w/v % in this hypothetical example). The smallest value for which these methods were feasible has been a 5 g/L difference between the supersaturated and the saturated state, which requires system solubilities at the order of 3–7 g/L or higher. In a similar way, solubility curves should be steep enough to allow for the full dissolution of the solute before reaching the solvent’s boiling point. If a system has a very low solubility (likely an antisolvent crystallization experiment) or a flat solubility curve, it is recommended to approach the experiment using controlled antisolvent addition and avoiding dissolution/crystallization cycles altogether. The approach is more labor-intensive, but it provides equivalent data if a reasonable induction time is maintained.

Fast Crystallization Kinetics

Due to the limitations of an image capture rate of 1 picture/second, it is important to select a supersaturation that ensures a batch crystallization time of ideally 60 s or longer between the onset of crystallization and the saturation of the camera. This may be difficult, especially for inorganic solutes, but slower kinetics ensure a larger amount of captured crystals in a given run. The shortest captured time for the systems investigated in the work was 80 s, which showed clear trends (Figure 8). This recommendation is subject to the assumption that the suspension density is high enough to reach a high number of crystals per picture, which may be difficult to achieve for fast-crystallizing systems like inorganic salts. For systems presenting a fast crystallization, it is recommended to run more than four replicate crystallization events and to combine those replicates in guiding parameter estimation.

Elongated Crystal Habits and Aggregation/Breakage

These methods were developed for crystals with low aspect ratios and with negligible agglomeration. Systems with high aspect ratios could be considered at the expense of lower accuracy (preferred orientations will affect the measured crystal size and the model assumptions for projected crystal volume) and adjusting the values for ka and kv to better capture the system’s aspect ratio. Similarly, models would need to be adapted for systems presenting crystal aggregation or breakage as these phenomena will affect the measured crystal moments. Expanding the methods to account for these systems fell out of the scope of this work, but it can be achieved with more advanced crystallization models and using the principles hereby described.

Conclusions

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Methods for the rapid determination of crystallization kinetic parameters from automated batch crystallization experiments at the 5 mL scale were developed and demonstrated for two model systems. The methods are based on tracking the crystal number and area from in situ images taken during batch crystallization. For dilute and well-mixed systems, and a camera magnification that allows the capture of a representative sample, trends are found to be reproducible, and they follow expected behaviors (different kinetics for different systems and increasing kinetics with supersaturation). A mathematical model was developed to extract crystallization parameters from imaging data, and the estimated parameters were tested for prediction across sites and for scalability. These methods are recommended as a high-throughput tool to obtain early kinetic data for model systems, with limited amounts of time and raw material. The captured trends can be used to inform process development and for the selection of suitable crystallization conditions that maximize kinetics and minimize system issues like aggregation or polymorphism. Collecting kinetic data for a variety of systems would be the first step toward building a database under consistent methods, for which new systems can be quickly classified for their crystallization kinetic behavior. This will aid the rapid development of crystallization processes through a kinetic-driven selection of the appropriate configuration and solvent and the early assessment of optimal crystallization strategies for novel systems based on kinetic similarity with existing solutes.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.cgd.3c00252.

  • Mathematical models for the parameter estimation, translation to gPROMS nomenclature, and scalability study (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
  • Authors
    • Ryan J. Arruda - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    • Paul A.J. Cally - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    • Anthony Wylie - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United StatesOrcidhttps://orcid.org/0000-0003-0866-4023
    • Nisha Shah - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    • Ibrahim Joel - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    • Zachary A. Leff - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    • Alexander Clark - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    • Griffin Fountain - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    • Layane Neves - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    • Joseph Kratz - Department of Chemical Engineering, Rowan University, Glassboro, New Jersey 08028, United States
    • Alpana A. Thorat - Pfizer Worldwide Research and Development, Groton, Connecticut 06340, United StatesOrcidhttps://orcid.org/0000-0002-3251-4255
    • Ivan Marziano - Pfizer Worldwide Research and Development, Sandwich, Kent CT13 9NJ, U.K.Orcidhttps://orcid.org/0000-0002-3759-0070
    • Peter R. Rose - Pfizer Worldwide Research and Development, Groton, Connecticut 06340, United States
    • Kevin P. Girard - Pfizer Worldwide Research and Development, Groton, Connecticut 06340, United StatesOrcidhttps://orcid.org/0000-0001-5821-4536
  • Author Contributions

    The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported by Pfizer Inc., Global Research & Development.

References

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This article references 45 other publications.

