0263–8762/02/$23.50+0.00
# Institution of Chemical Engineers
Trans IChemE, Vol 80, Part A, October 2002
www.catchword.com=titles=02638762.htm
CHARACTERIZING THE METASTABLE ZONE
WIDTH AND SOLUBILITY CURVE USING
LASENTEC FBRM AND PVM
P. BARRETT and B. GLENNON
Department of Chemical Engineering, University College Dublin, Dublin, Ireland
A
successful industrial crystallization typically requires the development of a robust
process in the laboratory. Knowledge of the solubility curve and the stability of the
solution in the vicinity of the equilibrium point, as indicated by the metastable zone
width, is essential to the successful development, optimization, and scale-up of a crystallization
process. Use of the Lasentec Focused Beam Re ectance (FBRM) system, with aqueous potash
alum solutions, to determine both the metastable zone width and solubility curve is demonstrated. The measured metastable zone width data are also used to estimate the nucleation
kinetics of the system. Lasentec Particle Vision and Measurement (PVM) images are also
employed to validate the results. The data collected using the FBRM system compare very well
with published literature values for potash alum solubility and metastable zone width in
aqueous solutions.
Keywords: nucleation; metastable zone width; solubility curve; Lasentec; FBRM; PVM.
INTRODUCTION
For the work presented in this paper, a Focused Beam
Re ectance (FBRM) probe (model M400LF, Lasentec Inc.,
USA) is used as the tool to help characterize both the
nucleation and dissolution properties of the material.
FBRM measures a chord length distribution (CLD),
which is a function of the number, size, and shape of
particles under investigation13 . FBRM uses a focused beam
of laser light, which scans in a circular path. As this light
scans across a particle or particle structure passing in front
of the probe window, light is scattered in all directions.
The light scattered back towards the probe is used to
measure a chord length off the given particle. Typically,
many thousands of chords are measured per second,
providing a robust measurement that is sensitive to the
change in the size or number of particles under investigation. Unlike, for example, optical turbidity or laser diffraction, FBRM does not depend on the presence of a
threshold nuclei concentration before a nucleation event
is detected—as soon as one particle is in the detectable
size range it will be detected. A more detailed description
of the operation of the FBRM probe is provided by other
authors 14 ,1 5 . FBRM has been used by previous researchers
to help characterize the metastable zone width1 6 and is
widely used as a tool for both batch and continuous
crystallization development and scale-up1 7,18 , crystallization control19 , and the troubleshooting and optimization of
downstream processing problems20 ,21 .
A Particle Vision and Measurement (PVM) probe (model
PVM 700L, Lasentec Inc., USA) was also integrated into
these experiments. PVM is a probe-based high resolution
in-situ video microscope providing images of crystals and
crystal structures as they exist in a process. PVM uses six
independent laser sources to illuminate a Ž xed area within
General Introduction
A solute will remain in solution until a sufŽ ciently high
level of supersaturation has been developed to induce
spontaneous nucleation. The extent of this supersaturation
is referred to as the metastable zone width. It will typically
be in uenced by a variety of process parameters including
saturation temperature, rate of supersaturation generation,
impurity level, mixing, and solution history1 . It is therefore
important to characterize the metastable zone width under a
speciŽ c set of operating conditions, which relate closely to
the conditions of the Ž nal scale crystallization. There are a
variety of correlations available in the literature, which can
be applied to help indicate the dominant nucleation mechanisms and can be used to predict the metastable zone width2 –4 .
An excellent overview of published metastable zone
width experiments is available in the literature5 . The polythermal technique6 is perhaps the most widely used technique for determining the metastable zone width. This
methodology involves cooling a saturated solution at a
Ž xed rate until nucleation occurs. This process is repeated
for a variety of cooling rates and saturation temperatures,
with the recorded nucleation temperature allowing the
calculation of the metastable zone width for a given cooling
rate, which in turn allows an estimation of the nucleation
kinetics6 . A wide variety of measurement techniques have
been applied to detect the onset of nucleation including
visualization7 , electrozone sensing8 , and optical turbidity9 .
