Preferential Crystallization of l-Asparagine in Water

ARTICLE pubs.acs.org/crystal

Preferential Crystallization of L-Asparagine in Water Katerina Petrusevska-Seebach, Andreas Seidel-Morgenstern, and Martin Peter Elsner* Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, 39106 Magdeburg, Germany ABSTRACT: Because of its simplicity and cost-effectiveness, preferential crystallization (PC) can be considered as one of the most attractive techniques available for enantioseparation. In this paper,the enantioseparation of the nonessential amino acid DL-asparagine (DL-Asn), which belongs to the group of conglomerate forming systems, is studied experimentally and theoretically. Goals of this work are to investigate the applicability of PC of L-Asn 3 H2O from an aqueous solution of racemic DL-Asn using simple isothermal batch preferential crystallization (SIB-PC) and to provide a reliable database for model validation based on essential model parameters identified. To further improve the performance of PC, two crystallizers can be connected in order to exchange continuously the mother liquors (CIB-PC, coupled isothermal batch preferential crystallization). This new configuration is tested and assessed.

’ INTRODUCTION The awareness for the discrimination of living systems toward pairs of enantiomers has led to a substantial preference of single enantiomers over the last few decades. In that manner, driven by highly influential regulatory authorities, the manufacture of enantiopure substances is increasing to a large extent in several industrial branches: pharmaceuticals, alimentary, etc.1 This tendency counts also for the essential group of chiral compounds — the amino acids. As final products or intermediates, they can be obtained either from the chiral pool or by catalytic asymmetric synthesis,2 biotechnologically,3 or via resolution of a racemic (1:1) mixture of enantiomers. In particular, the optical resolution of racemic mixtures is considered as a highly potential route for the production of pure enantiomers due to the rapid development of the separation techniques on analytical and preparative scale and their flexibility to accompany conventional organic syntheses and enzyme catalyzes.47 Among the available techniques, the so-called preferential crystallization (PC) is one of the more advantageous mostly due to its cost-effectiveness. This process is known and studied for more than one century.810 Nowadays, PC is an object of extensive investigation mostly due to the apparent simplicity and the advances in the quantitative analysis (powerful analytical measuring devices). The theoretical background of conventional crystallization processes including all kinetic phenomena such as crystal growth rate, nucleation rate, etc. has been established by several researchers.11,12 In recent years, the studies on crystallization processes have been emphasized much more on chemical engineering issues revealing the advantages of controlling and manipulating concentration and/or temperature profiles in batch crystallization.13,14 The concept of PC in terms of solubility phase diagram for systems where D- and L- enantiomers appear as homochiral crystals — conglomerate forming systems is described in Jacques et al.15 The solubility phase diagram of those systems exhibits a r 2011 American Chemical Society

eutectic at racemic composition. Although just 510% of the characterized racemates belong to this group of conglomerates, their relevance cannot be diminished16 — an inclusive overview of PC applied on conglomerates is given by Coquerel in Sakai et al.17 Lately, the simple isothermal batch preferential crystallization (SIB-PC) has undergone some drastic improvements regarding the 50% yield limitation, which is the major drawback of such resolution processes. For the enantioseparation of DL-threonine (i.e., an amino acid with two chiral carbon atoms which belongs to the most extensively studied cases1820), a concept of coupled isothermal batch preferential crystallization (CIB-PC) based on coupling two crystallizers for simultaneous crystallization of both enantiomers was proposed by Elsner et al.21 Another example is the work of Petrusevska-Seebach et al.22 and W€urges et al.23 which deals with a study of a one-pot process that integrates PC of the preferred and racemization of the unwanted enantiomer by using a biocatalyst for the model system of DL-asparagine/water. Besides the investigation regarding the racemization reaction, the particular work contains information for the solubility ternary phase diagram and an experimental feasibility study of PC for the examined model system. The current paper deals with a systematic experimental investigation and modeling of the process of PC of L-Asn 3 H2O. The goal of the experimental investigation is to determine the crystallization kinetics and to provide a reliable database for model validation based on essential model parameters identified. For the sake of simplicity, this investigation was mainly performed for aqueous L-Asn solutions being inoculated with LAsn 3 H2O crystals. To verify the influence of the counter enantiomer on the crystallization kinetics, the ratio of D- and LAsn in the initial solution was also changed. Furthermore, the Received: October 21, 2010 Revised: March 17, 2011 Published: April 28, 2011 2149

dx.doi.org/10.1021/cg101408e | Cryst. Growth Des. 2011, 11, 2149–2163

Crystal Growth & Design

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crystal growth in batch crystallization and of a single crystal was extensively studied. From the results obtained by this preliminary investigation, the experimental conditions for PC were set and the process was realized for several different supersaturation degrees and crystallization temperatures. Moreover, an experimental verification of the promising concept of CIB-PC was accomplished, revealing enhanced results (yield and purity) in comparison to SIB-PC.

’ THEORETICAL ASPECTS Crystal Growth. On the basis of the preliminary experimental study regarding the crystallization kinetics when crystallizing L-Asn 3 H2O from L-Asn/water solution, an indication of integration controlled crystal growth was observed. For a few surfaceintegration relations (power law, birth and spread - B&S and BurtonCabreraFrank - BCF11,12,24), a model discrimination was applied where statistical criteria (e.g., coefficient of determination) as well as the physical reasonability of the estimated parameters (inclusive their temperature dependence) were taken into consideration (results are not shown), implying that the common power law approach is the most appropriate for a quantification of the crystal growth. With respect to the indication that the examined system has not shown any growth anomalies (which could be approximated by a size-dependent growth) and by taking into consideration that there was only one enantiomer present (L-Asn; there is no inhibition of the counterenantiomer), the size-independent growth (SIG) approach can be expressed as

G0, eff ðtÞ ¼

dz ¼ kg , eff ðω, TÞðSðtÞ 1Þg dt

ð1Þ

where G0,eff is the effective linear crystal growth rate, z is the characteristic particle length, t is the time, kg,eff is the crystal growth rate constant which is usually highly influenced by the temperature T following an Arrhenius dependence and which might be in general also influenced by mass transport phenomena expressed by the stirrer speed ω (angular velocity) which could not be observed in our experiments, S is the degree of supersaturation and g is the order of the growth process. A common, empirical approach for the overall mass growth rate, best expressed as the total mass flux directed toward the crystal surface, shows in general a power-law dependency on the driving force ΔC = C Ceq 1 dmP ¼ km ðC Ceq Þg AP dt

ð2Þ

where AP is the surface area of one crystal, mP is the mass of one crystal, C is the actual mass concentration of the crystallizing species, and Ceq the equilibrium concentration. The total mass flux and the effective linear growth rate G0,eff can be related as follows 1 dmP 3kV FS dz 3kV FS ¼ ¼ G0, eff AP dt kA dt kA

1 dmP 1 dmS 1 dmL V L dC ¼ ¼ ¼ AP dt NAP dt NAP dt NAP dt

ð6Þ

with mS being the total mass of the solid phase (mS = NmP). A combination of eq 2 with eq 6 leads to dC km NAP km NAP ¼ ðC Ceq Þg ðC Ceq Þg dt VL VL ¼ KðC Ceq Þg

