On the metastable zone width of sparingly-soluble compounds during controlled addition of reactants

Two novel approaches of metastable zone width (MSZW) for sparingly-soluble compounds by reaction crystallization based on known concepts of crystallization processes are proposed. In these approaches theoretical equations relating the MSZW of sparingly-soluble compounds with the feeding rate R_B of one of the reactants are derived from consideration of the dependence of stationary three-dimensional (3D) nucleation rate J of the solute on the generating supersaturation lnS described by power-law relation and classical nucletion (CN) theory. The final equations of the models are then used to analyze the published experimental MSZW data of reaction crystallization of Li₂CO₃, having a negative temperature coefficient of solubility in water, obtained between 10 and 80 °C from aqueous LiCl solutions by addition of aqueous Na₂CO₃ solution at different feeding rate R_B. Both models are found to describe experimental MSZW data satisfactorily. Procedures for calculations of the constants (nucleation constant K and nucleation order m) of the power-law approach and the preexponential constant A and the parameter B, containing the interfacial energy γ, of the CN theory and relationships between different constants are described and discussed. The main findings of the study are as follows:

• (1)
  The nucleation constant K is related with the preexponential factor A, whereas the nucleation order m is related with the interfacial energy γ_eff.
• (2)
  The preexponential factor A rapidly decreases with an increase in solution temperature T of Li₂CO₃ is associated with a decrease in the radius r_c of 3D nuclei and the parameter f related with the solute solubility c₀ with increasing T.
• (3)
  The experimentally observed values of γ_eff are lower than the theoretical values of γ for all T and suggests that Li₂CO₃ crystallization occurs by 3D heterogeneous primary nucleation in the entire investigated temperature interval.