Crystal Growth - ETH Zürich - Homepage | ETH Zürich · 2020. 11. 4. · Crystal morphology...
Transcript of Crystal Growth - ETH Zürich - Homepage | ETH Zürich · 2020. 11. 4. · Crystal morphology...
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal Growth
Rate-Controlled Separations in Fine Chemistry
Crystallization
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Topics
1. Crystal growth: definition
2. Crystal surface
3. Crystal-fluid interface
4. Crystal growth: a 2-step process
5. Growth mechanisms: Continuous growth, Birth & spread (surface nucleation), Spiral growth (BFC)
6. Growth kinetics: experimental methods and parameter estimation
7. Crystal morphology: engineering and theoretical prediction
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal growth: single crystal (video)
Naphthalene in ethanol: single crystal growth
the fastest growing facet disappears
immediately and the crystal grows to a
regular shape
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal growth: definition
• The linear growth rate is the rate of growth of a face in the
direction normal to the face: velocity in the internal coordinate
• Growth is a kinetic phenomenon driven by supersaturation
(𝑆 > 1), that is determined by the thermodynamic data.
• Growth occurs independently for each face in layer-by-layer
fashion.
• The relative growth rates of the faces determine the crystal shape.
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal surface
• The ability of a surface to capture and integrate growth units into the crystal lattice depends upon the
strength and number of interactions that can form between the surface and the growth unit.
Molecules tend to bond at locations where they have
the maximum number of nearest neighbours.
• In a 2-D structure: the molecules are nodes of the structure, and a
new molecule connects expanding the regular structure:
• Case A: 1 bond is formed
• Case B: 2 bonds are formed. Favoured, since the system gains
more energy.
• The sites on the growing crystal surface can be classified as follows:
• Kink (K-face): when 3 bonds are possible
• Step (S-face): when 2 bonds are bonds possible
• Flat (F-face): when 1 bond is possible
With linear growth rate, 𝑣, proportional to the total binding energy:
B
A
Fast face B
disappears while
slow face A remains
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal-fluid interface
• Described by the “multilayer” model (Temkin, 1966): solid and fluid divided into blocks of equal size
Energy change (Δ𝐸) occurring when a perfectly flat surface is
roughened by removing one block (molecule) from the surface
and start a new layer.
solid-solid block interaction solid-fluid block interaction fluid-fluid block interaction
α-factor: indicates how easy a surface can form sites with multiple binding interactions (how easy a
surface can grow).
Rough surface fast growth
Intermediate
Flat surface slow growth
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal growth: a 2-step process
1. Mass transfer: desolvation and diffusion from the bulk solution to the interface (faster mass transfer,
faster growth).
2. Surface integration: inclusion in the crystal lattice: the more defects (inclusion sites), better
integration.
Adsorption layer
Desolvation
Diffusion
Inclusion
Step
Kink
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Growth mechanism: continuous growth (or rough growth)
• The energy for the formation of a step is low: surface with many kink and step sites (rough)
• Diffusion is the limiting step, since every unit reaching the surface will find a growth site.
Bulk concentration solubility
Rough surface
Diffusion
Inclusion
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Growth mechanism: birth and spread (surface nucleation)
• Roughness decreases
• Mass transfer is fast, but some units do not find an inclusion site:
they return to the fluid
Or join adsorbed growth units to form surface islands, disks or nuclei, binding to the surface, and
forming more step and kink sites, that promotes the growth of a new layer.
Ass: continuous
growth
Growth of the disk
Binding to
the crystal
Island diameter
Energy variation
related to the area related to the links
constants
Similar to the equation for homogeneous primary nucleation,
since the formation of critically sized 2D nuclei is needed Real: non-continuous growth
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Growth mechanism: spiral growth
• Surface is flat
• Growth can occur only if built-in lattice defects (dislocations) provide
energetically “cheap” processes for new molecule to be included in the
crystal and start a new layer
• Phenomenon may be controlled either by diffusion from the bulk solution
directly into the kink sites, or by two-dimensional diffusion across the
crystal surface (Burton, Cabrera and Frank 1951).
• Each crystal can have its own growth rate determined by its specific
dislocation structure.
Concentration of dislocation
Unitary growth of a single disk
Paloczi, et al., Applied Physics Letters, 1998, 73, 1658 LI, et al. Prog. Mater. Sci.., 2016, 82, 1-38.
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Growth mechanism: spiral growth (video)
Spiral growth of cysteine (oxidized dimer form of
the amino acid cysteine )
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal growth kinetics
Correlation between supersaturation and crystal growth can be incorporated in process models for
process design:
The growth rate can be measured as:
• Length/time: linear crystal growth. It is facet specific
• Mass/area time: mass rate of crystal growth
Temperature dependence
• Arrhenius equation: Activation energy of growth: it informs about the rate-limiting step (diffusion or surface integration)
• diffusion-limited growth
• integration-limited growth
Garside, J. et al Measurement of Crystal Growth and Nucleation Rates, 2nd ed.; IChemE: UK, 2002.
