Solubility and nucleation in l (+)-ascorbic acid–methanol–ethanol–water system

Chemical Engineering and Processing 46 (2007) 351–359

Solubility and nucleation in l(+)-ascorbic acid–methanol–ethanol–water system B. Wierzbowska a , A. Matynia a,∗ , K. Piotrowski b , J. Koralewska a a

b

Faculty of Chemistry, Wrocław University of Technology, 50-370 Wrocław, Poland Department of Chemical & Process Engineering, Silesian University of Technology, 44-101 Gliwice, Poland Received 18 April 2006; received in revised form 9 June 2006; accepted 10 July 2006 Available online 16 October 2006

Abstract The experimental data concerning the practical solubility, metastable zone width and nucleation kinetics in l(+)-ascorbic acid–methanol–ethanol–water system are presented. Measurements were performed in a laboratory cooled batch crystallizer with internal circulation of suspension. Practical solubility of l(+)-ascorbic acid in water solutions with addition of both methanol and ethanol was determined using the last crystal dissolution method within the temperature range of T = 313–353 K. Influence of solution composition and its cooling rate on the value of maximal supercooling of the system is presented and discussed. Nucleation kinetics was elaborated with the use of Kubota’s model of stochastic nucleation in the initial seeding system. Parameter values in the kinetic equations were determined with the method of maximal (critical) supercooling of the solution (constant cooling rates from RT = 4.17 × 10−3 –33.3 × 10−3 K s−1 range were applied). © 2006 Elsevier B.V. All rights reserved. Keywords: l(+)-Ascorbic acid; Methanol; Ethanol; Practical solubility; Critical (maximal) supercooling; Nucleation kinetics; Seeded system; DT batch crystallizer; Cooling rate

1. Introduction Vitamin C (l(+)-ascorbic acid [1,2], denoted later in the text as LAA) is usually made from d-glucose according to Reichstein procedure [3,4]. The raw product of synthesis, manufactured in industrial conditions, contains ca. 96–98 mass% of main component [5]. Required purity of LAA results the most often from its multistage batch crystallization from water solutions [6–13]. Moreover, the characteristic feature of LAA water solutions are extremely high values of maximal supercooling, considerable larger than these occurring in water solutions of inorganic salts [14–17]. Besides, these values are considerably depended on the solution’s composition, as well as on its cooling rate. In a less concentrated solutions (e.g. 30 mass% of LAA), cooled down with relatively high cooling rates (>30 × 10−3 K s−1 ), Tmax can even reach ca. 50 K value [6]. In these conditions batch crystallization time is short—thus a relatively low process yield can be expected. The undischarded supersaturation level in a

∗

Abbreviations: EtOH, ethanol; LAA, l(+)-ascorbic acid; MeOH, methanol Corresponding author. Tel.: +48 71 320 34 97; fax: +48 71 328 04 25. E-mail address: [email protected] (A. Matynia).

0255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2006.07.005

mother solution can even reach about a dozen mass%, increasing significantly the probability of sudden, spontaneous nucleation [7]. The crystal product withdrawn from the crystallizer is then characterized by small mean particle size [8]. It is also possible to run the crystallization process in an enhanced, LAA–aliphatic alcohol(s)–water system. Introduction of third component – aliphatic alcohol (in practice, one from the initial three alcohols in a homologous series, C1 –C3 ) – gives the opportunity to improve the process yield, quality of obtained crystal product and enables one to reduce the number of necessary batch crystallization stages [18–20]. It is of significant importance, regarding the biochemical activity (strong reducing properties) of Vitamin C [21], which after exposition to direct contact with air is quickly oxidized, losing partly its valuable bioactivity. This undesirable, side process is strongly catalyzed by copper, iron and other heavy metal ions, higher temperature, lower pH and presence of activated carbon, as well [22–26]. Some investigation results concerning LAA nucleation and crystal growth kinetics, both in pure distilled water and in selected three-component water solutions (addition of methanol (MeOH), ethanol (EtOH) or isopropanol, respectively) were

