Investigations of the Thermal Properties, Nucleation Kinetics, and Growth ofγ-Aminobutyric Acid in Aqueous Ethanol Solution

Wenge Yang, Ziyu Lei, Yonghong Hu,* Xiao Chen, and Shan Fu

College of Biotechnology and Pharmaceutical Engineering, Nanjing UniVersity of Technology,Nanjing 210009, China

DSC studies show that a sample starts to melt at 190.6 °C with a high melting enthalpy of 343.4 J/g. Usinga laser monitoring system, the solubility of γ-aminobutyric acid in aqueous ethanol solution was measuredby a synthetic method at temperatures ranging from 288.2 to 313.2 K and at atmospheric pressure; these areimportant data for the crystallization process of γ-aminobutyric acid from its aqueous solution. The measuredsolubility was correlated with the Buchowski-Ksiazczak equation and the modified Apelblat equation. Then,the induction of γ-aminobutyric acid in ethanol was estimated at different temperatures. The study revealsthat the induction period of γ-aminobutyric acid decreases with increasing supersaturation. Interfacial tensionwas estimated from the experimentally determined induction period values. Nucleation parameters were alsoinvestigated based on classical nucleation theory. The grown crystals were also subjected to structural andthermal studies.

1. Introduction

Amino acids, including glutamate, aspartic acid, γ-aminobu-tyric acid (GABA), and glycine, are major neurotransmitters inthe central nervous system. Glutamate and aspartic acid areexcitatory neurotransmitters, whereas GABA and glycine areinhibitory neurotransmitters. It has been known for a long timethat GABA is the major inhibitory neurotransmitter in themammalian central nervous system.1 GABA was first synthe-sized in 1883 and was first known only as a plant and microbemetabolic product. In 1950, however, GABA was discoveredto be an integral part of the mammalian central nervous system.GABA is found mostly as a zwitterion, that is, with the carboxylgroup deprotonated and the amino group protonated. It crystal-lizes in zwitterionic form [N+H3(CH2)3COO-] from aqueoussolution at the isoelectric point (pH 7.33), giving monoclinicprisms elongated along the c axis (space group P21/a; fourmolecules per unit cell; crystallographic parameters a ) 8.214Å, b ) 10.000 Å, c ) 7.208 Å, � ) 110.59°).2 Theconformational flexibility of GABA is important for its biologi-cal function, as it has been found to bind to different receptorswith different conformations. γ-Aminobutyric acid (GABA), anonprotein amino acid, is widely distributed among eukaryotesand prokaryotes. It has been known for a long time that GABAplays an important role in regulating neuronal excitabilitythroughout the nervous system. Thus, GABA has potential as afunctional component of foods and pharmaceuticals.

L-Glutamate can be converted to GABA through a processcatalyzed by glutamate decarboxylase, which is found inbacteria, animals, and higher plants. Compared to fermentation,the yields of GABA accumulated by fruit and vegetables arelow. Therefore, GABA produced through fermentation mightbe efficient to apply in industry.3 Because of the complexity ofthe fermentation broth composition, separation and purificationof GABA are needed. Because of the production costs and safetyproblems for food-grade GABA, synthetic or semisyntheticmedia are used for the fermentation of GABA.4 To cut downon the costs of separation and purification of GABA, crystal-lization can be used. As GABA belongs to a family of polar

organic compounds, its solubility in water is higher than thatin ethanol, and ethanol-water mixtures could be chosen as thesolvent for a cooling crystallization process. However, thenucleation kinetics and thermal properties of γ-aminobutyricacid crystals in ethanol-water mixtures have not yet beenreported. In this study, differential scanning calorimetry (DSC)was used to study the thermal behavior of γ-aminobutyric acid.The main melting point and the melting enthalpy of γ-ami-nobutyric acid were determined.

