Kinetics model of crystal nucleation and growth in supercooled water for designing ice-templating soft matter scaffold

Ice-templating technology has recently attracted extensive attention to achieve programed structure-property relationships in porous soft matter scaffolds. However, there is a huge gap existed between theoretical understanding and practical applications of nucleation kinetics and growth of ice crystals in supercooled water. This paper establishes a nucleation kinetics model of crystal growth in supercooled water, for designing ice-templating soft matter scaffolds with programmable structure-property relationship. A phase transition model was firstly formulated to characterize liquid-liquid phase transition of supercooled water, based on a two-state model and free-volume theory. Effects of diffusion coefficient and density of the supercooled water on ice nucleation kinetics and crystal growth were investigated, based on the classic nucleation theory. Analytical results showed excellent agreement with experimental data, with correlation indices of R²=90.7 % for diffusion coefficients and R²=94.0 % for densities, respectively. The model predicted a nucleation rate of 31.7 m⁻³∙s⁻¹ at 200 K and peak nucleation rate and crystal growth rates appearing at 183 K and 227 K. Constitutive relationships among mechanical behaviors, ice nucleus radius, nucleation ratio, and crystallization growth rate, were developed for the ice-templating scaffolds, based on the affine model theory and verified with finite element analysis results (R²= 99.9 %) and experimental results (R² = 95.8 %). Finally, the prediction results using the proposed model were further verified using the experimental data reported in the literature. This study provides a new methodology to describe the nucleation kinetics and growth of ice crystals in supercooled water and programmable structure-property relationships in ice-templating soft matter scaffolds.