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published by the authors previously (e.g. [13,20,27]). The research results have already found themselves useful in polish pharmaceutical industry in improvement of the technology of crystallization of Vitamin C from its water solutions. A new apparatus construction for a more effective process of mass crystallization of LAA from water (or water/methanol solutions) was also elaborated and successfully tested [28]. From the experiments performed up till now, concerning individual ternary systems, LAA–H2 O–(MeOH/EtOH), the profitable influences of these alcohols on the complex subprocesses of batch mass crystallization of LAA were confirmed. Similar observations (individual influence of methanol, ethanol or propanol) are reported by Smirnov, Suprunov et al. [18,19], as well as by Ulrich and Omar [29–32]. It seems purposeful to determine experimentally the influences of these both alcohols on the LAA solubility, metastable zone width and the nucleation rate. These technological factors influence both the batch process course and its final results (yield, crystal product quality) considerably. Supposing practical utility of the results – improvement of purification processes in pharmaceutical industry – the presented experiments were performed in enhanced, LAA–MeOH–EtOH–H2 O system intentionally assuming the ranges of initial concentrations of compounds, as well as its cooling rates to be compatible with industrial technological purification process conditions. Moreover, an direct comparison with the data corresponded to pure water LAA solutions and to water/alcohol (but only one) LAA solutions is thus possible. 2. Experimental setup and procedure 2.1. Experimental stand The experimental stand scheme is presented in Fig. 1. The experiments were performed in a laboratory batch Draft

Tube (DT) crystallizer of Vw = 0.6 dm3 working volume with internal circulation of solution/suspension. It was a hermetic, glass-made cylindrical tank (Vt = 1 dm3 , D = 120 mm, H = 123 mm) equipped with a cooling jacket (pipe-in-pipe type heat exchanger) embedded into a circulation profile element’s wall (d = 57 mm, h = 53 mm) coupled with thermostat, where an ice load was applied to cool the heat acceptor – circulating water – down to T = 275 K. A second thermostat was applied to heat the entire crystallizer content after the nucleation phenomenon occurrence (T = 360 K). The cooling/heating rates were precisely controlled by computer. In the tank axis, inside the circulation tube a three-paddle propeller mixer (dm = 55 mm) was installed. While all experiments the revolution number was assumed constant (10 ± 0.2 s−1 ) providing stable and intensive enough circulation of solution (after nucleation–suspension) inside the crystallizer working volume. Optimal value of revolution number was determined on the basis of initial test results [33]. 2.2. Experimental procedure Working solutions applied in the experiments, as biochemically active materials, were made just before their introduction into the crystallizer using LAA of the main component’s content above 99.7 mass% (GR for analysis and for biochemistry, MERCK, Germany), double distilled water, MeOH (p., POCH Gliwice, Poland) and EtOH (p.a., 96%, ZPS Polmos, Poland). An individual measurement procedure was as follows. The 0.7 kg of solution of known composition, after introduction into the crystallizer, was heated till its actual temperature value was by ca. 5 K higher than the expected solubility temperature, Ts (roughly estimated on the basis of initial test results). In this moment mixer was put in motion (preventing temperature and concentration gradients occurrence). After ca. 15 min of

Fig. 1. Laboratory batch crystallizer—an experimental setup: (1) DT crystallizer with internal circulation of the medium, (2) heating jacket, (3) cooler, pipe-in-pipe type heat exchanger, (4) thermostat (heating), (5) thermostat (cooling), (6) cooling coil, (7) cooling medium pump, (8) cooling water tank: ice + water, (9) PC computer, (M) stirrer speed control, (T) temperature control.