ð7Þ

where for small temporal changes of the surface area AP of a particle the last one can be replaced by its mean value Ap; thus the first expression on the right-hand side of eq 7 can be regarded as a constant denoted by K. A substitution of the concentration C by the supersaturation S(C(t) = S(t)Ceq) gives dSðtÞ ¼ KCgeq 1 ðSðtÞ 1Þg dt

ð8Þ

or in a linearized form dSðtÞ ln ¼ ln K þ ðg 1Þ ln Ceq þ g lnðSðtÞ 1Þ ð9Þ dt By plotting ln(dS(t)/dt) versus ln(S(t) 1), eq 9 enables an estimation of the order g for the growth process from the slope. The effective linear growth rate G0,eff can be determined by the measured temporal concentration changes dC/dt G0, eff ¼

dz kA V L dC kA V L dC ¼ dt 3kV FS NAP dt 3kV FS NAP dt VL dC ð10Þ ¼ 3NkV FS z2 dt

under the assumption that the surface area AP can be replaced by its mean value. Supposing, as already mentioned above that secondary nucleation can be neglected in accordance to our experiments, the total number of particles N crystallizing is related to the number of seeds introduced. Here, N was determined by means of the zeroth moment μo (eq 11) as well as of the third moment μ3 (eq 12): Z ¥ Z ¥ 0 f N, Seeds ðzÞ dz ¼ A f N, Seeds ðzÞ dz ð11Þ μ0 ¼ N ¼ 0

0

0

ð4Þ

where f N,Seeds(z) denotes the number density function of the experimentally investigated solid samples which is correlated with the number density function f0 N,Seeds(z) of the whole population used for seeding by the factor A. Moreover, this is correlated with the known amount of seeds mSeeds in order to obtain the factor A and subsequently, the particle number N Z ¥ 0 z3 f N, Seeds ðzÞ dz ð12Þ mSeeds ¼ FS kV μ3 ¼ FS kV A

ð5Þ

Process Model for SIB-PC of Asn from Racemic Asn/Water Solutions. Common feature of any PC process is that the

ð3Þ

with kA denoting the surface area shape factor according to AP ¼ kA z2

Furthermore, assuming a constant total number of particles N (i.e., no occurrence of nucleation, breakage and agglomeration according to our experimental observations), the overall mass flux can be correlated with the temporal change of the mass concentration C for the crystallizing species in the liquid phase (C = mL/VL) by the following equation

0

and kV denoting the volume shape factor V P ¼ kV z3

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dynamic behavior of the solid phase is described by a population balance based framework25,26 including two populations: one for the preferred (p) and another for the counter (c) enantiomer.27 The proportion of these both populations is reflected in the purity of the harvested solid product and determines eventually the efficiency of the process with regard to the enantioseparability. Considering ideally mixed batch suspension crystallizers, some assumptions (predominantly based on our experimental observations and conditions) have been made to simplify the mathematical model:11,12,26 (i) Crystal breakage and agglomeration are neglected which seems to be reasonable since the level of supersaturation is relatively low and the crystal suspension does not exceed more than 5%. (ii) The overall volume of the liquid and solid phase is constant. (iii) There is an inhibiting interdependence of both enantiomers on the growth rates of each component. (iv) Possible attrition effects are implicitly comprised in the effective (measured) growth rate expressions. (v) Nucleation phenomena take place at minimum crystal size which is actually negligible in comparison to the average size of the seeds. (vi) Because of our experimental observations secondary nucleation of the seeded, wanted p-species can be neglected. Under these assumptions and along with an isothermal operation mode, the resulting population balances for both enantiomers k are

Regarding the SIB-PC process, the corresponding mass balances for both components k in the liquid phase are Z ¥ dmL ðk; tÞ ¼ 3kV FS z2 Geff ðk; t, zÞf N ðk; t, zÞ dz dt 0 Z ¥ ¼ 3kV FS G0, eff ðk; tÞ z2 γðzÞf N ðk; t, zÞ dz 0

ð18Þ with initial data mL ðk; t ¼ 0Þ ¼ mL, 0 ðkÞ

where mL,0(k) is the initially dissolved mass of enantiomer k. Although the crystal growth rates of plenty organic crystalline substances reveal some growth anomalies such as growth rate dispersion and/or size-dependent growth,28 in the case of Asn in H2O such growth anomaly could not be observed. In addition, following our experimental observations an inhibiting effect of the c-enantiomer on the growth rate of the target enantiomer seems to play an important role. This might be approximately described by a simple power-law growth rate model assuming a first-order inhibition term Geff ðk; t, zÞ ¼ G0, eff ðk; tÞ with γðzÞ ¼ 1 and G0, eff ðk; tÞ ¼ kg, ef f ðTÞ

Df N ðk; t, zÞ D ¼ ðGeff ðk; t, zÞf N ðk; t, zÞÞ, k ∈ fp, cg ð13Þ Dt Dz where t and z represent the time and the characteristic particle size, Geff(k; t, z) is the overall growth rate and fN(k; t, z) denotes the number density function of each crystal population. The symbol k represents the p- and c-enantiomer, respectively. In general, the effective linear growth rate Geff(k; t, z) can be factorized by two terms: a size-independent one G0,eff(k; t) and a “size-dependent”, time-invariant factor γ(z), which is usually covering different growth rate anomalies such as crystal growth dispersion and/or size-dependent growth: Geff ðk; t, zÞ ¼ G0, eff ðk; tÞγðzÞ

f N ðk; t, z ¼ 0Þ ¼

Bðk; t, z ¼ 0Þ B0 ðk; tÞ ¼ Geff ðk; t, z ¼ 0Þ G0, eff ðk; tÞ

ð15Þ

Initial conditions (IC) f N ðk; t ¼ 0, zÞ ¼ f N, Seeds ðp; zÞ ¼ f N, Seeds ðzÞ f N ðk; t ¼ 0, zÞ ¼ f N, Seeds ðc; zÞ ¼ 0

ð16aÞ ð16bÞ

wherein fN,Seeds(z) characterizes the (initial) crystal size distribution (CSD0) of the seeds for the p-enantiomer which is directly linked with its mass mSeeds Z ¥ mSeeds ¼ mSeeds ðk ¼ pÞ ¼ kV FS z3 f N, Seeds ðzÞ dz ð17Þ 0

ðSðk; tÞ 1Þg 1 þ K inh ðh, h 6¼ kÞwðh, h 6¼ k; tÞ ð20Þ

In accordance to our experimental observations here kg,eff(T) is the (temperature T dependent and mass transport independent) crystal growth rate constant, whereas Kinh(h) is an inhibition constant concerning the counter enantiomer. S(k;t) denotes the degree of supersaturation of enantiomer k, that is, Sðk; tÞ ¼

ð14Þ

To solve these partial differential equations (PDE) (eq 13) following left boundary conditions in which the birth of new particles expressed by the nucleation rate B0(k; t) is incorporated and in addition, initial conditions are necessary: Boundary condition (BC)

ð19Þ

wðk; tÞ weq ðkÞ

ð21Þ

whereas w(k; t) is the mass fraction for component k defined as follows wðk; tÞ ¼

