Tong Zhou,Chunzhao Tu,Ya Sun,Linan Ji,Chuangxian Bian,Xiaohua Lu,Changsong Wang*

State Key Laboratory of Materials-Oriented Chemical Engineering,College of Chemical Engineering,Nanjing Tech University,Nanjing 211816,China

Keywords:Thiourea Metastable zone Induction time Cooling crystallization

ABSTRACT The solubility,metastable zone width(MSZW),and induction time of thiourea for cooling crystallization were experimentally determined in the temperature range of 283–323 K.The solubility data could be well described by the Apelblat equation model as lnx=-99.55+1071.66/T+16.27lnT.The determinations of the effects of various stirring and cooling rates indicated that the MSZW increased with increasing and decreasing cooling and stirring rates,respectively.Furthermore,the induction times at various temperatures and supersaturation ratios were also measured.The results indicated that homogeneous nucleation could occur at high supersaturation,whereas heterogeneous nucleation was more likely to occur at low supersaturation.Based on the classical nucleation theory and induction period data,the calculated solid–liquid interfacial tensions of thiourea in deionized water at 302.46 and 312.58 K were 2.86 and 2.94 mJ·m-2,respectively.

1.Introduction

Solution crystallization is a pivotal operating unit in separation and purification processes,which is widely employed in the production of high-quality products with the desired purity,crystalsize distribution,and shape [1,2].To satisfy the requirements of a high-quality product,the crystallization process should be fully controlled.

Nucleation and growth play vital roles in the determinations of the quality of a product and its crystal-size distribution during the crystallization process [3].The only driving force of crystallization is supersaturation,which controls nucleation and growth.The area ranging from the solubility curve to supersolubility is called the metastable zone width (MSZW) [4].An operation in this zone can avoid spontaneous nucleation and yield products with the required particle-size distribution (PSD) [5,6].However,MSZW is affected by several parameters,including the stirring rate,cooling rate,solvent species,and impurities [7,8].Therefore it is of great significance to determine MSZW,which is very beneficial to industrial amplification.The induction time of the crystallization process is defined as the time required by a supersaturated solution to attain the onset of nucleation,which is the ability of the solution to maintain a metastable state during crystallization [9,10].The induction time can also be employed to indicate the rate of nucleation.Thus,MSZW and the induction period are indispensable basic data for the crystallization process.

Thiourea is a crucial multifunctional chemical intermediate,which can be widely utilized in the synthesis of antihyperthyroidism drugs,resins,and sulfa drugs [11,12],and also in the manufacture of accelerators for the process of rubber vulcanization,metal-mineral-flotation agents,and so on [13–15].However,thiourea can easily absorb moisture,thus agglomerating because of its uneven PSD.Additionally,fine thiourea particles can be further aggravated in the above process.Therefore,the particle sizes of the products are generally controlled in the industrial crystallization process to mitigate the challenges of agglomeration[16].During the crystallization process,the acquisition of products with uniform particle sizes and specific crystal forms requires strict control of the operating parameters.Resultantly,the crystallization process is always performed in the metastable zone to avoid explosive nucleation [17–19].Consequently,to better the understanding the nucleation and growth of thiourea during the crystallization process,it is necessary to obtain a theoretical basis for the crystallization process and optimize the crystallizer and operating parameters.The solubility,metastable zone,and induction period of thiourea have been proven to be the most crucial factors of crystallization [19].Until now,the thiourea single crystal has been studied in-depth with the aids of the infrared(IR)diffraction spectroscopy,X-ray diffraction (XRD),and ultraviolet–visible(UV–Vis)spectroscopy,etc.[20].The results demonstrated that the inducers exhibited a great influence on the crystal form of thiourea in terms of changing the bulk density and improving the agglomeration of thiourea [21].However,only a few research focused on the solubility,metastable zones,and induction periods of thiourea in general.

In this study,the solubilities of thiourea were determined under different pH conditions with the static method[22,23],and the solubility data were fitted by the classical Apelblat theoretical model[24].Further,MSZW of thiourea in water and the effects of the stirring rates and cooling rates on MSZW were investigated by the turbidimetric method [25,26].The date of the induction period of thiourea in water were measured by the same method.Based on the above results,the theoretical basis for the industrial crystallization of thiourea was successfully obtained.

