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Modeling Approaches to Increase the Efficiency of Clear-Point-Based Solubility CharacterizationPaul Larsen, Dallin WhitakerCrop Protection Product Design & Process R&D
OCTOBER 4, 2018
TECHNO BIS CRYSTALLI Z ATI O N WORKSHOP
Agriculture Division of DowDuPont
Who is Corteva?
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Crystallization Background
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• Image Analysis
• Population Balance Modeling
• Statistical Estimation
PhD Thesis, UW-Madison 2007:http://jbrwww.che.wisc.edu/theses/larsen.pdf
Crystallization Background
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• Optimization of industrial crystallizers• Solubility characterization• Design and start-up of new, commercial-scale,
continuous crystallizer• Formulation product development
Early Stage Solvent Screening
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• Objective:• Identify promising solvents for crystallization and/or formulation
• Constraints:• Material availability• Time
• Considerations• Solvency for active ingredient• Solvent physical properties• Impact on product performance• Regulatory considerations• Cost/availability
Analytical method (aka slurry equilibration)• Add excess solids to solvent to create slurry• Equilibrate at desired temperature • Sample and analyze supernatant
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Solubility Measurement: Analytical Method
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Isothermal Clear-Point MethodLoading [wt%]
2 4 6 8 10 12 14 16
20 °C
40 °C
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Transmissivity
Temperature
Clear point
Cloud point
Lasersource
Detector
Polythermal Clear-Point Method
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Figure courtesy of Technobis Crystallization Systems
Polythermal Method: Crystal16
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Analytical method
Isothermal Clear point
Polythermal Clear point
Sample prep timeHeating/mixing equipment timeAnalytical analysis timeImpurity analysisCloud pointAccuracyMaterial Quantity
Method Comparison
Downsides of Polythermal Method
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Polythermal clear-point determination requires 1. a priori knowledge of the solubility in the various solvents of
interest2. a method to extrapolate the measured results to a specific
temperature of interest, 3. understanding of suitable temperature ramp rates for
adequate accuracy
Each of these challenges can be addressed by modeling.
A priori knowledge of solubility
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Options for solubility range-finding:1. Experimental 2. Semi-empirical
• Determine model parameters by regressing data in 4+ different solvents
• Examples: Hansen (HSPiP), Regressed UNIFAC (Dynochem), NRTL-SAC (AspenTech)
3. Quantum chemistry, ab initio• Determine solubility based on molecular structure,
quantum chemistry, and statistical thermodynamics• Examples: COSMO-RS (COSMOtherm), COSMO-SAC
hansen-solubility.com
AspenTech
COSMOtherm Approach
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StatisticalThermodynamics
polarization charge density (σ) calculation
σ-profilegeneration
Phase equilibrium predictionsVLE, SLE, LLE,
COSMOtherm Features
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1. Accuracy• Reasonably accurate relative solubility prediction based on molecular
structure alone – no data required• Sufficiently accurate absolute solubility prediction based on solubility data in
single solvent – even for complex molecules (Mw < 600 g/mol)
2. Less material usage and experimental effort than other approaches3. Useful for other applications (e.g. cocrystal screening, partition ratios)4. Speed
• May require days for quantum calcs for new molecule• Solubility prediction takes only minutes – hundreds/day
5. Ease-of-use• Software easy to use (but learning curve is steeper than other approaches)• Software designed for scripting and batch processing
COSMOtherm Accuracy
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Mea
sure
d M
ass F
ract
ion
Predicted Mass Fraction
Agrochemical Active Ingredient, Mw ~ 500 g/molHigh solubility in many organic solvents
COSMOtherm Accuracy
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Mea
sure
d M
ass
Frac
Predicted Mass Frac
Agrochemical Active Ingredient, Mw ~ 400 g/molHigh solubility in many organic solvents
COSMOtherm Accuracy
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Agrochemical Active Ingredient, Mw ~ 450 g/molLow solubility in many organic solvents
0
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Mea
sure
d M
ass F
ract
ion
Predicted Mass Fraction
COSMOtherm Accuracy
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Agrochemical Intermediate, Mw ~ 400 g/molHansen method ineffective (R2<0.3)
0.0
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Mea
sure
d M
ass F
ract
ion
Predicted Mass Fraction
COSMOtherm is not perfect, but good enough to get in the right ballpark for polythermal solubility measurement
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COSMOtherm and Solubility Workflow
