Estimation Of The Nucleation Kinetics For The Antisolvent Crystallization Of Paracetamol In Methanolwater Solutions
Journal of Crystal Growth 328 (2011) 50–57 Contents lists available at ScienceDirect Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgroEstimation of the nucleation kinetics for the anti-solvent crystallisation ofparacetamol 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, Irelandb Solid State Pharmaceuticals Cluster (SSPC), L1029, Lonsdale Building, Department of Mechanical, Aeronautical and Biomedical Engineering, University of Limerick, Castletroy,Co. Limerick, Irelanda r t i c l e i n f o a b s t r a c tArticle history: In this work the primary nucleation kinetics have been estimated for the anti-solvent crystallisation ofReceived 25 February 2011 paracetamol in methanol–water solutions from metastable zone widths (MSZW) and induction times atReceived in revised form 25 1C. Laser back-scattering via a focused beam reﬂectance Measurement (FBRMs) is utilised to detect4 May 2011 the onset of nucleation. The theoretical approach of Kubota was employed to estimate the nucleationAccepted 8 June 2011 kinetics, which accounts for the sensitivity of the nucleation detection technique. This approach isCommunicated by Y. FurukawaAvailable 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. TheKeywords: induction time in this paper was measured from 40% to 70% mass water and the MSZW is measuredA1. Nucleation from 40% to 60% mass water. The primary focus of the paper was to gauge the extent of how solventA1. Kinetics composition affects nucleation kinetics so that this effect may be incorporated into a populationA1. Anti-solvent crystallisationA1. Induction time balance model. Furthermore, the effects of solvent composition on the estimated nucleation rates areB1. 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 . 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 extensivelypharmaceutical and chemical industries for the production of high studied and its mechanism is poorly understood, compared to coolingquality product crystals. The process of crystallisation can involve crystallisation .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 optimisingdetermining the particle size and distribution of the ﬁnal product. The crystallisation processes. Due to a lack of theoretical models forability to measure the kinetics of these mechanisms is of crucial crystallisation kinetics, primary nucleation kinetics are usuallyimportance for process design and development. Cooling and solvent expressed as empirical power-law equations [4–6]. There are twoevaporation 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 sizeinducing supersaturation has been drawing increasing attention . distributions [7,8] or indirectly via measuring the metastableIn 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-solventthe solubility of the solute in the original solvent, consequently until a nucleation event is measured. Whereas induction timegenerating 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: firstname.lastname@example.org (C.T. O’Ciardha), In this work, a theoretical approach, previously suggested email@example.com (P.J. Frawley), firstname.lastname@example.org (N.A. Mitchell). Kubota, for the analysis of anti-solvent MSZW data, was utilised0022-0248/$ - see front matter & 2011 Elsevier B.V. All rights reserved.doi:10.1016/j.jcrysgro.2011.06.017
´ ´ 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 ð2ÞThe MSZW is deﬁned as the excessive anti-solvent composition atwhich the number density of grown primary nuclei reaches a Where DC is the supersaturation in terms of solute compositionﬁxed value, but unknown value . A cooling crystallisation is deﬁned as DC¼ (C1 À Cn), C1 is the initial solute concentration heldtreated in the same manner. In a cooling crystallisation a variety at the saturation point, deﬁned in terms of kg of solute in kg ofof temperature ranges are utilised to encompass a large range of solvent, which in this case is methanol and Cn is the solubility inthe solubility curve. In anti-solvent crystallisations, composition terms of anti-solvent composition, A. The solubility can beis analogous to temperature and a range of compositions is assumed to be a linear function of the anti-solvent compositionstudied in place of the temperature range of a cooling crystal- A  as follows:lisation. The composition range in this work of 40% to 70% masswater was chosen as this was the most desirable range to work in C n ¼ ÀaA þ C0 ð3Þterms of designing a crystallisation process whilst still capturingthe effect of the solubility gradient on nucleation kinetics. This Where a is the anti-solvent composition coefﬁcient of solubilityapproach is expanded in this work for the treatment of the and C0 is the solubility of an anti-solvent free solution (A¼ 0). Seeinduction time data for an anti-solvent crystallisation process. Fig. 1 for a graphical representation of this theoretical approachThe induction time is deﬁned as the time required for the number and how DC can be related to DA. The supersaturation DC can nowdensity of the grown primary nuclei to reach a ﬁxed value, once acertain level of supersaturation is induced in solution. The effectof solvent composition on the estimated nucleation parameters k0and n and hence nucleation rates are investigated. The MSZW andinduction time experiments are also compared as methods forevaluation of the nucleation kinetics for anti-solvent crystallisa-tion processes.2. Theory2.1. MSZW In this section the theoretical method suggested by Kubota ,employed for the estimation of the nucleation kinetic parameters,k0 and n from the MSZW data will be discussed. The cases weresolvent-free and solute-free anti-solvent is added into an initiallysaturated solution is considered. The speciﬁc anti-solvent addi-tion rate, RA, according to O’Grady et al.  is deﬁned as follows: d DARA ¼ ð1Þ dtWhere DA is the supersaturation in terms of excess anti-solventcomposition 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 initialsolution saturated with the solute. The primary nucleation rate, Jn, Fig. 1. A schematic diagram showing the relation between excessive anti-solventcan be described using the following power law expression as a composition DA and supersaturation DC .
