1. Journal of Crystal Growth 328 (2011) 50–57
Contents lists available at ScienceDirect
Journal of Crystal Growth
journal homepage: www.elsevier.com/locate/jcrysgro
Estimation of the nucleation kinetics for the anti-solvent crystallisation of
paracetamol in methanol/water solutions
´
Clifford T. O’Ciardha a,n, Patrick J. Frawley b, Niall A. Mitchell a
´
a
Solid State Pharmaceuticals Cluster (SSPC), L1025, Lonsdale Building, Department of Mechanical, Aeronautical and Biomedical Engineering, University of Limerick, Castletroy,
Co. Limerick, Ireland
b
Solid State Pharmaceuticals Cluster (SSPC), L1029, Lonsdale Building, Department of Mechanical, Aeronautical and Biomedical Engineering, University of Limerick, Castletroy,
Co. Limerick, Ireland
a r t i c l e i n f o a b s t r a c t
Article history: In this work the primary nucleation kinetics have been estimated for the anti-solvent crystallisation of
Received 25 February 2011 paracetamol in methanol–water solutions from metastable zone widths (MSZW) and induction times at
Received in revised form 25 1C. Laser back-scattering via a focused beam reflectance Measurement (FBRMs) is utilised to detect
4 May 2011
the onset of nucleation. The theoretical approach of Kubota was employed to estimate the nucleation
Accepted 8 June 2011
kinetics, which accounts for the sensitivity of the nucleation detection technique. This approach is
Communicated by Y. Furukawa
Available online 28 June 2011 expanded in this work to analyse the induction time for an anti-solvent crystallisation process. Solvent
composition is known to have a significant impact on the measured induction times and MSZW. The
Keywords: induction time in this paper was measured from 40% to 70% mass water and the MSZW is measured
A1. Nucleation
from 40% to 60% mass water. The primary focus of the paper was to gauge the extent of how solvent
A1. Kinetics
composition affects nucleation kinetics so that this effect may be incorporated into a population
A1. Anti-solvent crystallisation
A1. Induction time balance model. Furthermore, the effects of solvent composition on the estimated nucleation rates are
B1. Paracetamol investigated. The primary nucleation rates were found to decrease with dynamic solvent composition,
with the extent of their reduction linked to the gradient of the solubility curve. Finally, both MSZW and
induction time methods have been found to produce similar estimates for the nucleation parameters.
& 2011 Elsevier B.V. All rights reserved.
1. Introduction has a solubility that is a weak function of temperature, or is unstable
at high temperatures [2]. Although there are a number of industrial
Crystallisation from solution is an important unit operation in the applications of anti-solvent crystallisation, it has not been extensively
pharmaceutical and chemical industries for the production of high studied and its mechanism is poorly understood, compared to cooling
quality product crystals. The process of crystallisation can involve crystallisation [3].
several fundamental mechanisms, namely nucleation, growth and The determination of nucleation rates is integral to the devel-
agglomeration, with the relative magnitudes of these mechanisms opment of process models that are very useful in optimising
determining the particle size and distribution of the final product. The crystallisation processes. Due to a lack of theoretical models for
ability to measure the kinetics of these mechanisms is of crucial crystallisation kinetics, primary nucleation kinetics are usually
importance for process design and development. Cooling and solvent expressed as empirical power-law equations [4–6]. There are two
evaporation are two commonly employed ways of inducing super- ways in which parameters for these equations can be obtained,
saturation in solution. In the last decade, salting-out as a means of by combining population balance modelling and particle size
inducing supersaturation has been drawing increasing attention [1]. distributions [7,8] or indirectly via measuring the metastable
In this method, a secondary solvent known as anti-solvent or zone width or induction times [9–14]. In anti-solvent crystallisa-
precipitant is added to the solution. This results in the reduction of tions, estimating MSZW involves continuously adding anti-solvent
the solubility of the solute in the original solvent, consequently until a nucleation event is measured. Whereas induction time
generating a supersaturation driving force. Anti-solvent crystallisation experiments involve creating an initial supersaturation and measur-
is an advantageous method where the substance to be crystallised ing the time between the attainment of supersaturation in solution
and the nucleation event. Several methods exist to characterise the
MSZW and induction time, such as turbidity, FBRMs, ATR-FTIR,
n
Corresponding author. Tel.: þ353 61 213134; fax: þ353 61 202944.
which are known to affect measured data.