∑ ðkÞ

mL ðk; tÞ mL ðk; tÞ þ mSolvent

ð22Þ

with mL(k; t) being the mass of each dissolved enantiomer and msolvent representing the mass of the solvent (here: water). The quantity weq(k) denotes the equilibrium mass fraction describing the solubility. If this batch process is not interrupted in time, primary nucleation initiates the crystallization of the c-enantiomer which has a detrimental effect on the purity and thus on the process performance. The nucleation rate of this enantiomer is strongly influenced by the quantity and quality of the seeded enantiomer, and it is appropriately described by a heterogeneous mechanism (e.g., cf. Schubert and Mersmann34). Here, eq 27 was used to describe this phenomenon. The same follows from eq 23 which is based on a model proposed by Kind and Mersmann12,2932 grounded on primary homogeneous 2151



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(Ceq(k) = FL,eq 3 weq(k)). The heterogeneity of this mechanism is entirely attributed to the two parameters kb,prim,het and aprim,het which have to be estimated using the performed crystallization experiments. Since there is no significant indication for secondary nucleation, the overall nucleation rate B0(k; t) just consists of the primary heterogeneous contribution B0,prim,het(k; t), that is,

nucleation considerations J prim, het

rffiffiffiffiffiffiffiffi M γ ¼ 1:5ðcN A Þ7=3 D12 FS N A kB T 0 1 !2 3 16πγ M 1 A exp@φðθÞ 3ðkB TÞ3 FS N A ðln SÞ2

Fðμn ðh, h 6¼ k; tÞÞ

For the interfacial tension γ which is the most critical quantity in this model the following semiempirical correlation suggested by 0 1 Mersmann was used:33 FS 2=3 FS BMC NA ð24Þ γ ¼ a0 kB T ln@ A ceq M Supplementary, in order to capture the temperature dependence on the nucleation rate and to constrain the number of unknown parameters, the well-known Einstein relation was taken to approximate the binary diffusion coefficient which is primarily influenced by the viscosity η D12 ¼

B0 ðk; tÞ ¼ B0, prim, het ðk; tÞ

ð23Þ

kB T 2πηdm

ð25Þ

ð28Þ

From the mathematical point of view, the presented model for SIB-PC consists of two PDEs describing the temporal evolution of the number density functions for both, the population of the pas well as of the c-enantiomer and additionally two integrodifferential equations (IDE) to calculate the mass balances for each enantiomer remaining in the mother liquor. This distributed model can be greatly simplified by converting it into a moments model as it is described in the literature.25 From the PDE (eq 13) with boundary condition eq 15, a set of ordinary differential equations (ODEs) for the moments of the crystal size distribution (CSD) can be derived. In general, the moments are defined by Z ¥ zn f N ðk; t, zÞ dz, n ∈ N 0 ð29Þ μn ðk; tÞ ¼ z¼0

The viscosity was measured in our laboratory for a wider temperature and concentration range using an Ubbelohde capillary viscometer (Ubbelohde Viscometer 532 13/Ic, Schott Instruments, Mainz, Germany) and can be quantified by the following empirical equation in which KT and KW are fitted parameters (cf. Appendix A.3): 0 1 wðkÞ BðkÞ C KT C ð26Þ η ¼ η0 exp expB @ T Kw A

The zeroth moment corresponds to the overall number of k-crystals which is constant for the p-enantiomer, the second moment represents the total surface of the solid phase, whereas the third moment is proportional to the total volume of the crystalline material in the crystallizer. By partial integration, it follows from eq 13 and eq 15 that

The molar concentration c in eq 23 can be linked to the supersaturation degree S (c = ceqS; ceq denotes the solubility concentration at temperature T). Instead of the molar quantity, the extent of concentration can be also formulated by the mass concentration C (C = cM) which is directly associated with the mass fraction w of the dissolved species via the density (C = FLw). By neglecting the influence of the suspended crystals covered by the function F35 (i.e., F = 1) and by assuming a constant value for the function φ of the contact angle θ; when inserting the relations given above into eq 23 one gets after rearranging the following lumped (nonvolume-based) expression for the nucleation rate of the primary heterogeneous mechanism for each enantiomer k KT B0, prim, het ðk; tÞ ¼ kb, prim, het T exp T 0 1vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! wðk; tÞ u u B C FS ðkÞ B C t ln exp@ Ceq ðkÞ KW A

In the model, only the first four moments for each enantiomer are considered. With this notation and along with the above assumptions the mass balances eq 18 can be rewritten as follows:

∑

∑

ðSðk; tÞCeq ðkÞÞ7=3 exp

aprim, het ðlnðFS =Ceq ðkÞÞÞ3 ðln Sðk; tÞÞ2

! ð27Þ

Herein, Ceq(k) means the mass-based, equilibrium concentration which is directly linked to weq(k) by the density of the solution

dμn ðk; tÞ ¼ nG0, eff ðk; tÞμn 1 ðk; tÞ þ 0n B0 ðk; tÞ, n ∈ N 0 dt ð30Þ

dmL ðk; tÞ ¼ 3kV FS G0, eff ðk; tÞμ2 ðk; tÞ dt

ð31Þ

In order to estimate the unknown parameters characterizing the crystal growth as well as the nucleation, this reduced model has been implemented and then solved numerically over the temporal domain by Matlab (The MathWorks Inc., Natick, USA) using the therein available ode45 solver.36

’ EXPERIMENTAL SECTION Materials. D-, L-, and DL-Asn monohydrate were supplied by SigmaAldrich (Steinheim, Germany) and the water used for all experiments was purified using a Milli-Q gradient system (Millipore, Molsheim, France). HPLC grade ethanol was purchased from Merck (Darmstadt, Germany).

’ PROCEDURES Determination of the Metastable Zone Width. The wellknown Nyvlt’s polythermal method37 was used for an estimation of the width of the metastable zone. Saturated aqueous solutions (Tsat = 25, 35, 40, and 45 C) of L- and DL-Asn were placed in 2152



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Table 1. Summary for the Experiments Performed for the Study of the Influence of Some Basic Parameters on the Crystallization Kinetic (in All Cases Tcryst = 30 C) Tsat [C]

mSeeds,L [g]

SF [μm]

U [rpm]

