Determination of metastable zone and induction time of analgin for cooling crystallization☆

Ling Zhou ,Zhao Wang ,2,Meijing Zhang ,2,Mingxia Guo ,Shijie Xu ,Qiuxiang Yin ,2,*

1 School of Chemical Engineering and Technology,State Key Laboratory of Chemical Engineering,Tianjin University,Tianjin 300072,China

2 Collaborative Innovation Center of Chemical Science and Chemical Engineering,Tianjin 300072,China

1.Introduction

Solution crystallization is a pivotal operating unit for producing high-quality product with desired purity,crystal size distribution,and shape[1,2].The crystallization process should be entirely controlled for the product to meet the requirements.

Nucleation is important in determining the role of product quality and crystal morphology during crystallization[3].The discrepancy between concentration and saturation(i.e.,supersaturation)is the only driving force.This discrepancy could be produced using several methods(e.g.,evaporation,anti-solvent addition,and cooling).The region between the solubility equilibrium curve and the super solubility curve is called the metastable zone[4].Operating in this region could avoid spontaneous nucleation and may ensure that products meet the requirements of particle size distribution.Therefore,determining the metastable zone width is very essential.Furthermore,the information of metastable zone width is required for probing the nucleation mechanism[5,6]and the industrial amplification[7].The metastable zone width is not a thermodynamic property like solubility but influenced by several parameters including stirring rate,solvent species,cooling rate and so on[8].

The induction time during crystallization process is the time between a supersaturated solution reaching to the onset of nucleation[4].Therefore,the induction time can be analyzed through nucleation theory[7].The induction time influenced by several parameters including solvent species,temperature,concentration and so on.

Up to now,the most commonly determining method of the metastable zone width is polythermal technique.This method involves the measurement of the nucleation temperature through the cooling saturation solution with a certain rate[9].The metastable zone width is the discrepancy between the equilibrium temperature and the nucleation temperature for a cooling crystallization process.The metastable zone width can be determined using several methods,including laser,nephelometer conductivity meter,and focused beam reflectance measurement[10–13].This study usesin situRaman to monitor the onset of nucleation by observing the change in the analgin solution concentration and the solid crystal formation.

Analgin is a well-known and widely used analgetic and antipyretic drug employed for multicomponent preparations.Accordingly,the use of pure products has decreased because of some side effects.Analgin is one of the five active ingredients of Pentalgin-FS tablets produced by Farmstandart–Leksredstva[14].Some problems in the industrial production of analgin are long production periods,small particle sizes,maldistribution,and long drying and filtration times.Optimizing the cooling crystallization process and determining the optimum operating curve for producing high-quality products are important in solving these problems.Basic data,such as solubility,metastable zone width,and induction times,are all necessary for this goal[15].

Little data is available on the solubility,metastable zone width and nucleation parameters of analgin in the existing literature.In this study,the metastable zone width and the induction period of analgin in the ethanol–aqueous system are experimentally determined by thein situRaman method.The nucleation parameters are estimated using classical nucleation theory of Ny'vlt through the data of metastable zone width at different cooling rates.Interfacial energy and some nucleation parameters are subsequently calculated using classical nucleation theory relatingtindwith supersaturation.From the results of fitting the experimental data to the classical nucleation theory,the nucleation mechanism is identified,which can provide basic data for optimizing and controlling the analgin-crystallization process.

2.Theory

Similar to the Arrhenius reaction rate equation,Classical nucleation theory states that the nucleation rate(J)can be given as follows[7]:

wherekis the Boltzmann constant;Ais the pre-exponential factor;andTnis the nucleation temperature.Gibb's free energy,ΔG,is dependent on nucleus radiusrand can be written as follows:

where ΔGvis the free energy change;and γ is the interfacial energy.At pointd(ΔG)/dr=0,the nucleus reach the critical size,r*,free energy is maximum.