  1. 1
    Chen, J.; Sarma, B.; Evans, J. M. B.; Myerson, A. S. Pharmaceutical Crystallization. Cryst. Growth Des. 2011, 11, 887895,  DOI: 10.1021/cg101556s
  2. 2
    Khadka, P.; Ro, J.; Kim, H.; Kim, I.; Kim, J. T.; Kim, H.; Cho, J. M.; Yun, G.; Lee, J. Pharmaceutical Particle Technologies: An Approach to Improve Drug Solubility, Dissolution and Bioavailability. Asian J. Pharm. Sci. 2014, 9, 304316,  DOI: 10.1016/j.ajps.2014.05.005
  3. 3
    Azad, M. A.; Capellades, G.; Wang, A. B.; Klee, D. M.; Hammersmith, G.; Rapp, K.; Brancazio, D.; Myerson, A. S. Impact of Critical Material Attributes (CMAs)-Particle Shape on Miniature Pharmaceutical Unit Operations. AAPS PharmSciTech 2021, 22, 98,  DOI: 10.1208/s12249-020-01915-6
  4. 4
    O’Grady, D.; Barrett, M.; Casey, E.; Glennon, B. The Effect of Mixing on the Metastable Zone Width and Nucleation Kinetics in the Anti-Solvent Crystallization of Benzoic Acid. Chem. Eng. Res. Des. 2007, 85, 945952,  DOI: 10.1205/cherd06207
  5. 5
    Schall, J. M.; Mandur, J. S.; Braatz, R. D.; Myerson, A. S. Nucleation and Growth Kinetics for Combined Cooling and Antisolvent Crystallization in a Mixed-Suspension, Mixed-Product Removal System: Estimating Solvent Dependency. Cryst. Growth Des. 2018, 18, 15601570,  DOI: 10.1021/acs.cgd.7b01528
  6. 6
    Capellades, G.; Wiemeyer, H.; Myerson, A. S. Mixed-Suspension, Mixed-Product Removal Studies of Ciprofloxacin from Pure and Crude Active Pharmaceutical Ingredients: The Role of Impurities on Solubility and Kinetics. Cryst. Growth Des. 2019, 19, 40084018,  DOI: 10.1021/acs.cgd.9b00400
  7. 7
    Myerson, A. S.; Edemir, D.; Lee, A. Y. Handbook of Industrial Crystallization, 3rd Edit.; Cambridge University Press, 2019.
  8. 8
    Schall, J. M.; Capellades, G.; Mandur, J. S.; Braatz, R. D.; Myerson, A. S. Incorporating Solvent-Dependent Kinetics To Design a Multistage, Continuous, Combined Cooling/Antisolvent Crystallization Process. Org. Process Res. Dev. 2019, 23, 19601969,  DOI: 10.1021/acs.oprd.9b00244
  9. 9
    Power, G.; Hou, G.; Kamaraju, V. K.; Morris, G.; Zhao, Y.; Glennon, B. Design and Optimization of a Multistage Continuous Cooling Mixed Suspension, Mixed Product Removal Crystallizer. Chem. Eng. Sci. 2015, 133, 125139,  DOI: 10.1016/j.ces.2015.02.014
  10. 10
    Morris, G.; Power, G.; Ferguson, S.; Barrett, M.; Hou, G.; Glennon, B. Estimation of Nucleation and Growth Kinetics of Benzoic Acid by Population Balance Modeling of a Continuous Cooling Mixed Suspension, Mixed Product Removal Crystallizer. Org. Process Res. Dev. 2015, 19, 18911902,  DOI: 10.1021/acs.oprd.5b00139
  11. 11
    Capellades, G.; Duso, A.; Dam-Johansen, K.; Mealy, M. J.; Christensen, T. v.; Kiil, S. Continuous Crystallization with Gas Entrainment: Evaluating the Effect of a Moving Gas Phase in an MSMPR Crystallizer. Org. Process Res. Dev. 2019, 23, 252262,  DOI: 10.1021/acs.oprd.8b00376
  12. 12
    Nicoud, L.; Licordari, F.; Myerson, A. S. Polymorph Control in MSMPR Crystallizers. A Case Study with Paracetamol. Org. Process Res. Dev. 2019, 23, 794806,  DOI: 10.1021/acs.oprd.8b00351
  13. 13
    David, R.; Marchal, P.; Marcant, B. Modelling of Agglomeration in Industrial Crystallization from Solution. Chem. Eng. Technol. 1995, 18, 302309,  DOI: 10.1002/ceat.270180503
  14. 14
    Chung, S. H.; Lee, H. W.; Saleeby, E. G. Modeling a Cascade of Continuous Msmpr Crystallizers With Agglomeration. Chem. Eng. Commun. 1998, 163, 177200,  DOI: 10.1080/00986449808912350
  15. 15
    Hou, G.; Power, G.; Barrett, M.; Glennon, B.; Morris, G.; Zhao, Y. Development and Characterization of a Single Stage Mixed-Suspension, Mixed-Product-Removal Crystallization Process with a Novel Transfer Unit. Cryst. Growth Des. 2014, 14, 17821793,  DOI: 10.1021/cg401904a
