Crystallization Process Design Using Thermodynamics To Avoid

Article pubs.acs.org/crystal

Crystallization Process Design Using Thermodynamics To Avoid Oiling Out in a Mixture of Vanillin and Water Ian de Albuquerque and Marco Mazzotti* Institute of Process Engineering, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland ABSTRACT: Classical thermodynamics was used to model the vanillin and water phase diagram. Activity coefficient models, NRTL and UNIQUAC, were used to regress experimental equilibrium data. The vanillin and water mixture displays a liquid−liquid equilibrium that interacts with vanillin’s solid−liquid equilibrium, thus creating a challenge for crystallization processes. Using infrared spectroscopy we have experimentally shown that when the system entered the metastable liquid-liquid equilibrium region, by varying either composition or temperature, the phenomenon of oiling out could occur. By selecting operating points outside the metastable liquid−liquid equilibrium, oiling out was consistently avoided. Having validated the thermodynamic model’s accuracy and predictability, a robust process was designed allowing crystallized mass maximization while ensuring a direct route to crystallization. Utilizing a conceptual division of the desired portion of the phase diagram in operating zones, it was shown that a process can be qualitatively optimized with regard to process time, number of fines, and purity, concomitantly to crystallized mass maximization.

1. INTRODUCTION A homogeneous liquid mixture may undergo a phase transition yielding two or more stable liquid phases. Such phase transition arises due to the fact that the global minimum Gibbs free energy corresponds to a phase separated mixture, and this is the case for liquid−liquid equilibrium (LLE). Liquid−liquid extraction exploits the immiscibility between two liquid phases, and is widely used in organic chemistry to recover metals from mixtures,1 remove impurities,2 and separate proteins.3 According to Benedek et al.4 liquid−liquid phase separation (LLPS) is directly involved in cataract disease through LLE of γS-Crystallin and water. New polymeric materials have been designed using LLE knowledge by creating interpenetrating networks through spinodal decomposition.5,6 Superparamagnetic iron oxide nanoparticles were added in the inner phase of oil in water droplets, thus enabling the transport and release of the nanoparticles using a magnetic field.7 The set of applications and physical processes involving LLE is therefore extensive; however, in this work we focus on the challenges that LLPS creates when attempting to crystallize an organic molecule from solution. Upon cooling crystallization, a second liquid phase may emerge prior to crystal formation, a phenomenon known in the pharmaceutical community as oiling out, which is in fact a manifestation of LLPS.8 As opposed to the applications described above, LLPS is highly undesirable during crystallization since impurities are normally soluble in the solute-rich “oily” phase, hence leading to impure crystals.9 According to Groen et al.10 oiling out commonly causes major drawbacks in the industrial scale production of pharmaceuticals. A work by Lipinski 11 comparing recent drug types and discovery approaches of Pfizer and Merck, two major pharmaceutical © 2014 American Chemical Society

companies, showed that in recent years there is a trend to higher molecular weight APIs in both companies. Furthermore, in the search for more potent and target specific APIs a greater number of less hydrophilic and less polar molecules is evolving.12 In aqueous solution, larger and less hydrophilic molecules are more prone to oiling out,13 thereby making the development of novel crystallization strategies necessary and urgent. Several recent studies have reported oiling out of small organic molecules.8,9,14−22 Despite the need for modeling and understanding aimed at process control and scale-up, none of the reported studies have attempted to model the oiling out behavior from a thermodynamic point of view; in a few cases the oiling out region of the phase diagram was avoided by experimentally identifying permissible regions for crystal formation. The work of Kiesow et al.23 stands out, in the sense that it applied the PC-SAFT equation of state to qualitatively predict which mixtures would oil out, and validated predictions experimentally. Given the issues that might arise while crystallizing organic molecules, thermodynamics can play an important role in identifying operating conditions for a successful process. In this work, a widely used organic molecule, vanillin, was chosen due to its relative similarity with many organic molecules and APIs. Vanillin is an organic compound used industrially for over a century; currently it is used by the food, fragrance, pharmaceutical, and fine chemical industries. As of 2012 vanillin demand was greater than 16 000 tons and had total annual sales of approximately $650 million,24 thereby a compound of Received: June 20, 2014 Revised: September 1, 2014 Published: September 24, 2014 5617