2. Experimental Section

2.1. Materials. γ-Aminobutyric acid was purchased fromNanjing Xinbai Pharmaceutical Co. Ltd., with a purity of>99.5% (mass fraction). The main impurities were NaH2PO4

and threonine, as determined by mass spectrometry, colorimetryof phosphomolybdenum blue, and high-performance liquidchromatography measurements. Analytical-grade ethanol wasobtained from Shanghai Chemical Reagent Co. Ltd. and usedwithout further purification. In all experiments, doubly distilledwater was used.

2.2. Preparation and Characterization of γ-Aminobu-tyric Acid. The melting temperature (Tm) and latent heat ofmelting (4Hm) of γ-aminobutyric acid were measured with aDSC instrument (Netzsch DSC 204). The calibration run wasmade with the standard Al2O3 (sapphire). Analyses wereperformed at temperatures between 40 and 230 °C at a 2 °C/min heating rate. Aluminum crucibles containing the sampleswere purged with nitrogen at a flow rate of 30 mL/min. Theresults of DSC was shown in Figure 1.

2.3. Solubility Measurements. The solubility data of γ-ami-nobutyric acid in aqueous ethanol solution in the temperaturerange from 288.2 to 313.2 K were determined using a laserdetection system. The apparatus for solubility measurements isthe same as described in the literature.5The experiments werecarried out in a 50 mL jacketed glass vessel with a magneticstirrer; a constant temperature ((0.02 K) was maintained at therequired temperature by circulating water through the outerjacket from a thermoelectric controller. A glass bushing with amercury glass thermometer was inserted into the inner chamberof the vessels for the measurement of the temperature. The

* To whom correspondence should be addressed. Tel.: +86 02583587108. Fax: +86 025 83587108. E-mail: hyh@njut.edu.cn.

Ind. Eng. Chem. Res. 2010, 49, 11170–1117511170

10.1021/ie901517b 2010 American Chemical SocietyPublished on Web 10/15/2010

experimental temperature was measured using a digital ther-mometer with an uncertainty of 0.05 K. To improve the accuracyof the experimental results, three experiments were performedfor each data point. The relative standard deviations (RSDs) ofthe solubilities ranged from 0.71% to 2.71%.

The solubility data of γ-aminobutyric acid in aqueous ethanolsolution are given in Table 1. The solubility data in Table 1 aresaturated mole fraction solubilities (x2) of γ-aminobutyric acidin the ternary system and were obtained as follows

where C1, C2, and C3 represent the molar concentrations ofethanol, γ-aminobutyric acid, and water, respectively [mol/(100mL of solvent)].

2.4. Metastable Zone Width and Induction PeriodMeasurements. Nucleation experiments were carried out in aconstant-temperature bath with a control accuracy of (0.05 K,

provided with a cryostat for cooling below room temperature.A constant volume of 10 mL of solution was used in allmeasurements. The solution was preheated to 5 K above thesaturated temperature for homogenization and left at thesuperheated temperature for 1 h before being cooled. To measurethe metastable zone width, the conventional polythermal methodwas employed.6 The sample was continuously stirred to ensurehomogeneous concentration and temperature through the entirevolume of the solution. The solution was cooled at a rate of0.1 K/min from the overheating temperature until the first crystalappeared in the container, as detected by a laser monitoringsystem similar to the apparatus for solubility measurements.5

At that moment, the temperature was fixed, and the correspond-ing supersaturation was calculated. The metastable zone widthof γ-aminobutyric acid aqueous solution as a function oftemperature is shown in Figure 2.

The time required for the growth of the critical nucleus to adetectable size was negligibly small, so the time interval betweenthe achievement of supersaturation and the appearance of acrystal of detectable size was considered to be equivalent tothe induction period. To find the induction period for theγ-aminobutyric acid solution at different supersaturations, the

Figure 1. DSC curve of γ-aminobutyric acid.