  16. 16
    Rogers, L.; Briggs, N.; Achermann, R.; Adamo, A.; Azad, M.; Brancazio, D.; Capellades, G.; Hammersmith, G.; Hart, T.; Imbrogno, J.; Kelly, L. P.; Liang, G.; Neurohr, C.; Rapp, K.; Russell, M. G.; Salz, C.; Thomas, D. A.; Weimann, L.; Jamison, T. F.; Myerson, A. S.; Jensen, K. F. Continuous Production of Five Active Pharmaceutical Ingredients in Flexible Plug-and-Play Modules: A Demonstration Campaign. Org. Process Res. Dev. 2020, 24, 21832196,  DOI: 10.1021/acs.oprd.0c00208
  17. 17
    Cole, K. P.; Reizman, B. J.; Hess, M.; Groh, J. M.; Laurila, M. E.; Cope, R. F.; Campbell, B. M.; Forst, M. B.; Burt, J. L.; Maloney, T. D.; Johnson, M. D.; Mitchell, D.; Polster, C. S.; Mitra, A. W.; Boukerche, M.; Conder, E. W.; Braden, T. M.; Miller, R. D.; Heller, M. R.; Phillips, J. L.; Howell, J. R. Small-Volume Continuous Manufacturing of Merestinib. Part 1. Process Development and Demonstration. Org. Process Res. Dev. 2019, 23, 858869,  DOI: 10.1021/acs.oprd.8b00441
  18. 18
    Jiang, S.; ter Horst, J. H. Crystal Nucleation Rates from Probability Distributions of Induction Times. Cryst. Growth Des. 2011, 11, 256261,  DOI: 10.1021/cg101213q
  19. 19
    Kulkarni, S. A.; Kadam, S. S.; Meekes, H.; Stankiewicz, A. I.; ter Horst, J. H. Crystal Nucleation Kinetics from Induction Times and Metastable Zone Widths. Cryst. Growth Des. 2013, 13, 24352440,  DOI: 10.1021/cg400139t
  20. 20
    Tan, L.; Davis, R. M.; Myerson, A. S.; Trout, B. L. Control of Heterogeneous Nucleation via Rationally Designed Biocompatible Polymer Surfaces with Nanoscale Features. Cryst. Growth Des. 2015, 15, 21762186,  DOI: 10.1021/cg501823w
  21. 21
    Pons Siepermann, C. A.; Myerson, A. S. Inhibition of Nucleation Using a Dilute, Weakly Hydrogen-Bonding Molecular Additive. Cryst. Growth Des. 2018, 18, 35843595,  DOI: 10.1021/acs.cgd.8b00367
  22. 22
    Ildefonso, M.; Candoni, N.; Veesler, S. A Cheap, Easy Microfluidic Crystallization Device Ensuring Universal Solvent Compatibility. Org. Process Res. Dev. 2012, 16, 556560,  DOI: 10.1021/op200291z
  23. 23
    Ildefonso, M.; Revalor, E.; Punniam, P.; Salmon, J. B.; Candoni, N.; Veesler, S. Nucleation and Polymorphism Explored via an Easy-to-Use Microfluidic Tool. J. Cryst. Growth 2012, 342, 912,  DOI: 10.1016/j.jcrysgro.2010.11.098
  24. 24
    Laval, P.; Salmon, J.-B.; Joanicot, M. A Microfluidic Device for Investigating Crystal Nucleation Kinetics. J. Cryst. Growth 2007, 303, 622628,  DOI: 10.1016/j.jcrysgro.2006.12.044
  25. 25
    Briuglia, M. L.; Sefcik, J.; ter Horst, J. H. Measuring Secondary Nucleation through Single Crystal Seeding. Cryst. Growth Des. 2019, 19, 421429,  DOI: 10.1021/acs.cgd.8b01515
  26. 26
    Wang, X. Z.; Calderon De Anda, J.; Roberts, K. J. Real-Time Measurement of the Growth Rates of Individual Crystal Facets Using Imaging and Image Analysis. Chem. Eng. Res. Des. 2007, 85, 921927,  DOI: 10.1205/cherd06203
  27. 27
    Wu, K.; Ma, C. Y.; Liu, J. J.; Zhang, Y.; Wang, X. Z. Measurement of Crystal Face Specific Growth Kinetics. Cryst. Growth Des. 2016, 16, 48554868,  DOI: 10.1021/acs.cgd.6b00189
  28. 28
    Sangwal, K.; Wójcik, K.; Borc, J. In Situ Study of Growth and Dissolution Kinetics of Ammonium Oxalate Monohydrate Single Crystals from Aqueous Solutions Containing Cationic Impurities. Cryst. Res. Technol. 2007, 42, 12431251,  DOI: 10.1002/crat.200711013
  29. 29
    Quilló, G. L.; Bhonsale, S.; Gielen, B.; van Impe, J. F.; Collas, A.; Xiouras, C. Crystal Growth Kinetics of an Industrial Active Pharmaceutical Ingredient: Implications of Different Representations of Supersaturation and Simultaneous Growth Mechanisms. Cryst. Growth Des. 2021, 21, 54035420,  DOI: 10.1021/acs.cgd.1c00677
  30. 30