dx.doi.org/10.1021/cg500904v | Cryst. Growth Des. 2014, 14, 5617−5625

Crystal Growth & Design

Article

Figure 1. ATR-FTIR spectrum variation with (left) increasing vanillin concentration at 40 °C and (right) increasing temperature at 3.26 weight%. form I exclusively. Forms III and IV are unstable and were obtained during fusion studies.32 Form II is metastable and Hussain33 obtained it by seeding form II. Vanillin was used as purchased, and no polymorph studies were performed. 2.2. Experimental Setup. Experiments were carried out in a 250 mL jacketed glass reactor. A four blade impeller positioned 2 cm from the reactor’s bottom maintained a constant stirring rate of 375 rpm. Temperature was recorded and controlled every 30 s with a Huber Ministat cc3 using a Pt 100 temperature sensor. A ReactIR 45 m from Mettler-Toledo equipped with a 1.5 m long silver halide (AgX) fiber, 9.5 mm diameter probe, was used to collect infrared spectroscopy data. 2.3. ATR-FTIR Calibration. Spectroscopy techniques, such as ATRFTIR, are able to monitor vanillin vibrational modes.22 Building a calibration model for the mixture of vanillin and water allows in situ solution concentration monitoring. Due to the low infrared penetration depth, typically34 2−3 μm, the liquid phase is exclusively monitored despite presence of solids. This tool facilitates solubility measurements, allowing comparison with experimental data from other authors.25,35 ATR-FTIR is a powerful in situ technique that has been widely employed in studies aimed at concentration prediction,36 nucleation and growth monitoring,10 nucleation, growth, and agglomeration kinetics estimation,34,37−39 and crystal size distribution optimization.40−42 Building a regression model correlating the ATR-FTIR spectrum with the concentration of vanillin allows prediction of concentration. Commonly applied linear least-squares is not suitable for this problem since spectral data are highly correlated.42 Partial least squares regression (PLS) is suitable for ill-conditioned problems,43 and was the method of choice to correlate spectroscopic data and vanillin concentration.36 Spectra were collected every minute in the 750−2600 cm−1 range with a 4 cm−1 resolution, and were averaged over 64 scans. Absorbance in the fingerprint region of 1100−1680 cm−1 was used to correlate spectra and vanillin concentration, incorporating contributions from vanillin and water absorbance, resulting in 145 variables. Due to shifts that may occur over days, and even during the course of an experiment, a linear baseline was applied to the spectra. In addition, in order to reduce temperature effects on the spectra, smoothing and first derivative were taken using the Savitzky-Golay method. Figure 1(left) shows how the ATR-FTIR spectrum changes in a complex manner with respect to vanillin concentration. The range of 1100−1680 cm−1 was used because several vanillin absorbance fingerprints can be identified. Benzene ring CH stretching44 is observable at 1124 and 1300 cm−1. Stretching vibrations on the CC ring44 are seen at 1590, 1539, 1511, 1465, and 1372 cm−1. Aldehyde absorbance, due to in-plane CH deformation, is present at 1397 cm−1. The methoxy group absorbs at 1452 and 1430 cm−1, due to CH3 asymmetric deformation vibration.44 Water displays bending vibrations corresponding to a wavenumber of 1645 cm−1. Several of the above-mentioned fingerprints are indicated in Figure 1.

industrial interest. Recently, studies have been performed where liquid−liquid equilibrium was experimentally measured.25 Effects of LLPS on the crystallization of vanillin and water were also investigated.26 Vanillin and water constitute a common and relevant binary mixture, which can be used as a base model and can provide proof of concept on the use of thermodynamics to design robust crystallization processes that avoid oiling out. Our work aims at demonstrating a possible approach to circumvent oiling out. The approach is based on modeling the mixture’s phase diagram, with a unique set of parameters that is able to describe solid−liquid equilibrium, liquid−liquid equilibrium, and combinations thereof. Liquid−liquid equilibrium can be stable or metastable with respect to the solid phase, and regions of metastability can be fully predicted using an appropriate model. Such insight allows robust design of crystallization processes that avoid operating in the metastable LLE region, and can be combined with a seeding or cooling program. This strategy is particularly promising for predicting LLE when the LLPS envelope is completely submerged under the solubility curve,27 and when there is absence of experimental evidence or data for LLE. Since metastable LLE data is not available and is cumbersome to obtain, a sensible model capable of predicting metastable LLE is desirable. Two widely used activity coefficient models, NRTL28 and UNIQUAC,29 were implemented and compared to model the vanillin and water mixture. ATR-FTIR spectroscopy capabilities in identifying and characterizing LLPS were evaluated. ATR-FTIR calibration and solubility measurements for the vanillin and water mixture are described in section 2. Modeling and regressing statistically meaningful thermodynamic model parameters is crucial, and is discussed under Modeling, section 3. Model based regions where oiling out could and could not exist were experimentally validated in section 4. Oiling out may result in contaminated crystals,9,15,30 and slow down nucleation18 and growth kinetics,31 thereby affecting process time and the crystal size distribution. The trade-off between crystal size distribution, process time, and amount of fines is discussed in section 5.

2. EXPERIMENTAL SECTION 2.1. Materials. Vanillin (Eur. Ph. grade, Fluka) and deionized water were used for all experiments. Four vanillin polymorphs are known to occur.32,33 Form I is the stable and commercially used form purchased from Fluka. According to McCrone32 normal crystallization routes yield 5618



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Temperature effects at constant vanillin concentration are shown in Figure 1(right). Particularly for wavenumbers above 1500 cm−1, it is clear that temperature effects are significant. This strong temperature dependence can be observed, and was reported also for other substances.36,43 In the case of vanillin, temperature was normalized and included in the variable vector. This normalization consisted, for every experiment, of multiplying each temperature by the ratio of the largest absorbance to the largest temperature.43 Calibration experiments were performed by dissolving a known amount of vanillin and subsequently cooling the solution, at a rate of 5 °C/hour. Final temperature was roughly determined based on SLE and LLE points known from literature,25,32,35 attempting to avoid crystal nucleation and oiling out. Added vanillin weight fractions, measured with a balance, are shown as solid lines in Figure 2, while PLS regression results are shown as black circles.