From the previous equations,free energy change can be calculated as follows:

wherec*is solubility;Sis supersaturation;andVmis molar volume.Substituting Eqs.(5)and(6),

Therefore,the induction time can be expressed as supersaturation,

At constant temperature,lntindand 1/ln2Sshould be show a linear relationship.The slope can be obtained by:

3.Experimental Procedure

3.1.Materials

Analgin(purity:99.5%)was supplied by the Shandong Xinhua Pharmaceutical Co.,Ltd.,China.Anhydrous ethanol(purity:99.7%)was purchased from Tianjin Chemical Reagent Company.

3.2.Apparatus and procedure

3.2.1.Characterization of analgin

Powder X-ray diffraction(PXRD)pattern of the crystallinity of analgin was obtained using Cu Kαradiation(0.154nm)on Rigaku D/max-2500(Rigaku,Japan).The samples were conducted over a 2-theta range from 2°to 50°at a scanning rate of 1 step per second.

To determine the melting temperature and enthalpy fusion of analgin,a thermogravimetric/differential scanning calorimetry(Mettler-Toledo,Switzerland)was used for thermal analysis experiment under a nitrogen atmosphere.

3.2.2.Determination of solubility

The solubility data of analgin were measured by the gravimetric method previously described in literature[16–18].A 50 ml cylindrical double-jacketed glass was used.The jacketed temperature was controlled(±0.01 K)by a thermostat(XOYS-2006,Nanjing Xianou Instrument Manufacturing Co.,Ltd.,China).Stirring was stopped when the system reached the equilibrium,and the suspension stood for a while.The supernate was filtered with a filter membrane(0.22 μm).Subsequently,the filtrate was weighed as quickly as possible and dried at 50°C until no change was observed.The solubility data was obtained through repeating three times in each group to take the average value.

The molar fraction solubility of analgin in the ethanol–aqueous system can be obtained as follows:

wherem,mA,andmWare the mass of analgin,ethanol,and water respectively.M,MA,andMWare the molecule mass of analgin,ethanol,and water,respectively.

3.2.3.Determination of metastable zone width and induction time

The saturated solutions of the analgin ethanol aqueous system at certain temperatures were first prepared to determine the metastable zone width.To ensure complete dissolution,solutions were stirred for 20 min before each run at a temperature which is 5 K higher than the equilibrium temperature[19].Then,cool the solution with a certain cooling rate until the first crystal appeared.The metastable zone width is obtained through the difference between equilibrium temperature and nucleation temperature.

The induction time was experimentally measured over the supersaturation range from 1.1 to 1.4 at three different temperatures(i.e.,323.15 K,333.15 K,and 343.15 K).A saturated analgin solution at a particular experiment temperature is con figured according to the solubility data that has been determined by heating the suspension to 5 K higher than the equilibrium temperature and maintaining the solution in this state for 20 min.Rapid cooling the solution to experiment temperature to get the supersaturation level target.The solution was stirred at this temperature until nucleation occurred.The induction timetindwas the interval time between the creation of supersaturation and the nucleation point.

The Raman spectra could offer information about the solution and solid phases[20–24].Therefore,Raman spectroscopy,as a light scattering technique,could be easily exploited for monitoring phase changes in crystallization systems.The Raman spectra of different components exhibited some distinct differences that can be chosen as the characteristic peaks for each component[25–29].

This study employed in-situ Raman spectroscopy to determine the nucleation point using the Raman RXN2-HYBRID analyzer instrument.Raman spectroscopy was successfully used to identify the analgin solution and the solid(Fig.1).The peak at1002 cm?1(peak I)was chosen to represent the analgin solution,while that at 1630 cm?1(peak II)was selected to monitor the solid phase.Fig.2 shows the primary nucleation temperature when the solution equilibrium temperature is at 343.15 K and the cooling rate is at0.5 K/min which is shown as a typical measurement.The point at the characteristic peak intensity of the analgin solution started to decline and the solid peak intensity began to increase indicate the onset of nucleation.Fig.3 shows the comparative result of the nucleation temperatures measuring byin situRaman spectroscopy and the focused beam reflectance measurement(FBRM)(Mettler-Toledo,Switzerland).The two methods provided similar results of analgin in the ethanol–aqueous system.

Fig.1.Raman spectra of solution and suspension of analgin.