´ ´
E-mail addresses: clifford.ociardha@ul.ie (C.T. O’Ciardha), In this work, a theoretical approach, previously suggested by
patrick.frawley@ul.ie (P.J. Frawley), niall.mitchell@ul.ie (N.A. Mitchell). Kubota, for the analysis of anti-solvent MSZW data, was utilised
0022-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jcrysgro.2011.06.017

2. ´ ´
C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57 51
Nomenclature S scan speed (m/s)
WL width of laser (m)
A anti-solvent composition (kg/kg) k0 number-based nucleation rate constant (#/kg s)
A1 saturated anti-solvent composition (kg/kg) kn nucleation constant in Eq. (6) ( À)
DA excessive anti-solvent composition (kg/kg) n number-based nucleation order ( À)
DAm MSZW in terms of DA (kg/kg) n1 refractive index of liquid medium ( À)
C solute composition (kg/kg) n2 refractive index of crystal ( À )
Cn solubility (kg/kg) t time (s)
C1 saturated solute composition (kg/kg) tm time MSZW is reached (s)
DC supersaturation (kg/kg) a anti-solvent composition coefficient ((kg/kg)/(kg/kg))
Dp depth of penetration (m)
Jn primary number nucleation rate (#/kg s) Subscripts
N/V number density (#/m3)
V volume (m3) m detectable ( À)
Ra specific anti-solvent addition rate (kg/kg s) ind induction ( À )
R reflectance ( À )
to evaluate the nucleation kinetics of paracetamol in methanol function of supersaturation, DC, as follows:
and water mixtures. This approach takes into account the sensi-
tivity of the instrument employed to detect the nucleation event. Jn ¼ k0 ðDCÞn ð2Þ
The MSZW is defined as the excessive anti-solvent composition at
which the number density of grown primary nuclei reaches a Where DC is the supersaturation in terms of solute composition
fixed value, but unknown value [3]. A cooling crystallisation is defined as DC¼ (C1 À Cn), C1 is the initial solute concentration held
treated in the same manner. In a cooling crystallisation a variety at the saturation point, defined in terms of kg of solute in kg of
of temperature ranges are utilised to encompass a large range of solvent, which in this case is methanol and Cn is the solubility in
the solubility curve. In anti-solvent crystallisations, composition terms of anti-solvent composition, A. The solubility can be
is analogous to temperature and a range of compositions is assumed to be a linear function of the anti-solvent composition
studied in place of the temperature range of a cooling crystal- A [11] as follows:
lisation. The composition range in this work of 40% to 70% mass
water was chosen as this was the most desirable range to work in C n ¼ ÀaA þ C0 ð3Þ
terms of designing a crystallisation process whilst still capturing
the effect of the solubility gradient on nucleation kinetics. This Where a is the anti-solvent composition coefficient of solubility
approach is expanded in this work for the treatment of the and C0 is the solubility of an anti-solvent free solution (A¼ 0). See
induction time data for an anti-solvent crystallisation process. Fig. 1 for a graphical representation of this theoretical approach
The induction time is defined as the time required for the number and how DC can be related to DA. The supersaturation DC can now
density of the grown primary nuclei to reach a fixed value, once a
certain level of supersaturation is induced in solution. The effect
of solvent composition on the estimated nucleation parameters k0
and n and hence nucleation rates are investigated. The MSZW and
induction time experiments are also compared as methods for
evaluation of the nucleation kinetics for anti-solvent crystallisa-
tion processes.
2. Theory
2.1. MSZW
In this section the theoretical method suggested by Kubota [3],
employed for the estimation of the nucleation kinetic parameters,
k0 and n from the MSZW data will be discussed. The cases were
solvent-free and solute-free anti-solvent is added into an initially
saturated solution is considered. The specific anti-solvent addi-
tion rate, RA, according to O’Grady et al. [11] is defined as follows:
d DA
RA ¼ ð1Þ
dt
Where DA is the supersaturation in terms of excess anti-solvent
composition defined as DA ¼A ÀA1, A is the anti-solvent composi-
tion at a time t and A1 is the anti-solvent composition of an initial
solution saturated with the solute. The primary nucleation rate, Jn, Fig. 1. A schematic diagram showing the relation between excessive anti-solvent
can be described using the following power law expression as a composition DA and supersaturation DC [3].

3. 52 ´ ´
C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57
be related to DA as follows: composition, DA, and Eq. (11) can be integrated to give
DC ¼ a DA ð4Þ N
¼ kn ðDAÞn tind ð12Þ
V m
Inserting Eq. (4) into Eq. (2) yields the following:
Jn ¼ kn ðDAÞn ð5Þ Rearranging Eq. (12) yields induction time as a function of
excess anti-solvent composition as follows:
Where kn ¼ ank0. The MSZW was newly defined by Kubota [3], as
ðN=VÞm
the excess anti-solvent composition at which the number density tind ¼ ðDAÞÀn ð13Þ
kn
of grown primary nuclei reaches a fixed value of (N/V)m, corre-
sponding to the detectable number density of the nucleation The above equation can be fitted to a trendline of a plot of the
detection technique employed. The number density can be induction time, tind, versus the excess anti-solvent composition,
evaluated by integrating the nucleation rate (Jn ¼ d(N/V)/dt) from DA. The nucleation order, n, and the expression (N/V)m/kn can be
time zero to the time the MSZW is reached, tm: estimated from the power and constant of this trendline, respec-
Z ðN=V Þm Z tm tively. The expressions in Eq. (13) are the same as those in Eq.