The method of detection frequently has an in uence on the
success of the kinetics estimation, as often there is a time lag
following nucleation as the material grows to a detectable
size range1 0– 1 2 .
799
800
BARRETT and GLENNON
the slurry. Light scattered back towards the probe is used in
conjunction with a CCD element to produce an image. The
image has a Ž eld of view of 860 mm £ 645 mm, with the
pixel size on the CCD array 0:67 mm, with allowing image
resolution down to approximately 5 mm. The software allows
up to 10 images per second to be stored. These images help
validate particle shape and give an indication of particle
dimension and structure following nucleation and during
dissolution.
Nucleation Kinetics
Utilizing classical nucleation theory, it can be shown that
the nucleation rate, or rate of change in the number of
crystals, can be expressed as6
dN
ˆ k00 Dcn
…1†
dt
When a solution is cooled, the rate of supersaturation
generation can be expressed as a function of the cooling
rate, r1 ; 12
J ˆ
dDc
dc¤
ˆ r1
…2†
dt
dT
With knowledge of the solubility curve, the temperature
coefŽ cient of solubility is simply the slope for a given
saturation temperature.
When nucleation occurs, the maximum possible undercooling is given as
DTmax ˆ T ¤ ¡ Tnuc
This corresponds to the maximum supersaturation
…3†
dc¤
…4†
dT
At the point of nucleation it is assumed that the rate of
formation of new crystals equals the rate of supersaturation
generation. The mass of nuclei formed relates directly to the
number of crystals formed6 :
Dcmax ˆ DTmax
dM
ˆ k0 arr3 Dcm ˆ kN Dcm
dt
Combining equations (2), (4) and (5) yields,
µ³ ¤ ´
¶m
³ ¤´
dc
dc
m
DTmax ˆ r1
e
kN D c ˆ kN
dT
dT
…5†
solutions were prepared using reagent grade potash alum
and 0:22 mm Millipore Ž ltered water.
The crystallization vessel used has a maximum working
volume of 2 L, but the starting volume used was about 1 L.
The agitated jacketed vessel had an inner diameter of 13 cm
with a domed bottom and is equipped with a standard
Ruston turbine, of diameter 5 cm. The crystallizer has
ports to accommodate the FBRM and PVM probes, which
were positioned to ensure good  ow against the probe
windows, allowing a representative sample of the particle
system to be measured (Figure 1). For this work, the vessel
was operated with four standard baf es, with both probes
themselves offering additional baf ing. An impeller speed
of 400 rpm was employed for all experiments, which helped
ensure adequate mixing, but also avoided excessive splashing in the vessel. The vessel was sealed and operated with a
condenser at 10¯ C. Programmed cooling and heating
proŽ les were implemented using a Julabo HP50 Heating=
Cooling system. Temperature data were recorded on PC via
a PT-100 probe which was in the crystallizer and connected
to the Julabo heating=cooling system.
To minimize the amount of material consumed and to
help aid in the future automation of the process, the same
saturated solution was ‘recycled’ batch to batch. Solution
history is known, in some cases, to have a bearing on the
measured metastable zone width2 2 . Prior to completing the
proposed experiments, the effect, if any, of solution history
on the nucleation behaviour of potash alum in water was
investigated.
A potash alum solution saturated at approximately 35¯ C
was heated to 50¯ C and aged for 1.5 hours to help ensure
full dissolution. A similar protocol was recommended by
previous researchers on the nucleation behaviour of the
potash alum system23 . The solution was then cooled, at
¡
0.7¯ C min 1 , to 20¯ C. At this point the solution is reheated,
¡
again at 0.7¯ C min 1 , to 50¯ C and the aging and cooling
process is repeated. This process is then repeated eight times
using the same ‘recycled’ solution, with FBRM used to
monitor the system.