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the mixing the cooling process started (a constant cooling rate value, RT , was assumed). When solution attained a temperature value by 1 K lower than the expected solubility temperature, Ts , dozens of well shaped LAA crystals (ca. 0.1 g of total mass, mean crystal size 900 ␮m) were introduced into the mixed system (heterogeneous/surface nucleation [14,34]). Identical seeding procedure was applied in two compounds (water–LAA) [6–8] and three compounds (water–LAA–MeOH/EtOH) [13,20,27,28] solutions. While further cooling of the system, a continuous observation of the solution was realized till a moment of characteristic, spontaneous nucleation was attained (noticeable, sudden turbidity in the bulk solution [34]; the latent heat of phase change (crystallization) liberated, producing in result a clearly observable increase of solution temperature, recorded by the computer measurement system—see Fig. 1). The corresponded temperature value can be interpreted as the spontaneous crystallization temperature, Tcr (this characteristic temperature value is also termed: nucleation temperature, maximal supercooling temperature or limiting supersaturation temperature). The current flow (cooling medium, water of temperature ca. T = 275 K) was then stopped and the heating medium was connected (water of temperature ca. T = 360 K). The suspension in the crystallizer was slowly heated till the turbidity disappeared. The corresponded temperature is the practical solubility temperature, Ts [35]. The processed solution was further heated up till temperature higher by 5 K compared to Ts temperature was reached. After 15 min the subsequent cooling process (to temperature Tcr ) was started, with the same cooling rate and in the manner described above. Both heat transfer operations – heating and cooling of the processed solution – were used once again. Applying this experimental procedure one can dispose two values of Ts and three values of Tcr . For assumed composition of the mixture, the measurement procedure described above was repeated twice (reproducibility test). Their average values (based on four values of Ts and six values of Tcr ) enabled one to calculate the average maximal supercooling value [36]: Tmax = Ts − Tcr . The experimental tests of practical solubility in LAA–MeOH–EtOH–H2 O systems were performed within the following compound concentration ranges: • 30 mass% ≤ cLAA ≤ 50 mass%, • cMeOH + cEtOH composition ranges: 12 mass% ≤ cMeOH + cEtOH ≤ 40 mass% for cLAA = 30 and 40 mass%, 12 mass% ≤ cMeOH + cEtOH ≤ 30 mass% for cLAA = 45 mass%, 12 mass% ≤ cMeOH + cEtOH ≤ 20 mass% for cLAA = 50 mass%, • distilled water—a complement to a 100 mass%. The solutions containing 45 or 50 mass% of LAA were mixed with lower amounts of MeOH–EtOH mixtures than it was in case of 30 and 40 LAA mass% solutions. Higher concentrations of these alcohols caused the solution boiled in the temperature lower than the LAA solubility temperature, Ts .

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The 39 diversified compositions of four-compound solutions (LAA–MeOH–EtOH–H2 O) were tested. For each composition, Ts and Tcr (thus Tmax ) values were determined experimentally. In this, first set of experiments, a constant linear cooling rate was assumed (RT = 8.33 × 10−3 K s−1 ). Kinetic parameter values of LAA nucleation process in a linearly cooled, batch seeded crystallizer with internal circulation of suspension were elaborated on the basis of data corresponded to three solutions of the following compositions: - LAA 40 mass%, MeOH 10 mass%, EtOH 10 mass%, water 40 mass%, - LAA 45 mass%, MeOH 10 mass%, EtOH 10 mass%, water 35 mass%, - LAA 50 mass%, MeOH 10 mass%, EtOH 10 mass%, water 30 mass%. For each composition tested the solution in the crystallizer was cooled down with five linear cooling rate values, selected as follows: RT = (4.17, 8.33, 16.7, 25.0, 33.3) × 10−3 K s−1 (second set of experiments). 3. Solubility and maximal supercooling in LAA–MeOH–EtOH–H2 O system 3.1. Solubility Practical solubilities of LAA in four-component (LAA– MeOH–EtOH–H2 O) solutions were investigated. The experimental data are collected in Table 1. On the basis of 39 experimental data sets (solution compositions) an empirical correlation in the form of cLAA = f(Ts , cMeOH , cEtOH ) was elaborated as: cLAA = 0.527Ts − 0.283cMeOH − 0.386cEtOH − 129.75