N N
¼ d ¼ Jn dt ð6Þ (10), providing an important link between MSZW and the induc-
V m 0 V 0
tion time of the nucleation process for anti-solvent crystallisation.
Where N is the number of grown primary nuclei and V is the However, in both the MSZW and induction time theories the
solution volume, both of which increase over the course of an nucleation constant, kn, cannot be evaluated without first assum-
anti-solvent crystallisation process. For the determination of the ing a value for the detectable number density of the detection
MSZW, the anti-solvent is added at a constant specific rate, RA, the technique utilised.
above equation can be rearranged, using Eq. (1) as follows:
Z DAm 2.3. FBRMs: detectable number density
N
¼ Jn =RA dðDAÞ ð7Þ
V m 0
In the approach of Kubota in order to evaluate a value for kn, a
Where DAm is the MSZW in terms of excess anti-solvent composi- value for the detectable number density, Nm/V, for the nucleation
tion DA and corresponds to the time the MSZW is reached, tm. detection technique employed must be assumed. In the LabMaxs
Inserting Eq. (5) into Eq. (7) and integrating, assuming kn and n reactor system, an FBRMs probe is employed to detect the point
remain constant, yields the following: of nucleation. As described in Section 3.2.1, the FBRMs probe
provides a measurement of the particle chord lengths, dependent
N kn
¼ ðDAm Þðn þ 1Þ ð8Þ on the optical properties of crystals and the liquid medium. The
V m ðn þ 1ÞRA
probe has a precision of 1 mm and the chord counts in the
Rearranging Eq. (8) gives 10–50 mm range were utilised to indicate the nucleation point.
For this work, nucleation of the solution was taken to be when the
ðN=VÞm 1=ðn þ 1Þ 1=ðn þ 1Þ
DAm ¼ RA ð9Þ counts in the specified range were greater than or equal to
kn
2 counts per second. This value was chosen as it detected the
The MSZW is now dependant on the nucleation kinetics onset of nucleation before other chord lengths, while avoiding the
(kn and n), the specific anti-solvent addition rate, RA, and the noise generated by the agitation of the impeller and by the anti-
method of nucleation detection, (N/V)m. Taking the logarithms of solvent addition. In order to evaluate the detectable number
both sides and rearranging yields the following: density, Nm/V, of the probe FBRMs, its measurement volume, V,
per second must be estimated.
1 ðN=VÞm 1
logðDAm Þ ¼ log ðn þ 1Þ þ log RA ð10Þ The method for measuring the measurement volume is out-
nþ1 kn nþ1
lined according to Mitchell et al. [16]. This approach has been
The above equation can be fitted to a trendline of a logarithmic modified in order to take into account the refractive indices and
plot of the MSZW, DAm, versus the specific anti-solvent addition depth of penetration of the respective systems. Using the above
rate, RA. The nucleation order, n, and the expression, (N/V)m/kn can method, a value of 268 mm was arrived at for the depth of
be estimated from the slope and constant of this trendline, penetration, for the assumed detectable size of 10 mm. The
respectively. refractive indices of methanol and water are 1.329 and 1.333,
respectively. It is possible to combine these as the difference in
2.2. Induction time refractive index is negligible. In this work the nucleation rate is
expressed as #/kg solvent s; however, the measurement volume
The induction time is defined as the time required for ‘first was evaluated in m3 in the method of Mitchell et al. [16]. The
nucleation events’ to be detected in a solution kept at a constant nucleation kinetics in this work are calculated in terms of kilo-
level of supersaturation. Kubota [15] previously defined the gram of solvent.
induction time, tind, for a cooling crystallisation process, to In order to evaluate the measurement mass of the FBRMs in
correspond to the time required for the number density, Nm/V, terms of kg of solvent (methanol), the volume in m3 is first
of grown crystals to reach a fixed value. In this work this divided by the density of the total solution. The density of the
theoretical treatment of the induction time has been extended total solution is dependent on the composition studied and was
for an anti-solvent crystallisation process. Assuming primary evaluated using the approach of [17]. This yields a measurement
nucleation can be described in terms of excess anti-solvent mass in terms of kg of total solution. This value is then multiplied
composition by Eq. (5), the number density, (N/V)m, can be by the mass fraction of solvent (methanol) in solution, giving a
written as follows: measurement mass in terms of kg of solvent. In turn this results in
Z tind Z tind a different measurement mass for the FBRMs depending on the
N
¼ Jn dt ¼ kn ðDAÞn dt ð11Þ initial mass fraction of water present.