resulting in a relative accuracy of ±0.54%, and an average deviation of ±0.21 g/kg. 2.4. Solid−Liquid Equilibrium (SLE) Measurements. The PLS model obtained from the calibration shown in Figure 2 was used to measure SLE of the vanillin and water mixture. Starting from a saturated suspension, containing excess vanillin solids, and slowly heating was shown to be a reliable method for solubility measurements.37,45 A rate of 2 °C/h was employed in this work, covering a temperature range from 5 to 45 °C. Gravimetric solubility measurements were also performed and are represented by hollow circles in Figure 3(left). Only points drawn in yellow were used for parameter estimation in section 3. Figure 3(right) shows heating and temperature plateaus, ensuring equilibrium conditions, along with estimated concentrations. For comparative purposes, data measured by Cartwright35 and Mange et al.46 are shown in Figure 3(left). Cartwright35 measured vanillin’s solubility in water by taking averages between crystal dissolution and crystal formation temperatures, with a standard deviation of ±0.5 °C; note that since nucleation is an activated process, crystal formation times may differ significantly, thereby raising questions regarding this method’s accuracy. Mange et al.46 recorded the temperature at which a known amount of vanillin crystals would dissolve. To further validate his measurements, Mange stirred a vanillin and water solution at a fixed temperature for 14 h, followed by filtering and weighing of the solids. From our analysis, Mange’s46 solubility data is more reliable and in reasonable agreement with our data. Additionally, the SLLE was experimentally measured. A mixture of vanillin and water was stirred at a given temperature for 6 h and then held without stirring for equilibration over at least 2 days. After the equilibration time, phases were inspected and if SLLE was not present the procedure was repeated with a new temperature until the SLLE temperature was found. The obtained temperature was TSLLE = 50.7 °C, in comparison with a value of 51 °C reported in the literature.25 2.5. Liquid−Liquid Equilibrium (LLE) Measurements. Liquid− liquid equilibrium data reported in the literature25 was used in this work, without repeating any experiment. Averages were taken when experimental results were given as ranges, and water mole fractions are given by vanillin’s mole fraction complement to unity (see Table 1).

Figure 2. Vanillin and water mixture calibration using ATR-FTIR. Black lines represent experimentally added vanillin concentration, while black circles indicate calculated concentrations using the PLS model.

3. MODELING 3.1. Phase Equilibrium. Accurate phase equilibrium calculations require robust solution methods for minimizing the total Gibbs free energy or, alternatively, for solving the isofugacity equation(s). Solving the isofugacity equation(s)

PLS was performed using MATLAB 7.14 and PLS_Toolbox 5.8 developed by Eigenvector Research Inc. Six latent variables were used

Figure 3. Solubility measurement using ATR-FTIR. On the left, ATR-FTIR and gravimetric measurements of vanillin solubility are shown. Comparison with literature data obtained by Cartwright35 and Mange et al.46 is shown by diamond and square symbols, respectively. Points represented in yellow were used for parameter estimation in section 3. ATR-FTIR solubility measurement was carried out with a heating rate of 2 °C/h and constant temperature plateaus, and is shown on the right. 5619



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Table 1. LLE Experimental Data Obtained by Svärd25 et al. for a Binary Mixture of Vanillin and Watera T [°C]

xI2 [−]

xII2 [−]

60 65 70 75 80 90

6.85 × 10−3 7.90 × 10−3 8.50 × 10−3 8.80 × 10−3 1.00 × 10−2 1.23 × 10−2

3.94 × 10−1 3.08 × 10−1 3.08 × 10−1 3.08 × 10−1 3.08 × 10−1 2.78 × 10−1

FSLE(p) =

1 V

V

⎡

v=1

⎣

N

m

∑ ⎢⎢ln(x2vγ2v(x v , Tv , p)) −

⎞⎤ ΔHm ⎛ Tv − 1⎟⎥ ⎜ RTv ⎝ Tm ⎠⎥⎦

2

(1a) FLLE(p) =

1 2N

∑ ∑ [ln(xikI γikI (x k I, Tk , p)) − ln(xikIIγikII(x k II, Tk , p))]2 k=1 i=1

(1b)

where V is the number of SLE experimental points, N is the number of experimental LLE tie-lines yielding 2N experimental points, and m is the number of components. The subscripts i, k, and v indicate the component, tie-line, and SLE experimental point, respectively. The melting temperature and enthalpy of vanillin, which in this mixture corresponds to the solute, are indicated as Tm and ΔHm, respectively. Experimental mole fractions and temperatures are used in eq 1a and 1b, and parameters are contained in vector pNRTL and pUNIQUAC. The objective function to be minimized is defined as

a Data given in mole fractions of vanillin x2. Water, x1, mole fraction is given by the complement of x2 to unity.

coupled with the tangent plane criterion allows distinction between stable and unstable states.47,48 Total Gibbs free energy minimization is computationally expensive, and for this reason we tackled phase equilibrium calculations using the isofugacity equation(s). In this work solid−liquid equilibrium (SLE), liquid−liquid equilibrium (LLE), and combinations thereof were relevant. The governing equations for all types of equilibrium considered (SLE, LLE, SLLE, and SSLE) are given in the Appendix (Table 5). Note that all phase equilibrium conditions are computed at atmospheric pressure. It is important to mention that without a stability test47,48 distinction between a stable, unstable or metastable phase is not possible; therefore, any solution to an equilibrium calculation can only be accepted after verifying that it is stable through the stability test, in this work performed as indicated by Michelsen.47 3.2. Activity Coefficient Models. Two widely used activity coefficient models, UNIQUAC and NRTL, were investigated for modeling the vanillin and water mixture for comparative purposes. The functional form of both models can be found in Prausnitz.28 Minor modifications were made defining, for the NRTL model, the quantity τij = gij/T, and for UNIQUAC an additional parameter was introduced, i.e., τij = aij/T + bij. 3.3. Parameter Estimation. The parameter estimation for the NRTL and UNIQUAC models was based on the leastsquares minimization of the logarithm of activities, as described by Sørensen et al.49 The least-squares minimization problem was formulated in terms of logarithmic difference, such that small and large activities are equally weighted.49 Parameters accurately describing the phase diagram of vanillin and water in the SLE and LLE regions are sought, therefore minimizing errors in both regions is necessary. SLE errors, FSLE(p), are calculated based on the Schröder-van Laar equation as shown in eq 1a, whereas LLE errors, FLLE(p), are calculated based on the isofugacity condition as shown in eq 1b. Activity coefficient γ(x, T, p), is a function of solution composition x, temperature T, and parameter set p. Compositions in mole fraction and temperatures are known from experiments and are used for parameter estimation, whereas the parameter set p that minimizes SLE and LLE errors is sought.