(1)

where cLAA —saturation (practical solubility) concentration of LAA in temperature Ts , mass%; Ts —temperature corresponded to the last crystal dissolution (Ts = 313–353 K); cMeOH , cEtOH —concentrations of MeOH and EtOH, respectively, mass%. Concentration ranges of the solution compounds (thus Eq. (1) applicability area) were presented in previous section. Correlation coefficient value of Eq. (1) was R = 0.997, while its mean relative error sr = ±2.1%. Eq. (1) can be also presented as a solubility temperature in the function of the solution composition, Ts = f(cLAA , cMeOH , cEtOH ): Ts = 1.897cLAA + 0.537cMeOH + 0.732cEtOH + 246.20

(1a)

Eq. (1a) with Eq. (3) can be applied for the calculation of maximal supercooling, Tmax (see resulting Eqs. (4) and (5)). In Fig. 2, a comparison of solubility temperature Ts values: experimental (Table 1) and calculated with Eq. (1a) is presented. Compatibility between the experimental and calculated data can be regarded satisfactory. Density values of the investigated (saturated) solutions, corresponded to the crystal dissolution temperature (Ts ), were also determined with the use of density bottle equipment. The

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Table 1 Experimental test data concerning the metastable zone width in a LAA–MeOH–EtOH–H2 O system (batch cooling DT crystallizer) Composition of solution (mass%)

Practical solubility temperature

Nucleation temperature

Critical supercooling

LAA

MeOH

EtOH

H2 O

Ts (K)

Tcr (K)

Tmax (K)

30 30 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 40 40 40 40 40 45 45 45 45 45 45 45 45 45 50 50 50 50 50 50

2 6 10 5 10 15 10 15 20 10 20 30 2 6 10 5 10 15 10 15 20 10 20 30 2 6 10 5 10 15 10 15 20 2 6 10 5 10 15

10 6 2 15 10 5 20 15 10 30 20 10 10 6 2 15 10 5 20 15 10 30 20 10 10 6 2 15 10 5 20 15 10 10 6 2 15 10 5

58 58 58 50 50 50 40 40 40 30 30 30 48 48 48 40 40 40 30 30 30 20 20 20 43 43 43 35 35 35 25 25 25 38 38 38 30 30 30

313.5 313.0 312.5 316.5 316.0 315.0 321.5 320.5 320.0 329.0 327.0 325.0 331.0 330.0 329.0 335.5 335.0 334.0 341.5 340.0 339.0 353.0 351.0 348.0 339.0 339.0 339.0 343.5 343.0 342.5 353.0 352.0 349.0 349.0 348.0 347.5 353.5 353.0 352.5

279.5 278.5 278.0 279.5 279.0 278.0 283.0 282.5 280.5 291.5 289.0 286.5 306.0 303.0 301.0 308.5 306.0 304.0 315.5 313.0 311.5 333.0 329.0 325.0 317.5 317.5 316.5 323.5 320.5 320.0 335.0 333.5 329.5 329.5 327.0 327.5 336.5 335.0 333.5

34.0 34.5 34.5 37.0 37.0 37.0 38.5 38.0 39.5 37.5 38.0 38.5 25.0 27.0 28.0 27.0 29.0 30.0 26.0 27.0 27.5 20.0 22.0 23.0 21.5 21.5 22.5 20.0 22.5 22.5 18.0 18.5 19.5 19.5 21.0 20.0 17.0 18.0 19.0

a

b

Cooling rate, RT = 8.33 × 10−3 K s−1 . a Average with four experimental data. b Average with six experimental data.

measurement results can be described with the use of empirical correlation: ρsol = 1.569Ts − 3.898cMeOH − 4.789cEtOH + 651.43

