crystallization. crystallization principle primary nucleation: can be either homogeneous or...
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Crystallization
Crystallization Principle
Primary nucleation: Can be either homogeneous or heterogeneous
The rate of primary nucleation modeled by power law expression:
No foreign particles present
Foreign particles present
B = no. of nuclei formed per unit volume per unit timeN = no. of nuclei per unit volumekn = rate constantc = instantaneous solute conc.c* = solute conc. at saturation(c – c*) = supersaturationn = exponent typically 3 to 4.
Crystallization Principle
Secondary nucleation (usually predominates):
The rate of secondary nucleation:
Shear nucleation
Contact nucleation
K1 = rate constantMT = suspension densityb = exponent typically 2.j= 1 (most probable value)
Occurs as a result of fluid shear on
growing crystal faces
Occurs because of crystals colliding with each other and with impeller and other vessel internal surfaces
Crystallization Principle- As in precipitation, the solution must be supersaturated in order
for particles to form crystal (c – c*) in both Eqs.- Supersaturation must be above a certain value before nucleation
will begin.
Crystallization Principle
1• In Metastable region, the
supersaturation is so low that nucleation will not start.
2• The supersaturation is raised to Labile
region, nucleation can begin. • At this point, crystals begin to grow, and
the supersaturation decreases.• Point • is possible way of carrying out a
crystallization.
3• If the supersaturation becomes too
high, the nucleation rate will be too great, and an amorphous precipitate will result.
Crystallization Principle3) Crystal Growth- Crystal growth is the post-nucleation process in which the
molecules in solution are added to the surface of existing crystals.
- For designing a crystallizer, the useful relationship describing the rate of mass deposition, R during crystal growth is:
W = mass of crystals per volume of solvent
A = surface area of crystals per volume of solvent kG = overall mass transfer coefficient (depend on T, crystal size, hydrodynamic conditions, and presence of impurities.) g = the order usually between 0 – 2.5 (near unity is most common)
Crystallization Principle3) Crystal Growth- Also, to express overall linear growth rate as (delta L law):
L = characteristic single dimension of the crystal, such as length
It is shown that geometrically similar crystals of the same material grow at the rate described by Eq 9.2.4.
Crystallization Principle3) Crystal Growth- Crystal growth is actually a process that consists of two steps
in series.
(1) Solute molecules must reach the crystal surface by means of diffusion.
(2) At the surface, the solute must be integrated into the crystal lattice.
Crystallization Principle3) Crystal Growth
Where ci = concentration at the interface between liquid and solid phase. kd & kr = mass transfer coefficients.
- When the exponents are unity, combining Eqs (9.2.3), (9.2.5) & (9.2.6) gives:
Thus, if surface integration is very fast compared with bulk diffusion, then, and
Crystallization Principle4) Crystallization Kinetics from Batch Experiment
Process Crystallization of ProteinWhy use crystallization for purification of protein?
1) One or more expensive chromatography steps possibly can be eliminated.
2) Relatively inexpensive to carry out, since costly adsorbents are not required (as in chromatography)
3) Proteins crystals often can be stored for long periods at low T without being degraded or denatured after the addition of stabilizing agents such as ammonium sulfate, glycerol, or sucrose.
Process Crystallization of ProteinHow to crystallize protein?- Adjustment of pH to isoelectric point (isoelectric precipitation)- Addition of organic solvents- Addition of salts (salting-out)- Addition of non-ionic polymers.
Another way to crystallize protein?- Reduction of ionic strength by dialysis or diafiltration, which
relies on the limited solubility of many proteins at low ionic strength (reverse of “salting-in” effect).
- Key strategy: move the system very slowly to a state of min. solubility of the desired protein until a limited degree of supersaturation is reached.
Process Crystallization of ProteinStudy case:
1) Alcohol oxidase enzyme - from Pichia pastoris yeast
- grown in a 100-L pilot plant fermentor- crystallized by lowering ionic strength by diafiltration with deionized water- crystallization was preceded by lysis of yeast cells, diafiltration with microfilter to obtain alcohol oxidase in the permeate, and concentration and then diafiltration with an ultrafilter.
Process Crystallization of ProteinStudy case:
2) Ovalbumin - crystallized in the presence of conalbumin and lysozyme by
addition of 2.5 µm seed crystals to a solution (600 mL) that had been made supersaturated by slowly adding ammonium sulfate solution. - the supersaturation was kept in the metastable region to avoid nucleation.- the crytals growth rate is a second-order dependence on ovalbumin supersaturation, and the presence of the other 2 proteins did not affect the growth rate constant.
Crystallizer Scale-up & DesignImpurity is a problem in crystallization, can be in the
following locations in crystal sample:
1) Deposited on crystal surfaces due to incomplete removal of impure mother liquor.
2) Trapped within voids between separate crystals in materials that agglomerate.
3) Contained in inclusions of mother liquor within individual crystals.
4) Distributed throughout the crystals by molecular substitution at the lattice sites.
Crystallizer Scale-up & DesignIt is recommended that geometric similarity and
constant power per volume be used in scale-up of crystallizers.
For turbulent flow in vessels (Reynolds number >
10,000), constant power per volume:
For an agitated tank, the Reynolds number is:
Ni = impeller rotation ratedi = impeller diameter
Ni = rev. per minρ = fluid densityµ = fluid viscosity
Crystallizer Scale-up & Design2 additional strategies also used in Scale-up:
1) Maintaining constant impeller tip speed;
2) Scale-up at the minimum speed required for particle suspension;
Practice 1: Solubility in Crystallization
Given solubility data for Phthalic acid as follows:
18 g / 100 mL water at 100 ºC
0.54 g / 100 mL water at 15 ºC
A student obtained 3.2 g of crude phthalic acid. After recrystallization and drying, 2.5 g of pure acid was obtained. Calculate:
a) The percent recovery
2.5g/3.2gx100 =78%
b) Amount of water needed for recrystallization
100mL/18gx3.2g = 17.7mL
c) Amount of product lost to the filtrate.
0.54g/100mLx17.7mL=0.1g