Effects of quenched disorder on the kinetics and pathways of phase transition in a soft colloidal system

Although impurities are unavoidable in real-world and experimental systems, most numerical studies on nucleation focus on pure (impurity-free) systems. As a result, the role of impurities in phase transitions remains poorly understood, especially for systems with complex free energy landscapes featuring one or more metastable intermediate phases. In this study, we employed Monte-Carlo simulations to investigate the effects of static impurities (quenched disorder) of varying length scales and surface morphologies on the nucleation mechanism and kinetics in the Gaussian Core Model (GCM) system, a model for soft colloidal systems. We first explored how the nucleation free energy barrier and critical cluster size are influenced by the fraction of pinned particles ($f_{\rm p}$) and the pinned cluster size ($n_{\rm p}$). Both the nucleation free energy barrier and critical cluster size increase sharply with increasing $f_{\rm p}$ but decrease as $n_{\rm p}$ grows, eventually approaching the homogeneous nucleation limit. On examining the impact of surface morphology on nucleation kinetics, we observed that the nucleation barrier significantly decreases with increasing the spherical pinned cluster (referred to as "seed") size of face-centred cubic (FCC), body-centred cubic (BCC), and simple cubic (SC) structures, with BCC showing the greatest facilitation. Interestingly, seeds with random surface roughness had little effect on nucleation kinetics. Additionally, the polymorphic identity of particles in the final crystalline phase is influenced by both seed surface morphology and system size. This study further provides crucial insights into the intricate relationship between substrate-induced local structural fluctuations and the selection of the polymorphic identity in the final crystalline phase, which is essential for understanding and controlling crystallization processes in experiments.