(2)

valid within the presented in previous section parameter ranges (correlation coefficient R = 0.991, mean relative error sr = ±0.6%). Solubility isotherms in the form of cLAA = f(cMeOH + cEtOH )T=const . dependency are presented in Fig. 3 (for clarity of the presentation a constant concentration, 10 mass%, of one of the alcohols is assumed). Concentration values of LAA, necessary while the preparation of the isotherms, were calculated with the use of Eq. (1) in the temperature range of Ts = 323–343 K (every 5 K), for the total concentration of both alcohols in the

solution within a 12–40 mass% range. As it results from Eq. (1), these isotherms are straight, parallel lines. Presence of aliphatic alcohol in the system effects in decreasing of the LAA solubility (see Eq. (1), Fig. 3). For example: in temperature Ts = 343 K the practical solubility (equilibrium concentration) of LAA in water solution is ca. cLAA = 49.7 mass% [6], however it is ca. 38.7 mass% in the water solution composed additionally of: 30 mass% of MeOH and 10 mass% of EtOH. On the other hand, for reverse proportions of these additives (water solution containing 10 mass% of MeOH and 30 mass% of EtOH) this value is ca. cLAA = 36.6, mass% (see the coefficient values in empirical Eq. (1), thus different slopes for MeOH and EtOH in Fig. 3). For comparison it may be noted, that when the solution has the same content (40 mass%) of one, single alcohol – but

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however in the restricted range. On the other hand this tendency causes simultaneously decrease of supersaturation, which is a main driving force in the mass crystallization processes. Moreover, the rise of temperature favours the LAA thermal decomposition (biologically active substance). Addition of aliphatic alcohols advantageously decreases the boiling temperature of the solution. Considering these complex, opposite interactions, practical application of aliphatic alcohol additives should be recommended (or restricted) only to LAA water solutions with the alcohols which total concentration does not exceed 20 mass%. 3.2. Maximal supercooling (metastable zone width)

Fig. 2. Comparison of practical solubility temperature (Ts ) and nucleation temperature (Tcr ) values determined experimentally (Table 1) and calculated: Ts with the use of Eq. (1a) and Tcr with the use of Eq. (3), respectively.

only MeOH – the LAA solubility is higher (40.7 mass% [20]) than it can be achieved using any aliphatic alcohol mixtures. This phenomenon is not advantageous considering the practical application of the aliphatic alcohols in the purification processes of a technical grade Vitamin C. Lower LAA concentration in the crystallizer feeding stream, as a consequence of decrease of its solubility in this system, limits the process yield, influences the mother liquor balance, as well as affects the number of the process stages. On the other hand, presence of aliphatic alcohol(s) in the system makes the process of mother solution concentration more complicated since it requires extra hermetic apparatus and installation, additionally of special construction providing security in the plant work with some danger (flammable and explosive) organic solvents. Increase of the process temperature brings about the increase of LAA solubility (see Eq. (1)),

Alcohol(s) presence alters the LAA maximal supercooling temperature, Tcr , as well. Individual, separate influences of MeOH or EtOH on the nucleation kinetics in the discussed systems are described in details in the authors’ previous works [13,20]. Simultaneous influence of both these alcohols on the temperature Tcr , thus on the metastable zone width in the water–aliphatic alcohols solutions of LAA appears to be a considerable more complex phenomenon than it is in case of an individual alcohol action. Some extremes in Tcr = f(cLAA , cMeOH , cEtOH ) or Tmax = f(cLAA , cMeOH , cEtOH ) complex functions are clearly observable in the raw laboratory data (Table 1). Estimation of these relationships with the use of artificial neural networks was presented in the other authors’ works (e.g. [37,38]). However, with some simplifying assumptions the experimental data of Tcr = f(cLAA , cMeOH , cEtOH ) can be accurately enough fitted by the empirical relationship: Tcr = 2.932cLAA + 0.671cMeOH + 0.883cEtOH + 174.78