V m 0 0
For example, for a 50% initial mass water composition with a
For anti-solvent crystallisation processes, induction time total solution density of 883.3 kg/m3, results in a measurement
experiments are conducted at a constant excess anti-solvent mass of 2.664 Â 10 À 6 kg total solution. Taking the mass fraction of

4. ´ ´
C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57 53
0.5 into account yields a measurement mass of 1.332 Â 10 À 6 kg of vital process parameters and full walk away operation. A custom
solvent. This results in a detectable number density of 1.50 Â 106#/kg wall baffle described previously [16] was employed in all experi-
solvent for the FBRMs probe, for 2 counts per second in the ments to improve the level of mixing in the reactor, and to make
10–50 mm size range. the estimated nucleation kinetics from the online FBRMs probe
more representative of the process. Anti-solvent (water) addition
into the solution was achieved using a ProMinent beta/4 peristal-
3. Experimental tic pump, which was found to be capable of a maximum addition
rate of 30 g/min. An electronic balance (Mettler Toledo XS60025
The solubility of paracetamol in methanol/water mixtures was Excellence) was used for recording the amount of the anti-solvent
determined gravimetrically in a range of water mass fractions added to the solution.
from 0 to 1 at a temperature of 25 1C. First, the solvent/anti-
solvent mixture was prepared, and excess solute was then added.
The slurry was then sealed within a closed container in a 3.2.1. FBRMs probe
temperature controlled water bath for 48 h, to allow the solution A Mettler-Toledo Focused Beam Reflectance Measurement
to reach equilibrium. Afterward, the saturated solution was (FBRMs) D600L probe was utilised in this work to provide in-
filtered, weighed, and put into an oven to separate the liquid situ detection of nucleation as discussed previously [16]. For all
from the solid phase at 45 1C for 48 h. The weight of the FBRMs measurements, the fine detection setting was employed,
remaining dry solute particles together with the weight of the as the detection setting was found to produce a significant level of
saturated solution yielded the solubility at a given solvent–anti- noise due to the agitation of the impeller. A measurement
solvent composition, as shown in Fig. 2. The average standard frequency of 10 s was employed for all FBRMs measurements,
deviation across all compositions is 0.0004 kg/kg with a max- with a chord count of 2#/s in the 10–50 mm range taken to
imum of 0.0017 kg/kg. It can be seen from Fig. 2 that the solubility correspond to the point of nucleation in the system. This value
passes through a maximum at an anti-solvent mass fraction of was chosen as it detected the onset of nucleation before other
approximately 0.1, after which it is observed to decrease chord lengths, while avoiding the noise generated by the agitation
significantly. of the impeller and by the anti-solvent addition.
3.1. Materials 3.3. Experimental procedure
The experimental work outlined was performed on Acetami- 3.3.1. Induction time
nophen (paracetamol), with a purity of Z99%, sourced from The reactor was filled with a saturated solution of paracetamol
Sigma Aldrich. The methanol employed in this work was of ACS for a given methanol–water mixture. The solution was then
reagent grade with a purity of Z99%, sourced from VWR. heated to a 30 1C for 15 min under agitation to ensure complete
Deionised water was used in all experiments. dissolution. The solution was then cooled to the temperature of
the actual experiment, 25 1C. All experiments conducted in this
3.2. Apparatus work were carried out at a solution temperature of 25 1C. An
initial supersaturation is generated by quickly adding a known
A LabMaxs reactor system from Mettler-Toledo is utilised in amount of water, with a constant impeller speed of 250 rpm. After
this work to estimate the kinetics of the paracetamol and this initial supersaturation has been induced no additional
methanol/water solution system. The reactor is a 1 L round- anti-solvent is introduced into the vessel. Induction time experi-
bottomed borosilicate glass jacketed reactor, allowing controlled ments were carried out at initial absolute supersaturation values
heating and cooling of solutions. Agitation of the solution is ranging from 0.014 to 0.034 kg/kg yielding a supersaturation ratio
provided by means of an overhead motor and a glass stirrer, with range of 1–1.3. Absolute supersaturation is defined in Section 2 as
four blades at a pitch of 451. The system allows fluid dosing and the difference of the solute concentration at saturation (Cn) to
the use of in-situ immersion probes. The system comes with solute concentration (C). The supersaturation ratio is defined as
iControl LabMaxTM Software enabling real-time measurement of the ratio of solute concentration (C) to solute concentration at
saturation (Cn). In the case of an experiment starting at an initial
composition of 40% mass water and charging in 90 g of water to
induce nucleation, the value for absolute supersaturation would
correspond to 0.034. The induction time experiments were con-
ducted in four different initial solvent compositions including
40%, 50%, 60% and 70% mass water, to investigate its effect of the
measured induction times. This range of solvent compositions
was chosen as it was an optimal range with respect to its gradient
whilst still showing the effect of the solubility gradient on
nucleation kinetics. The induction time was determined by an
increase in chords counts in the 10–50 mm range, as shown in
Fig. 3. The solution temperature and the solvent composition
were held constant over the course of the experiment.
