Secondary Nucleation by Interparticle Energies. I. Thermodynamics

Secondary nucleation, in the absence of attrition, is known to be dependent on external fields, such as contact forces, shear, or interparticle forces. In this contribution, the thermodynamic effect of the presence of the seed crystal surface on secondary nucleation is derived in the context of the classical nucleation theory. The Gibbs free energy for the formation of a cluster close to a seed crystal is calculated with the addition of interparticle energies, namely, van der Waals attractive forces and Born repulsive forces. This results in the stabilization of a subcritical cluster close to the seed surface that can become a secondary nucleus more easily than under homogeneous nucleation conditions. Far from the seed surface, the developed model is reduced to the homogeneous nucleation described by the classical nucleation theory. The crystallization of paracetamol from an ethanol solution is taken as a case study, and the stabilization effect, given by the presence of interparticle energies, can be observed at different values of supersaturation. Three key indicators have been defined and calculated to describe the intensity of the stabilization effect, two of which, namely, the distance from the seed surface where the stabilization is active and the enhancement factor for supersaturation, are used in Part II of this series to describe the kinetics of secondary nucleation by interparticle energies.