(3)

valid within the parameter ranges presented above (R = 0.996, sr = ±3.5%, see Fig. 2). For the solution of assumed composition one can approximately calculate from the Eq. (1a) and Eq. (3) (average error: ca. ±5%; maximal error: ca. ±20%) the maximal supercooling value, defined as: Tmax = Ts − Tcr

(4)

using the resulting, detailed empirical formula: Tmax = f (cLAA , cMeOH , cEtOH ) = 71.42 − 1.035cLAA −0.134cMeOH − 0.151cEtOH

(5)

In the form of maximal supersaturation (applying Eq. (1) for the zone limiting temperature values, Ts and Tcr ) one obtains: cmax (T, cMeOH , cEtOH ) = cLAA (Ts , cMeOH s , cEtOH s ) −cLAA (Tcr , cMeOH cr , cEtOH cr )

(6)

Additionally assuming: cMeOH , cEtOH = const. (hermetic apparatus, no vapors produced while cooling, no changes in the mass inside this closed system) one can directly apply the simplified form of Eq. (6): Fig. 3. Solubility isotherms in the LAA–MeOH–EtOH–H2 O system (calculated with Eq. (1)).

cmax (T ) = cLAA (Ts ) − cLAA (Tcr ) = 0.527Tmax

(6a)

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50 mass% causes ca. 2 times decrease in Tmax and cmax values. On this basis it can be concluded, that it is advantageous to introduce the concentrated solutions of LAA into the crystallizer. Assuming constant cooling rate (RT ), the period of batch crystallization process (after fast nucleation event) enlarges, what enables one to acquire a higher process yield and larger sizes of the product crystals, more convenient in the consecutive processes of their mechanical separation from the mother liquor and effectively washing. 4. Kinetics of the LAA nucleation

Fig. 4. Metastable zone in the LAA–MeOH–EtOH–H2 O system (assumed constant concentration of MeOH 10 mass% and EtOH 10 mass%). Comparison of experimental and calculated data: (1) practical solubility line—Eq. (1); (2) spontaneous nucleation line—rearranged Eq. (3). Cooling rate RT = 8.33 × 10−3 K s−1 .

It seems interesting to mention, that LAA solutions tend to form stable supersaturated solutions, of relatively high values of maximal supercooling (thus with strongly enhanced metastable zone width, practically non-comparable with these in inorganic compounds solutions; heterogeneous limit exceeds the homogeneous one corresponding to inorganic species, see Fig. 4) [6,13,20,27]. Even introduction of tens of seeding LAA crystals (although heterogeneous or heterogeneous-surface nucleation mechanisms can be theoretically expected for these specific process conditions) does not cause the occurrence of an vigorous evolution of nuclei, although the nucleation temperature is then in water solutions of LAA by up to 10 K higher compared to nucleation temperature without seeding (homogeneous nucleation) and above 5 K higher in case of alcohol(s) presence [6]. As it was stated above, the solubility temperature (Ts ) was determined with so-called last crystal dissolution method [34]. However, the temperature determined this way, termed here practical solubility temperature, should not be directly identified with the thermodynamic-based temperature of the saturated solution since it is dependent, among other things, on the process parameter values, as: heating/cooling rate (heat transport intensity), crystal dissolution rate, intrinsic dynamic stability of the supersaturated solutions, etc. Its value, however important for practical application of presented technology, is usually by 1–2 K higher than the exact, physicochemical saturation temperature of the solution (in some cases the differences can be even higher). In Fig. 4 there is presented the metastable zone limits of the water–alcohols solutions of LAA. Total concentration of both alcohols in the solution was assumed constant (20 mass%, distributed as: 10 mass% of MeOH and 10 mass% of EtOH). Both exemplary, selected experimental data (see Table 1) and the values calculated with Eq. (1) and rearranged Eq. (3) – as solid and dashed lines – are presented. From Fig. 4 it results, that the increase of LAA concentration in the solution from 30 to