Φ(p) = FSLE(p) + FLLE(p)

(2)

NRTL parameters α12, g12, and g21 and UNIQUAC parameters a12, b12, a21, and b21 were found by minimization of eq 2 using a genetic algorithm implemented through the function ga of MATLAB 7.14. Metastable LLE data is not available, and additionally due to the metastable character measuring its equilibrium compositions is not straightforward; therefore, we resort to predicting the metastable LLE using the regressed parameters. 3.4. Results. Parameter estimation was carried out by minimizing the objective function given by eq 2 using a genetic algorithm. Physical properties for vanillin and water are given in Table 2. In the case of the NRTL model, the nonrandomness parameter α12 was given an initial guess of 0.47, as recommended by Prausnitz50 for the type of mixture consisting of vanillin and water. Optimum parameters resulted in an objective function value of ΦNRTL(p*) = 0.006. Table 2 reports the estimated parameters along with a 95% confidence interval. Parameter estimation in the case of the UNIQUAC model resulted in an objective function value of ΦUNIQUAC(p*) = 0.01, and the parameters are reported in Table 2. Due to the use of two additional parameters, the confidence intervals for the UNIQUAC model were very broad, thus indicating large uncertainties in the obtained parameters. Figure 4 shows phase diagrams obtained using the optimal NRTL and UNIQUAC parameters. UNIQUAC results are shown by orange curves, while NRTL results are shown by black curves. For both models LLE dashed lines correspond to metastable LLE; thermodynamic modeling is particularly useful when dealing with oiling out due to its capability to predict the conditions where metastable LLPS occurs. All experimental points represented by circles in Figure 4 were used in the parametric regressions, while points represented by stars were not; therefore, stars can test model predictions. Experimental data of SLE at temperatures lower than TSLLE was measured using

Table 2. Physical Properties for Vanillin25 and Water, and Optimum Parameters Found Using UNIQUAC and NRTL Models Physical Properties UNIQUAC NRTL

ΔHm [(kj/mol)] 22 a12[K] −695 ± 1.4 × 104 α12[−] 0.53 ± 0.03

Tm [°C] 80 b12[K] 3 ± 87 g12[K] 1402 ± 7 5620

ΔHm,solv [(kj/mol)] 6.010 a21[K] 664 ± 7.9 × 103 g21[K] 497 ± 245

Tm,solv [°C] 0 b21[K] −3 ± 2



Article

Case A shows how to avoid oiling out based on the phase diagram. An undersaturated solution is prepared and cooled to a temperature so as not to reach the LLPS envelope. While cooling the solution becomes supersaturated, but still homogeneous. Eventually the supersaturated solution undergoes crystal nucleation and growth until supersaturation is completely depleted. The process is monitored using ATR-FTIR spectra, and upon crystallization vanillin absorbance is decreased. Figure 5a,b,c shows the experimental design for case A using the phase diagram, the ATR-FTIR time-resolved spectra of the vanillin fingerprint region, and the temperature profile, respectively. In Figure 5a initial and final temperatures are shown, connected via a vertical dashed line. The homogeneous mixture, undersaturated or supersaturated, is identified with the Greek letter α. The final state, reached after a certain period of time at the final temperature, consists of a saturated solution of composition ω in equilibrium with the pure solid θ. Since the ATRFTIR exclusively monitors absorbance contributions due to the liquid phase, only states α and ω are shown in the ATR-FTIR time-resolved spectra Figure 5b. The phase transition from a homogeneous solution to SLE occurs at about 0.8 h and 34 °C, as can be seen by the decrease in ATR-FTIR vanillin absorbance. Case B is designed to access the region of metastable LLPS. This experiment is aimed at demonstrating that oiling out occurs inside the region predicted by the model and that, due to the metastable character of the LLE, crystallization follows LLPS. Initially the undersaturated mixture is cooled until the final temperature, and after a given amount of time LLPS occurs. Figure 6a,b,c shows the experimental design for case B using the phase diagram, the ATR-FTIR time-resolved spectra of the vanillin fingerprint region, and the temperature profile, respectively. In Figure 6a the initial homogeneous solution, α, is shown along with the metastable LLE; at the final temperature the phase split is expected to yield two liquid phases, a solvent-rich phase of composition β and a solute-rich phase of composition δ. Crystallization is expected to happen after a certain amount of time, resulting in a saturated solution of composition ω in equilibrium with the pure solid phase θ. By following vanillin’s infrared fingerprint the exact time when oiling out occurs can be determined by a large increase in that region’s absorbance due to the high absorbance of the vanillin-rich δ phase; crystallization, on the other hand, would result in a decrease in vanillin absorbance. A large increase in vanillin absorbance is observed at 1.8 h and 31 °C, indicating the onset of LLPS into phases of compositions approaching β and δ; note that upon LLPS both liquids wet the ATR-FTIR probe and contribute to the overall measured absorbance. Subsequent to oiling out the mixture crystallized, as can be verified by the decrease in absorbance, particularly visible at the wavenumber of 1300 cm−1. Finally, case C demonstrates the analogy between stable and metastable LLPS. By cooling an initially undersaturated solution until a region of stable LLPS, stable LLE is observed. The mixture is then heated in order to validate the lack of hysteresis, and the undersaturated solution is recovered (see Figure 7).

