The title of my Ph.D. thesis is "Identifying the mechanisms of complex transformations: From transition pathways to reaction coordinates".


In this doctoral thesis, I investigate the crystallization mechanisms and search for reaction coordinates in two different physical systems. In both cases, we observe transitions from an unordered, liquid-like state to an ordered, crystalline state. The first system is a polymer chain consisting of identical monomers interacting via a square-well potential. For a sufficiently small well width, the polymer undergoes a first-order freezing transition from an expanded, unordered phase to a compact, crystalline state. Using transition path sampling in combination with a new path generation algorithm developed specifically for polymers, we study this freezing transition. We find that typical transition states, located between the two stable phases, consist of a single crystalline nucleus attached to one or more chain fragments. The second system consists of soft particles with purely repulsive interactions. Due to the finite value of the pair potential for zero separation, the GEM-4 system can form a cluster crystal. In such a crystal, a number of particles sit on top of each other at the same lattice site. Hopping events occur where a particle jumps from its cluster to an adjacent one at another lattice site. We investigate which microscopic mechanisms lead to the formation of cluster crystal structures from a supercooled liquid. We also compare our simulation results with predictions from classical nucleation theory. For both systems, we calculate free energy landscapes as a function of different order parameters and optimize the reaction coordinate. In the case of the polymer we find that the total potential energy combined with a measure of its overall crystallinity is a better indicator of the progress of the transition than the size of its crystalline nucleus, which is used in classical nucleation theory. For the cluster crystal system, we place particular emphasis on investigating the role of various structural compositions during the freezing transition. We find that even for conditions where a multiply-occupied fcc crystal is the thermodynamically stable phase, kinetically, the nucleation into bcc cluster crystals is strongly preferred.


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