    Randolph, A. D.; Larson, M. A. Theory of Particulate Processes - Analysis and Techniques of Continuous Crystallization; Academic Press, Inc., 1971.
  31. 31
    Deck, L. T.; Mazzotti, M. Conceptual Validation of Stochastic and Deterministic Methods To Estimate Crystal Nucleation Rates. Cryst. Growth Des. 2022, 23, 899914,  DOI: 10.1021/acs.cgd.2c01133
  32. 32
    Maggioni, G. M.; Bosetti, L.; dos Santos, E.; Mazzotti, M. Statistical Analysis of Series of Detection Time Measurements for the Estimation of Nucleation Rates. Cryst. Growth Des. 2017, 17, 54885498,  DOI: 10.1021/acs.cgd.7b01014
  33. 33
    Kail, N.; Briesen, H.; Marquardt, W. Analysis of FBRM Measurements by Means of a 3D Optical Model. Powder Technol. 2008, 185, 211222,  DOI: 10.1016/j.powtec.2007.10.015
  34. 34
    Barrett, P.; Glennon, B. In-Line FBRM Monitoring of Particle Size in Dilute Agitated Suspensions. Part. Part. Syst. Charact. 1999, 16, 207211,  DOI: 10.1002/(SICI)1521-4117(199910)16:5<207::AID-PPSC207>3.0.CO;2-U
  35. 35
    Yenkie, K. M.; Diwekar, U. Stochastic Optimal Control of Seeded Batch Crystallizer Applying the Ito Process. Ind. Eng. Chem. Res. 2012, 52, 108122,  DOI: 10.1021/ie300491v
  36. 36
    Ottens, E. P. K.; de Jong, E. J. A Model for Secondary Nucleation in a Stirred Vessel Cooling Crystallizer. Ind. Eng. Chem. Fund. 1973, 12, 179184,  DOI: 10.1021/i160046a006
  37. 37
    Evans, T. W.; Sarofim, A. F.; Margolis, G. Models of Secondary Nucleation Attributable to Crystal-crystallizer and Crystal-crystal Collisions. AIChE J. 1974, 20, 959966,  DOI: 10.1002/aic.690200517
  38. 38
    Schall, J. M.; Capellades, G.; Myerson, A. S. Methods for Estimating Supersaturation in Antisolvent Crystallization Systems. CrystEngComm 2019, 21, 58115817,  DOI: 10.1039/c9ce00843h
  39. 39
    dela Cruz, I. J. C.; Perez, J. V.; Alamani, B. G.; Capellades, G.; Myerson, A. S. Influence of Volume on the Nucleation of Model Organic Molecular Crystals through an Induction Time Approach. Cryst. Growth Des. 2021, 21, 29322941,  DOI: 10.1021/acs.cgd.1c00101
  40. 40
    Sangwal, K. Novel Approach to Analyze Metastable Zone Width Determined by the Polythermal Method: Physical Interpretation of Various Parameters. Cryst. Growth Des. 2009, 9, 942950,  DOI: 10.1021/cg800704y
  41. 41
    Pascual, G. K.; Donnellan, P.; Glennon, B.; Kamaraju, V. K.; Jones, R. C. Experimental and Modeling Studies on the Solubility of 2-Chloro-N-(4-Methylphenyl)Propanamide (S1) in Binary Ethyl Acetate + Hexane, Toluene + Hexane, Acetone + Hexane, and Butanone + Hexane Solvent Mixtures Using Polythermal Method. J. Chem. Eng. Data 2017, 62, 31933205,  DOI: 10.1021/acs.jced.7b00288
  42. 42
    Valavi, M.; Svärd, M.; Rasmuson, A. C. Improving Estimates of the Crystallization Driving Force: Investigation into the Dependence on Temperature and Composition of Activity Coefficients in Solution. Cryst. Growth Des. 2016, 16, 69516960,  DOI: 10.1021/acs.cgd.6b01137
  43. 43
    Romdhani, A.; Martínez, F.; Almanza, O. A.; Jouyban, A.; Acree, W. E. Solubility of Acetaminophen in (Ethanol + Propylene Glycol + Water) Mixtures: Measurement, Correlation, Thermodynamics, and Volumetric Contribution at Saturation. J. Mol. Liq. 2020, 318, 114065,  DOI: 10.1016/j.molliq.2020.114065
  44. 44
    Ni, X. W.; Valentine, A.; Liao, A.; Sermage, S. B. C.; Thomson, G. B.; Roberts, K. J. On the Crystal Polymorphic Forms of L-Glutamic Acid Following Temperature Programmed Crystallization in a Batch Oscillatory Baffled Crystallizer. Cryst. Growth Des. 2004, 4, 11291135,  DOI: 10.1021/cg049827l
  45. 45
    Nicoud, L.; Licordari, F.; Myerson, A. S. Estimation of the Solubility of Metastable Polymorphs: A Critical Review. Cryst. Growth Des. 2018, 18, 72287237,  DOI: 10.1021/acs.cgd.8b01200