Table 1. Mole Fraction Solubility (xi) of γ-Aminobutyric Acid inAqueous Ethanol Solution from 288.2 to 313.2 K

T (K) xi × 103 RSD (%) T (K) xi × 103 RSD (%)

xe ) 0.00 xe ) 0.18

288.2 4.563 1.86 288.2 3.956 1.53293.2 5.242 1.13 293.2 4.272 2.55298.2 6.646 2.19 298.2 5.253 1.81303.2 7.628 2.57 303.2 6.446 2.27308.2 8.477 0.71 308.2 7.583 1.64313.2 9.334 2.21 313.2 8.361 1.36

xe ) 0.43 xe ) 0.57

288.2 3.662 1.10 288.2 2.532 2.25293.2 3.679 1.11 293.2 3.358 1.52298.2 4.348 2.21 298.2 3.582 2.62303.2 5.452 1.35 303.2 4.274 2.60308.2 6.583 1.89 308.2 4.795 2.01313.2 7.265 1.01 313.2 5.643 1.79

xe ) 0.81 xe ) 1.00

288.2 1.936 2.71 288.2 0.825 1.32293.2 2.575 2.53 293.2 1.253 1.44298.2 2.754 2.13 298.2 2.175 1.88303.2 3.854 2.52 303.2 2.643 2.31308.2 4.362 2.16 308.2 3.432 1.37313.2 5.267 1.44 313.2 4.152 2.57

x2 )C2

C1 + C2 + C3(1)

Figure 2. Metastable zone width of γ-aminobutyric acid in water.

Ind. Eng. Chem. Res., Vol. 49, No. 22, 2010 11171

conventional isothermal method was used.7 As shown in Figure3, the induction period was measured for various supersatura-tions.

3. Data Regression and Discussion

3.1. Model of Solubility and Regression. Figure 1 showsthe DSC curve of γ-aminobutyric acid. It can been seen thatmelting starts at 190.6 °C, with a maximum at 192.4 °C. Asshown in Figure 1, the melting enthalpy of γ-aminobutyric acidis 343.4 J/g.

It can be seen that the solubility of γ-aminobutyric acidincreases with increasing temperature over the range of solventcompositions studied. At a given constant temperature, thesolubility data of γ-aminobutyric acid in aqueous ethanolsolution decreases with increasing ethanol content.

To describe solid-liquid equilibrium, the relationship be-tween solubility and temperature can be described as8

where γx is the activity coefficient on a mole fraction basis, xis the mole fraction solubility, ∆fusH is the fusion enthalpy, ∆Cp

is the heat capacity difference between the solid and the liquid,T is the equilibrium temperature (K), Tt is the triple-pointtemperature, and R is the gas constant. The value of ∆Cp is sosmall in comparison to ∆fusH that the second and third terms ineq 2 can be neglected. Because solid-liquid equilibrium dataare not often available, especially in mixed solvents, correlationand prediction schemes are frequently employed.

The λh equation, which was originally proposed by Bu-chowski et al.,9 can be used to correlate most solid-liquidequilibrium systems. The λh equation is given by

where λ and h are two adjustable parameters obtained from thesolubility data and the parameter h is related to the enthalpy ofsolution per mole of solute.10-13 In the λh equation, x is themolar fraction of solute at saturation temperature T.

Transforming eq 3 for an explicit form of x yields

The ability of λh equation to represent the experimentalsolubility of γ-aminobutyric acid in aqueous ethanol solutionis summarized in Table 2, in the form of “curve-fit” parametersand percentage deviations in back-calculated solubilities. Theroot-mean-square deviations (rmsd’s) of λh equation can bedescribed as follows

where N is the number of experimental points and xicalc denotes

the back-calculated solubility data from λh equation.Based on eq 2, a simple relationship can be adopted for the

infinite-dilution activity coefficient as follows

Then, the following simple expression of the Apelblat model14-16

for the solubility in such systems can be obtained

where x is the mole fraction of solute; T is the absolutetemperature; and a, b, and c are the model parameters, with

The equation is simple and easy to apply to engineering.Therefore, we used the Apelblat equation to correlate thesolubility data of γ-aminobutyric acid in aqueous ethanolsolution. The values of the three parameters a, b, and c togetherwith the root-mean-square deviations (rmsd’s) of the Apelblatequation are listed in Table 3.