D-/L-Asn

34

0.6

200255

250

0/100

36

0.6

200255

250

0/100

40

0.6

200255

250

0/100

36

0.2

200255

250

0/100

36 36

0.6 1

200255 200255

250 250

0/100 0/100

36

0.6

90150

250

0/100

36

0.6

200255

250

0/100

36

0.6

355500

250

0/100

36

0.6

200255

250

0/100

36

0.6

200255

375

0/100

36

0.6

200255

500

0/100

34 34

0.6 0.6

200255 200255

250 250

0/100 50/50

50 mL thermostatted double-jacketed vessels provided with a magnetic stirrer, heated up a few degrees higher than Tsat to ensure a clear solution and subsequently cooled down by using different cooling rates (5, 7.5, 10, and 20 K/h). Four cycles were performed for each experiment. The nucleation — designating the end of the metastable region — was detected by an in-line turbidity sensor integrated in a low pressure auto-MATE reactor system (HEL Limited, Hertfordshire, England). The temperature was measured in-line by a PT-100 sensor. The difference between Tsat and the temperature Tnuc at which the first crystals were detected refers to the maximum subcooling ΔTmax. Effect of Subcooling, Mass of Seeds, Sieve Fraction, Stirrer Speed, and the Presence of the Counter Enantiomer on the Kinetics. For a system of L-Asn/water seeded with L-Asn 3 H2O, a preliminary study was performed with regard to the effect of subcooling ΔT, the mass of seeds mSeeds, the sieve fraction of the seeds SF and the stirrer speed U. Additionally, the ratio of D- and LAsn in the initial solution was changed to verify the influence of the counter enantiomer on the crystallization kinetics of L-Asn 3 H2O. The experimental conditions are summarized in Table 1. The batch crystallization has been carried out in a stirred, jacketed glass vessel of 450 mL total volume. Information for the progress of the concentration of the enantiomers was obtained by online measurements of the optical rotation angle using a polarimeter (POLARmonitor, IBZ Messtechnik, Hannover, Germany) and the density of the liquid phase (Density Meter DE40, Mettler-Toledo, Giessen, Germany). The combination of polarimetry and densitometry has already been established for a reliable online monitoring of PC for several enantiomers.20,21,38 The temperature was measured in-line using a PT-100 sensor. The experimental setup is depicted in Figure 1. For each parameter set given in Table 1 a saturated solution was prepared and placed into the crystallizer, heated up to approximately 15 deg above the saturation temperature and maintained at this temperature in order to ensure complete dissolution. After cooling down to Tsat, a particular subcooling was applied to reach the crystallization temperature Tcryst. The cooling rate was 10 K/h. Prior to the occurrence of primary nucleation, seed crystals of L-Asn 3 H2O were added into the system. During the whole time crystal-free solution was pumped

Figure 1. Experimental setup for SIB-PC.

out from the crystallizer with a constant flow rate of 3.6 mL/min by a circulation pump (Heidolph PD 5201, SP Quick 1.6, Heidolph Electro GmbH & Co. KG, Kelheim, Germany) via an insulated line through the polarimeter and density meter and lead back to the vessel. The temperature of the analytical devices and the pipelines was 10 deg higher than Tcryst. The data for the density and the optical rotation angle were constantly recorded and used for the calculation of the mass fractions of each enantiomer in the liquid phase. Study of the Growth Rate Constant (Batch Crystallization). Because of different dependencies on the temperature, size, supersaturation, etc., a certain set of conditions is required for an evaluation of the growth rate. Here, for crystallization of L-Asn 3 H2O from L-Asn/water system initiated by adding seeds of L-Asn 3 H2O, the progress of the growth rate was examined for several different crystallization temperatures and different subcoolings: Tcryst = 20 C (for ΔT = 6 and 10 K), 25, 30, and 35 C (for ΔT = 4, 6, and 10 K). Initially, for each experimental data set the “reaction order” was determined using the relationship given by eq 9. Subsequently, G0,eff was determined according to eq 10. For an estimation of N (eq 11), the number density function was created from a control sample of 200 crystals belonging to the sieve fraction which was most frequently used in this work (200255 μm). For each of the cylindrical particles (V = (π/4)LD2), the diameter D and the length L was measured manually and the equivalent length was calculated by correlating their form with an ideal cube shape (z = ((π/4)LD2)1/3). Because of this investigation is very time-consuming, it has been performed for only one experimental data set at the beginning of the experiment. Furthermore, the density of the solid was determined experimentally using a pycnometer. For the change of the liquid phase density, experimental data recorded during the experiments was used while for hz an average value determined at the beginning and at the end of the experiment has been taken. On the basis of the experimental results, the degree of supersaturation can be calculated as well as the values for G0,eff and g. The crystal growth rate constant kg,eff was estimated from the slope of a fitted linear function for each experimental data set according to eq 1. Furthermore, its value was taken as average when different ΔT's have been applied for each examined temperature and was assumed to follow an Arrhenius type dependence (kg,eff = kg,eff,0 exp(EA/RT)). 2153


Crystal Growth & Design Study of the Growth Rate Constant of a Single Crystal. For aqueous solutions of L-Asn, the growth of a single crystal of L-Asn 3 H2O was measured for different supersaturations (ΔT = 2, 4, and 6 K) at Tcryst = 30 C as well as for different crystallization temperatures (20, 30, 35, and 40 C) with ΔT = 4 K. A scheme of the experimental setup is shown in Figure 2. For each experimental data set, a saturated solution was prepared and pumped through a tube (approximately volume of 10 mL) with a flow rate of 13 mL/min to the cell (volume of 5.4 mL, in-house manufactured) where a single crystal was fixed. The cell was kept at the corresponding temperature Tcryst which was measured by an in-line PT-100 sensor. The growth of the crystal was observed under a microscope (Stemi 2000-C microscope and AxioVision Rel. 4.6 software, Carl Zeiss GmbH, Jena, Germany). An image of one of the examined crystals at the beginning and near the end (after 960 min) of one of the performed runs is presented in Figure 3a,b, respectively. The diameter D and the length L of the characterized crystals with nearly cylindrical shape were determined by image analysis and the equivalent length was calculated by correlating its form with an ideal cube shape. For each experiment, the crystal growth was estimated from the slope of the progression of z over time (G0,eff = dz/dt), while the overall “reaction order” was determined from the experiments performed for different supersaturations at Tcryst = 30 C. The growth rate constants for Tcryst = 20, 30, 35, and 40 C (ΔT = 4 K) were calculated using eq 1. Furthermore, by using the above-mentioned, well-known Arrhenius approach the activation energy EA could be estimated.

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Simple Isothermal Batch Preferential Crystallization (SIBPC). The PC of L-Asn 3 H2O from aqueous solution of racemic

DL-Asn

was performed at several different conditions listed in Table 2. All experiments were carried out utilizing the same procedure and setup as for the L-Asn/water system. With regard to the response of the polarimeter, a few trials of PC were terminated when the signal for the optical rotation angle was relatively close to its maximum in order to ensure pure product. After the deliberate end, the solid phase was filtrated and washed using ice-cold water and ethanol, dried, and dissolved. Subsequently, they were analyzed by HPLC (HP 1100 liquid chromatograph, Hewlett-Packard, Waldbronn, Germany). The chromatographic investigation was performed on a Chirobiotic T column, 250 4.6 mm, 5 μm particles (Astec, Whippany, NJ, USA) at T = 25 C using a mixture of ethanol/water = 70/30 v/v as mobile phase with a flow rate of 0.5 mL/min. Coupled Isothermal Batch Preferential Crystallization (CIB-PC). The coupled preferential crystallization CIB-PC offers a possibility of simultaneous crystallization of each enantiomer in a separate vessel. As already demonstrated by Elsner et al.,21 this concept seems to be superior to the simple batch crystallization in terms of the yield of enantiopure components. A schematic illustration of the configuration for CIB-PC is shown in Figure 4. Compared to the simple batch PC, in this coupled configuration there are two vessels, tank A and tank B, in which both enantiomers E1 and E2 are being simultaneously crystallized in a preferable manner (E1 in tank A and E2 in tank B) under exactly the same conditions (except for the nature of the initially introduced homochiral seed crystals). Both batch crystallizers are coupled by an exchange of crystal-free liquid phase providing an increase of the concentration of the preferred enantiomer in the particular vessel. Assuming that the kinetics of PC for L-Asn 3 H2O and for D-Asn 3 H2O are identical, a racemic Table 2. Summary of the Experiments Performed for Preferential Crystallization of L-Asn 3 H2O from Aqueous Solution of Racemic DL-Asn

Figure 2. Experimental setup for the single crystal growth measurement.

run

Tcryst [C]

ΔT [K]

S

mSeeds,L [g]

SF [μm]

U [rpm]