Predicting solubility at specific temperature
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ln 𝛾𝛾𝑥𝑥 =∆𝐻𝐻𝑓𝑓𝑅𝑅
1𝑇𝑇𝑓𝑓−
1𝑇𝑇
𝑐𝑐 = 𝐴𝐴 + 𝐵𝐵𝑇𝑇 + 𝐶𝐶𝑇𝑇2
ln 𝑥𝑥 = 𝐴𝐴 +𝐵𝐵𝑇𝑇 + 𝐶𝐶 ln𝑇𝑇
…and many other variations
Recommend semi-empirical because Schroder-Van Laar often not adequate and empirical may produce non-physical results
Simplified Schroder-Van Laar
Empirical
Semi-empirical
Selecting a suitable ramp rate for polythermal clear-point method
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Factors that determine suitable temperature ramp rate:• Intrinsic dissolution rate• Initial particle size distribution (PSD)• Solubility
Approach: Use simulation to characterize impact of these factors on measurement accuracy
Particle size, [um]
Characterizing measurement accuracy via simulation
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Type Equation Key Assumptions
Population Balance
Size-independent dissolution rate
Dissolution rate
Well-mixed, no mass transfer limitations
Mass Balance Constant slurry volume
Transmittance(Beer-Lambert)
Dilute slurry, single-scattering
Model solution via method of characteristics and method of moments
D
D
𝐷𝐷 = 𝑘𝑘𝑑𝑑 �̂�𝐶 − �̂�𝐶∗
H. B. Matthews, Model Identification and Control of Batch Crystallization for an Industrial Chemical System, PhD thesis, University of Wisconsin-Madison, April 1997.
Example Simulation Output
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t = 0 min
t = 900 min
t = 1150 min
Particle size, [um]
PSD
Time [min]
Time [min]
solubility
Liquid phase conc.
end of transitionstart end
DOE: impact of variables on measurement accuracy
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Objective: Determine relative significance of variables impacting accuracy of polythermal clear-point-based solubility measurement
Factors:1. Ramp rate [C/min]2. Mean particle size [um]3. PSD shape [unitless]4. Dissolution rate constant [cm/min]5. Solubility at 0 C [mass fraction]6. Slope of solubility curve [1/C]
Design: full-factorial (64 simulations)
Characteristic Length [µm]
Particle Size Distribution
DOE: impact of variables on measurement accuracy
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Objective: Determine relative significance of variables impacting accuracy of polythermal clear-point-based solubility measurement
Factors:1. Ramp rate [C/min]2. Mean particle size [um]3. PSD shape [unitless]4. Dissolution rate constant [cm/min]5. Solubility at 0 C [mass fraction]6. Slope of solubility curve [1/C]
Design: full-factorial (64 simulations)
Characteristic Length [µm]
Particle Size Distribution
Solubility Curve
DOE Results
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Mean particle sizeDissolution rate constantRamp rateSlope of solubility curvePSD shape
Solubility at 0 C
Some Practical Questions
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1. What systems are suitable for clear-point-based measurement?2. How small should particles be to obtain accurate
measurement?3. What ramp rate is needed for worst-case scenario (low
solubility, low dissolution rate)?4. What can we learn from the shape of the transmittance
profile?
Impact of Particle Size and Ramp Rate
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Mean size = 100 µm
50 µm
10 µm
Mean size = 100 µm
50 µm
10 µm
Impact of Particle Size and Ramp Rate
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Mean size = 100 µm
50 µm
10 µm
Mean size = 100 µm
50 µm
10 µm
For systems with solubility <1 wt%, it is recommended to use particles with size ~10um.
Impact of Particle Size and Ramp Rate
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Mean size = 100 µm
50 µm
10 µm
Polythermal clear point method not recommended for systems with solubility < 1000ppm.
What determines the shape of the transmittance profile?
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narrow wide
Tran
smitt
ance
time time
Hypothesis: Measurement error correlates with transition width.
Transition width = Temp at end – Temp at start
Measurement error vs transition width
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Wide transition does not necessarily indicate low accuracy
Measurement error vs transition width
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Purple: low solubilityBlue: medium solubilityYellow: high solubilityMarker size: particle size
Transition width depends on many factors Generally increases with decreasing solubility and increasing particle size
Measurement error vs transition width
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Purple: low dissolution rate constantYellow: high dissolution rate constantMarker size: ramp rate
Transition width also affected by Ramp rate and dissolution rate
Summary
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1. Polythermal clear point method has many advantages for early-stage solvent screening.
2. Predictive tools such as COSMOtherm increase the experimental efficiency of clear point methods.
3. Measurement accuracy depends not only on ramp rate but also on initial PSD, intrinsic dissolution rate, and solubility curve.
4. Keep ramp rate and initial particle size as small as feasible to increase accuracy.