Experimental Determination of Metastable Zone Width, Induction

Article pubs.acs.org/jced

Experimental Determination of Metastable Zone Width, Induction Period, and Primary Nucleation Kinetics of Cytidine 5′Monophosphate Disodium Salt in an Ethanol−Aqueous Mixture Jin Yu, An Li, Xiaochun Chen, Yong Chen, Jingjing Xie, Jinglan Wu, and Hanjie Ying* College of Biotechnology and Pharmaceutical Engineering, Nanjing University of Technology, Xin mofan Road 5, Nanjing 210009, People’s Republic of China ABSTRACT: A systematic investigation was carried out to determine the metastable zone width (MSZW) and induction period values of cytidine 5′monophosphate disodium salt (5′-CMPNa2) in an ethanol + water mixture solution. Experimental determination of the MSZW was performed using a laser method. The two factors solution temperature and agitation were evaluated in this study to measure the MSZW. It was observed that the MSZWs decreased when the agitation levels increased and were little affected by solution temperature. The induction period was combined with the classical theory of nucleation. The various critical nucleation parameters, such as the interfacial tension (γ), the radius of critical nucleus (r*), the critical free energy of nucleus (ΔG*) and the molecular number of critical nucleus (i*) were evaluated in the controlled nucleation condition. The critical nucleation parameters varied with increased temperature, and the nucleation rate increased with increased supersaturation.

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INTRODUCTION Cytidine 5′-monophosphate (5′-CMP) is one of four common ribonucleotides that constitute ribonucleic acids (RNAs) and may be a substrate for the preparation of cytidine-5′diphosphate choline (CDP-choline), cytidine triphosphate (CTP), and other medicinal derivatives which are widely used in the food and pharmaceutical industries.1 Its disodium salt cytidine 5′-monophosphate disodium (5′-CMPNa2) can be prepared by enzyme synthesis, enzymatic hydrolysis of RNA and synthetic processes. The molecular structure of cytidine 5′monophosphate disodium (5′-CMPNa 2 ) (sodium((2R,3S,4R,5R)-5-(4-amino-2-oxopyrimidin-1(2H)-yl)-3,4-dihydroxytetrahydrofuran-2-yl) methyl phosphate, CAS registry no. 6757-06-8, molecular mass: 367.16) is shown in Figure 1.

industrial applications, it is difficult to control the crystallization processes. Nevertheless, the aim of this work was to study the metastable zone width, induction period, and primary nucleation kinetics of 5′-CMPNa2 in order to control the crystallization processes. Water and ethanol are widely used as industrial solvent. Ethanol is selected as an effective antisolvent for the crystallization of 5′-CMPNa2, which is inexpensive, has low toxicity compared with other organic solvents, and furthermore can be dissolved in water in any proportion. In industrial production where there is high partial oversaturation in which it is difficult to avoid a sharp nucleation, the formation of amorphous precipitate leads to particle aggregation and impurities. Therefore, there is a need to focus on solution supersaturation and metastable zone control. In this study, metastable zone width (MSZW) and induction periods were determined experimentally. The MSZW is an important parameter in the design and optimization of crystallization processes.3 To provide a controlled nucleation rate, a nucleation study is beneficial to determine the correct supersaturation where good quality 5′-CMPNa2 crystals can be obtained. In our work, the induction period was combined with the classical theory of nucleation. From the experimentally determined induction period values, the interfacial energy was calculated which was compared with the theoretical values derived from solubility data. Many important properties involved in the primary nucleation of the solution were studied.

Figure 1. Structure of cytidine 5′-monophosphate disodium salt.

Very few studies have focused on the separation and crystallization of 5′-CMPNa2. To date, the crystal data of 5′CMPNa2 has been reported.2 Previously, it was reported that in the humidity range 0 to 90 %, the crystallographic data of crystal water molecules per CMP changed from approximately one to nine. The crystal structures of three different hydrates have been determined, and the number of water molecules per nucleotide was 9.25, 8.125, and 6.5, respectively.2 However, in © XXXX American Chemical Society

Received: January 10, 2013 Accepted: March 16, 2013

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The evaluation of nucleation parameters, including the free energy of the radius of critical nucleus (r*), the free energy of the critical nucleus (ΔG*), and the molecular number of critical nucleus (i*) were calculated using the interfacial tension value for the controlled nucleation conditions of 5′-CMPNa2 in an ethanol + water mixture.