Figure 4. Binary phase diagram as a function of vanillin mass fraction. Comparison between optimal descriptions obtained with NRTL, shown in black, and UNIQUAC, shown in orange. SLE experimental data is shown by yellow points, LLE by blue points, and the temperature where SLLE is observed is represented by a green point. The calculated eutectic temperature is shown by a black horizontal line connecting pure solvent and solute. Water SLE is not visible due to the proximity between its melting temperature and the eutectic temperature. Experimental points shown by circles were used for parameter estimation, whereas points shown by stars were not.

ATR-FTIR while the TSLLE temperature was measured following the procedure described in section 2.4. Liquid−liquid equilibrium and vanillin-rich SLE data were obtained from the literature.25 Both models, NRTL and UNIQUAC, provided a reasonable description of SLE and LLE data. SLLE temperature and vanillin rich SLE data were more accurately predicted by the NRTL model. Given that the NRTL model provided a superior quality of interpretation and prediction of the experimental data, and additionally narrower confidence intervals, the NRTL model along with the parameters reported in Table 2 is used in the following.

4. EXPERIMENTAL PROOF OF CONCEPT The working hypothesis is that entering the metastable or stable LLPS region might lead to oiling out, while on the other hand, avoiding it leads to a direct route to crystallization. As detailed in the Results section the NRTL model was chosen and is used for process design considerations of the vanillin and water mixture; from now on, the phase diagram is shown as colored regions. Three experiments labeled A, B, and C were chosen to demonstrate our working hypothesis (see Table 3): each case corresponds to a different initial concentration c0, and different initial and final temperature Tinit, Tfinal. Case A, Figure 5, was chosen such that regions of stable and metastable LLE are entirely avoided, thus leading to crystallization without oiling out. In case B, Figure 6, the operating point enters the metastable LLE region of the phase diagram, whereas in case C, Figure 7, the stable LLE region is entered.

5. PROCESS DESIGN Using the thermodynamic knowledge obtained in section 3 the region of metastable LLE can be mapped and, in conjunction with the solubility curve and the eutectic point, used for process design. A crystallization process can be optimized using a variety of objectives, such as crystallized mass, yield, crystal size distribution, crystal shape, and process time. Crystal size distribution, crystal shape, and process time depend on crystallization kinetics; since the focus here is on thermodynamics, these objectives will not be quantitatively discussed further. Crystallized mass and yield are properties dependent on thermodynamics that can be optimized using the phase diagram; crystallized mass M is defined as

Table 3. Design for Proof of Concept Experimentsa case

c0 [−]

Tinitial [°C]

Tfinal [°C]

comment

fig

A B C

0.0263 0.0403 0.0504

45 60 65

27 30 65

SLE metastable LLE and SLE stable LLE

5 6 7

M(c0 , T ) = c0 − c*(T )

a

All cases are identified in terms of initial concentration c0 in mass fraction, initial and final temperature Tinitial, Tfinal, corresponding observations, and figure where each experiment is given.

(3)

where c0 represents the initial solute’s concentration in mass fraction, and c*(T) indicates the solubility in mass fraction at 5621



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Figure 5. (a) Phase diagram showing case A. State α represents a homogeneous solution, and ω represents the composition of a saturated solution in SLE with pure solid phase θ. (b) and (c) show ATR-FTIR spectra of the vanillin fingerprint over time and the corresponding temperature profile, respectively. Crystallization without oiling out occurs as can be verified by the decrease in ATR-FTIR absorbance.

Figure 6. (a) Phase diagram showing case B. State α represents a homogeneous solution, ω represents the composition of a saturated solution in SLE with pure solid phase θ, whereas β and δ are compositions of phases in metastable LLE. (b) and (c) show ATR-FTIR spectra of the vanillin fingerprint over time and the corresponding temperature profile, respectively. Oiling out is detected via the increase in ATR-FTIR vanillin absorbance starting at 1.8 h. Afterwards, crystallization occurs as can be observed via the decrease in vanillin absorbance, particularly at the wavenumber 1300 cm−1.

temperature T. Yield is defined as crystallized mass divided by c0. The crystallized mass is typically maximized by cooling the solution to the eutectic temperature. However, in cases where oiling out might occur, operating temperatures leading to a stable

or metastable LLPS must be avoided. Therefore, the phase diagram provides a simple recipe for designing robust processes with regard to oiling out. If a particular objective is desired in terms of crystal size for instance, kinetic information would be 5622