52 ´ ´ C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57be 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 , as ðN=VÞmthe excess anti-solvent composition at which the number density tind ¼ ðDAÞÀn ð13Þ knof 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 thedetection 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 betime 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 thesolution 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 detectionMSZW, 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, aWhere DAm is the MSZW in terms of excess anti-solvent composi- value for the detectable number density, Nm/V, for the nucleationtion DA and corresponds to the time the MSZW is reached, tm. detection technique employed must be assumed. In the LabMaxsInserting Eq. (5) into Eq. (7) and integrating, assuming kn and n reactor system, an FBRMs probe is employed to detect the pointremain 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 1ÞDAm 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 numberboth 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 1logðDAm 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. . 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 andplot of the MSZW, DAm, versus the speciﬁc anti-solvent addition depth of penetration of the respective systems. Using the aboverate, 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 ofbe estimated from the slope and constant of this trendline, penetration, for the assumed detectable size of 10 mm. Therespectively. refractive indices of methanol and water are 1.329 and 1.333, respectively. It is possible to combine these as the difference in2.2. 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. . Thenucleation 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  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 incorrespond to the time required for the number density, Nm/V, terms of kg of solvent (methanol), the volume in m3 is ﬁrstof grown crystals to reach a ﬁxed value. In this work this divided by the density of the total solution. The density of thetheoretical treatment of the induction time has been extended total solution is dependent on the composition studied and wasfor an anti-solvent crystallisation process. Assuming primary evaluated using the approach of . This yields a measurementnucleation can be described in terms of excess anti-solvent mass in terms of kg of total solution. This value is then multipliedcomposition by Eq. (5), the number density, (N/V)m, can be by the mass fraction of solvent (methanol) in solution, giving awritten 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 measurementexperiments are conducted at a constant excess anti-solvent mass of 2.664 Â 10 À 6 kg total solution. Taking the mass fraction of
´ ´ C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57 530.5 into account yields a measurement mass of 1.332 Â 10 À 6 kg of vital process parameters and full walk away operation. A customsolvent. This results in a detectable number density of 1.50 Â 106#/kg wall bafﬂe described previously  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 make10–50 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-solventdetermined 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 probetemperature controlled water bath for 48 h, to allow the solution A Mettler-Toledo Focused Beam Reﬂectance Measurementto 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 . For allfrom 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 ofsaturated solution yielded the solubility at a given solvent–anti- noise due to the agitation of the impeller. A measurementsolvent 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 toimum 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 valuepasses through a maximum at an anti-solvent mass fraction of was chosen as it detected the onset of nucleation before otherapproximately 0.1, after which it is observed to decrease chord lengths, while avoiding the noise generated by the agitationsigniﬁcantly. 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 timenophen (paracetamol), with a purity of Z99%, sourced from The reactor was ﬁlled with a saturated solution of paracetamolSigma Aldrich. The methanol employed in this work was of ACS for a given methanol–water mixture. The solution was thenreagent grade with a purity of Z99%, sourced from VWR. heated to a 30 1C for 15 min under agitation to ensure completeDeionised 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 this3.2. 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. Afterthis work to estimate the kinetics of the paracetamol and this initial supersaturation has been induced no additionalmethanol/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 valuesheating and cooling of solutions. Agitation of the solution is ranging from 0.014 to 0.034 kg/kg yielding a supersaturation ratioprovided by means of an overhead motor and a glass stirrer, with range of 1–1.3. Absolute supersaturation is deﬁned in Section 2 asfour blades at a pitch of 451. The system allows ﬂuid dosing and the difference of the solute concentration at saturation (Cn) tothe use of in-situ immersion probes. The system comes with solute concentration (C). The supersaturation ratio is deﬁned asiControl 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 theFig. 2. Gravimetrically determined solubilities for paracetamol in methanol and FBRMs probe. The corresponding anti-solvent composition waswater mixtures at 25 1C. recorded and utilised in the estimation of nucleation kinetic
54 ´ ´ C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57parameters. The MSZW experiments were carried out at addition induction time to exclude any mixing effects. The shortest inductionrates 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 involves4. 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 power4.1. 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 askinetics. The induction times were plotted as a function of the kn ¼ ank0. This implies that the slope of the solubility curve needsexcess 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 andsolvent charged into the vessel to generate the initial super- anti-solvent; however, in the work of Kubota  the solubility issaturation. This term is used to differentiate the anti-solvent mass expressed as anti-solvent free solubility. This way of expressingalready present in the vessel. It should be noted that the mass of solubility is advantageous in representing MSZW points on athe solvent does not change throughout the experiments. The solubility plot as the anti-solvent mass can be plotted linearly, seeformulation 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 thistion. The experimental excessive anti-solvent masses used were solubility plot was used to calculate the value for k0. The values offrom 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 andnoted 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 theinitial supersaturation must be short in comparison to theFig. 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 watervarying compositions. solution.