1

30

6

1.30

0.6

200255

250

2

30

5

1.25

0.6

200255

250

3

30

4

1.20

0.6

200255

250

4

35

4

1.20

0.6

200255

250

5

40

4

1.20

0.6

200255

250

Figure 3. Illustration of a crystal at the beginning (a) and near the end (b) of an experiment performed for analysis of the single crystal growth. 2154



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Figure 4. Experimental setup for CIB-PC.

composition is expected in the liquid phase. The continuous exchange of the liquid phases has been devised to achieve higher driving forces for the crystallization of the p-enantiomer which is beneficial for the concept of PC. This configuration can be described as mimicking racemization on apparatus level and can provide an even more extended time period in which PC will take place on a high purity level. With the exception of the sieve fraction (SF), all parameters for the CIB-PC experiment were the same as for run 3 (see Table 2). The experimental equipment, the treatment, and the analysis of the solid phase after the experiment was finished following the same procedure as described in the section for batch crystallization. Because of some inconveniences possibly caused by the insuperable difference of the crystals’ shape of D- and L-Asn 3 H2O, for a successful operation, self-grown homochiral crystals of each enantiomer with SF > 500 μm were seeded in the particular crystallizer. The liquid phases from both vessels were exchanged with a flow rate of 37.5 mL/min.

’ RESULTS AND DISCUSSION Metastable Zone Width. Figure 5 depicts the solubility and

the metastable zone curves for aqueous solutions of L- and The mass fractions of L- and D-Asn for the MZW curves have been calculated for the maximum possible nucleation-free subcooling at cooling rate zero (ΔTmax,0). In both cases, the estimated values for ΔTmax,0 were in a range of ∼710 K (details are given in Appendix A.1). According to the fact that even small disturbances can cause primary nucleation when the system is thermodynamically unstable, working at the limit is definitely not recommendable. Thus, in the forthcoming kinetic studies mostly a lower subcooling was tested (applied cooling rate was 10 K/h). Effect of Subcooling, Mass of Seeds, Sieve Fraction, Stirrer Speed, and Presence of the Counter Enantiomer on the Kinetics. In Figure 6ad, the change of the mass fraction of L-Asn in the liquid phase is presented vs time for different ΔT, mSeeds, SF, and U, respectively. In all cases, time zero designates the seeding time and instantaneous crystallization of L-Asn 3 H2O which is noticeable from the decrease of its mass fraction in the liquid phase. DL-Asn.

Figure 5. Solubility and metastable zone curves for L-Asn/water and DL-Asn/water systems.

The most distinguishable effect on the crystallization kinetic was observed when different subcooling was applied (Figure 6a). The initial slopes imply that a higher amount of L-Asn can be obtained in a shorter time when the supersaturation is larger. By increasing the mass of seeds, the crystallization rate was only slightly enhanced (Figure 6b). The impact of the sieve fraction of the seeds and the stirrer speed was found to be negligible (Figure 6c,d). Observing no effect on the crystallization kinetics even when the stirrer speed was increased by factor 2 might indicate a crystallization process which may be controlled by integration (negligible diffusion in the liquid phase) and is not influenced by secondary nucleation (higher stirrer speed often causes breakage of the existing crystals and formation of new ones). The progress of the mass fraction curves of L-Asn was compared for two cases (composition of the initial solution D-/L-Asn = 0/100 and 50/50, both seeded with L-Asn). The results are depicted in Figure 7 where a significant effect of the counter enantiomer on the kinetics can be observed. This implies that the conclusions drawn from the previous experimental investigation can serve only as an approximation. 2155



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Figure 6. Influence of (a) subcooling, (b) mass of seeds, (c) sieve fraction of the seeds, and (d) stirrer speed on the kinetics when crystallizing L-Asn 3 H2O from aqueous L-Asn solutions (a summary of the remaining parameters is given in Table 1; the mass fractions for this binary system were obtained from the measured densities).

Figure 8. Number density function of 200 analyzed particles.

Figure 7. Influence of the presence of the counter enantiomer for PC of L-Asn 3 H2O from D-/L-Asn/water system.

Table 3. Some Parameters Relevant for the Calculation of the Crystal Growth Rate (eq 10)

Growth Rate Study (Batch Crystallization). The results from

the estimation of the reaction order have led to an average value of 1 ((0.3). The number density function required for calculation of G0,eff is depicted in Figure 8. Subsequently, for the determination of G0,eff, the growth rate constant was estimated according to eq 1. The results and some additional parameters related to eqs 1012 are listed in Tables 3 and 4.

FS [g/cm3]

mSeeds [g]

kV

N

0.112

0.6

1

393114

The dependence of kg,eff on the temperature is presented in Figure 9a. From the slope of a fitted linear function to the experimental data, a value of 49.1 kJ/mol was obtained for the activation energy EA. This value implies that the growth process is predominantly controlled by surface integration (EA of 2156



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∼4060 kJ/mol).39 In addition, the negligible influence of the stirrer speed on the concentration profiles is a further indication for this assumption. Single Crystal Growth Rate Study. The dependence of the growth rate constant on the temperature for the single crystal growth study is depicted in Figure 9b. Interestingly, the results from single crystal growth and growth in batch mode show a similar trend which suggests independency on the fluid dynamics, the setup and type of crystallization (mass and single crystal) where different phenomena can have an impact on the EA. In this case, similar results have been obtained for the “reaction order” and the activation energy (58.8 kJ/mol). Table 4. Average Equivalent of the Crystal Lengtha ΔT = 4 K [mm] Tcryst [C]

z [mm]

20

a

ΔT = 6 K

ΔT = 10 K

z [mm]

z [mm]

0.327

0.336

25

0.364

0.312

0.314

30

0.390

0.377

0.345

35

0.408

0.408

0.408

That is, the mean value of the crystal size at the beginning and at the end of the experiment.

The observations of the performed studies were useful for the model development — the indications for negligible diffusion in the liquid phase and absence of secondary nucleation allowed for neglecting the respective kinetics in the dynamic model. Simple Isothermal Batch Preferential Crystallization (SIBPC). Experimental Results. In order to attain familiarity with the duration of PC, the first experiment (Tcryst = 30 C, ΔT = 6 K (run 1) (Another experiment of PC with parameters equal as for run 1 has been already published by Petrusevska-Seebach et al.22) was carried out up to thermodynamic equilibrium, meaning that pure product was not obtained. The results of run 1 are given in Figure 10a,b where the change of the polarimeter signal and mass fractions over time are presented, respectively. Time zero in both figures is the seeding time. Obviously L-Asn 3 H2O begins to crystallize right after the seeds are introduced in the solution. The phenomenon is observable by the increase of the polarimeter signal — left-hand figure — and the decrease of the mass fraction of L-Asn in the liquid phase — righthand figure. Until the PC period is over, D-Asn does not crystallize, and consequently, its spontaneous primary nucleation arises. The reproducibility of the same experiment was tested several times, showing satisfactory results (Figure 15, Appendix A.2). For the same set of parameters, a few experiments have been terminated at different points of time when the signal of the optical rotation angle was close to the maximum. After 80, 100,

Figure 9. Arrhenius plot for (a) mass crystallization and (b) single crystal growth.