Quantitative, mathematical description of a stochastic, heterogeneous process of creation a new solid phase composed of the smallest-size crystals in a batch crystallizer is a complex problem. The proposed methods of the experimental results elaboration [34–36] do not lead to the unequivocal interpretation of the test data. It seems, that for practical applications (estimation of the kinetic parameters) an stochastic model of nucleation process in a seeded solution, proposed by Kubota et al. [39], Eq. (7), can be recommended with an acceptable accuracy: B = kb (T )n

(7)

The parameter values in Eq. (7) can be calculated from Eq. (8) on the basis of measurement data of maximal supercooling in the solution (Tmax ) while using diversified values of cooling rate (RT ): Tmax =

Γ ((n + 2)/(n + 1)) (kb /[RT (n + 1)])1/(n+1)

(8)

The relatively complex Eq. (8) can be also presented in a simplified form: 1/(n+1)

Tmax = kT RT

(8a)

which enables one to conveniently predict, having known kT and n, the values of maximal supercooling in the solution for the assumed cooling rate. In Fig. 5 there are presented the experimental results concerning maximal supercooling in the LAA–MeOH–EtOH–H2 O solutions (LAA concentration: 40, 45 and 50 mass%, 10 mass% of MeOH and 10 mass% of EtOH), cooled with RT from the 4.17 × 10−3 to 33.3 × 10−3 K s−1 range. Calculated on this basis the nucleation order (n) and kinetic constant (kb ) values (see Eq. (8)), as well as a constant kT (see Eq. (8a)), are presented in Table 2. Analyzing these data (see Fig. 5, Table 2) it can be concluded, that the kinetic constant kb value increases with the temperature Ts increasing (thus with the increase of LAA concentration in solution introduced into the batch crystallizer as a result of the equilibrium concentration increase), while the nucleation order slightly decreases (n = 1.99 → 1.90). Considering the accuracy and precision of the analytical procedure [13] while determining the maximal supercooling Tmax and repeatability of the test results it can be, approximately, assumed as n = 2. As it results from Fig. 5, the water–alcohols solutions of LAA are characterized by relatively high values of the maximal

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Table 2 Kinetic parameters of the nucleation in the: LAA–MeOH–EtOH–H2 O system Composition of solution (mass%) LAA 40 45 50

MeOH 10 10 10

EtOH 10 10 10

H2 O 40 35 30

Practical solubility temperature

Eq. (7) parameter values

Ts (K)

kb

n

335 343 353

7.57 × 10−7

1.99 1.92 1.90

Fig. 5. Influence of cooling rate, RT , on the maximal supercooling Tmax in the water–alcohols solutions of LAA (assumed constant concentration of MeOH 10 mass% and EtOH 10 mass%).

supercooling Tmax —even to ca. 46 K (depending on LAA concentration in the solution and its cooling rate, see also Table 1). The higher is the LAA concentration in the process solution and the lower is its cooling rate, the lower values of Tmax can be expected. For example: for the solution of composition: cLAA = 50 mass%, cMeOH = 10 mass%, cEtOH = 10 mass% and cH2 O = 30 mass%, cooled down with the constant linear cooling rate RT = 4.17 × 10−3 K s−1 the expected maximal supercooling is Tmax = 15 K. This conclusion is of essential significance in selection of the optimal technological parameter values for the complex batch LAA crystallization process with seeding. Lower values of supercooling Tmax , thus lower maximal supersaturation cmax correspond to longer times of the mass transfer between the supersaturated solution and newly created solid phase, more convenient, milder conditions for the supersaturation reduction, thus a more convenient possibilities of acquire the expected quality of LAA crystal product [40].

