Year: 2025
Type: article
Abstract: Supersaturation, nucleation, and phase separation are ubiquitous phenomena of great interest in both science and industry. However, a unified, quantitative understanding of these phenomena has yet to be achieved for mesoscopic systems. Here, we present a set of general equations that determine the monomer saturation degree, the size distribution, and the free energy of mesoscopic systems, as well as their phase-transition conditions. These equations reveal that, under supersaturation, the largest cluster size (LCS) is an important state variable; the supersaturation degree decreases with the LCS, approaching unity in the macroscopic limit. We identify the critical supersaturation, at which the nuclei undergo the phase transition to form large crystals. Below this critical supersaturation, the nucleus size distribution is either a unimodal function or a monotonically decreasing function of size, depending on the system and temperature. We also predict the most probable nucleus size and the direction of spontaneous changes of the LCS. Our theory provides a unified, quantitative explanation of the nucleus-size-distribution across six different systems, including nanoparticles and biological condensates. This work serves as a general theoretical framework useful for understanding and designing nucleation and phase transitions of mesoscopic systems.
DOI: 10.1021/jacs.5c10868
Institutions: Chung-Ang University, Lawrence Berkeley National Laboratory, University of California, Berkeley, Korea Advanced Institute of Science and Technology, Pohang University of Science and Technology, Seoul National University, Soongsil University, Institute for Basic Science, Pusan National University, Chungbuk National University, Institute of Engineering Research, Advanced Institute of Convergence Technology
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,500
OpenAlex ID: W4416951813