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Figure 7. (a) Phase diagram showing case C. State α represents a homogeneous solution, and β and δ are compositions of phases in stable LLE. (b) and (c) show ATR-FTIR spectra of the vanillin fingerprint over time and the corresponding temperature profile, respectively. LLPS is detected via the increase in ATR-FTIR vanillin absorbance starting at 0.45 h, whereas a homogeneous solution is recovered at 0.53 h.

required. Nonetheless, however, by using the phase diagram it is possible to qualitatively design a process that aims at minimizing process time, minimizing fines, or maximizing crystal purity; the concept is demonstrated in Figure 8 and Table 4. For a given initial concentration c0 the operating part of the phase diagram is upper-bounded by c0, Figure 8, and is conceptually divided in three operating zones labeled I, II, and III (the boundaries of these zones are defined qualitatively as discussed in the

Table 4. Qualitative Process Design Based on the Phase Diagram of Vanillin and Water objective

operate in region

drawbacks

min process time max purity no fines

I II, III III

purity is critical, fines are found long process time, possibly fines in II max process time

following). Region I maintains the greatest supersaturation throughout the process. High supersaturation results in greater nucleation and growth rates; therefore, region I is expected to minimize process time. Since region I is close to the metastable LLE boundary, fluctuations in the temperature control of a large reactor as well as model inaccuracies could compromise purity due to oiling out. Furthermore, many fines would be generated due to the high supersaturation and nucleation rate. Region III mitigates the issues of fines and purity due to low supersaturation and to the fact that the region is far from the metastable LLE boundary. On the other hand, process time may be significantly larger than in region I. Finally, region II has the promise of containing the optimum trade-off in terms of process time, purity, and amount of fines; however, the boundaries of region II must be defined based on crystallization kinetics.

6. CONCLUSION Phase diagrams were generated based on thermodynamic activity coefficient models, NRTL and UNIQUAC, applied to the vanillin and water mixture. The NRTL model was found to be more accurate and predictive for this mixture; therefore, it was used for process design considerations. ATR-FTIR spectroscopy was the tool used to identify oiling out in situ and monitor vanillin concentration. As experimentally demonstrated, oiling out only occurs within the stable or metastable liquid−liquid

Figure 8. Vanillin and water phase diagram modeled using NRTL. Maximum crystallized mass M is obtained by cooling the solution with initial concentration c0 down to the eutectic temperature while avoiding the metastable LLE boundary (dashed blue line). A portion of the phase diagram, upper-bounded by c0 and lower-bounded by the eutectic temperature, is divided in three operating regions I, II, and III as described in Table 4. 5623



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Table 5. Phase Equilibrium Conditions Considereda

phase separation regions. Considering that avoiding oiling out is a priority, a process concept was developed so as the crystallized mass and yield could be maximized, while at the same time fulfilling, according to the crystallization path within the phase diagram, specifications regarding crystal purity, amount of fines, and process time. All quantitative considerations were performed based on thermodynamics; however, droplet and crystal nucleation kinetics knowledge would allow further insights on the interplay between crystallization and oiling out. Thermodynamic knowledge is, however, crucial for computing supersaturations in highly nonideal mixtures; supersaturation is an essential variable for estimating crystallization kinetic parameters, and therefore an additional advantage of a thermodynamic modeling approach. Applying thermodynamics to a mixture where liquid−liquid phase separation poses a challenge for crystallization enabled a process design that consistently avoided oiling out. The goal is that a greater number of mixtures including small organic molecules,21,22 proteins,51−53 and polymers54,55 are thermodynamically described, thus enabling robust process design that avoids liquid−liquid phase separation.

■

LLE

(x I , x II , f : 2m + 1 unknowns)

isofugacity

xiIγi I(T , x I ) = xiIIγi II(T , x II ) ∀ i

material balance

zi = fxiI + (1 − f )xiII ∀ i m

stoichiometry

∑ xiI = 1 i=1

SLE

(s : 1 unknown)

isofugacity

⎡ ΔH (T ) ⎛ T ⎞⎤ m m γm(T , x)xm = exp⎢ − 1⎟⎥ ⎜ ⎢⎣ RT ⎝ Tm ⎠⎥⎦

material balance

zi = (1 − s)xii ∈ [1, m − 1]

zm = (1 − s)xm + s SLLE

(x I , x II , f1 , f2 : 2m + 2 unknowns)

isofugacity

xiIγi I(T , x I ) = xiIIγi II(T , x II ) ∀ i ⎡ ΔH (T ) ⎛ T ⎞⎤ m m γm(T , x)xm = exp⎢ − 1⎟⎥ ⎜ ⎢⎣ RT ⎝ Tm ⎠⎥⎦

APPENDIX

material balance

zi = f1 xiI + f2 xiIIi ∈ [1, m − 1]

A.1. Phase Equilibrium Equations

zm = f1 xmI + f2 xmII + (1 − f1 − f2 )