With reference to Figure 2, initially as the solution is
cooled and becomes supersaturated, FBRM detects no
particles and the count data indicate no change in particle
number. However, as soon as nucleation occurs, crystals are
formed, and there is a corresponding increase in counts in
…6†
where e is deŽ ned as1 2
eˆ
100R
‰100 ¡ c…R ¡ 1†Š2
…7†
Rearranging equation (6) and taking logarithms yields,
³ ¤´
dc
¡ ln e
ln…r1 † ˆ m ln…DTmax † ‡ ln kN ‡ …m ¡ 1† ln
dT
…8†
Therefore, a plot of r1 versus DTmax will yield the apparent
nucleation order, m, and the nucleation rate constant, kN .
MATERIALS AND EXPERIMENTAL METHODS
Kinetic studies were performed on aluminum potassium
sulphate KAl(SO4 )2¢12H 2 O (potash alum) in water. All
Figure 1. Schematic drawing of probe positions relative to the impeller.
Trans IChemE, Vol 80, Part A, October 2002
FBRM, PVM, AND METASTABLE ZONE WIDTH AND SOLUBILITY CURVE
801
Figure 2. FBRM data and temperature proŽ le for a typical batch.
the FBRM data. An advantage of using FBRM is that the
measured count data can be split into speciŽ c population
regions, permitting the isolation of the size range in which a
change occurs. A 10-s measurement duration was used for
all FBRM measurements. As the FBRM measures over a
10-s period, the number of counts in the 0–20 mm range was
used as the indication of nucleation. Published growth data
for potash alum2 4 predict that nuclei may grow by up to
15 mm in this 10-s period.
Zooming in on the region around the point of nucleation
(Figure 3) will illustrate the sensitivity of FBRM to the
nucleation event, and the importance of selecting the most
suitable statistic. FBRM is used to detect the point of
nucleation for all batches, and the temperature of nucleation
is recorded on the PC and tabulated for this process
(Table 1).
Ignoring the one outlier (batch 5), the point of nucleation
is taken as 26.4¯ C (average of all batches) with a standard
deviation of 0.34¯ C. The reproducibility, therefore, from
batch to batch is excellent. In this case, the potash alum
nucleated consistently at the same temperature, validating
that, for this material at the conditions under examination,
solution history did not have a bearing on the point of
nucleation.
Figure 3. FBRM data and temperature data at the point of nucleation.
Trans IChemE, Vol 80, Part A, October 2002
802
BARRETT and GLENNON
Table 1. Nucleation temperatures for initial trials.
Batch #
1
2
3
4
5
6
7
8
Nucleation temperature (¯ C)
26.07
26.06
26.35
27.06
29.12
26.22
26.58
26.42
Immediately following nucleation, the FBRM reports a
rapid increase in coarse chords counts (Figure 3) indicating
the presence of large crystals, either through rapid growth or
agglomeration. To validate this rapid increase in dimension,
a series of PVM images were captured within the Ž rst few
minutes of nucleation (Figure 4), highlighting the presence
of Ž nes, but also the presence of both large single crystals
and agglomerates.
Figure 4. PVM images taken within 2 minutes of the point of nucleation for
a typical batch.
Following the cooling period, the slurry is reheated.
During this reheating process, the material will begin to
dissolve. PVM images taken during this dissolution period
give an indication of the complexities of the dissolution
mechanism. There is a clear transition from the distinctive
octahedral shape of the potash alum crystals to a more
rounded structure (Figure 5). Extensive investigation
conŽ rmed that this transition was indeed due to dissolution,
and not to crystal breakage or attrition.
Fine particles have a high surface area to volume ratio in
comparison with coarse particles, and by applying basic
thermodynamic theory, these Ž ne particles will have a
tendency to dissolve before the coarser particles. Therefore
to successfully track when the material goes back into
solution ( point of disappearance) counts in a coarse size
range (50–250 mm) are used, and the point of disappearance
is detected using these coarse counts in a similar manner to
the nucleation work above.