3.3.2. Metastable zone width
The above procedure is repeated; however, in these experi-
ments the anti-solvent is added at a constant rate until an
increase in chords in the 10–50 mm range is observed by the
Fig. 2. Gravimetrically determined solubilities for paracetamol in methanol and FBRMs probe. The corresponding anti-solvent composition was
water mixtures at 25 1C. recorded and utilised in the estimation of nucleation kinetic

5. 54 ´ ´
C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57
parameters. The MSZW experiments were carried out at addition induction time to exclude any mixing effects. The shortest induction
rates ranging from 2 to 10 g/min. time encountered in this work was 380 s. The time taken to generate
an initial supersaturation for this case was 160 s.
Fig. 5 shows experimental averaged induction times for 50%
mass. The process of estimating nucleation parameters involves
4. Evaluation of kinetic parameters and results
fitting the induction time data, plotted as a function of excess
anti-solvent composition (kg anti-solvent/kg solvent), with power
4.1. Induction time
law expressions and solving Eq. (13) for kn with the knowledge of
the number density of the FBRMs, as mentioned in Section 2. The
Induction time experiments were carried out in order to
value of the exponent is taken directly as n as per Eq. (13).,
investigate the effect of solvent composition on nucleation
However, the value for kn has to be further numerically treated as
kinetics. The induction times were plotted as a function of the
kn ¼ ank0. This implies that the slope of the solubility curve needs
excess anti-solvent composition as shown in Fig. 4. Excess anti-
to be known in order to calculate the value for k0.
solvent composition is defined as the excessive anti-solvent mass
Solubility can be expressed in a variety of ways. In Section 2,
per solvent mass. Excessive anti-solvent mass is the mass of anti-
Fig. 2, the solubility is expressed as a function of the solvent and
solvent charged into the vessel to generate the initial super-
anti-solvent; however, in the work of Kubota [3] the solubility is
saturation. This term is used to differentiate the anti-solvent mass
expressed as anti-solvent free solubility. This way of expressing
already present in the vessel. It should be noted that the mass of
solubility is advantageous in representing MSZW points on a
the solvent does not change throughout the experiments. The
solubility plot as the anti-solvent mass can be plotted linearly, see
formulation of the theory by Kubota requires that the induction
Fig. 1. The anti-solvent free solubility of paracetamol in methanol/
time is plotted as a function of excessive anti-solvent composi-
water mixtures is shown in Fig. 6. The instantaneous slope of this
tion. The experimental excessive anti-solvent masses used were
solubility plot was used to calculate the value for k0. The values of
from 20 to 90 g in order to avoid any mixing issues. It must be
n and k0 for all solvent compositions are shown in Table 1 and
noted that in order to produce precise and repeatable measure-
plotted in Figs. 9 and 10.
ments of the induction time, the time needed to generate the
initial supersaturation must be short in comparison to the
Fig. 3. Time evolution of the FBRMs signal at an initial mass composition of 50%. Fig. 5. Induction time as a function of excessive anti-solvent mass for an initial
composition of 50% mass water.
Fig. 4. Induction time as a function of various excessive anti-solvent masses at Fig. 6. Anti-solvent free solubility for paracetamol in methanol and water
varying compositions. solution.

6. ´ ´
C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57 55
Table 1
Nucleation parameters estimated from induction time data at varying
compositions.
Parameters 40% mass 50% mass 60% mass 70% mass
water water water water
k0 5.12 Â 1007 3.37 Â 106 9.67 Â 1005 3.39 Â 103
n 3.314 2.426 1.895 0.6091
‘‘It can be seen from Fig. 4 that solvent composition has a
significant impact on induction time. The largest impact is seen in
experiments starting at a 70% initial mass water composition. The
induction times for 70% initial mass water are large in contrast
with those encountered from 40% to 60% mass water composi-
tions. The solubility gradient is significantly reduced from 70%
mass water to 100% mass water leading to a reduced driving force
and supersaturation. Due to this reduced driving force, the time
taken for the system to nucleate is significantly longer. A decrease
Fig. 7. Metastable zone width as a function of addition rate at various solvent
in induction time and hence the values of k0 and n with solvent compositions.
composition complies with theory and this will be discussed in
more detail in Section 4.3. When the nucleation kinetic para-
meters are estimated from the above induction time experiments,
similar trends are observed. Fig. 9 demonstrates that the nuclea-
tion constant k0 decreases with solvent composition with the
largest decrease observed from 60% to 70% mass water. It must be
noted that k0 is a numerically derived value. Fig. 10 shows the
effect of solvent composition on the nucleation order n. The value
of n is an experimentally derived value and it can be seen that it is
a linear function of solvent composition. Fig. 11 shows how
solvent composition affects the nucleation rate. This figure
demonstrates that nucleation rates are slower for higher water
mass fractions and there is a drop from 40% mass water to 50%
and that 50–60% mass water are similar in magnitude. This
complies with effect of the solubility gradient and interfacial
energy which will be discussed further in Section 4.3.’’