Fig.2.Measured change of the characteristic peak intensity with temperature during the cooling of a solution saturated at 343.15 K and cooled with a 0.5 K·min?1 rate.

Fig.3.Comparison of the nucleation points of analgin from the Raman and FBRM measurements.

4.Results and Discussion

4.1.Material characterization

Fig.4 is the PXRD pattern of analgin,there was no polymorphism in the experiments.

Fig.4.Power X-ray diffraction pattern of analgin.

The TGA analysis(Fig.5)shows two stages in the thermal decomposition process.The crystal water is lost in the first stage with the weight decreasing by about 4.8%and the second step from 510.15 K with a weight loss as the decomposition.The DSC analysis shows that both the exothermic and endothermic peaks appear from 505 K to 525 K which indicate that analgin should be decomposed with melting.Therefore,the melting temperature and the enthalpy of fusion of analgin could not be got by the thermal analysis experiment.

4.2.Solubility

The solubility data of analgin in 85%ethanol–aqueous system over the temperature range from 283.15 K to 353.15 K were experimentally determined.According to the Van't Hoff equation,the solubility mole fraction solubility values(C0)could be described as follows[7]:

Fig.5.Thermal analysis(TGA/DSC)of analgin.The solid and dashed lines are the DSC and TGA curves,respectively.

whereRis the ideal gas constant;anda,b,andhare the parameters.The enthalpy changes of solution ΔHS*and the specific heat capacity of analginCp*can be estimated by the parametersaandbas follows:

Fig.6 shows the above equation can predict solubility data well.The apparent solution enthalpy and the specific heat capacity at 298 K were obtained using Eqs.(15)(16)[7]:

Fig.6.Van't Hoff plot for the correlation of the analgin solubility data.

The obtained specific heat capacity is consistent with the data determined by indirect method of DSC,464.64 J·mol?1·K?1.

4.3.Metastable zone width

Supersaturation is the discrepancy between concentration and saturation and it is the fundamental driving force of the crystallization process.The metastable zone is the area between the super solubility curve and the solubility curve.Operating in this region could avoid spontaneous nucleation and may ensure that products meet the requirements of particle size distribution.The base data of the metastable zone width will be used for getting better control of nucleation[30].

According to the classical approach of Ny'vlt,the relationship between primary number nucleation rate(Jn)and supersaturation(Δc)can be described as[3]:

The value of dc*/dTcan be obtained is the slope of the solubility curve.On the point of nucleation,the relationship of the maximum supersaturation(Δcmax)and the maximum supercooling degree(ΔTn)can be described as follows:

Assuming that supersaturation generated rate is equal to the primary nucleation,the mass of the formed nuclei(M)can be given as follows,

where α is the volume shape factor,knis the mass nucleation rate constant and ρcis density.Combining previous equations,we obtain:

By linear fitting of lnRcand ln(ΔTn),the parametersmandkncan be obtained.

The metastable zone width in the analgin ethanol–aqueous system is measured at various cooling rates to determine the nucleation kinetic parameters.It is can be seen from Fig.7 and Table 1 that the experimental data can be fitted to Eq.(23)satisfactorily.Accordingly,the nucleation rate constant increases and the nucleation order decreases with equilibrium temperature increase.

Fig.7.Apparent nucleation orders estimated from the MSZW data using Ny'vlt theory.

Table 1Nucleation kinetic parameters evaluated by fitting the MSZW experimental data