2.21 × 10−6 3.61 × 10−6

kT , Eq. (8a)

R, Eq. (8a)

144.7 112.1 97.1

0.999 0.994 0.997

compared to water or water–one alcohol solutions of LAA. Increase (assumed Ts = const.) of the concentration of one of the alcohols by 10 mass% – with the constant value of the second alcohol’s concentration – effects either in LAA solubility decrease by ca. 2.8 mass% (MeOH) or by ca. 3.9 mass% (EtOH). Practical solubility of LAA in this four-component liquid system can be calculated from Eq. (1), since the corresponded density of solution in temperature Ts —from Eq. (2). The practical solubility courses were determined experimentally in the laboratory batch crystallizer (Vw = 0.6 dm3 ) with internal circulation of suspension using the last crystal dissolution method. The experimental data presented confirmed also that the presence of aliphatic alcohols in the crystallizing system modifies the nucleation temperature, Tcr , thus the corresponding metastable zone width. The value of this temperature can be calculated (approximately) from the empirical Eq. (3) for the assumed chemical composition of the solution, since the value of maximal supercooling, Tmax , from Eq. (5) and maximal supersaturation cmax from Eq. (6) or Eq. (6a). It was concluded, that the water–aliphatic alcohols solutions of LAA can be characterized by high values of maximal supercooling Tmax = 15–46 K, depending on LAA concentration, type and concentrations of alcohols in the solution (Table 1, Eq. (5), Figs. 4 and 5), as well as on its cooling rate (see Eq. (8) or Eq. (8a), Table 2, Fig. 5). Nucleation kinetics of LAA was described quantitatively assuming validity of the Kubota’s stochastic model of nucleation process in a seeding solution. The values of constant (kb ) and nucleation order (n) in kinetic equation (Eq. (7)) were determined. It was concluded, that with the temperature increase the kb value increases, too, while the nucleation order n slightly decreases (see Table 2). Taking under consideration unavoidable experimental error while determining the Ts and Tcr values, the nucleation order n = 2 can be approximately assumed. Considering the calculated values of n, kT and kb (see Table 2), the detailed relationships valid for the solution of recommended, optimal composition: LAA 50 mass%, MeOH 10 mass%, EtOH 10 mass% and water 30 mass%) are as follows: B = 3.6 × 10−6 (T )2

(7a)

and 1/3

5. Conclusions

Tmax = 97RT

Practical solubility in LAA–MeOH–EtOH–H2 O system was determined within the temperature range of T = 313–353 K. It was concluded, that presence of both aliphatic alcohols in this four-component system effects in decrease of LAA solubility

The relationships presented above enable one to estimate the probability (rate) of nucleation (Eq. (7a)), as well as to calculate the value of maximal supercooling of the solution as the function of cooling rate in a seeded batch crystallizer (Eq. (8b)).

(8b)

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Acknowledgement This work was supported by the Ministry of Science and Higher Education of Poland under grant No. 3T09B 122 27. Appendix A. Nomenclature

B cEtOH cLAA cMeOH cmax D d dm H h kb kT N n RT R sr Tcr Ts T Tmax

Vt Vw yi yˆ i

nucleation probability, nucleation rate (s−1 m−3 ) concentration of ethanol in a solution (mass%) concentration of l(+)-ascorbic acid (LAA) in a solution (mass%) concentration of methanol in a solution (mass%) critical, maximal supersaturation in solution (mass%) crystallizer’s diameter (m) draft tube’s diameter (m) propeller mixer’s diameter (m) crystallizer’s height (m) draft tube’s height (m) constant in equation of nucleation probability (rate) B (s−1 K−n ) constant in Eq. (8a) (s1/(n+1) K−(n/(n+1)) ) number of observations exponent (nucleation order) in the equation of nucleation probability (nucleation rate) B cooling rate (K s−1 ) correlation coefficient mean relative error defined by  N 2 100 1/N i=1 [(ˆyi − yi )/ˆyi ] (%) nucleation temperature (K) (practical) solubility temperature (K) supercooling in the solution (K) critical, maximal value of supercooling in the solution (maximum allowable supercooling) defined as Ts − Tcr (K) crystallizer’s total volume (m3 ) crystallizer’s working volume (m3 ) observed value estimated value

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