3.3 Solubility and metastable zone width (MSZW) measurement.
Thiourea was dissolved by stirring in water at the respective temperature over 12 h. The solutions were filtrated to remove the dissolved solids. The concentration of the solution was measured by an Abbe refractometer (Shanghai Precision Instrument Co., Ltd., China, 2WAJ) through a concentration−refractive index standard curve to determine the solubility. Measurement error is ± 0.00002 nD. The classic MSZW measurement method was introduced46.
All measurements were implemented in a 100 mL double-jacketed crystallizer. Easymax (Mettler Toledo Ltd., US, 102 HFCal) was used for temperature control and the stirring speed control. Laser transmitting and receiving devices (Thorlabs GmbH, PM100USB) were applied to determine the MSZW in the experiment based on the detective shape decrease in the laser light transmission intensity.
The solubility data of thiourea in water were measured by author and fitted via Apelblat simplified empirical equation2,6,47with a good agreement (R2=0.99998),
\(lnx=115.39-\frac{8872.01398796}{(T+\mathrm{273})}-14.54862211ln(T+\mathrm{273})\)(23)
where x is solubility of thiourea in water, g/100g water;T is temperature, °C.
The MSZW (ΔTmax) was determined by the following equation:
\(\Delta T_{\max}=T_{\text{eq}}T\) (24)
where T eq is the equilibrium temperature of the thiourea aqueous solution at a certain concentration and T denote the detected initial nucleation temperature. As reported by Sangwal48, the theoretical model of the metastable zone width can be expressed as,
\(\mathrm{\ln}\Delta T_{\max}=K+\frac{1}{m}\mathrm{\ln}\nu-\frac{n}{m}\mathrm{\ln}N_{r}\)(25)
where \(\nu\) is cooling rate and \(N_{r}\) is stirring speed; K ,m , n are experimental data regression parameters. A single-factor experiment was carried out to investigate the effect of operational conditions on MSZW, including cooling rate and stirring speed; the cooling rate ranged from 0.1 to 1 °C min−1; the stirring speed ranged from 100 to 500 rpm.