As shown in Table 3, the Apelblat equation can well regressthe solubility data of γ-aminobutyric acid in aqueous ethanolsolution.

Based on eq 2, a modified Apelblat equation was designedto correlate the solubility data of γ-aminobutyric acid in aqueousethanol solution considering the change of the density of ethanoland water along with the change of temperature. The densityof ethanol and water was determined by the densimeter in thecrystallizer, and the relation between density and temperaturecan be described as in eqs 8 and 9

Table 2. Regressed Parameters and Absolute Average Deviationsfor γ-Aminobutyric Acid in Aqueous Ethanol Solution from 288.2 to313.2 K Calculated by the λh Equation

xe λ h rmsd (×105)

0.00 0.03 11708.58 3.560.18 0.03 13448.29 4.120.43 0.04 13331.85 4.250.57 0.05 12416.70 4.870.81 0.04 16599.35 5.251.00 0.02 23064.60 4.32

ln( 1γxx) )

∆fusH

RTt(Tt

T- 1) -

∆Cp

Rln(Tt

T- 1) +

∆Cp

Rln

Tt

T(2)

ln[1 + λ(1 - x)x ] ) λh(1

T- 1

Tm) (3)

x ) λexp[λh(T-1 - Tm

-1)] - 1 + λ(4)

rmsd ) [1n ∑

i)1

n

(xicalc - xi

exp)2]1/2

(5)

ln γ1∞ ) A + B

T(6)

ln x ) a + bT+ c ln T (7)

a )∆fusH1

RTt1-

∆fusCp1

R(ln Tt1 + 1) - A

b )∆fusH1

R+

∆fusCp1

RTt1 - B

c )∆fusCp1

R

Table 3. Regressed Parameters and Absolute Average Deviationsfor γ-Aminobutyric Acid in Aqueous Ethanol Solution from 288.2 to313.2 K Calculated by the Apelblat Equation

xe a b (×10-3) c rmsd (×105)

0.00 143.55 -7.805 -14.07 0.380.18 24.12 -2421.22 -1.77 0.450.43 -103.61 -9.146 -15.6 0.360.57 -1.35 -1145.26 0.77 1.200.81 5.36 -1894.05 0.22 0.741.00 379.3 -20167.6 -37.9 0.61

F1 ) 8.855 × 104/T + 490.3 (8)

11172 Ind. Eng. Chem. Res., Vol. 49, No. 22, 2010

where F1 and F3 represent the densities of ethanol and water,respectively; M1 and M3 represent the molecular weights ofethanol and water, respectively; V1 and V3 refer to the volumesof ethanol and water, respectively; and V refer to the totalvolume of the ternary system.

Substitution of eqs 10 and 11 into eq 1 and subsequentrearrangement results in eq 12

In addition, the total molar concentration can be regarded asa function of temperature T and volume ratio of ethanol andwater ω

Therefore, we used this modified Apelblat equation tocorrelate the solubility data of γ-aminobutyric acid in aqueousethanol solution. The values of the three parameters A, B, andC together with the root-mean-square deviations (rmsd’s) of themodified Apelblat equation are listed in Table 4.

3.2. Metastable Zone Width. The metastable zone widthof the γ-aminobutyric acid aqueous solution as a function oftemperature is shown in Figure 2. The metastable zone widthdecreases slightly with increasing temperature, which indicatesthat the higher the solubility, the smaller the metastable zonewidth. It is also evident that γ-aminobutyric acid is easily solublein water; thus, water can be used to grow crystals of a suitableparticle size. To obtain crystals of a suitable particle size, thevalue of the solubility should be maintained in the metasta-ble zone width.

