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Separation Processes Laboratory - Prof. Mazzotti - Rate Controlled Separations

Crystal Growth

Rate-Controlled Separations in Fine Chemistry

Crystallization


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


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


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.


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


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


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


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


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


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.


Growth mechanism: spiral growth (video)

Spiral growth of cysteine (oxidized dimer form of

the amino acid cysteine )


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.


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.


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


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


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


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


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


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


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


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


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.


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.


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


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.


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.

crystal growth - eth zürich - homepage | eth zürich · 2020. 11. 4. · crystal morphology...

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