2.Experimental

2.1.Materials

Thiourea (purity,99%),calcium hydroxide (purity,A.R.),and hydrochloric acid (purity,A.R.) were purchased from Sinopharm Chemical Reagent Co.,Ltd.,China,and all of them were utilized without further purification. Deionized water(conductivity ＜5 μS·cm-1) was employed for all the tests.

2.2.Apparatus and experimental setup

Fig.1 shows the schematic diagram of the experimental devices for the measurements of the solubility,MSZW,and induction period of thiourea.The cooling rate of thiourea was controlled by the cooling rate of an Ultra-precision thermostatic bath.

2.3.Determination of solubility curves

The static method was employed to determine the solubility of thiourea in deionized water.A certain amount of thiourea particles was accurately weighed on an electronic balance(the accuracy was 0.1 mg),after which they were poured into a jacketed beaker.The liquid in the beaker was kept at a temperature than was to be measured by a low-temperature thermostat.During the tests,the temperature was measured by a precision thermometer,which was placed in the thiourea solution,with an error of ±0.05 K.The temperature ranged from 280 to 325 K.After the addition of thiourea,the blend was stirred at a speed of 400 r·min-1for 3 h to attain a dissolution equilibrium.Next,the stirring blade was stopped,and the blend was allowed to stand for 2 h to observe if there were undissolved crystals.In the case of observed crystals,the mixture was filtered to remove them and achieve a saturated thiourea solution weighted m1.The solution was dried afterward at 100 °C to remove the solvent (water) and obtain the solute (thiourea)weighted m2.Finally,the solubility mole fraction x,was calculated according to Eq.(1).Three parallel experiments were conducted at different temperatures,and the average x value was recorded.

Fig.1.Apparatus for the measurement of solubility,MSZW,and induction period of thiourea.1.Turbidity meter controller;2.Overhead electronic stirrer;3.Precision digital temperature thermometer;4.500 ml jacketed beaker;5.Ultra-precision thermostatic bath.

where M1and M2are the relative molecular masses of the solvent(water) and solute (thiourea),respectively.

2.4.Determination of MSZW

To determine the MSZW of the thiourea solution,400 ml of a saturated thiourea solution was prepared and cooled at the desired rate.Based on the measured solubility data,the saturated solution of thiourea was accurately prepared at a certain temperature,and the experimental temperature of the low-temperature thermostat was adjusted to be 5 K higher than that of the saturated solution to completely dissolve the thiourea crystals in the solution.Thereafter the solution was cooled at a cooling rate of 10 K·h-1.The employed stirring speeds were 200,300,and 400 r·min-1at pH=7.Briefly,the procedure was as follows:the turbidity meter and stirring blade were turned on,and the low-temperature thermostat and stirring blade were adjusted to run at certain cooling stirring rates.At first,the turbidity meter reading was stable at a certain value,which indicated that there was no evident formation of thiourea crystals in the solution.Subsequently,the turbidity meter reading suddenly increased,implying that a large number of crystals had been precipitated.Through this approach the temperature at which the precipitation occurred was obtained at this time.The differences between the precipitation saturation temperatures were designated as MSZW.Parallel experiments were performed three times at the same saturation temperature,and the average value of MSZW was finally obtained.Furthermore,the cooling rates of 5,10,and 15 K·h-1were selected to determinate MSZW at a stirring speed of 300 r·min-.1

2.5.Determinations of the induction time

To determine the induction time of the thiourea solution,400 ml of a thiourea solution was stirred at a speed of 300 r·min-1.The changes in the crystal particles of the supersaturated solution obtained by cooling and the corresponding time were detected and determined by the turbid meter and a stopwatch,respectively.Firstly,the thiourea solution was quickly poured into the jacketed beaker at a certain temperature,and the timing started immediately until the particles appeared in the solution.This period between the beginning when the solution was poured into the jacketed beaker and the appearance of particles was recorded as the induction time.The parallel experiments were repeated three times under each condition and the average value was obtained as the final induction time.The experimental temperatures were set at 302.46 K and 312.58 K,respectively.

3.Results and Discussions

3.1.Solubility

The solubilities of thiourea under different pH conditions were shown in Fig.2.They demonstrated that the solubility increased evidently as the temperatures increased,while the change in pH exhibited only a minimal influence on the solubility of thiourea at the same temperature.