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This article is cited by 1 publications.

  1. Andrew Cashmore, Russell Miller, Hikaru Jolliffe, Cameron J. Brown, Mei Lee, Mark D. Haw, Jan Sefcik. Rapid Assessment of Crystal Nucleation and Growth Kinetics: Comparison of Seeded and Unseeded Experiments. Crystal Growth & Design 2023, 23 (7) , 4779-4790. https://doi.org/10.1021/acs.cgd.2c01406
  • Abstract

    Figure 1

    Figure 1. Methods overview including the required hardware and software for each step.

    Figure 2

    Figure 2. Example event for crystallization of l-glutamic acid from water, tracking the increase in the total number of crystals per picture and the subsequent drop due to crystal overlap. Only the highlighted area is considered acceptable for parameter estimation, covering an active crystallization event for a dilute system.

    Figure 3

    Figure 3. Block diagram of the data flow for estimation of kinetic parameters in the gPROMS model, including necessary experimental data and its potential sources.

    Figure 4

    Figure 4. Example of the program results for crystallization of l-glutamic acid in water, with a sample concentration of 35 mg/g solvent, Tc = 10 °C, and Tmax = 80 °C. Highlighted areas represent a typical induction time measurement in green (optional for this work, if primary nucleation kinetics are desired), and a typical crystallization event (purple) as it would be cropped by the user. The latter is the same 20 min event included in Figure 2.

    Figure 5

    Figure 5. Removal of outliers for an acetaminophen crystallization event (40 mg/g solvent, 25% ethanol in water, 10 °C) that used an overhead hook for stirring. (a) Raw data for the number of crystals per picture during the event. (b) Data for the same event after outlier removal. Outliers were removed if they were found below 70% of the moving average’s value.

    Figure 6

    Figure 6. Processed trends for an acetaminophen crystallization event (40 mg/g solvent, 25 vol % ethanol in water, 10 °C) after outlier removal, showing the evolution of the total number, length, area, and volume of crystals on camera. The fraction of points removed as outliers is illustrated from the counts at 0 crystals/picture.

    Figure 7

    Figure 7. Solubility curve for acetaminophen in 25 vol % ethanol and 75 vol % water. Data was obtained from polythermal solubility screening that was integrated with the Crystalline program.

    Figure 8

    Figure 8. Overlay of the raw data (before outlier removal) for all 13 successful crystallization events for acetaminophen, with starting times adjusted at the equivalent initial signal. Concentrations are organized by color and individual crystallization events are organized by marker shape.

    Figure 9

    Figure 9. Best fits for acetaminophen parameter estimation. (a) Total number of crystals per picture (Ntot); (b) total crystal area per picture (Atot).

    Figure 10

    Figure 10. Reproducibility of the methods: using parameters estimated from experiments at Rowan University to predict kinetic trends obtained from experiments at Pfizer, with a corrected θ of 2.26 mg/picture due to the higher magnification in the Crystalline. (a) total number of crystals per picture (Ntot); (b) total crystal length per picture (Ltot).

    Figure 11

    Figure 11. Comparison of crystal habits obtained during crystallization of l-glutamic acid from water at 35 and 40 mg/g (solvent basis).

    Figure 12

    Figure 12. Form transition from α-l-glutamic acid to β-l-glutamic acid during polythermal solubility screening and subsequent dissolution of the β form at a higher saturation temperature.

    Figure 13

    Figure 13. Overlay of the raw data for all 10 successful crystallization events for α-l-glutamic acid, with starting times adjusted at the equivalent initial signal. Concentrations are organized by color (labeled), and individual crystallization events are organized by marker shape.

    Figure 14

    Figure 14. Best fits for parameter estimation for crystallization kinetics of the α form of l-glutamic acid. (a) Total number of crystals per picture (Ntot); (b) total crystal area per picture (Atot).

    Figure 15

    Figure 15. Comparison of the performance of the 4 μm/pixel camera against the 1.9 μm/pixel camera for two separate crystallization events of 35 mg/g of l-glutamic acid in water at 10 °C. At the higher magnification, the camera gets saturated sooner and with approximately 1/4 of the number of crystals per picture, limiting both the duration and the amount of valid imaging data obtained from a crystallization event.

  • References

    ARTICLE SECTIONS
    Jump To

    This article references 45 other publications.