16πγ 3Vm 2

ln t ind = K +

2 3 3

3υ κ T (ln S)2

(3)

Therefore, under the above assumptions the tind can be written as

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⎤ ⎡ γ3 ln t ind ∝ ⎢ 3 2⎥ ⎣ T (ln S) ⎦

THEORY Metastable Zone Width. The state of supersaturation is an essential requirement for all crystallization processes. In 1897, the terms “labile” and “metastable” supersaturation were first introduced to classify supersaturated solutions in which spontaneous nucleation would or would not occur,4 respectively. For each system, the MSZW could be considered a characteristic property of crystallization. It is a region bounded by the solubility curve and the metastable limit which can be seen in Figure 2 section A.4 The solution was supersaturated;

(4)

At constant temperature, a straight line for ln tind against 1/(ln S)2 should be obtained from eq 4.9 ln(t ind) ∼

1 (ln S)2

(5)

The slope of this straight line can be given by α=

16πγ 3Vm 2 3ν 2κ 3T 3

(6)

Therefore, the interfacial tension is evaluated from ⎛ 3αν 2κ 3T 3 ⎞1/3 ⎟ γ=⎜ 2 ⎝ 16πVm ⎠

(7)

The Arrhenius reaction velocity relationship written in terms of the induction time is as follows: t ind = A exp(ΔG /κT )

(8)

where ΔG is the free energy.5 Figure 2. Saturation−supersaturation diagram cited by ref 5.

ln t = ln A +

however, spontaneous nucleation did not occur in a sufficiently short time.5 The metastable zone width (MSZW) is usually influenced by temperature, initial concentration, cooling rate, stirring rate, impurities, etc.6 In this study, the factors of temperature and stirring rate were considered in the metastable zone width measurement. During industrial crystallization processes, the MSZW is an extremely important parameter in analyzing the product crystal size distribution, crystal size, and crystal shape which is helpful in crystal growth.7 Induction Period and Interfacial Tension. The period between the instant when the supersaturated state is generated and the time instant when the particles become detectable is defined as the induction time.8 The induction time tind is an important nucleation parameter which can be used to describe the nucleation rate J, and is considered to be inversely proportional to the nucleation rate. t ind ∝ J −1

ΔG* =

(9)

16πγ 3 3ΔGν 2

(10)

where A is a constant and ΔGν is the bulk energy change per unit volume and is given by10

ΔGν = −(κT ln S /V )

(11)

In the above expression, V is the molar volume of the crystal. Evaluation of Nucleation Parameters.11 The change in Gibb’s free energy (ΔG) between the crystalline phase and the surrounding mother liquor results in a driving force, which stimulates crystallization. For rapid crystallization ΔG should be < 0. The energy required to form 5′-CMPNa2 nuclei is given by12 ΔG =

(1)

4 3 πr ΔGυ + 4πr 2γ 3

(12)

where ΔGν is the energy change per unit volume, γ is the interfacial tension, and r is the radius of the nucleus. The first term represents the formation of the new surface and the second term represents the difference in the chemical potential between the crystalline phase and the surrounding mother liquor. At the critical state, the free energy formation obeys the condition: d(ΔG)/dr = 0. Hence, the radius of the critical nucleus was expressed as13,14

The nucleation rate may be expressed by ⎡ 16πγ 3Vm 2 ⎤ ⎥ J = A exp⎢ − 3ν 2κ 3T 3(ln S)2 ⎦ ⎣

ΔG* κT

(2)

Where κ is the Boltzmann constant, T is absolute temperature, S is the degree of supersaturation, Vm is the volume of the molecule, γ is interfacial tension, and ν is the moles of ions per mole of electrolyte. This is the rate equation for homogeneous nucleation. From eqs 1 and 2, the relationship between induction period and supersaturation can be expressed as

r* =

−2γ ΔGν

or

r* =

−2νγ Δμ

(13)

The nucleation rate J was calculated using the equation B

dx.doi.org/10.1021/je4000263 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data ⎡ −ΔG* ⎤ J = A exp⎢ ⎣ κT ⎥⎦

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stirrer, and a thermometer. The temperature of the crystallizer was controlled by a thermostatic bath.15 The stirring speed was set to 200 rpm. In this study, all experiments were conducted in a temperature-controlled room and solutions were prepared in the same room. The crystallizer was filled with a saturated solution of 5′CMPNa2 to a known mass of ethanol + water mixture. The saturated solution was heated to 15 °C above the saturation temperature under agitation for at least 40 min. At a constant cooling rate, the solution was then quickly cooled to the experiment temperature. The induction time (tind) was the time which elapsed between when the stirring started and the particles become detectable.16 Thus, the time between reaching the target supercooling and detection of the first nucleation events was taken as the induction time for the nucleation process. The plot of ln(tind) against 1/(ln S)2 is shown in Figure 6.

