On the interpretation of metastable zone width in anti-solvent crystallization

Considering nonlinear dependence of solute concentration on anti-solvent solvent composition a modified Nyvlt-like equation based on traditional power-law relation between nucleation rate and developing supersaturation and a new equation based on the classical theory of three-dimension nucleation are proposed to explain the dependence of anti-solvent addition rate on metastable zone width defined as excessive anti-solvent composition in anti-solvent crystallization. The experimental data on the metastable zone width in anti-solvent crystallization of benzoic acid are analyzed and discussed from the standpoint of these equations. It is found that the new approach based on the classical nucleation theory provides better insight into the processes involved in anti-solvent crystallization. Analysis of the experimental results on anti-solvent crystallization of benzoic acid [D. O'Grady, M. Barret, E. Casey, and B. Glennon, Trans. IChemE A 85, 945, (2007)] revealed that: (1) the value of metastable zone width for a solvent anti-solvent system is determined by the solute solvent and solute anti-solvent interactions, (2) the dependence of the metastable zone width on stirring is associated with the enthalpy of mixing, and (3) the new approach predicts a threshold anti-solvent addition rate associated with the setting up of an equilibrium between solvent and anti-solvent and a maximum anti-solvent addition rate connected with the induction period t(ind) for the onset of crystallization. (c) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim