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.