Figure 10. Progression of (a) the polarimeter signal and (b) the mass fractions of D- and L-Asn over time for PC of L-Asn 3 H2O from aqueous racemic DL-Asn solution for run 1. 2157



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and 120 min, a product with purity of 98.4%, 97.6%, and 99.6% has been harvested as was already expected from the mass fraction progress curves of run 1. However, a small inconsistency between the duration time and the purity was noticed which may be a consequence of the downstream process, that is, the posttreatment of the harvested solid product (filtration and washing) or a consequence of the reproducibility. The influence of the degree of supersaturation was tested mostly because it is the driving force for crystallization and its intensity can have significant impact on the outcome of PC. For that purpose, two additional trials of PC (runs 2 and 3) have been performed and compared with run 1. The results are presented in Figure 11, demonstrating faster spontaneous nucleation of the counter enantiomer for higher supersaturation. Theoretically, it was expected that all mass fraction trends would end at equilibrium composition (at Tcryst = -/L-Asn 3 H2O = 3.51 mass%), but only for run 3 this is 30 C, WDcryst probable. The others differ slightly, for example, for run 1 the -/L-Asn 3 H2O = 3.7 mass% which corresponds to Tcryst value for WDcryst of approximately 1 C higher than the current set-point, while for run 2 the curves proceed below this point. From a practical point of view, when a product with high purity is desired (>98% or >99%) the accuracy of the progression curves after the start of the nucleation of the c-enantiomer is not of much interest since the process should be terminated before this happens. On the other hand, their accuracy becomes relevant when estimations for the yield and the purity are required.

For clarity reasons, from the experimental results shown in Figure 11, the expected values for the mass of solid product mS, and the corresponding purity of L-Asn 3 H2O the yield Y(DL) S PuL-Asn 3 H2O for several points of time are presented in Table 5. When harvesting a product after crystallization, one has to take into account that there will be some losses due to the washing of the crystals from the mother solution. This factor is quite significant for the purity of the product, because the small nuclei of the counter enantiomer which were just developed can be easily washed out. Another critical aspect for the examined case is the reproducibility, meaning that calculations made for one run will not always give very precise expectation for another. These effects are observable when the product purity of run 1 calculated after 80 min (93%, Table 5) is compared with the purity which has been examined via HPLC analysis when the process was deliberately terminated (98.4%; please note that the calculated purity is also much lower than the product purity when the process was terminated after 100 and 120 min). Another issue which cannot be omitted is that for asparagine the specific optical rotation angle is very small ([R]25 D = 5.6), meaning that small interruptions during the measurement, for example, small polarimeter signal offset, can have an impact on the results and mislead the conclusions to a certain extent. Model Validation. A trial for the prediction of the progress of PC was made based on a model which is rather challenging because (1) the process operates in a thermodynamically unstable range where different phenomena can provoke different effects; thus, one cannot give consolidated statements and (2) the reproducibility is still an issue. The experimentally obtained data points were another concern for the modeling. They contained a moderate number of outliers due to air bubbles and small offsets. When the model based on moments was developed, some of the observations and relations which have been taken into account are described in Process Model for SIB-PC of Asn from Racemic Asn/water Solution. Apart from that, a few incorporated parameters were difficult to be predetermined: the pre-exponential crystal growth rate constant for L-Asn included in the -Asn Arrhenius dependence kLg,eff, 0, the inhibition constant for L-Asn -Asn , the nucleation constant included in the growth of D-Asn KLinh D-Asn for the counter enantiomer kb,prim,het and the constant for the -Asn . These have been estimated by exponential law for D-Asn aDprim,het fitting the model individually to the progress curves obtained from three experiments for PC of L-Asn (run 3 as well as run 4 and run 5) by means of least-squares. The differential equations have been calculated using the ode45 solver, while the parameters were estimated by utilizing the lsqcurvefit function, both implemented in MATLAB. The model parameters and the minimized objective function OF are shown in Table 6.

Figure 11. Experimental results for the dependence of the mass fraction of each enantiomer on time at different supersaturations (run 1 squares, run 2 triangles and run 3 circles).

Table 5. Expected Values for the Mass and Yield of Solid Product Accompanied with the Purity of L-Asn 3 H2O for Run 1, 2 and 3a Run 1 t [min]

ms [g]

Y(DL) s

[%]

Run 2 PuL-Asn 3 H2O [%]

ms [g]

Y(DL) s

[%]

Run 3 PuL-Asn 3 H2O [%]

ms [g]

Y(DL) s

[%]

PuL-Asn 3 H2O [%]

80

1.1

3.4

93

1.0

3.2

91

1.0

2.9

100

180

2.4

7.7

87

1.9

6.1

90

1.8

5.1

100

300

3.0

12.0

68

2.4

7.9

86

2.3

6.5

100

a

The yields for SIB-PC are calculated with respect to the initial mass of DL-Asn 3 H2O introduced in the crystallizer (indicated with the superscript (DL)) for a better comparison with the CIB-PC results. Y(DL) = (mS,L-Asn 3 H2O þ mS,D-Asn 3 H2O)/(minit,DL-Asn 3 H2O); PuL-Asn 3 H2O= (mS,L-Asn 3 H2O)/(mS,L-Asn 3 H2O þ s mS,D-Asn 3 H2O). 2158



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-Asn For the unwanted enantiomer the value for KLinh is relatively low, implying negligible crystal growth inhibition in particular for the lower examined temperatures. The estimated progress curves based on the experimental results and the dependencies of the mass fraction for D- and L-Asn over time predicted by the model for runs 3, 4, and 5 are depicted in Figure 12, panels a, b, and c, respectively. With respect to the curves predicted by the model, in all three cases their agreement with the experimental results for the L-form is better than for the ones of the D-form which is not favorable since the course of the counter enantiomer curve sets the limitations on the duration of PC. There is even a disparity in the tendency when comparing Figure 12, panels a and b with c — in the first two the period of PC is overestimated in comparison to the third which may lead to false expectations for the purity of the product.

Table 6. Parameters Obtained by Individual Fitting of the Model to the Estimated Progress Curves of run 3 (Tcryst = 30 C), run 4 (Tcryst = 35 C), and run 5 (Tcryst = 40 C)a

-Asn -Asn run kLg,eff,o [m/s] KLinh []

a

-Asn kDb,prim,het 1 [s 3 K1 7

7/3

3 m 3 kg

-Asn ] aDprim,het []

OF

3

67.53

0.63

791

0.106

4.4 105

4

80.92

1.64

774

0.434

1.2 104

5

72.13

24.98

894

0.559

2.5 104

For all cases is ΔT = 4 K.