(14)

where A is the pre-exponential factor (∼10 for solution).10 The number of molecules in the critical nucleus is expressed as 30

i* =

■

4π (r *)3 3υ

(15)

EXPERIMENTAL SECTION Materials. Cytidine 5′-monophosphate disodium salt (5′CMPNa2) (purity >0.99) was prepared by our lab. Ethanol used in the experiments was of analytical reagent grade, and the mass fraction was 0.997. Distilled deionized water was used in all cases. It was obtained from the triple distilled water generator (SZ-97, Shanghai Yarong Biochemical Instrument Co. Ltd., China). Metastable Zone Width Measurement. The composition of the solvent mixture (x0) is defined by eq 16. x0 =

m2 /M 2 m1/M1 + m2 /M 2

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RESULTS AND DISCUSSION The temperature dependence of the solubility of 5′-CMPNa2 in ethanol + water solvent mixture is shown in Figure 3. From the graph it can be seen that the solubility increased with increasing temperature. The MSZW experiments of 5′-CMPNa2 were conducted using a similar program format at different temperatures and different agitation speeds. The results are shown in Figure 4 and Figure 5. The corresponding supersaturation ratio S can be calculated from the concentration values which was directly affected the nucleation process and the process of crystal growth. c S= (17) c*

(16)

where m1 and m2 represent the mass of the solute (water and ethanol). M1 and M2 are the respective molecular masses. The isothermal method was applied to measure the solubility of 5′-CMPNa2 (Figure 3.) in ethanol + water solvent mixture (x0 = 0.198) at different temperatures.

From Figure 4, it can be seen that the MSZWs were little affected by solution temperature. According to eq 17, for the constant proportion, both the supersolubility and solubility lie along the same trendline in the measured MSZW observed from the graph. However, the MSZWs were decreased when agitation rates increased in Figure 5. The nucleation was influenced by the supersaturation ratio S. When the temperature and the ethanol adding rate were fixed, the low agitation rate would lead to a partial supersaturation. The system was easy to nucleate in this condition. However, a high agitation rate continuously mixes the system and redissolves nuclei leading to a difficult nucleation. The metastable zone width is related to the nucleation rate. In this study, the induction period was determined experimentally for 5′-CMPNa2 at different supersaturations. It was noted that the plot of ln(tind) against 1/(ln S)2 was a straight line (Figure 6). On the basis of this straight line, its slope was calculated to determine interfacial tension according to eq 7. The measured interfacial tension varied from 0.899 mJ/ m2 to 1.28 mJ/m2. The interfacial tension values estimated in this study are compared with literature data listed in Table 1. The interfacial tension values are larger than that of asiaticoside,17 but smaller than those of L-arginine phosphate18 and dexamethasone sodium phosphate.19 This implies that the crystallization of the salts is much easier than that of the pure compound. However, the crystallization of cytidine 5′-monophosphate disodium salt (5′-CMPNa2) is much more difficult than that of other salts. The induction period, a measure of nucleation rate, was decreased exponentially with supersaturation. This suggested that the nucleation rate increased exponentially.

Figure 3. The solubility (sol) of 5′-CMPNa2 in water + ethanol solvent mixture at various temperatures (T). x0 = 0.198 calculated from eq 16.

The measurement of MSZW was carried out in a constant temperature bath, where the uncertainty in temperature was ± 0.1 K. The desired quantity of the solution of 5′-CMPNa2 in water was poured into the crystallizer and mixed with a stirrer. The rotation rate was maintained at 150 rpm and 350 rpm, respectively. When the solution temperature was steady, ethanol was added into the crystallizer by a slow pump. A laser was used to determine the appearance of the first nucleus in solution and the volume of ethanol. Determination of Induction Time. The induction time experiments were conducted in a 250 mL round-bottomed jacketed crystallizer. The crystallizer was equipped with a lid, a C

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Figure 5. (a) Metastable zone width of 5′-CMPNa2 in water + ethanol solvent mixture with an agitation speed of 150 rpm: ▲, this work, supersolubility; Δ, this work, solubility. (b) Metastable zone width of 5′-CMPNa2 in water + ethanol solvent mixture with an agitation speed of 350 rpm: ▲, this work, supersolubility; Δ, this work, solubility.