    1. 1
      Chen, J.; Sarma, B.; Evans, J. M. B.; Myerson, A. S. Pharmaceutical Crystallization. Cryst. Growth Des. 2011, 11, 887895,  DOI: 10.1021/cg101556s
    2. 2
      Khadka, P.; Ro, J.; Kim, H.; Kim, I.; Kim, J. T.; Kim, H.; Cho, J. M.; Yun, G.; Lee, J. Pharmaceutical Particle Technologies: An Approach to Improve Drug Solubility, Dissolution and Bioavailability. Asian J. Pharm. Sci. 2014, 9, 304316,  DOI: 10.1016/j.ajps.2014.05.005
    3. 3
      Azad, M. A.; Capellades, G.; Wang, A. B.; Klee, D. M.; Hammersmith, G.; Rapp, K.; Brancazio, D.; Myerson, A. S. Impact of Critical Material Attributes (CMAs)-Particle Shape on Miniature Pharmaceutical Unit Operations. AAPS PharmSciTech 2021, 22, 98,  DOI: 10.1208/s12249-020-01915-6
    4. 4
      O’Grady, D.; Barrett, M.; Casey, E.; Glennon, B. The Effect of Mixing on the Metastable Zone Width and Nucleation Kinetics in the Anti-Solvent Crystallization of Benzoic Acid. Chem. Eng. Res. Des. 2007, 85, 945952,  DOI: 10.1205/cherd06207
    5. 5
      Schall, J. M.; Mandur, J. S.; Braatz, R. D.; Myerson, A. S. Nucleation and Growth Kinetics for Combined Cooling and Antisolvent Crystallization in a Mixed-Suspension, Mixed-Product Removal System: Estimating Solvent Dependency. Cryst. Growth Des. 2018, 18, 15601570,  DOI: 10.1021/acs.cgd.7b01528
    6. 6
      Capellades, G.; Wiemeyer, H.; Myerson, A. S. Mixed-Suspension, Mixed-Product Removal Studies of Ciprofloxacin from Pure and Crude Active Pharmaceutical Ingredients: The Role of Impurities on Solubility and Kinetics. Cryst. Growth Des. 2019, 19, 40084018,  DOI: 10.1021/acs.cgd.9b00400
    7. 7
      Myerson, A. S.; Edemir, D.; Lee, A. Y. Handbook of Industrial Crystallization, 3rd Edit.; Cambridge University Press, 2019.
    8. 8
      Schall, J. M.; Capellades, G.; Mandur, J. S.; Braatz, R. D.; Myerson, A. S. Incorporating Solvent-Dependent Kinetics To Design a Multistage, Continuous, Combined Cooling/Antisolvent Crystallization Process. Org. Process Res. Dev. 2019, 23, 19601969,  DOI: 10.1021/acs.oprd.9b00244
    9. 9
      Power, G.; Hou, G.; Kamaraju, V. K.; Morris, G.; Zhao, Y.; Glennon, B. Design and Optimization of a Multistage Continuous Cooling Mixed Suspension, Mixed Product Removal Crystallizer. Chem. Eng. Sci. 2015, 133, 125139,  DOI: 10.1016/j.ces.2015.02.014
    10. 10
      Morris, G.; Power, G.; Ferguson, S.; Barrett, M.; Hou, G.; Glennon, B. Estimation of Nucleation and Growth Kinetics of Benzoic Acid by Population Balance Modeling of a Continuous Cooling Mixed Suspension, Mixed Product Removal Crystallizer. Org. Process Res. Dev. 2015, 19, 18911902,  DOI: 10.1021/acs.oprd.5b00139
    11. 11
      Capellades, G.; Duso, A.; Dam-Johansen, K.; Mealy, M. J.; Christensen, T. v.; Kiil, S. Continuous Crystallization with Gas Entrainment: Evaluating the Effect of a Moving Gas Phase in an MSMPR Crystallizer. Org. Process Res. Dev. 2019, 23, 252262,  DOI: 10.1021/acs.oprd.8b00376
    12. 12
      Nicoud, L.; Licordari, F.; Myerson, A. S. Polymorph Control in MSMPR Crystallizers. A Case Study with Paracetamol. Org. Process Res. Dev. 2019, 23, 794806,  DOI: 10.1021/acs.oprd.8b00351
    13. 13
      David, R.; Marchal, P.; Marcant, B. Modelling of Agglomeration in Industrial Crystallization from Solution. Chem. Eng. Technol. 1995, 18, 302309,  DOI: 10.1002/ceat.270180503
    14. 14
      Chung, S. H.; Lee, H. W.; Saleeby, E. G. Modeling a Cascade of Continuous Msmpr Crystallizers With Agglomeration. Chem. Eng. Commun. 1998, 163, 177200,  DOI: 10.1080/00986449808912350
    15. 15
      Hou, G.; Power, G.; Barrett, M.; Glennon, B.; Morris, G.; Zhao, Y. Development and Characterization of a Single Stage Mixed-Suspension, Mixed-Product-Removal Crystallization Process with a Novel Transfer Unit. Cryst. Growth Des. 2014, 14, 17821793,  DOI: 10.1021/cg401904a