Fig.2.Solubility of thiourea under different pH.

The Apleblat model [24]is a semi-empirical equation that correlates the solubility and temperature,and its expression is shown in Eq.(2) as follows:

where x is the molar solubility of the solute;T is the experimental temperature;A,B,and C are the parameters in the Apleblat model.

The Apleblat model was applied to correlate the solubility data of thiourea to obtain A,B,C,and the correlation coefficient,R2.The root mean square deviation (RMSD) was calculated by Eq.(3) as follows:

where xiis measured from the experiments;xcalwas calculated by the model and n is the number of data measured in the experiments.

The results revealed that the fitting errors (R2=0.9995 and RMSD=6.63×10-4)of the data of thiourea solubility by the Apleblat model are acceptable,thus indicating that the model and its corresponding parameters (A=-99.55,B=1071.66,and C=16.27) were suitable for the solubility modeling of thiourea.This model could be applied to calculate the solubility of thiourea at other temperatures,and it availed theoretical support for the cooling crystallization of thiourea.

3.2.Metastable zone widths

3.2.1.The influences of stirring speed and saturation temperature on MSZW

As shown in Fig.3,as the stirring rates increased at the same temperature,the MSZW became significantly narrow,and the mass transfer rate in the system also increased as the stirring rate was augmented.Additionnally,the probability of collision between the molecules also increased.Additionally,the rate of heat transfer also increased as the stirring rates increased,thus increasing the probability of nucleation.Kubota [27]noted that the intensity of stirring would increase the rate of secondary nucleation and change the number of crystal nuclei that could be detected in the solution by the turbidity meter.Fig.3 also revealed that constant stirring and cooling rates,MSZW decreased significantly with the augmentations of the saturation temperatures.This phenomenon could be explained by the solubility curves of thiourea (Fig.2).The solubility of thiourea increased significantly as the temperature increased,indicating increments in the probabilities of collision and nucleation of the molecules in the solution due to high temperature,and these resulted in the easy growths of crystal nuclei in the solution.

Fig.3.MSZW of thiourea in different speeds (cooling rate 10 K·h-1).

3.2.2.The effects of cooling rates on MSZW

By plotting ln(ΔTmax/T0) against lnb,as shown in Fig.4,it was revealed that at constant saturation temperature (T0),ln(ΔTmax/T0)increased as the cooling rates(lnb)increased.Further,it also revealed that at a constant cooling rate,MSZW decreased as

T0increased.This is because the concentration of the solution increased correspondingly as T0increased,and this resulted in a decrease in the distance between the solute molecules in the solution,thereby enhancing the probabilities of collisions between the solute molecules and consequent nucleation.

Fig.4.MSZW of thiourea in different cooling rates (speed rate 300 r·min-1).

where m is the apparent nucleation progression and K is the nucleation constant.RGis the ideal gas constant and f is a constant calculated from the concentration of the solute.T0is the saturation temperature and Tnucis the nucleation temperature.ΔHdis the enthalpy of dissolution,which could be calculated from the solubility data by the Vant’s Hoff equation.

Taking the logarithms of both sides of Eq.(4),the relationship between ΔTmax/T0and b could be expressed by Eq.(5):

MSZWs at different saturation temperatures were fitted according to Eq.(5) to obtain m at different temperatures,as seen in Table 1.The fitting results indicated that ln(ΔTmax/T0) exhibited a good linear relationship with lnb at different temperatures,and m exhibited a downward trend from 1.65 to 0.63 as T0s increased.

It was also noticed that the overall values of m were relatively small.Generally,a low m value represented the strong solute–solvent interaction in the solution system.The small m value at a high temperature indicated that it was beneficial to the aggregation of the growth unit in the solution to form a stable 3D crystal nucleus[30],and this also indicated that the formation of a large number of crystal nuclei was controlled by the explosive nucleation mechanism [32].Therefore,in the thiourea crystallization process,an appropriate b should be selected according to the specific production requirements to avoid explosive nucleation and achieve the particle-size requirement.