During the heating process, as the point of saturation is
approached, the rate of dissolution decreases. Therefore, for
fast heating rates, the temperature measured at the point of
Figure 5. PVM image sequence taken during dissolution process.
Trans IChemE, Vol 80, Part A, October 2002
FBRM, PVM, AND METASTABLE ZONE WIDTH AND SOLUBILITY CURVE
Figure 6. Calculating the saturation temperature via extrapolation.
disappearance may be signiŽ cantly greater than the actual
saturation temperature. For this work, the point of disappearance is tracked using FBRM for a variety of different
heating rates. As the heating rate is reduced, the temperature
of the point of disappearance approaches the saturation
temperature. Extrapolation of the data back to an inŽ nitely
slow heating rate will yield an estimate of the point of
solubility (Figure 6).
The cooling=heating rates used for these experiments are
0.7, 0.6, 0.5, 0.4, 0.3, 0.2, and 0.15¯ C per minute. The
experimental protocol used is similar to the initial nucleation
trials, with the saturated solution heated to 15¯ C above the
estimated point of solubility, holding for 1.5 hours and then
cooling at a Ž xed rate to 5–10¯ C below the detected point of
nucleation, and then reheating at the same Ž xed rate back to
15¯ C above the estimated point of solubility and again
holding for 1.5 hours. This process is repeated for each of
the temperature rates and the order in which they are
performed is randomized. Each rate is repeated at least
three times to ensure good reproducibility. FBRM and
temperature data are recorded throughout this process at
10-s intervals.
Following the completion of the heating=cooling cycles,
the concentration is adjusted by addition of water to the
crystallizer. The experiments outlined above are then
repeated for the new concentration. Repeated dilutions
were made until the total volume in the crystallizer was
2 L. At this point, a fresh 1 L solution at a lower concentration was made and the process repeated. Experiments with
different liquid volumes but the same concentration, while
maintaining a constant impeller speed, show no signiŽ cant
variation in the measured nucleation temperature. This
indicates that the power input per unit volume does not
have a marked effect on the point of nucleation for this
material.
Figure 7. Measured and literature solubility data.
available for relating solubility, typically in the format of
mole fraction, to temperature1 2 . Assuming ideal solution
behaviour, the original van’t Hoff solubility relationship2 5
can be used to correlate the solubility of any substance in
any solvent26 . Extrapolation via the van’t Hoff solubility
curve is often subject to errors and an overview of how to
treat, extrapolate, and interpret measured solubility data is
available in the literature27 .
In this case, the solubility data are Ž tted to equation (9)2 7
using a non-linear regression:
ln…x† ˆ
12:10
‡ 10:47 ln…T † ¡ 65:73
T
Trans IChemE, Vol 80, Part A, October 2002
…9†
Figure 7 shows the excellent correlation obtained between
the experimental data, the Ž tted solubility curve, and literature values2 8 .
The metastable zone width is calculated as the difference
between the point of solubility and the measured point of
nucleation. The solubility curve and the metastable zone
width data measured for two cooling rates over the entire
experimental temperature range are plotted in Figure 8.
Figure 9 shows the measured metastable zone width for a
variety of cooling rates as a function of the saturation
temperature. There is a clear trend of a widening of the
EXPERIMENTAL RESULTS
Applying the technique described in the previous section
to solutions of varying concentrations, the metastable zone
width and solubility curve over a wide temperature range
can be generated. It is often useful to Ž t a solubility curve to
measured solubility points and extrapolate the curve over a
wide range of temperatures. There are many relationships
803
Figure 8. Measured solubility and metastable zone width data.
804
BARRETT and GLENNON
CONCLUSIONS
Figure 9. Metastable zone width as function of saturation temperature.