´ ´ C.T. O’Ciardha et al. / Journal of Crystal Growth 328 (2011) 50–57 55Table 1Nucleation parameters estimated from induction time data at varyingcompositions. 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 asigniﬁcant impact on induction time. The largest impact is seen inexperiments starting at a 70% initial mass water composition. Theinduction times for 70% initial mass water are large in contrastwith 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 forceand supersaturation. Due to this reduced driving force, the timetaken for the system to nucleate is signiﬁcantly longer. A decrease Fig. 7. Metastable zone width as a function of addition rate at various solventin induction time and hence the values of k0 and n with solvent compositions.composition complies with theory and this will be discussed inmore 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 thelargest decrease observed from 60% to 70% mass water. It must benoted that k0 is a numerically derived value. Fig. 10 shows theeffect of solvent composition on the nucleation order n. The valueof n is an experimentally derived value and it can be seen that it isa linear function of solvent composition. Fig. 11 shows howsolvent composition affects the nucleation rate. This ﬁguredemonstrates that nucleation rates are slower for higher watermass fractions and there is a drop from 40% mass water to 50%and that 50–60% mass water are similar in magnitude. Thiscomplies with effect of the solubility gradient and interfacialenergy 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 efﬁcientmethod for estimating the dependency of nucleation kinetics on Table 2solvent 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 wateron solvent composition. MSZW data was measured for threeinitial 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 3.10parameters estimated. Fig. 8 is a plot of the logarithm of speciﬁcanti-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% massand values for slope and intercept are used to calculate kinetic water. This observation is also seen in parameters estimated fromparameters from Eq. (10) with the knowledge of the detectable induction time and is related to the solubility gradient. Thesenumber density of the FBRMs and the instantaneous solubility observations are discussed more in detail in Section 4.3. Fig. 9 isgradient as discussed in Section 4.1. These kinetic parameters are plotted on a logarithmic scale due to the large magnitude ofshown 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 compositionthe induction time data the nucleation parameters k0 and n werefound to decrease with solvent composition. Similar trends were It has been found that solvent composition has a large impactascertained when ﬁtting MSZW data to theoretical models. on nucleation kinetics estimated from both MSZW data andFigs. 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 methodscomposition from 40% mass water to 50% mass water. However applied. These trends can be seen in Figs. 9–11.
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 . Granberg et al.  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 . 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 . 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 , 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 massFig. 11. Nucleation rate as a function of supersaturation ratio for various initial % fraction for both methods; however, the order is lower in datamass 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 waternucleation and growth is still unclear . 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 ratesfaces leading to a reduced solid–liquid interfacial energy. Davey can result in higher levels of localised supersaturation leading to proposed that the net effect of changing the solvent, such spontaneous nucleation and hence a faster nucleation rate.
´ ´ 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. AcknowledgementsFig. 12. Nucleation rate estimated from MSZW and induction time experiments asa function of supersaturation ratio for 40% and 50% initial mass water This research has been conducted as part of the Solid Statecomposition. Pharmaceuticals Cluster (SSPC) and funded by Science Foundation Ireland (SFI).5. Best practise: nucleation kinetics References Estimation of nucleation kinetics in general for crystallisingsystems is not a trivial matter; however, for anti-solvent systems  S.M. Nowee, A. Abbas, J.A. Romagnoli, Anti-solvent crystallisation: modelit 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.  N. Doki, N. Kubota, M. Yokota, S. Kimura, S. 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