Figure 4. (a) Metastable zone width of 5′-CMPNa2 in water + ethanol solvent mixture at 298 K: ▲, this work, supersolubility; Δ, this work, solubility. (b) Metastable zone width of 5′-CMPNa2 in water + ethanol solvent mixture at 293 K: ▲, this work, supersolubility; Δ, this work, solubility.

For the classical homogeneous nucleation theory, the radius of critical nucleus (r*) was calculated according to eq 13, using the corresponding interfacial tension (γ), temperature T, and the known values of supersaturation ratio S. Both free energy of the critical nucleus (ΔG*) and the molecular number of critical nucleus (i*) were evaluated according to eq 12 and eq 15 for 5′-CMPNa2. These findings are shown in Table 2. The radius of critical nucleus (r*) decreased with the increasing of supersaturation and accordingly the nucleation rate (J) increased with increasing of supersaturation. The free energy of the critical nucleus (ΔG*) and the critical nucleus molecular number (i*) increased exponentially with the decrease of the supersaturation and also varies with different temperature.

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CONCLUSIONS Experimental determination of the MSZW was performed by a laser method which can be applied as a fast check on solution behavior. The results indicate that the MSZWs of 5′-CMPNa2 were decreased when agitation rates increased, but were little affected by solution temperature. Determination of the induction period of the supersaturated solution was a useful aid in ascertaining the maximum allowable supersaturation.20 In

Figure 6. Plot of 1/(ln S)2 versus ln(tind) at various temperatures: ■, T = 303 K; ●, T = 305 K; ▲, T = 308 K. Supersaturation ratio S calculated from eq 17. Induction time tind elapsed between when the stirring started and the particles become detectable.

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(2) Sugawara, Y.; Nakamura, A.; Iimura, Y.; Kobayashi, K.; Urabe, H. Crystallographic investigation of humidity-induced phase transition of disodium cytidine 5′-monophosphate and crystal structure of three hydrates. J. Phys. Chem. B 2002, 106, 10363−10368. (3) O’Grady, D.; Barrett, M.; Casey, E.; Glennon, B. The effect of mixing on the metastable zone width and nucleation kinetics in the anti-solvent crystallisation of benzoic acid. Chem. Eng. Res. Des. 2007, 85, 945−952. (4) Mullin, J. W. Crystallization, 3rd ed.; Butterworth-Heinemann: London, 1993. (5) Nývlt, J.; Sohnel, O.; Matuchova, M.; Broul, M. The Kinetics of Industrial Crystallization. Amsterdam: The Netherlands, 1985. (6) Peng, J. Y.; Dong, Y. P.; Nie, Z.; Kong, F. Z.; Meng, Q. F.; Wu, Li. Solubility and metastable zone width measurement of borax decahydrate in potassium chloride solution. J. Chem. Eng. Data 2012, 57, 890−895. (7) Kim, K.-J.; Mersmann, A. Estimation of metastable zone width in different nucleation processes. Chem. Eng. Sic. 2001, 56, 2315−2324. (8) Nagy, Z. K.; Fujiwara, M.; Woo, X. Y.; Braatz, R. D. Determination of the kinetic parameters for the crystallization of paracetamol from water using metastable zone width experiments. Ind. Eng. Chem. Res. 2008, 47, 1245−1252. (9) Bromberg, L.; Rashba-Step, J.; Scott, T. Insulin particle formation in supersaturated aqueous solutions of poly(ethylene glycol). Biophys. Chem. 2005, 89, 3424−3433. (10) Balu, T.; Rajasekaran, T. R.; Murugakoothan, P. Nucleation studies of ZTC doped with L-arginine in supersaturated aqueous solutions. Phys. B 2009, 404, 1813−1818. (11) Rajasekaran, R.; Rajendiran, K. V.; Mohan Kumar, R.; Jayavel, R.; Dhanasekaran, R.; Ramasamy, P. Investigation on the nucleation kinetics of zinc thiourea chloride (ZTC) single crystals. Mater. Chem. Phys. 2003, 82, 273−280. (12) Nielsen, A. E.; Sarig, S. Homogeneous nucleation of droplets and interfacial tension in the liquid system methanol−water− tribromomethane. J. Cryst. Growth 1971, 8, 1−7. (13) Rajesh, N. P.; Kannan, V.; Raghavan, P. S.; Ramasamy, P.; Lan, C. W. Nucleation studies and crystal growth of (NH4)H2PO4 doped with thiourea in supersaturated aqueous solutions. Mater. Chem. Phys. 2002, 76, 181−186. (14) Joseph Kumar, F.; Jayaraman, D.; Subramanian, C.; Ramasamy, P. Nucleation kinetic study of KTiOPO4 crystallizing from high temperature solution. J. Cryst. Growth 1994, 137, 535−537. (15) Teychené, S.; Biscans, B. Nucleation kinetics of polymorphs: Induction period and interfacial energy measurements. Cryst. Growth Des. 2008, 8, 1133−1139. (16) Iqbal, H.; Bhuiyan, M.; Mavinic, D. S.; Beckie, R. D. Nucleation and growth kinetics of struvite in a fluidized bed reactor. J. Cryst. Growth 2008, 310, 1187−1194. (17) Zheng, X. F.; Fu, J.; Lu, X. Y. Solubility and Induction Period Study of Asiaticoside and Madecassoside in a Methanol + Water Mixture. J. Chem. Eng. Data 2012, 57, 3258−3263. (18) Arunmozhi, G.; Jayavel, R.; Subramanian, C. Experimental determination of metastable zone width, induction period and interfacial energy of LAP family crystals. J. Cryst. Growth 1997, 178, 387−392. (19) Hao, H.; Wang, J.; Wang, Y. Determination of induction period and crystal growth mechanism of dexamethasone sodium phosphate in methanol−acetone system. J. Cryst. Growth 2005, 274, 545−549. (20) Kind, M.; Mersmann, A. On Supersaturation during mass crystallization from solution. Chem. Eng. Technol. 1990, 13, 50−62.