4.4.Induction time

Fig.8 shows the induction time is dependent on supersaturations in analgin.The induction timetindis plotted against the supersaturation ratiosSat three different temperatures.The induction time increases when decrease the supersaturation ratio for a particular temperature and increases when decrease the temperature for a certain supersaturation.Fig.9 shows the result of linear fitting on ln(tind)and 1/ln2Sat three different temperatures.It is observed that the slope is higher at higher supersaturation regions and the slope is lower at lower supersaturation regions.Other investigators reported the similar results for various organic chemicals[30–33].It attributed this to different nucleation mechanisms at different supersaturation regions.Homogeneous nucleation occurred at the region of high supersaturation as well as heterogeneous nucleation more likely happen at the region of low supersaturation.Heterogeneous nucleation occurred in the already existing surface such as the surface of crystals,crystallizer walls,impellers and so on.In crystallization process,the free energy barrier is reduced to already existing nucleation sites.Therefore,heterogeneous nucleation is more likely to occur if there are nucleation sites than homogeneous nucleation.When supersaturation is high,the nucleation is dominant because of high homogeneous nucleation rate.At the region of low supersaturation,the homogeneous nucleation rate is low,which results in the heterogeneous nucleation to predominate[7].Table 2 shows the fitting results according to the Eq.(10).The interfacial tension(γ)can be estimated from the slope of straight line according to homogeneous nucleation according to Eq.(11).Table 3 presents the values of interfacial energy.Some papers have also used this method to determine thermodynamic parameters for other systems[7,34].The value of the interfacial energy can reflect the ability of the spontaneous nucleation of the solute.Accordingly,the higher the value of the interfacial energy is,the more difficult to crystallize.Therefore,this is a significant parameter for the selection of solvent in the crystallization process.

Fig.8.Isothermal dependence of the induction time on analgin supersaturations.

Fig.9.Plot of ln(t ind)versus 1/ln2S for analgin at different temperatures.

Table 2Parameters and correlation indices in Eq.(10)at different temperatures

Table 3Interfacial analgin energy

5.Conclusions

The solubility,metastable zone width,and induction time of analgin in an ethanol–aqueous system for batch cooling crystallization were determined.The analgin solubility in the selected solvents increases with temperature increase,which means that analgin could be efficiently separated using mixing solvent of ethanol and water through cooling crystallization.Fitting the solubility data with the Van't Hoff equation,the apparent solution enthalpy and the specific heat capacity can be estimated.The metastable zone width significantly broadens with the cooling rate increase and the saturation temperature decrease.Furthermore,the nucleation kinetic parameters are achieved through the Ny'vlt model fitting.The induction period was experimentally measured over a supersaturation range at three different temperatures.According to classical nucleation theory,nucleation parameters and interfacial energy are calculated by analyzing the induction time data.The nucleation parameters vary with temperature.Moreover,the nucleation rate increases with increasing temperature.Homogeneous nucleation tended to occur when the supersaturation is high,whereas heterogeneous nucleation was more likely to occur when the supersaturation is low.This finding can provide basic data for optimizing and controlling the analgin-crystallization process.

Nomenclature

Apre-exponential factor,m3·s?1

a,b,hempirical constant for van't Hoff equation

C0mole fraction solubility,mol·mol?1

Cp*apparent heat capacity,J·mol·K?1

c* equilibrium concentration,mol·mol?1

Δcthe supersaturation(Δc=c?c*),mol·mol?1

Δcmaxmaximum supersaturation,mol·mol?1

ΔGGibb's free energy,J·mol?1

ΔG* free energy to form the critical size nucleus,J·mol?1

ΔGvfree energy change per unit volume,J·mol?1

ΔHS*apparent enthalpy of solution,J·mol?1

Jnnucleation rate,m3·s?1

Kempirical constant for the relationship between induction time and supersaturation

kBoltzmann constant,1.38 × 10?23J·K?1

knthe mass nucleation rate constant

k'n the number nucleation rate constant

Mamolecule mass of analgin,g·mol?1

Memolecule mass of ethanol,g·mol?1

Mwmolecule mass of water,g·mol?1

mamass of analgin,g

memass of ethanol,g

mwmass of water,g

nnucleation order

Rideal gas constant,8.3145 J·mol·K?1

Rccooling rate,K·s?1

rradius of the nucleus,nm

r* critical radius of the nucleus,nm

Ssupersaturation ratio,S=c/c*

Ttemperature,K

Tnnucleation temperature,K

T0solubilization temperature,K

ΔTnmetastable zone width,K

tindinduction time,s

Vmmolar crystal volume,m3

α slope of this straight line for lntindagainst 1/ln2S

γ interfacial energy,mJ·m?2

ρcdensity,kg·m?3

? volume shape factor

Superscripts

a analgin

c cooling

e ethanol

ind induction

n nucleation

w water

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