Effects of Cooling Rate on the Size of Heterogeneities of Gels formed by Arrested Spinodal Decomposition

Protein gelation poses a challenge in materials science due to the lack of first-principles theories for predicting the properties of out-of-equilibrium amorphous states. This study examines the kinetics of gels formed through arrested spinodal decomposition and explores the influence of cooling rate on their structural and dynamical properties over waiting time. For the first time we apply the Non-equilibrium Self-Consistent Generalized Langevin Equation (NESCGLE) theory to describe the effects of finite cooling rates on the spinodal decomposition process. This approach allows us to describe the temporal evolution of heterogeneity sizes. Our NESCGLE theory predictions are successfuly compared with the experimental data of lysozyme solutions during gel formation [Gibaud and Schurtenberger, J. Phys.: Condens. Matter 21, 322201 (2009)], thus improving our understanding of gelation in nonequilibrium conditions and emphasizing the critical role of cooling rate as a key parameter.