    16. 16
      Rogers, L.; Briggs, N.; Achermann, R.; Adamo, A.; Azad, M.; Brancazio, D.; Capellades, G.; Hammersmith, G.; Hart, T.; Imbrogno, J.; Kelly, L. P.; Liang, G.; Neurohr, C.; Rapp, K.; Russell, M. G.; Salz, C.; Thomas, D. A.; Weimann, L.; Jamison, T. F.; Myerson, A. S.; Jensen, K. F. Continuous Production of Five Active Pharmaceutical Ingredients in Flexible Plug-and-Play Modules: A Demonstration Campaign. Org. Process Res. Dev. 2020, 24, 21832196,  DOI: 10.1021/acs.oprd.0c00208
    17. 17
      Cole, K. P.; Reizman, B. J.; Hess, M.; Groh, J. M.; Laurila, M. E.; Cope, R. F.; Campbell, B. M.; Forst, M. B.; Burt, J. L.; Maloney, T. D.; Johnson, M. D.; Mitchell, D.; Polster, C. S.; Mitra, A. W.; Boukerche, M.; Conder, E. W.; Braden, T. M.; Miller, R. D.; Heller, M. R.; Phillips, J. L.; Howell, J. R. Small-Volume Continuous Manufacturing of Merestinib. Part 1. Process Development and Demonstration. Org. Process Res. Dev. 2019, 23, 858869,  DOI: 10.1021/acs.oprd.8b00441
    18. 18
      Jiang, S.; ter Horst, J. H. Crystal Nucleation Rates from Probability Distributions of Induction Times. Cryst. Growth Des. 2011, 11, 256261,  DOI: 10.1021/cg101213q
    19. 19
      Kulkarni, S. A.; Kadam, S. S.; Meekes, H.; Stankiewicz, A. I.; ter Horst, J. H. Crystal Nucleation Kinetics from Induction Times and Metastable Zone Widths. Cryst. Growth Des. 2013, 13, 24352440,  DOI: 10.1021/cg400139t
    20. 20
      Tan, L.; Davis, R. M.; Myerson, A. S.; Trout, B. L. Control of Heterogeneous Nucleation via Rationally Designed Biocompatible Polymer Surfaces with Nanoscale Features. Cryst. Growth Des. 2015, 15, 21762186,  DOI: 10.1021/cg501823w
    21. 21
      Pons Siepermann, C. A.; Myerson, A. S. Inhibition of Nucleation Using a Dilute, Weakly Hydrogen-Bonding Molecular Additive. Cryst. Growth Des. 2018, 18, 35843595,  DOI: 10.1021/acs.cgd.8b00367
    22. 22
      Ildefonso, M.; Candoni, N.; Veesler, S. A Cheap, Easy Microfluidic Crystallization Device Ensuring Universal Solvent Compatibility. Org. Process Res. Dev. 2012, 16, 556560,  DOI: 10.1021/op200291z
    23. 23
      Ildefonso, M.; Revalor, E.; Punniam, P.; Salmon, J. B.; Candoni, N.; Veesler, S. Nucleation and Polymorphism Explored via an Easy-to-Use Microfluidic Tool. J. Cryst. Growth 2012, 342, 912,  DOI: 10.1016/j.jcrysgro.2010.11.098
    24. 24
      Laval, P.; Salmon, J.-B.; Joanicot, M. A Microfluidic Device for Investigating Crystal Nucleation Kinetics. J. Cryst. Growth 2007, 303, 622628,  DOI: 10.1016/j.jcrysgro.2006.12.044
    25. 25
      Briuglia, M. L.; Sefcik, J.; ter Horst, J. H. Measuring Secondary Nucleation through Single Crystal Seeding. Cryst. Growth Des. 2019, 19, 421429,  DOI: 10.1021/acs.cgd.8b01515
    26. 26
      Wang, X. Z.; Calderon De Anda, J.; Roberts, K. J. Real-Time Measurement of the Growth Rates of Individual Crystal Facets Using Imaging and Image Analysis. Chem. Eng. Res. Des. 2007, 85, 921927,  DOI: 10.1205/cherd06203
    27. 27
      Wu, K.; Ma, C. Y.; Liu, J. J.; Zhang, Y.; Wang, X. Z. Measurement of Crystal Face Specific Growth Kinetics. Cryst. Growth Des. 2016, 16, 48554868,  DOI: 10.1021/acs.cgd.6b00189
    28. 28
      Sangwal, K.; Wójcik, K.; Borc, J. In Situ Study of Growth and Dissolution Kinetics of Ammonium Oxalate Monohydrate Single Crystals from Aqueous Solutions Containing Cationic Impurities. Cryst. Res. Technol. 2007, 42, 12431251,  DOI: 10.1002/crat.200711013
    29. 29
      Quilló, G. L.; Bhonsale, S.; Gielen, B.; van Impe, J. F.; Collas, A.; Xiouras, C. Crystal Growth Kinetics of an Industrial Active Pharmaceutical Ingredient: Implications of Different Representations of Supersaturation and Simultaneous Growth Mechanisms. Cryst. Growth Des. 2021, 21, 54035420,  DOI: 10.1021/acs.cgd.1c00677
    30. 30
