Nucleation rate and Gibbs free energy of nucleation of APIs, large molecule, amino acid and inorganic materials in solution at different cooling rates

Abstract

We propose a new mathematical model based on the classical nucleation theory to predict the nucleation rate, kinetic constant, and Gibbs free energy of nucleation using metastable zone width (MSZW) data as a function of solubility temperature. Unlike widely used models by Nyvlt, Kubota, and Sangwal, which are limited in capturing the impact of varying cooling rates, the proposed model allows direct estimation of nucleation rates from MSZW data obtained under different cooling conditions. This is particularly advantageous for continuous or semi-batch crystallisation design, where cooling rate is a critical variable. The model has been successfully validated using experimental data from 22 solute–solvent systems, including 10 APIs, one API intermediate, lysozyme, and glycine, as well as 8 inorganic compounds. Predicted nucleation rates span from 1020 to 1024 molecules/m3s for APIs, and up to 1034 molecules/m3s for lysozyme, the largest molecule studied. Gibbs free energy of nucleation varies from 4 to 49 kJ/mol for most compounds, reaching 87 kJ/mol for lysozyme. The model also enables accurate prediction of induction time and key thermodynamic parameters such as surface free energy, critical nucleus size, and number of unit cells—based solely on MSZW data obtained at different cooling rates.

Supplementary files

Article information

Article type
Communication
Submitted
05 May 2025
Accepted
16 Jul 2025
First published
16 Jul 2025
This article is Open Access
Creative Commons BY-NC license

CrystEngComm, 2025, Accepted Manuscript

Nucleation rate and Gibbs free energy of nucleation of APIs, large molecule, amino acid and inorganic materials in solution at different cooling rates

M. Vashishtha and V. K. Kannuchamy, CrystEngComm, 2025, Accepted Manuscript , DOI: 10.1039/D5CE00467E

This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. You can use material from this article in other publications, without requesting further permission from the RSC, provided that the correct acknowledgement is given and it is not used for commercial purposes.

To request permission to reproduce material from this article in a commercial publication, please go to the Copyright Clearance Center request page.

If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given.

If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party commercial publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page.

Read more about how to correctly acknowledge RSC content.

Social activity

Spotlight

Advertisements