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Measurement of crystal growth rates
The experimental methods for growth rate estimation can be classified as:
• Direct methods
Single crystal growth: length- or mass-based rate
Growth of suspension of crystals: mass-based rate
• Indirect methods
Concentration monitoring over time
Ochsenbein, et al. Chem. Eng. Sci., 2015, 133, 30-43.
Different growth mechanisms as a function of S
Desupersaturation curve
LI, et al. Prog. Mater. Sci.., 2016, 82, 1-38.
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Direct methods: single crystal experiments
• Monitoring over time the growth of a large single crystal in supersaturated
conditions with optical microscopy techniques or atomic force microscopy (AFM).
• The growth mechanism and rate can be estimated for each facet.
Theoretical predictions are compared to experimental kinetic measurements in a
range of supersaturations.
Alternatively, a mass-based rate can be computed by weighing the crystal before
and after the experiment
Davey et al., J. Phys. Chem., 1988, 92, 2032-2036
Succinic acid
α-resorcinol
BCF
Birth&spreadSalicylamide
Lynch & Rasmuson, Cryst. Growth Des. 2019, 19, 7230−7239
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Single crystal experiments: devices
• Constant temperature
• Large volume of solution to ensure constant supersaturation
• Not stagnant solution in order to prevent diffusion from controlling the crystal growth rate
Stirred solution
Pumped solution: increase chance of nucleation
Rotating disk: the crystal is fixed on a disk that moves instead of the liquid
Myerson et al., Handbook of Industrial Crystallization, 2019
To minimize the effect of bulk diffusion,
the growth rate is measured as a function of
flow rate (or stirring speed, at constant S).
The growth rate increases with increasing
flow rate, if mass transfer is controlling, until
a constant value.
A flow rate is chosen in the range where
constant rate is detected (no mass-transfer
controlled).
Lynch & Rasmuson, Cryst. Growth Des. 2019, 19, 7230−7239
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Direct methods: crystal suspension
Conditions more similar to an industrial environment:
• Fluidized-bed crystalliser: solution is recirculated and seeds suspended in the vessel.
Constant temperature and supersaturation
• MSMPR operating at steady state: growth rates obtained based on population balance concepts.
Temmel et al., Crystals, 2020, 10, 394
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Indirect methods: desupersaturation experiments
• Batch seeded isothermal experiment
• Monitoring over time the concentration profile of the bulk solution with spectroscopical techniques, at
conditions where only growth occurs (nucleation is avoided).
• A model (no nucleation) is fitted to the experimental data for the estimation of the growth rate.
Procedure:
1. Equilibration of the saturated solution of known
concentration, cooled to the desired supersaturation.
2. Addition of the seeds to the clear solution at
constant temperature: they will grow until reaching
the solubility concentration.
3. Monitoring the desupersaturation with IR (or
densitometer, sampling) in the presence of the
FBRM (counting the crystal number to detect
nucleation and discard the experiment in case it
occurs)
1. Cooling
2. Seeding
3. Growing
IR
FBRM
t
c
t#
1
2
3
1
2
3
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Parameter estimation
• Growth experiments are run at conditions at which nucleation is negligible.
• A PBE model is used to describe the process and solved assuming that nucleation is not occurring.
• Several models can be used to fit the experimental desupersaturation data, and the appropriate one
should be chosen.
For example:
• Isothermal case [length or mass based G rate]
• Temperature dependent growth rate
Arrhenius type T-dependence
Schöll et al, Faraday Discuss., 2007, 136, 247–264
Growth rate estimated
from experiments
Extrapolated, in
agreement with
previous
experimental results
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal morphology
Crystal size and shape can affect:
• Processability: filterability, tableting
• Dissolution
Crystals having the same internal structure can have different external shape.
• “equilibrium” habit: crystal shape when it is allowed to equilibrate with its surroundings. Minimization of the
surface energy
• “Growth” habit: crystal shape developed when kinetics dominate.
Slow growing facets
Fast
growing
facets
It is determined by:
1. The internal crystal structure
2. Relative growth rates of the facets
3. External factors: solvent, supersaturation,
temperature, solution purity/additives. Slow growing
facets
Fast growing
facets
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Morphology engineering
Different strategies can be implemented to modify the crystal morphology
• Milling: mechanical action promoting crystal breakage and defects formation.
• Temperature cycling: heating and cooling cycles.
• Solvent selection: solute-solvent interaction can promote growth of different facets.
• Habit modifiers:
Tailor-made additives: usually one part is structurally similar to the crystallizing molecule,
while another is dissimilar.