      Randolph, A. D.; Larson, M. A. Theory of Particulate Processes - Analysis and Techniques of Continuous Crystallization; Academic Press, Inc., 1971.
    31. 31
      Deck, L. T.; Mazzotti, M. Conceptual Validation of Stochastic and Deterministic Methods To Estimate Crystal Nucleation Rates. Cryst. Growth Des. 2022, 23, 899914,  DOI: 10.1021/acs.cgd.2c01133
    32. 32
      Maggioni, G. M.; Bosetti, L.; dos Santos, E.; Mazzotti, M. Statistical Analysis of Series of Detection Time Measurements for the Estimation of Nucleation Rates. Cryst. Growth Des. 2017, 17, 54885498,  DOI: 10.1021/acs.cgd.7b01014
    33. 33
      Kail, N.; Briesen, H.; Marquardt, W. Analysis of FBRM Measurements by Means of a 3D Optical Model. Powder Technol. 2008, 185, 211222,  DOI: 10.1016/j.powtec.2007.10.015
    34. 34
      Barrett, P.; Glennon, B. In-Line FBRM Monitoring of Particle Size in Dilute Agitated Suspensions. Part. Part. Syst. Charact. 1999, 16, 207211,  DOI: 10.1002/(SICI)1521-4117(199910)16:5<207::AID-PPSC207>3.0.CO;2-U
    35. 35
      Yenkie, K. M.; Diwekar, U. Stochastic Optimal Control of Seeded Batch Crystallizer Applying the Ito Process. Ind. Eng. Chem. Res. 2012, 52, 108122,  DOI: 10.1021/ie300491v
    36. 36
      Ottens, E. P. K.; de Jong, E. J. A Model for Secondary Nucleation in a Stirred Vessel Cooling Crystallizer. Ind. Eng. Chem. Fund. 1973, 12, 179184,  DOI: 10.1021/i160046a006
    37. 37
      Evans, T. W.; Sarofim, A. F.; Margolis, G. Models of Secondary Nucleation Attributable to Crystal-crystallizer and Crystal-crystal Collisions. AIChE J. 1974, 20, 959966,  DOI: 10.1002/aic.690200517
    38. 38
      Schall, J. M.; Capellades, G.; Myerson, A. S. Methods for Estimating Supersaturation in Antisolvent Crystallization Systems. CrystEngComm 2019, 21, 58115817,  DOI: 10.1039/c9ce00843h
    39. 39
      dela Cruz, I. J. C.; Perez, J. V.; Alamani, B. G.; Capellades, G.; Myerson, A. S. Influence of Volume on the Nucleation of Model Organic Molecular Crystals through an Induction Time Approach. Cryst. Growth Des. 2021, 21, 29322941,  DOI: 10.1021/acs.cgd.1c00101
    40. 40
      Sangwal, K. Novel Approach to Analyze Metastable Zone Width Determined by the Polythermal Method: Physical Interpretation of Various Parameters. Cryst. Growth Des. 2009, 9, 942950,  DOI: 10.1021/cg800704y
    41. 41
      Pascual, G. K.; Donnellan, P.; Glennon, B.; Kamaraju, V. K.; Jones, R. C. Experimental and Modeling Studies on the Solubility of 2-Chloro-N-(4-Methylphenyl)Propanamide (S1) in Binary Ethyl Acetate + Hexane, Toluene + Hexane, Acetone + Hexane, and Butanone + Hexane Solvent Mixtures Using Polythermal Method. J. Chem. Eng. Data 2017, 62, 31933205,  DOI: 10.1021/acs.jced.7b00288
    42. 42
      Valavi, M.; Svärd, M.; Rasmuson, A. C. Improving Estimates of the Crystallization Driving Force: Investigation into the Dependence on Temperature and Composition of Activity Coefficients in Solution. Cryst. Growth Des. 2016, 16, 69516960,  DOI: 10.1021/acs.cgd.6b01137
    43. 43
      Romdhani, A.; Martínez, F.; Almanza, O. A.; Jouyban, A.; Acree, W. E. Solubility of Acetaminophen in (Ethanol + Propylene Glycol + Water) Mixtures: Measurement, Correlation, Thermodynamics, and Volumetric Contribution at Saturation. J. Mol. Liq. 2020, 318, 114065,  DOI: 10.1016/j.molliq.2020.114065
    44. 44
      Ni, X. W.; Valentine, A.; Liao, A.; Sermage, S. B. C.; Thomson, G. B.; Roberts, K. J. On the Crystal Polymorphic Forms of L-Glutamic Acid Following Temperature Programmed Crystallization in a Batch Oscillatory Baffled Crystallizer. Cryst. Growth Des. 2004, 4, 11291135,  DOI: 10.1021/cg049827l
    45. 45
      Nicoud, L.; Licordari, F.; Myerson, A. S. Estimation of the Solubility of Metastable Polymorphs: A Critical Review. Cryst. Growth Des. 2018, 18, 72287237,  DOI: 10.1021/acs.cgd.8b01200
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