Kinetics of homogeneous nucleation of monodisperse spherical sulphur and anatase particles in water–acid systems

Abstract Homogeneous nucleation and growth of monodisperse spherulites of sulphur and hydrated titanium dioxide in anatase structure was studied using an original optical method for measuring relative scattering coefficient (RSC), based on alternative application of coherent radiation of two lasers with different wavelengths. Application of Mie's theory on calculation of relative scattering cross-section RSCS and data on RSC provide possibility for simultaneous obtaining of numerical data on the duration of induction period t ∗ , change in the diameter d ( t ) and number N ( t ) of critical nuclei of a new phase by varying temperature–concentration conditions during homogeneous mass (industrial) crystallization. The procedure reliably registers d ( t ) and N ( t ), starting with the size of d ∼30 nm and allows investigation of the kinetics of various phenomena in colloid systems prior to the beginning of particles precipitation. In the system Na 2 S 2 O 3 +HCl+H 2 O, assuming that the number of nuclei during their growth from critical size d ∗ to d ∼30 nm remained the same, we for the first time succeeded in estimating the upper and lower limits for d ∗ value. During the hydrolysis of titanium oxysulphate sulphuric acid solutions (TiOSO 4 +H 2 SO 4 +H 2 O), monodisperse spherulites of hydrated anatase composition were obtained and the dependence of t ∗ value on supersaturation value γ was studied. We have determined the critical size d ∗ and surface energy σ of nuclei as well as functions d ( t ) and N ( t ) of colloid spherulites TiO 2 · n H 2 O.