4.2. MSZW
In the section above we applied the model developed by Fig. 8. Kubota’s method for estimating nucleation kinetics for an initial composi-
Kubota to estimate the anti-solvent nucleation kinetic parameters tion of 50% mass water.
from induction time data and showed that it is an efficient
method for estimating the dependency of nucleation kinetics on Table 2
solvent composition. In this section, MSZW will be analysed for its Nucleation parameters estimated from MSZW data at varying compositions.
efficacy in estimating nucleation kinetics and their dependence
Parameter 40% mass water 50% mass water 60% mass water
on solvent composition. MSZW data was measured for three
initial solvent compositions, shown in Fig. 7. k0 3.01 Â 1008
5.86 Â 106
5.85 Â 106
This data is then fitted to theoretical models and nucleation n 3.63 3.29 3.10
parameters estimated. Fig. 8 is a plot of the logarithm of specific
anti-solvent addition rate versus logarithm of the MSZW, respec-
tively, for 40% mass water. The plot is fitted with a linear trend there is only a minimal difference between 50% and 60% mass
and values for slope and intercept are used to calculate kinetic water. This observation is also seen in parameters estimated from
parameters from Eq. (10) with the knowledge of the detectable induction time and is related to the solubility gradient. These
number density of the FBRMs and the instantaneous solubility observations are discussed more in detail in Section 4.3. Fig. 9 is
gradient as discussed in Section 4.1. These kinetic parameters are plotted on a logarithmic scale due to the large magnitude of
shown in Table 2. nucleation constant k0 and nucleation rate values. This enables all
By applying this method to three different initial solvent data to be visualised whilst preserving trends.
compositions shown in Fig. 7, the effect of the solvent composi-
tion on the nucleation rate can be evaluated. In Section 4.1, from 4.3. Effect of solvent composition
the induction time data the nucleation parameters k0 and n were
found to decrease with solvent composition. Similar trends were It has been found that solvent composition has a large impact
ascertained when fitting MSZW data to theoretical models. on nucleation kinetics estimated from both MSZW data and
Figs. 9 and 10 demonstrate a decrease of nucleation parameters induction time data. Both data sets show similar trends. Nuclea-
k0 and n with solvent composition. Fig. 9 demonstrates a large tion kinetics have been shown to reduce with solvent composi-
difference in magnitude for k0 values as a function of solvent tion regardless of the experimental or theoretical methods
composition from 40% mass water to 50% mass water. However applied. These trends can be seen in Figs. 9–11.

7. 56 ´ ´
C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57
that the solubility increases, results in an increase of the nuclea-
tion rate at a constant supersaturation, due to a decrease in
interfacial tension. This theory is supported by experimental
results [20]. Granberg et al. [18] showed an increase in measured
interfacial tension from 65% to 85% mass water, which was
attributed to an increase in reported induction times. It was also
found that the critical radius and the number of molecules needed
to nucleate decrease with decreasing water content and increas-
ing solubility, due to a decreasing interfacial energy [18]. The low
interfacial energy reflects that the free energy difference between
the crystal surfaces at the interface to the solution and the
crystalline structure in the interior is low [18].
Along with interfacial energy, one must also consider the effect
of the solubility gradient. In an anti-solvent crystallisation, the
concentration of the solute is reduced due to dilution. In some
cases the solution will become diluted before it becomes super-
saturated and this is due to an insufficient gradient and hence
driving force. In essence, adding anti-solvent decreases the
Fig. 9. Nucleation constant k0 as function of solvent composition. concentration faster than it decreases the solubility. Referring to
Fig. 2, we can see that the gradient is less pronounced at higher
water compositions. The instantaneous solubility gradient for 40%
mass water is three times larger than that for 70% mass water.
