A polymer functionalized nanosphere of diameter 2. The polymer is modeled as 8 soft sphere (WCA) beads connected by FENE springs.
Two views of a simulation cell containing 2000 TNS in the H phase. NS are blue; Tethers are not shown. The NS in this system have polydispersity Δ = 20%.
The top panel shows 8 unit cells of a double gyroid (DG) phase. The NS are monodisperse and shown in blue and white. Tethers are not shown. The bottom panel shows the same 8 unit cells from a side perspective.
The top panel shows 2000 TNS that have self-assembled to the L phase by a conventional path. The NS in this system have polydispersity Δ = 3%. The bottom panel shows 2000 TNS that have self-assembled to the PLH phase by an alternate path. The NS in this system have polydispersity Δ = 10%.
Schematic showing the two paths, the conventional path (CP) and the alternate path (AP), used in the present study.
Schematic of paths used in determining the quasiequilibration properties of polydispersity.
The CP and AP phase diagrams (T * versus Δ) are shown in overlay for the volume fraction ϕ = 0.25 and ϕ = 0.3 ± 0.01. The region where the CP indicates the phases to be stable is contained within the region where the AP indicates the phase to be stable. Thus the darker shaded region is labeled both conventional and alternate. The bottom graph shows for DG the relative likelihood of the DG phase self-assembling via the CP as a function of polydispersity.
The (a) CP and (b) AP phase diagrams (T * versus Δ) are shown for the volume fraction ϕ = 0.4. The arrows illustrate the path used to explore the phase diagram.
The effect of polydispersity on (a) the crystalline vs (b) icosahedral local packing, (c) the potential energy of the NS-NS interaction, (d) the coordination, and (e) packing fraction of the particles, as determined by a radical tessellation, is compared at ϕ = 0.25, 0.3, and 0.4. The phases found along each curve are indicated in parentheses in the legend. The dashed arrows indicate the collapse of QEΔ↓ data onto QEΔ↑ data at ϕ = 0.4.
A series of snapshots of the L phase is shown at polydispersity 0%, 6%, 10%, and 12% as polydispersity is grown into a monodisperse cooled system. At each polydispersity, the system was allowed to relax for 10 × 106 time steps. Nanospheres are colored red if locally crystalline, light blue if unidentifiable, and dark blue if icosahedral. Tethers are not shown. Initially, the system is in a totally crystalline state, with a few non-crystal NS found at grain boundaries and defects in the lamellae. At 6%, the system is still crystal, although the number non-crystal NS at grain boundaries and lamellae defects has increased. At 10%, the lamellae is mostly liquid and disordered, with a few small islands of crystal bilayer remaining. At 12%, the system is fully in the PLH phase. Note that although “red” particles are still present, they are not spatially correlated and represents the limitations of the identification algorithm.
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