Use of averaged local bond order parameters in order to determine the crystalline structures. The particles in this simulation snapshot are color-coded according to .
Effective free energies associated with straightening of individual chains (blue squares) and alignment of neighboring chains (red circles) as a function of the size of clusters of aligned segments n. The colored segments in the sketches represent the selection criteria used for the computation of the corresponding probabilities. 6
Relative variation of several observables (O) from the melt to the formation of a critical nucleus for the particles involved in the nucleus: the nematic order parameter S 2 (black, continuous), the radius of gyration R g (red, dotted), the inverse of the Voronoi cell volume V (blue, dashed), and the crystallinity order parameter (purple, dashed-dotted) corresponding to the largest cluster size. The curves are averaged over 25 independent trajectories progressing backward in time from the nucleation time t = t 0 in steps Δt to t = −50Δt. On the right side, we present three snapshots of the nucleus chains. The particles that form the nucleus at time t 0 are highlighted in gray. The chains are already initially prolate and undergo orientational ordering before they straighten further. Finally, a cluster of aligned, hexagonally placed chains is formed.
Probability distributions of the averaged local bond order parameter computed at different times for those particles that form the crystallite at t 0.
(a) Top view of a cluster. Crystalline particles (blue) and surface chains (red). Note the hexagonal arrangement of the chains and the relatively low coverage of the top surface by surface chains. (b) Normalized histograms of the surface particles versus label of a particle in the chain (0 to 19): all surface particles (filled histogram) and only those that belong to chains successfully attached after τ D (dashed histogram).
Trajectory of a chain attaching via the sliding process: ((a)–(d)) Snapshots of the time evolution, with big red beads representing the attaching chain, medium sized gray beads being the cluster of crystalline particles, and small gray beads being particles that belong to the cluster chains but are not crystalline; (e) Time evolution of the order parameter for every particle in the chain, with black dots highlighting particles that are identified as crystalline according to the alignment criterion (Eq. (1) ). Every iteration corresponds to a single Δt = τ D /20.
(a) Correlation between attachment events: The dark (blue) bars represent the distribution of neighboring attachment events as resulting from the analysis of 30 growth trajectories of length 30Δt. The light (red) color bars represent the distribution of neighboring attachment events for a Monte Carlo sampling of non-interacting cylinders attached at random sites picked uniformly on the surface of the crystal. Simultaneous attachment of neighboring chains is more likely to occur in the interacting system than in the non-interacting system. (For detailed definition of terms, please see the main text.) Isolated (b) and multiple (c) attachment events are shown in the insets. (d) Schematic illustration of a configuration of random segments placed at the surface of the crystalline cluster. Their direction corresponds to the average direction of the end-to-end vectors of the cluster chains.
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