Despite that, the experimental results obtained from the first trial of run 3 (Figure 11, symbols marked by circles) and the estimated progress curves based on the experimental results obtained from the second (Figure 12a) show different behavior. In the first trial, the period of PC is clearly visible for a longer time, while in the second it can be assumed that PC may be accomplished up to approximately 100 min. A similar trend was observed also for run 4 where hardly any period of PC is visible, in contrast to run 5 where for up to 200 min the process is feasible. Because of the reasons mentioned above, the results from this study can serve only for a rough estimation of the progress of PC. Coupled Isothermal Batch Preferential Crystallization (CIB-PC). The changes of the mass fractions of the enantiomers over time in each vessel shown in Figure 13 are a result of the CIB-PC experiment. The mass fraction profiles reveal nearly racemic composition in the liquid phase in both tanks during the whole time which is favorable for achieving a higher supersaturation level and therefore a higher driving force for crystallization.40 The CIB-PC experiment was terminated after approximately 800 min (tend, Tank1 = 800 min and tend,Tank2 = 820 min) leading to mS,Tank 1 = (DL) 3.4 g (Y(DL) S,TANK 1 = 10.2%) and mS,Tank 2 = 3.2 g (YS,TANK 2 = 9.7%) with purities PuD-Asn 3 H2O = 100% and PuL-Asn 3 H2O = 98%. Although the process in tank 2 was terminated some minutes later, the yield and the product purity revealed values which were moderately smaller than for the tank where D-Asn 3 H2O was crystallized. A disparity of this type, but with higher intensity, was also observed for some preliminary trials whereupon it was

Figure 12. Estimated progress curves based on the experimental data (symbols) and model predictions (lines) for D- and L-Asn for run 3 (a), 4 (b), and 5 (c). 2159



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Figure 13. Coupled mode preferential crystallization of D-Asn 3 H2O in TANK 1 and L-Asn 3 H2O in TANK 2 at Tcryst = 30 C, ΔT = 4 K, mSeeds,L = mSeeds,D = 0.6 g, SF > 500 μm and 250 rpm.

Figure 14. Dependence of the maximum subcooling on the applied cooling rate for (a) L-Asn/water and (b) DL-Asn/water.

In order to check the superiority of CIB-PC over SIB-PC, the results presented above were compared to values estimated from = 1.5% the progress curves of run 3: 0.5 g of solid product, Y(DL) S and 98% purity of L-Asn 3 H2O (note that for this experiment the sieve cut was slightly different and there was no pretreatment of the seeds). Under the examined conditions, the CIB-PC was proven to be far more advantageous than SIB-PC; that is, the coupled configuration has led to more than a 6-fold increase of the yield (PuL-Asn 3 H2O = 98%).

Figure 15. Reproducibility of run 1 (polarimeter signal vs time).

assumed that the main reason is the different crystal shape of the enantiomers which were introduced as seeds. As mentioned before, for the presented experiment this problem was challenged by using self-grown homochiral crystals, but obviously that did not fulfill the expectations completely.

’ CONCLUSIONS Preferential crystallization of L-asparagine monohydrate from racemic aqueous solution of DL-asparagine has been modeled and realized successfully for different supersaturation degrees and crystallization temperatures. In preliminary investigations, the widths of the metastable zones and the influence of various process parameters on the crystallization kinetic were quantified. For quantitative description of the process, a mathematical model based on moments was developed and applied. This model and the estimated parameters were applicable to predict important features of the process. However, in order to reach high levels of purity, the process had to be terminated earlier than expected. Finally, a more advanced configuration was studied experimentally using two coupled crystallizers in which the mother 2160



Figure 16. Dependence of the density of water and aqueous solutions of DL-Asn on the temperature.

liquors were exchanged continuously. The results obtained show that preferential crystallization in such a coupled mode (CIBPC) is feasible and can outperform the standard simple batch mode (SIB-PC) with respect to productivity and purity.

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Figure 17. Temperature dependence of the dynamic viscosity of aqueous solutions of DL-Asn.

the densitytemperature for water (eq A.1) and for the densitymass fractiontemperature relation for the solution (eq A.2) the experimental data were corrected with respect to the offset. Fwater ¼

’ APPENDIX A.1. Metastable Zone Width (MZW). The dependencies of the maximum subcooling (ΔTmax = Tsat Tnuc; the experimental data for Tnuc are average values of four cycles) on the cooling rate (CR) for the systems L-Asn/water and DL-Asn/water are shown in Figure 14, panels a and b, respectively. The intercept of a fitted linear function to the experimental data gives an estimation of the maximum possible nucleation-free subcooling at cooling rate zero (ΔTmax,0). A.2. Reproducibility of Preferential Crystallization. Figure 15 shows the reproducibility of run 1. The experimental data set under which the experiments have been performed is given in Table 2. A.3. Physical Properties of the Solution. For the calculation of particular parameters during PC, for example, concentrations, densities etc., inclusive amount of measurements for the change of the density, and the viscosity of the solution have been performed covering a broad temperature and concentration range. For the relation of the saturation concentration as a function of concentration and temperature, the experimental data obtained for the solubility measurements have been utilized (these data are published in ref 22). All these dependencies and relations are given in the following. Density. For the density-mass fraction of the enantiomerstemperature dependence, the density of several aqueous solutions of DL-Asn (wDL-Asn = 1, 2, 3, 4, 5, 7, 8, 9, 10 mass%) was measured in a temperature range between 20 and 50 C. The results, accompanied with the density of water, are depicted in Figure 16. The reliability of the results was tested by comparing the experimentally determined densities of water with their reference values41 whereby a minor offset has been observed (Fwater,exp Fwater,ref was in a range ∼0.0020.004 g/cm3). Subsequently, the Fwater,ref values were used for defining the correlation of

1 cm3 cm3 þ 4:911 100:6 2 ðT 273:15 KÞ2 0:9999 g gK ðA.1Þ FL ¼ Fwater þ 0:3572

g wDL-Asn cm3

ðA.2Þ

Herein Fwater is the density of water, T indicates the temperature, FL is density of the solution and wDL-Asn is mass fraction of the DLAsn. Viscosity. For the correlation between the dynamic viscosity, the temperature and the mass fraction, the kinematic viscosity ν was experimentally determined for several solutions of DL-Asn with concentration varying from approximately 1 to 9 mass% in a temperature range of T = 2040 C with step ΔT = 5 C. Consequently, the dynamic viscosity η was calculated using the results for ν and the density of the particular solution (determined by eq A.2). The results are presented in Figure 17. The expression which correlates their dependence is described by eq A.3 η ¼ 2:9542

kg 1724:8 K wDL-Asn exp exp 10 m3s T 0:6641 6

ðA.3Þ

Solubility. The relation describing the dependence of the solubility of L-Asn 3 H2O as a function of the temperature and the concentration of the other enantiomer is given by eq A.4

w L-Asn ¼ K 1 þ 0:030482wD-Asn eq

ðA.4Þ

For determination of K1 the following expression was used in 2161



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order to describe its relation with the temperature: K 1 ¼ 0:0092 expð0:0443T=CÞ

ðA.5Þ

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors would like to acknowledge the support of Polina Peeva, Noelia Melero Pereira, Luise Borchert, and Madeleine B€uttner during performing the measurements. ’ SYMBOLS: a0 parameter [] aprim,het lumped constant within exponential term for primary heterogeneous nucleation [] A scaling factor [] surface area of a solid particle [m2] AP B0 overall nucleation rate at negligible particle size z = 0 [s1] B0,prim,het nucleation rate for primary, heterogeneous mechanism [s1] c molar concentration [mol/m3] (molar) solubility concentration at temperature T ceq (equilibrium) [mol/m3] C mass concentration [kg/m3] (mass) solubility concentration at temperature T Ceq (equilibrium) [kg/m3] molecular diameter [m] dm binary diffusion coefficient [m2/s] D12 number density function [m1] fN F function considering solid phase properties of seeded p-enantiomer on heterogeneous nucleation of c-enantiomer [] g exponent in crystal growth term [] G0,eff effective, size-independent linear growth rate [m/s] Geff effective linear growth rate [m/s] h enantiomer h ∈ {p,c} (p: preferred, c: counter) J nucleation rate (per volume) [s1 3 m3] k enantiomer k ∈ {p,c} (p: preferred, c: counter) surface area shape factor [] kA Boltzmann constant [1.38 1023 J/K] kB kb,prim,het lumped constant for nucleation rate [s1 3 K1 7 7/3 ] 3 m 3 kg effective crystal growth constant [m/s] kg,eff crystal growth constant for mass-based approach km [kg1-g 3 m3g-2 3 s1] volume shape factor [] kV K constant [kg1-g 3 m3(g-1) 3 s1] inhibition constant [] Kinh (fitted) parameter for temperature dependence [K] KT (fitted) parameter for mass fraction dependence [] KW m mass [kg] total mass of the crystallizing species in the liquid mL phase [kg] mass of a solid particle [kg] mP total mass of the crystallizing species in the solid mS phase [kg]