3.3. Nucleation Kinetics of γ-Aminobutyric Acid Crystals.For homogeneous nucleation,17 the nucleation rate is inverselyproportional to the induction period, that is, J ∝ τ-1, and it canbe expressed as

where k is the Boltzmann constant (1.38 × 10-23 J/K); V is themolecular volume of a γ-aminobutyric acid molecule; γ is theinterfacial tension; and S is the degree of supersaturation, S )C/C*, where C is the actual concentration of the solution andC* is the equilibrium concentration of the solution.

In the present investigation, the interfacial tension wascalculated using the experimentally determined induction periodvalues in the following relation, which is based on the classicaltheory of homogeneous spherical nucleus18

where B is a constant, NA is Avogadro’s number, and τ is theinduction period of the solution at temperature T. A plot of lnτ versus 1/(ln S)2 is a straight line with a slope given by

Because ln B weakly depends on temperature, the interfacialtension of the solid relative to this solution can be calculatedfrom the slope of the line with

According to the theories of homogeneous nucleation devel-oped by Beckers and Doring19 and Nielsen,20 the change inGibbs free energy between the crystalline phase and thesurrounding mother liquor is given by

where Gv ) -(kT ln S/V).At the critical state, the free energy obeys the condition

d(∆G)/dr ) 0.The radius of the critical nucleus can be expressedas

The interfacial tension (γ), volume free energy (∆Gv), criticalfree energy (∆Gc), and radius of the critical nucleus (rc) ofγ-aminobutyric acid were calculated at different supersaturationratios and are given in Table 5.

A study of the induction period versus supersaturation wasconducted for various supersaturations at different temperatures.In Figure 3, it is clear that the induction period decreases withincreasing supersaturation, which suggests that the nucleationrate increases with increasing supersaturation. It is also possiblethat increasing the supersaturation enhances the formation rateof the nucleus and shortens the induction period.

Based on classical homogeneous nucleation theory, theinduction period (τ) is related to the interfacial tension (γ).Based on eqs 19 and 20, the interfacial tension was calculatedfrom the slope of the straight-line fit to the ln τ versus 1/(lnS)2 data (Figure 4). Based on the above eqs 21-23, nucleation

F3 ) 3.570 × 104/T + 876.5 (9)

C1 )F1V1/M1

V)

F1

M1

V1

V) f1(T)

V1

V(10)

C3 )F3V3/M3

V)

F3

M3

V3

V) f3(T)

V3

V(11)

x2 )C2

f1(T)V1

V+ f3(T)

V3

V

)C2

F(T,ω)(12)

V1

V) 1

1 + ω(13)

V3

V) ω

1 + ω(14)

F(T,ω) ) 11 + ω

[f1(T) + f3(T)ω] (15)

C2 ) exp[A + BT+ C ln(T)]F(T,ω) (16)

Table 4. Regressed Parameters and Absolute Average Deviationsfor γ-Aminobutyric Acid in Aqueous Ethanol Solution from 288.2 to313.2 K Calculated by the Modified Apelblat Equation

xe A B (×10-3) C rmsd (×105)

0.00 143.55 -7.805 -14.07 0.380.18 24.12 -2421.22 -1.77 0.450.43 -103.61 -9.146 -15.6 0.360.57 -1.35 -1145.26 0.77 1.200.81 5.36 -1894.05 0.22 0.741.00 379.3 -20167.6 -37.9 0.61

J ) A exp[- 16πγ3V2

3k3T3(ln S)2] (17)

ln τ ) -ln B +16πγ3V2NA

3R3T3(ln S)2(18)

m )16πγ3V2NA

3R3T3(19)

γ ) RT( 3m

16πV2NA)1/3

(20)

∆G ) 43

πr3∆Gv + 4πr2γ (21)

rc ) - 2γ∆Gv

(22)

∆Gc )43

πrc2γ ) 16πγ3V2

3k2T2 ln2 S(23)

Ind. Eng. Chem. Res., Vol. 49, No. 22, 2010 11173

parameters such as the critical radius of nucleus (rc), theGibbs free energy per unit volume (∆Gv), and the criticalfree energy barrier (∆Gc) of γ-aminobutyric acid werecalculated at different supersaturations using the interfacialtension value and are shown in Table 5.