Phase equilibrium calculations were performed for 1 mol of an mcomponent mixture of mole fraction z by combining the isofugacity condition(s) with the mass balances. In order to obtain a closed system of equations a stoichiometric balance was included in the cases of LLE and SLLE. After liquid−liquid phase separation the initial mixture would be split into two liquid mixtures with f and 1 − f mol, respectively. For SLLE, the initial mixture would be split into mixtures with number of moles f1, f 2, and 1 − f1 − f 2, for the first liquid phase, the second liquid phase, and the pure solid phase, respectively. In the case of SLE, phase separation results in a solid phase of s number of moles and a liquid phase of 1 − s mol. Similarly, for SSLE the mixture is split in fractions with s, ssolv, and 1 − s − ssolv number of moles, corresponding to the pure solid solute, the pure solid solvent, and the liquid phase, respectively. Table 5 summarizes all treated equilibrium relationships, and applicable isofugacity equations, mass balance, and stochiometry condition. The NewtonRaphson method was used to numerically solve LLE and SLLE problems. Roots of the tangent plane distance function47,48 were used as initial composition guesses for each phase. SLE and SSLE calculations reduce to one and two equations, respectively. Coupling SLE with the mass balance allows solving SLE problems with a single unknown, i.e., the solid number of moles s∈[0,1], thus reducing the problem to one equation and one unknown; the liquid composition is calculated through the mass balance. SSLE has an additional equation and unknown corresponding to the additional solid compound. These types of equilibrium problems were solved using the LevenbergMarquardt algorithm within MATLAB 7.14.

m

stoichiometry

∑ xiI = 1 i=1

SSLE

(s , ssolv : 2 unknowns)

isofugacity

⎡ ΔH (T ) ⎛ T ⎞⎤ m m γm(T , x)xm = exp⎢ − 1⎟⎥ ⎜ ⎢⎣ RT ⎝ Tm ⎠⎥⎦

⎡ ΔH ⎛ T ⎞⎤ m , solv(Tm , solv) ⎜⎜ γm , solv(T , x)xm , solv = exp⎢ − 1⎟⎟⎥ ⎢⎣ RT ⎝ Tm , solv ⎠⎥⎦ material balance

zi = (1 − s − ssolv)xii ∈ [1, m − 2] zm − 1 = (1 − s − ssolv)xm − 1 + ssolv

zm = (1 − s − ssolv)xm + s a

Unknown variables are identified next to each type of equilibrium. xF is a composition vector in mole fraction for phase F, γi(T,x) is the activity coefficient of component i at temperature T and composition x, ΔHm(Tm) and ΔHm,solv(Tm,solv) correspond to the melting enthalpy at the melting temperature of the solute and solvent, respectively. The assumed 1 mol initial mixture with composition z is split into, e.g., f and 1−f, where f∈[0,1], for all resulting mixtures.

X = ∇p η(p*)

(4)

the functional dependence of X on p was omitted for simplicity. Variance of residuals is computed as σ2 =

(Y − Ŷ )T (Y − Ŷ ) 2N + V − n

(5)

where n represents the number of elements in vector p*, and the column vector Y − Ŷ is a deviation vector corresponding to the difference between experimental and calculated activities. In the case of SLE, (Y − Ŷ )T(Y − Ŷ ) = VFSLE, analogously for LLE it is equivalent to 2NFLLE. The covariance matrix can then be computed:

A.2. Approximate Confidence Intervals

Approximate confidence intervals were calculated based on the optimized parameters found by minimizing eq 2. Assumptions of uncorrelated and constant variance measurement errors were applied. As discussed in the algorithm section, the logarithm of activities was used for regression purposes, i.e., η(x, T; p) = ln (xiγi(x, T;p)). First, a sensitivity matrix X with respect to η is calculated for every experimental measurement by estimating the derivatives in the neighborhood of the optimum parameter vector p*, with respect to model parameters.

cov(p*) = (XT X)−1σ 2

(6)

the standard error in parameter pk is given by the kth diagonal of the square root of the covariance matrix sk = [covk,k(Φ(p*))]1/2. 5624



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With the previously indicated assumptions, and an 100(1 − α)% confidence interval, the parameters are given by

pk* ± skt1 − α /2

(29) Abrams, D. S.; Prausnitz, J. M. AIChE J. 1975, 21, 116−128. (30) Codan, L.; Bäbler, M. U.; Mazzotti, M. Org. Process Res. Dev. 2012, 16, 294−310. (31) Lai, S. M.; Yuen, M. Y.; Siu, L. K. S.; Ng, K. M.; Wibowo, C. AIChE J. 2007, 53, 1608−1619. (32) McCrone, W. C. Anal. Chem. 1950, 22, 500. (33) Hussain, K.; Thorsen, G.; Malthe-Sø renssen, D. Chem. Eng. Sci. 2001, 56, 2295−2304. (34) Cornel, J.; Lindenberg, C.; Mazzotti, M. Cryst. Growth Des. 2009, 243−252. (35) Cartwright, L. C. Agricultural and Food Chemistry 1950, 312−314. (36) Togkalidou, T.; Fujiwara, M.; Patel, S.; Braatz, R. D. J. Cryst. Growth 2001, 231, 534−543. (37) Lindenberg, C.; Krattli, M.; Cornel, J.; Mazzotti, M. Cryst. Growth Des. 2009, 9, 1124−1136. (38) Lindenberg, C.; Mazzotti, M. J. Cryst. Growth 2009, 311, 1178− 1184. (39) Lindenberg, C.; Vicum, L.; Mazzotti, M. Cryst. Growth Des. 2008, 8, 224−237. (40) Saleemi, A. N.; Rielly, C. D.; Nagy, Z. K. Cryst. Growth Des. 2012, 12, 1792−1807. (41) Nagy, Z. K.; Braatz, R. D. Annu. Rev. Chem. Biomol. Eng. 2012, 3, 55−75. (42) Fujiwara, M.; Nagy, Z. K.; Chew, J. W.; Braatz, R. D. Journal of Process Control 2005, 15, 493−504. (43) Cornel, J.; Lindenberg, C.; Mazzotti, M. Ind. Eng. Chem. Res. 2008, 47, 4870−4882. (44) Gunasekaran, S.; Ponnusamy, S. Indian Journal of Pure & Applied Physics 2005, 43, 838−843. (45) Vetter, T.; Mazzotti, M.; Brozio, J. Cryst. Growth Des. 2011, 11, 3813−3821. (46) Mange, C. E.; Ehler, O. Ind. Eng. Chem. 1924, 16, 1258−1260. (47) Michelsen, M. L. Fluid Phase Equilib. 1982, 9, 1−19. (48) Wasylkiewicz, S. K.; Sridhar, L. N.; Doherty, M. F.; Malone, M. F. Ind. Eng. Chem. Res. 1996, 35, 1395−1408. (49) Sørensen, M. J.; Magnussen, T.; Rasmussen, P. F. A. Fluid Phase Equilib. 1979, 3, 47−82. (50) Renon, H.; Prausnitz, J. M. AIChE J. 1968, 14, 135−144. (51) Asherie, N. Methods 2004, 34, 266−72. (52) Lomakin, a.; Asherie, N.; Benedek, G. B. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 9465−8. (53) Thomson, J. A.; Schurtenberger, P.; Thurston, G. M.; Benedek, G. B. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 7079−83. (54) Kim, S. S.; Lloyd, D. R. J. Membr. Sci. 1991, 64, 13−29. (55) Lee, H. K.; Myerson, A. S.; Levon, K. Macromolecules 1992, 25, 4002−4010.