There is a large reduction in nucleation order from 40% to 70%
mass water, in data estimated from both MSZW and induction
time experiments shown in Fig. 10. The nucleation rates esti-
mated from these parameters also show a decrease with increas-
ing mass fraction of water. Fig. 11 is a plot of nucleation rate as a
function of relative supersaturation for various percentage water
mass compositions. This plot follows the theories of interfacial
tension and that of the solubility gradient. A large decrease can be
seen for nucleation rates measured between 40% and 50% mass
water, the rate slows between 50% and 60% mass water corre-
sponding to a minimal change in solubility gradient followed by a
large decrease between 60% and 70% mass water due to a lower
solubility gradient in this region. While the values of k0 and n
have no physical significance [21], the values of n indicate the
dependence of the nucleation rate on the levels of supersatura-
tion. It is evident that at higher water mass compositions there is
Fig. 10. Nucleation order n as function of solvent composition. a lower order of supersaturation driving force. This result
complies with the combined effects of solubility gradient and
interfacial energy.
4.4. Metastable zone width vs induction time
In this section a comparison will be made between MSZW and
induction time as methods for estimating nucleation kinetics. As
can be seen in Figs. 9 and 10 both show similar trends. Fig. 9 is a
plot of nucleation constant k0 estimated from induction time data
and MSZW data. Both methods demonstrate that the nucleation
constant k0 decreases with increasing water mass fraction. It can
be seen from both sets of data that there is a significant reduction
in the nucleation constant from 40% to 50% mass water. This level
of reduction in nucleation constant is not seen from 50% mass
water to 60% mass water. This observation follows the gradient
theory discussed in Section 4.3, where the solubility gradient is
similar in this region of the solubility curve. Fig. 10 shows that the
nucleation order scales linearly with increasing water mass
Fig. 11. Nucleation rate as a function of supersaturation ratio for various initial % fraction for both methods; however, the order is lower in data
mass water compositions. estimated from the induction time method. A similar trend is
observed when comparing nucleation rates obtained from both
methods. Fig. 12 is a plot of nucleation rates estimated from
The role played by the solvent regarding its influence on MSZW and induction time data for 40% and 50% initial water
nucleation and growth is still unclear [18]. One theory involves mass. This may be a result of the dependency of MSZW on mixing.
favourable interactions between solute and solvent on specific Addition of anti-solvent into a mixing vessel at high addition rates
faces leading to a reduced solid–liquid interfacial energy. Davey can result in higher levels of localised supersaturation leading to
[19] proposed that the net effect of changing the solvent, such spontaneous nucleation and hence a faster nucleation rate.

8. ´ ´
C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57 57
estimated in order to evaluate the nucleation parameters. The
dependence of nucleation kinetic parameters k0 and n on solvent
composition and hence nucleation rate have been evaluated and
been found to decrease with higher anti-solvent mass fractions. A
link is established between these observed trends and a solubility
gradient along with theories on interfacial tension. MSZW and
induction time have been compared as methods to obtain
nucleation kinetics and shown to be in reasonable agreement.
Both methods show that nucleation rate decreases with increas-
ing anti-solvent composition. These observations provide a
valuable insight into the effect of solvent composition on nuclea-
tion kinetics and thus its inclusion in a population balance model
to describe an anti-solvent crystallisation process would signifi-
cantly improve its predictive ability.
Acknowledgements
Fig. 12. Nucleation rate estimated from MSZW and induction time experiments as
a function of supersaturation ratio for 40% and 50% initial mass water This research has been conducted as part of the Solid State
composition. Pharmaceuticals Cluster (SSPC) and funded by Science Foundation
Ireland (SFI).
5. Best practise: nucleation kinetics
References
Estimation of nucleation kinetics in general for crystallising
systems is not a trivial matter; however, for anti-solvent systems [1] S.M. Nowee, A. Abbas, J.A. Romagnoli, Anti-solvent crystallisation: model
it is a magnitude more difficult due to the addition of another identification, experimental validation and dynamic simulation, Chem. Eng.
liquid into the solution. In this section, the common pitfalls to Sci. 63 (2008) 5457–5467.
[2] N. Doki, N. Kubota, M. Yokota, S. Kimura, S. Sasaki, Production of sodium
avoid and best practices to employ will be discussed with regard chloride crystals of uni-modal size distribution by batch dilution crystal-
to the evaluation of nucleation kinetics for anti-solvent crystal- lization, J. Chem. Eng. Jpn. 35 (11) (2002) 1099–1104.
lisation processes. Firstly, the placement of the addition pipe for [3] N. Kubota, An interpretation of the metastable zone width concerning
primary nucleation in anti-solvent crystallisation, J. Cryst. Growth 310
the anti-solvent is crucially important. It should be placed in a (2008) 4647–4651.
high velocity zone near the impeller to ensure that the [4] J.W. Mullin, Crystallization, third ed., Butterworth-Heinemann, London, 1993.
anti-solvent is incorporated into the solution as quickly as [5] A. Mersmann, Supersaturation and nucleation, Chem. Eng. Res. Des. 74 (1996)
812–820.
possible, with mixing having minimal impact on the measured
[6] J. Nyvlt, Kinetics of nucleation in solutions, J. Cryst. Growth 3/4 (1968)
data. It is also advisable to place the nucleation detection device, 377–383.