FBRM demonstrated that it is a valuable tool to aid in
determining both the solubility curve and nucleation properties of the potash alum water system. FBRM as a measurement technique offers the advantage of sensitivity to Ž nes
for detecting a nucleation event, but also one can isolate and
track the coarse material during dissolution. PVM images
helped illustrate the shape of the crystals, but more importantly showed the presence of large crystals after nucleation,
conŽ rming the rapid growth expected. The solubility data
collected via the FBRM technique showed excellent correlation with literature values.
The measured nucleation order will help give an indication
of the ease at which material will nucleate. This should serve as
a useful parameter to help assess the effect of different solvents
or solvent compositions on the metastability of a solution.
The metastable zone width and solubility technique
presented lends itself to easy automation, which should
prove invaluable, particularly in a pharmaceutical development laboratory where many solutes=solvents are screened
for both solubility and metastable zone width. In these
experiments, the solution was recycled batch to batch and
a series of dilutions were made to the system to change the
concentration. This approach used less material and allowed
the rapid screening of the solubility curve. However, it is
recommended that the effect of both solution history and
mixing on the measured metastable zone width be considered. If metastable zone width is in uenced on a laboratory
scale, it is likely that this effect will be exacerbated during
process scale-up, and is worthy of further investigation.
NOMENCLATURE
Figure 10. Nucleation order for a typical batch.
measured metastable zone width as the saturation temperature decreases.
Using equation (8), a plot of the cooling rate versus the
metastable zone width allows an estimate of the nucleation
order (Figure 10). Therefore, in this case the apparent
nucleation order is 2.03. The nucleation constant is also
calculated using equation (8), with the temperature coefŽ cient of solubility estimated from the slope of the solubility
curve at a particular temperature. This data analysis is
applied to all the batches, to give an indication of nucleation
properties over a variety of concentrations. Table 2 shows
the calculated nucleation parameters for this material over
the conditions examined. The nucleation order ranged from
1.57–2.03, which is in good agreement with previously
reported values of 1.1–3.5 for this material2 3 .
Table 2. Calculated nucleation parameters.
T (K)
322
318
313
309
306
298
m
kN
1.86
1.83
1.78
2.03
1.97
1.57
10.39 £ 10 6
¡
11.79 £ 10 6
¡
£
12.58 10 6
¡
8.87 £ 10 6
¡
7.53 £ 10 6
¡
7.28 £ 10 6
¡
A1 , A2 , A3
c
c¤
Dc
Dcmax
dM =dt
dN =dt
constants
¡
concentration, g solute (100 g solvent) 1
¡
saturation concentration, g solute (100 g solvent) 1
¡
supersaturation , g solute (100 g solvent) 1
supersaturation at point of nucleation, g solute (100 g
¡
solvent) 1
¡ ¡
nucleation rate, m 3 s 1
constant
nucleation rate constants
apparent nucleation order
nucleation order
¡
cooling rate, K s 1
nuclei size, m
ratio of molecular weight of hydrate: anhydrou s
temperature, K
saturation temperature, K
nucleation temperature, K
maximum undercooling, K
solute mole fraction
temperature coefŽ cient of solubility, g solute (100 g
¡
solvent K) 1
¡
mass nucleation rate, g crystal (g free solvent s) 1
¡3 ¡1
nucleation rate, m s
Greek symbols
a
e
r
crystal shape factor
conversion factor deŽ ned by equation (7)
¡
density, kg m 3
J
k
kN , k0
m
n
r1
r
R
T
T¤
Tnuc
DTmax
x
dc¤ =dT
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ADDRESS
Correspondence concerning this paper should be addressed to
Dr B. Glennon, Department of Chemical Engineering, University College
Dublin, BelŽ eld, Dublin 4, Ireland.
E-mail: brian.glennon@ucd.i e
The manuscript was received 19 March 2002 and accepted for publication
after revision 6 August 2002.