3.3.Nucleation induction time

The nucleation induction periods of thiourea were measured by a turbidimeter at 302.46 and 312.58 K,after which ln-2S–lntindwas plotted,as shown in Fig.5.At a constant temperature,the rate of thiourea nucleation increased with the increase in the supersaturation,i.e.,the ln-2S coordinates moved to the left,and the induction period was reduced.At the same supersaturation,the increase in the temperature resulted in an increase in the nucleation rates and a reduced induction period.

According to the reports of Mullin et al.[33],the nucleation rates for spherical nuclei could be expressed as follows:

in Eq.(8),J is the nucleation rate,S is the supersaturation,v is the molecular volume,kBis the Boltzmann constant,γ is the solid–liquid interfacial tension,and T is the thermodynamic temperature.

The relationship between the induction period(tind)and S could be obtained from the following:

Eq.(9) shows that at a constant temperature,ln(tind) and ln-2S are in a linear relationship,the slope of α and intercept of β.Therefore,at a given temperature and solvent composition,γ in the system could be determined by tindaccording to Eq.(10):

Table 1 Fitting results of thiourea MSZW at different temperatures

Fig.5.Relationship between ln(tind ) with ln-2S.

Applying Eq.(9) to correlate tindat different temperatures,two straight lines with different slopes appeared,and they corresponded to the homogeneous(Fig.5,left zone)and heterogeneous nucleations (Fig.5,right zone),respectively.At high supersaturation,before the nucleus appeared in the solution,the primary nucleation rate was very high,indicating that the nucleation was mainly homogeneous [34].At low supersaturation where the nuclei have already appeared in the solution,the emergence of new nuclei was dominated by heterogeneous nucleation.

The parameters of Eq.(10) are shown in Table 2.According to the parameters,the calculated γ in the thiourea solution at 302.46 and 312.58 K were 2.86 and 2.94 mJ·m-2,respectively.During the homogeneous nucleation,γ was an important factor for nucleation and growth.It indicated the ability of the solute molecules to crystallize from the solvent;the smaller γ was,the easier it was for the solute to precipitate out of the solution [35,36].

3.4.Discussion for thiourea industrial crystallization

During thiourea crystallization in the industry,the temperatures are generally controlled;they are uniformly reduced from 323 to 283 K.However,the above determinations revealed that the solubility curve of thiourea could be divided into two parts:283.76–302.38 K and 302.38–321.82 K.The change in the solubility rate in the high-temperature region (302.38–321.82 K) was higher than that in the low-temperature one (283.76–302.38 K)where the phenomenon of supersaturation was more likely to occur.Therefore,supersaturation must be controlled at a lowered b in the high-temperature region.The low-temperature region could accelerate b and result in adequate supersaturation to promote crystal growth.

These inferences could also be obtained from the experiments on thiourea MSZW and tind.MSZW in the high-temperature region was narrower than that in the low-temperature one,and tindwas shorter in the high-temperature region than in the lowtemperature one.Therefore,at the various stages of thiourea crystallization,the different bs should be controlled to prevent the solution state from exceeding the supersaturation curve,which might result in explosive nucleation.

It was also proven that the operation parameters,such as band stirring rate,exhibited great influences on the crystal sizes of thiourea,which requires further optimization in practical industrial production.

Table 2 Parameters of Eq.(10) at different temperatures

4.Conclusions

The solubility of thiourea has been tested at different temperatures and pH values.The results demonstrated that the solubility of thiourea increased as the temperature increased and that pH exhibited a very minimal effect on the solubility.The solubility data was accurately described by the Apelblat equation model.The obtained Apleblat equation was applied to estimate the molar solubility of thiourea at multiple temperatures.

MSZW decreased as the temperature increased,and it was gradually narrowed at a high temperature-drop rate at constant T0.The classical Nvlt model was applied to fit MSZW and b,and the obtained m was 0.99–1.65.

It was found that the higher the supersaturation in the solution,the shorter tindwould be for thiourea.tindand supersaturation were fitted as two linear regions because of the homogeneous and heterogeneous nucleations of the thiourea crystallization process.γs of thiourea at 302.46 and 312.58 K were also calculated,and they yielded the values of 2.86 and 2.94 mJ·m-2,respectively.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by Top-notch Academic Programs Project of Jiangsu Higher Education Institution(TAPP),Priority Academic Program Development of Jiangsu Higher Education Institutions (PPZY2015A044).Appreciation the support from Jingbo-Nanjing Tech University Research Institute (JBNT-2020-003).