M N NA S t T U VL VP w z γ γ(z) η η0 θ μn FL FS φ ω

molar mass [kg/mol] number of particles [] Avogadro constant [6.022 1023 mol1] supersaturation degree [] time [s] temperature [K] stirrer speed [rpm] volume of the liquid phase [m3] volume of a solid particle [m3] mass fraction [] characteristic particle size [m] interfacial tension [N/m] size-dependent function for (size-dependent growth) SDG model [] dynamic viscosity [m2/s] (fitted) prefactor for dynamic viscosity [m2/s] contact angle [deg] nth moment [mn] density of solution [kg/m3] density of solid phase [kg/m3] function of the contact angle stirrer speed (angular velocity) ω = (2πU/60) min/s [s1]

’ REFERENCES (1) Caner, H.; Groner, E.; Levy, L.; Agranat, I. Drug Discovery Today 2004, 9 (3), 105–110. (2) Najera, C.; Sansano, J. M. Chem. Rev. 2007, 107, 4584–4671. (3) Leuchtenberger, W.; Huthmacher, K.; Drauz, K. Appl. Microbiol. Biotechnol. 2005, 69, 1–8. (4) Meier, N. M.; Franco, P.; Lindner, W. J. Chromatogr. A 2001, 906, 3–33. (5) Fogassy, E.; N ogradi, M.; Kozma, D.; Egri, G.; Palovics, E; Kiss, V. Org. Biomol. Chem. 2006, 4, 3011–3030. (6) Ward, T. J.; Baker, B. A. Anal. Chem. 2008, 80, 4363–4372. (7) Ahuja, S. Chiral Separations, Applications and Technology; American Chemical Society: Washington DC., 1996. (8) Secor, R. M. Chem. Rev. 1963, 63 (3), 297–309. (9) Harada, K. Bull. Chem. Soc. Jpn. 1965, 38 (9), 1552–1555. (10) Yamada, S.; Yamamoto, M.; Chibata, I. J. Org. Chem. 1973, 38 (26), 4408–4412. (11) Mullin, J. W. Crystallization, 4rd ed.; Butterworth-Heinemann: Oxford, 2001. (12) Mersmann, A. Crystallization Technology Handbook, 2nd ed.; Marcel Dekker, Inc.: New York, 2001. (13) Jones, A. G. Crystallization Process Systems; ButterworthHeinemann: Oxford, 2002. (14) Yu, Z. Q.; Chew, J. W.; Chow, P. S.; Tan, R. B. H. Chem. Eng. Res. Des. 2007, 85 (7), 893–905. (15) Jacques, J.; Collet, A.; Wilen, S. H. Enantiomers, Racemates and Resolutions; Krieger Publishing Company: Malabar, FL, 1994. (16) Collet, A. Enantiomer 1999, 4, 157–172. (17) Sakai, K.; Hirayama, N.; Tamura, R. Novel Optical Resolution Technologies; Springer-Verlag: Berlin, Heidelberg, 2007. (18) Profir, V. M.; Matsuoka, M. Colloids Surf. A-Physicochem. Eng. Aspects 2000, 164 (23), 315–324. (19) Rodrigo, A. A.; Lorenz, H.; Seidel-Morgenstern, A. Chirality 2004, 16, 499–508. (20) Elsner, M. P.; Fernandez Menendez, D.; Alonso Muslera, E.; Seidel-Morgenstern, A. Chirality 2005, 17, S183–S195. (21) Elsner, M. P.; Ziomek, G.; Seidel-Morgenstern, A. AIChE J. 2009, 55 (3), 640–649. (22) Petrusevska-Seebach, K.; W€urges, K.; Seidel-Morgenstern, A.; L€utz, S.; Elsner, M. P. Chem. Eng. Sci. 2009, 64, 2473–2482. 2162



ARTICLE

(23) W€urges, K.; Petrusevska-Seebach, K.; Elsner, M. P.; L€utz, S. Biotechnol. Bioeng. 2009, 104 (6), 1235–1239. (24) Kitamura, M.; Ishizu, T. J. Cryst. Growth 2000, 209 (1), 138–145. (25) Randolph, A. D.; Larson, M. A. Theory of Particulate Processes; Academic Press: San Diego, 1988. (26) Ramkrishna, D. Population Balances: Theory and Applications to Particulate Systems in Engineering; Academic Press: New York, 2000. (27) Angelov, I.; Raisch, J.; Elsner, M. P.; Seidel-Morgenstern, A. Ind. Eng. Chem. Res. 2006, 45 (2), 759–766. (28) Kougoulos, E.; Jones, A. G.; Wood-Kaczmar, M. W. J. Cryst. Growth 2005, 273 (34), 520–528. (29) Kind, M.; Mersmann, A. Chem.-Ing.-Tech. 1983, 55 (9), 720–721. (30) Mersmann, A. Trans IChemE 1996, 74 (A), 812–820. (31) Mersmann, A.; Bartosch, K. J. Cryst. Growth 1998, 183 (12), 240–250. (32) Mersmann, A.; Bartosch, K.; Braun, B.; Eble, A.; Heyer, C. Chem.-Ing.-Tech. 2000, 72 (12), 17–30. (33) Mersmann, A. J. Cryst. Growth 1990, 102 (4), 841–847. (34) Schubert, H.; Mersmann, A. Trans IChemE 1996, 74 (A), 821–827. (35) Kawajiri, Y.; Angelov, I.; Ziomek, G.; Elsner, M. P.; Seidel-Morgenstern, A. Parameter estimation for preferential crystallization by nonlinear programming. Chem. Eng. Sci. 2011, submitted. (36) Dormand, J. R.; Prince, P. J. J. Comp. Appl. Math. 1980, 6, 19–26. (37) Nyvlt, J.; S€ohnel, O.; Matuchova, M.; Broul, M. The Kinetics of Industrial Crystallisation; Elsevier: Amsterdam, Netherlands, 1985. (38) Lorenz, H.; Polenske, D.; Seidel-Morgenstern, A. Chirality 2006, 18, 828–840. (39) Mullin, J. W. Crystallization, 3rd ed.; Butterworth-Heinemann: Oxford, 1993. (40) Elsner, M. P.; Ziomek, G.; Seidel-Morgenstern, A. Chem. Eng. Sci. 2011, 66 (6), 1269–1284. (41) Perry, R. H. Green, D. W. Perry’s Chemical Engineers’ Handbook, 7th ed.; McGraw-Hill Companies, Inc.: USA, 1997.

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Preferential Crystallization of l-Asparagine in Water

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