Table 1. Comparison of the Interfacial Tension Value of 5′CMPNa2 with those of Other Compounds interfacial tension solute

mJ·m−2

solution

17

asiaticoside cytidine 5′-monophosphate disodium salt 18 L-arginine phosphate dexamethasone sodium phosphate19

methanol−water ethanol−water

0.55 to 0.86 0.899 to 1.28

water methanol− acetone

2.5 to 5.0 3.5 to 9

Table 2. Summary of Nucleation Data for Cytidine 5′Monophosphate Disodium Salt T/K

S

ΔG*·10−22/J

J ·1029/N·m−3·s−1

r*·10−10/m

i*

303.15

2.50 2.07 1.72 1.47 1.97 1.75 1.53 1.31 1.64 1.50 1.33 1.28

4.364 6.943 12.501 24.461 3.672 5.386 9.311 22.970 4.989 7.478 14.714 20.517

9.01 8.47 7.42 5.57 9.15 8.78 7.99 5.75 8.86 8.34 6.99 6.07

2.86 3.61 4.84 6.78 2.97 3.60 4.74 7.44 3.64 4.46 6.25 7.38

0.23 0.46 1.11 3.05 0.26 0.46 1.04 4.04 0.47 0.87 2.40 3.95

305.15

308.15

this study, induction period values for 5′-CMPNa2 were determined in an ethanol + water mixture. Using the experimentally determined induction period values, the interfacial tensions were calculated, which are in the range of 0.899 mJ/m2 to 1.28 mJ/m2. Fundamental growth parameters were also investigated. The various critical nucleation parameters, such as the radius of critical nucleus (r*), the critical free energy of nucleus (ΔG*), and the molecular number of critical nucleus (i*) were evaluated in the controlled nucleation condition. The critical nucleation parameters varied with increased temperature, and the nucleation rate increased with increased supersaturation. To avoid uncontrollable spontaneous nucleation, this study was very useful in providing a controlled nucleation rate to obtain good quality crystals.

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AUTHOR INFORMATION

Corresponding Author

*Tel.:+86 25 86990001. Fax: +86 25 58139389. E-mail: [email protected]. Funding

The work was supported in part by the grand from the National Outstanding Youth Foundation of China (Grant No.: 21025625), the PCSIRT, 12KJB530003, and the PAPD. We would like to acknowledge the financial support provided by the National High-Tech Research and Development Plan of China (863 Program, 2012AA021202) as well. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Borodi, Gh.; Hernanz, A.; Bratu, I.; Pop, Mihaela; Navarrob, R. Hydrated sodium cytidine-5′-monophosphate. Acta Crystallogr. 2001, E57, 514−516. E

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