Impurities and process by-products (ex. Biuret promotes better processable habit for urea)
Others: dyes, polymers, surfactans.
• Spherical crystallization
Sperical agglomeration
Emulsion solvent diffusion
• Sonocrystallization: induced nucleation at low supersaturation, that can be convenient for the desired shape
Salvatori & Mazzotti Ind. Eng. Chem. Res. 2017, 56, 32, 9188–9201
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal morphology prediction
• Thermodynamic model for morphology prediction: minimization of the
energy (Wulff construction), but this results to be wrong.
• Other models have been developed (for example Bravais-Friedel-Donnay-
Harker, specific force field)
Reasonable good prediction in case of crystals grown from vapor or
sublimation, and in case of weak solute-solvent interactions.
Large deviation in case of strong solute-solvent interactions, since the
models usually neglect the effects of solvents and additives.
Improvement: simplified kinetic model with a solvent dependent parameter that
can be determined from molecular dynamics simulations of the surface–
solution interface.
Different faces have different growth rates, due to the different functional groups exposed. The energy for
the formation of a crystal is:
surface energy per unit area of the face 𝑖
of the th crystal face and is the area of said face
area of the face 𝑖
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Kinetic model: shape evolution model
• Describes the temporal evolution of the perpendicular distance of all the crystal faces. Prediction of
appearance and disappearance of crystal faces.
• Required: unit cell and symmetry data, likely crystallographic faces and their associated growth rates.
• Model totally independent of any physical model used to describe the
growth rate of faces, as long as the previously described time
transformation has no time reversal.
Assumption: the crystal is faceted for all time.
• Successful prediction of steady state shapes confirmed experimentally
(adipic acid and glycine in water).
Zhang et al., AIChEJ, 2006, 52, 1906
Gadewar & Doherty, Journal of Crystal Growth, 2004, 267, 239–250
Li, et al. Prog. Mater. Sci.., 2016, 82, 1-38.
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Kinetic model: shape evolution model
Introducing non-dimensional variables, the fact that crystals evolve to self-similar shape (steady state shape) can be captured.
Perpendicular distance of face 𝑖 [μm]
Growth rate of face 𝑖 [μm/s]
Dimensionless perpendicular
distance of face 𝑖
Relative growth rate
Dimensionless wrapped time
At steady state: constant relative growth rate
Reference face never disappears,
such that 𝑡 → 𝜉 has no time reversal
Dynamic model for each crystal face
Introducing the dimensionless time
It describes the crystal shape
Frank-Chernov condition
Frank F. C. Growth and Perfection of Crystals, Wiley: New York 1958.
Chernov A. A. Soviet Physics-Crystallography 1963, 7, 728-730.
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Shape evolution model: example
Case 1: large , blue facet disappear Case 2: large , red facet disappear
Same crystal shape, but different functional groups at the surface
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
Crystal growth in summary
• 𝑺 > 𝟏 for crystal growth to occur.
• The growth rate is the velocity in the internal coordinate:
• Each facet has a different growth rate, and this determines the crystal shape.
• Growth is a 2-step process: diffusion, inclusion.
• Depending on the roughness of the crystal surface, different growth mechanism can be identified:
Continuous growth (or rough growth)
Birth & spread (surface nucleation)
Spiral growth (BCF)
• The growth can be measured experimentally, with direct (single crystal or suspension) or indirect
methods (desuperaturation curve), at iso- or poly-thermal.
• The crystal morphology can be modified with different methods.
• Several models aim at predicting the crystal morphology: thermodynamic or kinetic models.
Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations
References
• Davey & Garside, From molecules to Crystallizers, 2000
• Paloczi, et al., Applied Physics Letters, 1998, 73, 1658
• Ochsenbein, et al. Chem. Eng. Sci., 2015, 133, 30-43.
• Davey et al., J. Phys. Chem., 1988, 92, 2032-2036
• Lynch & Rasmuson, Cryst. Growth Des. 2019, 19, 7230−7239
• Myerson et al., Handbook of Industrial Crystallization, 2019
• Temmel et al., Crystals, 2020, 10, 394
• Schöll et al, Faraday Discuss., 2007, 136, 247–264
• Salvatori & Mazzotti Ind. Eng. Chem. Res. 2017, 56, 32, 9188–9201
• Zhang et al., AIChEJ, 2006, 52, 1906
• Gadewar & Doherty, Journal of Crystal Growth, 2004, 267, 239–250
• Frank F. C. Growth and Perfection of Crystals, Wiley: New York 1958.
• Chernov A. A. Soviet Physics-Crystallography 1963, 7, 728-730
• Li, et al. Prog. Mater. Sci.., 2016, 82, 1-38.
• Garside, J et alJ. Measurement of Crystal Growth and Nucleation Rates, 2nd ed.; IChemE: UK, 2002.