an FBRMs in this case, away from the addition pipe as noise from [7] M. Aoun, E. Plasari, R. David, J. Villermaux, A simultaneous determination of
nucleation and growth rates from batch spontaneous precipitation, Chem.
bubbles can mimic the onset of nucleation. Secondly, the MSZW
Eng. Sci. 54 (1999) 1161–1180.
approach to evaluating the nucleation kinetics for an anti-solvent [8] A.F. Blandin, D. Mangin, V. Nallet, J.P. Klein, J.M. Bossoutrot, Kinetics
system involves varying the anti-solvent addition rates, which identification of salicylic acid precipitation through experiments in a batch
can be troublesome at higher addition rates. For instance, if a stirred vessel and a T-mixer, Chem. Eng. J. 81 (2001) 91–100.
[9] M. Knox, M. Trifkovic, S. Rohani, Combining anti-solvent and cooling crystal-
peristaltic pump is employed for anti-solvent dosing as was the lization: effect of solvent composition on yield and metastable zone width,
case in this work, ensure that a minimum pulse rate is utilised, to Chem. Eng. Sci. 64 (2009) 3555–3563.
reduce the level of noise generated by the anti-solvent addition. ´ ¨
[10] J. Nyvlt, O. Sohnel, M. Matuchova, M. Broul, The Kinetics of Industrial
Crystallization, Elsevier, Amsterdam, The Netherlands, 1985.
Finally, for induction time experiments the time required to [11] D. O’Grady, M. Barrett, E. Casey, B. Glennon, The effect of mixing on the
generate an initial supersaturation must be short in comparison metastable zone width and nucleation kinetics in the anti-solvent crystal-
to the measured induction time. The supersaturation working lisation of benzoic acid, Chem. Eng. Res. Des. 85 (2007) 945–952.
¨ ¨
[12] J. Scholl, L. Vicum, M. Muller, M. Mazzotti, Precipitation of L-glutamic acid:
range for the induction time experiments was effectively limited determination of nucleation kinetics, Chem. Eng. Technol. 29 (2) (2006) 257–264.
by the robustness of the dosing pump employed. However, the ¨
[13] J. Scholl, C. Lindenberg, L. Vicum, M. Mazzotti, J. Brozio, Anti-solvent
supersaturation range encountered in these induction time precipitation of PDI 747: kinetics of particle formation and growth, Cryst.
Growth Des. 7 (9) (2007) 1653–1661.
experiments is comparable to that encountered in a typical
[14] M. Trifkovic, M. Sheikhzadeh, S. Rohani, Determination of metastable zone
anti-solvent process. The maximum addition rate utilised in this width for combined anti-solvent/cooling crystallisation, J. Cryst. Growth 311
work was 10 g/min. In the case where the values of the para- (2009) 3640–3650.
[15] N. Kubota, A new interpretation of metastable zone widths measured for
meters are being utilised in a population balance model to
unseeded solutions, J. Cryst. Growth 310 (2008) 629–634.
describe the crystallisation process, these addition rates are more ´ ´
[16] N.A. Mitchell, P.J. Frawley, C.T. O’Ciardha, Nucleation kinetics of
than sufficient as processes with high addition rates tend to suffer paracetamol–ethanol solutions from induction time experiments, using
s
from spontaneous nucleation leading to poor crystal yields. Lasentec FBRM , J. Cryst. Growth 321 (2011) 91–99.
[17] Z.K. Nagy, M. Fujiwara, R.D. Braatz, Modelling and control of combined cooling
and antisolvent crystallization processes, J. Process Control 18 (2008) 856–864.
˚
[18] R.A. Granberg, C. Ducreux, S. Gracin, A.C. Rasmuson, Primary nucleation of
6. Conclusions paracetamol in acetone–water mixtures, Chem. Eng. Sci. 56 (2001)
2305–2313.
[19] R.J. Davey, Solvent effects in crystallization processes, in: E. Kaldis (Ed.),
The nucleation kinetic parameters of paracetamol in methanol
Current Topics in Materials Science, vol. 8, North-Holland Publishing Com-
and water solutions were estimated from the MSZW and induc- pany, Amsterdam, 1982, pp. 429–479.
tion time data measured by an FBRMs probe. Both MSZW and [20] F.-M. Lee, C.E. Stoops, L.E. Lahti, An investigation of nucleation and crystal
induction time data were fitted to theoretical models which growth mechanism of urea from water–alcohol solutions, J. Cryst. Growth 32
(1976) 363–370.
accounted for the sensitivity of the nucleation detection techni- [21] A.S. Myerson, Handbook of Industrial Crystallization, second ed., Butter-
que utilised. The measurement volume of the FBRMs has been worth-Heinemann, Boston, 2002.