(7)

where t1−α/2 is the relevant quantile of Student’s t distribution. Intervals are reported for a 95% confidence interval.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The authors are thankful to the Swiss National Science Foundation for their support (project number 200021-143270). REFERENCES

(1) Wei, G.-T.; Yang, Z.; Chen, C.-J. Anal. Chim. Acta 2003, 488, 183− 192. (2) DeSimone, J. M. Science 2002, 297, 799−803. (3) Goklen, K. E.; Hatton, T. A. Sep. Sci. Technol. 1987, 22, 831−841. (4) Annunziata, O.; Ogun, O.; Benedek, G. B. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 970−4. (5) Inoue, T. Prog. Polym. Sci. 1995, 20, 119−153. (6) Sperling, L. H. Adv. Chem. 1994, 1−38. (7) Sander, J. S.; Erb, R. M.; Denier, C.; Studart, A. R. Adv. Mater. 2012, 24, 2582−7 2510.. (8) Codan, L.; BaIL̀ ́bler, M. U.; Mazzotti, M. Cryst. Growth Des. 2010, 10, 4005−4013. (9) Duffy, D.; Cremin, N.; Napier, M.; Robinson, S.; Barrett, M.; Hao, H.; Glennon, B. Chem. Eng. Sci. 2012, 77, 112−121. (10) Groen, H.; Roberts, K. J. J. Phys. Chem. B 2001, 105, 10723− 10730. (11) Lipinski, C. A. Journal of pharmacological and toxicological methods 2001, 44, 235−49. (12) Stahl, P. H. In Handbook of Pharmaceutical Salts: Properties, Selection, and Use; Wiley-VCH: Weinheim, 2002; pp 135−160 (13) Derdour, L. Chem. Eng. Res. Des. 2010, 88, 1174−1181. (14) Codan, L.; Casillo, S.; Bäbler, M. U.; Mazzotti, M. Cryst. Growth Des. 2012, 12, 5298−5310. (15) Deneau, E.; Steele, G. Org. Process Res. Dev. 2005, 9, 943−950. (16) Lafferrère, L.; Hoff, C.; Veesler, S. Cryst. Growth Des. 2004, 4, 1175−1180. (17) Lafferrère, L.; Hoff, C.; Veesler, S. J. Cryst. Growth 2004, 269, 550−557. (18) Lu, J.; Li, Y.-P.; Wang, J.; Ren, G.-B.; Rohani, S.; Ching, C.-B. Sep. Purif. Technol. 2012, 96, 1−6. (19) Lu, J.; Li, Y.-P.; Wang, J.; Li, Z.; Rohani, S.; Ching, C.-b. Org. Process Res. Dev. 2012, 442−446. (20) Revalor, E.; Bottini, O.; Hoff, C. Org. Process Res. Dev. 2006, 10, 841−845. (21) Yang, H. Org. Process Res. Dev. 2012, 16, 1212−1224. (22) Zhao, H.; Xie, C.; Xu, Z.; Wang, Y.; Bian, L.; Chen, Z.; Hao, H. Ind. Eng. Chem. Res. 2012, 51, 14646−14652. (23) Kiesow, K.; Tumakaka, F.; Sadowski, G. J. Cryst. Growth 2008, 310, 4163−4168. (24) Evolva, 2012, Annual Report. (25) Svärd, M.; Gracin, S.; Rasmuson, A. C. J. Pharm. Sci. 2007, 96, 2390−2398. (26) Parimaladevi, P.; Kavitha, C.; Srinivasan, K. CrystEngComm 2014, 16, 2565. (27) Bonnett, P. E.; Carpenter, K. J.; Dawson, S.; Davey, R. J. Chem. Commun. (Cambridge) 2003, 698−9. (28) Prausnitz, J. M. Molecular thermodynamics of fluid-phase equilibria; Prentice-Hall, Inc., 1986. 5625


Crystallization Process Design Using Thermodynamics To Avoid

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