As the supersaturation increased, the radius of the criticalnucleus (rc) and the critical energy barrier (∆Gc) decreased. Itis necessary to note that the minimum Gibbs free energy barrieroccurs at the interfacial tension value when a particularsupersaturation is fixed. Hence, we conclude that the interfacialtension plays a vital role in the nucleation mechanism. In thiscase, the crystal growth is generally controlled by the birth andspread, and the crystal surface becomes smoother.

4. Conclusions

DSC studies show that a sample starts to melt at 190.6 °Cwith a high melting enthalpy of 343.4 J/g. For ethanol-waterbinary solvents, the solubility of γ-aminobutyric acid was foundto decrease with increasing concentration of ethanol. For thetemperature range investigated, the solubility of γ-aminobutyricacid in the solvents increased with increasing temperature. Thesolubility data were correlated with the Buchowski-Ksiazczakλh equation, the Apelblat equation, and a new modified Apelblatequation. The modified Apelblat equation can regress thesolubility data much better than the λh equation. The solubilitymeasured in this study can be used for γ-aminobutyric acidpurification or its optical resolution by the preferential crystal-lization procedure.

The metastable zone width and induction period of γ-ami-nobutyric acid crystals were determined experimentally. Theinduction period was measured under various supersaturationconditions. The induction period, which is inversely proportionalto the nucleation rate, was used to estimate the interfacial tensionbetween γ-aminobutyric acid crystals and the solution; thenucleation parameters, such as the radius of the critical nucleus(rc), the volume free energy (∆Gv), and the critical free energy(∆Gc) of γ-aminobutyric acid crystals were also calculated. Therelationship between the high melting enthalpy of γ-aminobu-tyric acid and its structure was also explained. In later research,we will study the enthalpy of the hydrogen bonding inγ-aminobutyric acid.

Acknowledgment

This research work was financially supported by the Depart-ment of Science and Technology of Jiangsu Province in China(No. BE2008399), as well as by the 863 Project (No.2007AA02Z211), Ministry of Science and Technology, People’sRepublic of China.

Supporting Information Available: Supersaturated concen-tration of γ-aminobutyric acid (Table S1). This information isavailable free of charge via the Internet at http://pubs.acs.org/.

List of Symbols

C ) molar concentrationk ) Boltzmann constant (1.38 × 10-23 J/K)R ) gas constantrc ) radius of the critical nucleus of γ-aminobutyric acid crystalsS ) degree of supersaturationT ) temperatureTm ) melting pointTt ) triple-point temperatureV ) molecular volume of a γ-aminobutyric acid moleculex ) mole fraction of solutex2 ) saturated mole fraction solubilityx2

calc ) back-calculated solubility data from the λh equation or theApelblat equationx2

exp ) experimental solubilityγ ) interfacial tensionγx ) activity coefficient on a mole fraction basis∆Cp ) heat capacity difference between the solid and the liquid∆Gc ) critical free energy barrier of γ-aminobutyric acid crystals∆Gv ) volume free energy of γ-aminobutyric acid crystals∆fusH ) fusion enthalpy∆Hm ) latent heat of melting

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Table 5. Kinetic Parameters of γ-Aminobutyric Acid CrystalNucleation in Water

S interfacial tension,γ (mJ/m2)

volume free energy,∆Gv (×10-6J/m3)

critical radius,rc (nm)

critical free energy,∆Gc (×10-23 J)

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Figure 3. Effect of supersaturation on induction period at differenttemperatures.

Figure 4. Plot of ln τ versus 1/(ln S)2 for γ-aminobutyric acid.

11174 Ind. Eng. Chem. Res., Vol. 49, No. 22, 2010

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ReceiVed for reView September 27, 2009ReVised manuscript receiVed August 22, 2010

Accepted September 26, 2010

IE901517B

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