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Micellar crystals in solution from molecular dynamics simulations
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10.1063/1.2913522
/content/aip/journal/jcp/128/18/10.1063/1.2913522
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/18/10.1063/1.2913522

Figures

Image of FIG. 1.
FIG. 1.

Mean squared displacement averaged over all beads in the simulation box. These data were obtained from the initial simulation runs of the polymer at and . The origin of the time axis is time steps which indicates that the recording of these results began after the system reached equilibrium. In the case of , this equilibrium is a metastable state, and the beads are not diffusing. The simulation run performed at formed a fcc lattice around time step which persisted until the end of the run at , and the mean squared displacement shows a characteristic diffusive behavior.

Image of FIG. 2.
FIG. 2.

Snapshot of a polymer simulation run at , , , taken after the fcc lattice formed. beads are represented by orange spheres, and are shown with a reduced radius so they do not obscure important details. Orange lines indicate bonds between these beads. beads are shown in blue with a radius of . Large yellow spheres are placed on the lattice reconstructed from . Every yellow sphere is sitting on a micelle, visually confirming a perfect fcc crystal. The beads have been removed around a single unit cell of the lattice and yellow lines added to guide the eye. All snapshots are generated using PYMOL (Ref. 25).

Image of FIG. 3.
FIG. 3.

Examples of the behavior of during a simulation run of the polymer. Results are shown here for two independent runs with , , and . The origin of the time axis indicates the time step where the entire simulation started from a random initial configuration. Note how both systems eventually plateau at the same state , although it occurs at different times.

Image of FIG. 4.
FIG. 4.

Snapshot of a polymer simulation run at , , and taken after the lattice formed. The resulting lattice in this system is a body centered tetragonal with . Coloring conventions are identical to Fig. 2.

Image of FIG. 5.
FIG. 5.

Snapshot of a simulation run at , , and , taken after the bcc lattice formed. Coloring conventions are identical to Fig. 2.

Image of FIG. 6.
FIG. 6.

Polymer transfer vs temperature calculated from simulation runs of the polymer at and . All simulations start from an already equilibrated bcc phase. Results are included for the Nosé–Hoover thermostat and Langevin thermostat with two different values of . The inset plots the same data as a plot of vs to show that the slopes of the resulting lines are universal.

Image of FIG. 7.
FIG. 7.

Number of micelles in the ordered phase as a function of time for a single simulation run of the polymer at and temperature . The origin of the time axis on this plot indicates the time step where the simulation was started from a random configuration.

Image of FIG. 8.
FIG. 8.

Structure factor calculated after the lattice formed for the polymer simulation run at , , and . The full 3D is plotted as a scatter plot of vs . The multiplicity of the various peaks can be seen. Vertical dotted lines indicate the location of identified peaks, and their positions relative to are also noted (the factor of 4 is included because there are four unit cells along the box length ).

Image of FIG. 9.
FIG. 9.

Fluctuations in micelle positions vs temperature calculated for a polymer simulation run at , , and . The micellar crystal was formed at and then cooled to the target temperature without disrupting the lattice. Simulation runs heated to a higher temperature do disrupt the lattice and becomes ill-defined. Fluctuations on the axis are plotted as a ratio relative to , the nearest neighbor distance in the lattice.

Image of FIG. 10.
FIG. 10.

Radial density distribution for two nearest neighbor micelles superimposed with a separation of the nearest neighbor distance in the bcc lattice. The axis plots the volume fraction of the different beads belonging to a micelle in the local environment around the micelle. The results were calculated from a simulation run at , , and averaged over all micelles and time steps after the micellar crystal has formed.

Image of FIG. 11.
FIG. 11.

Summary of the phase diagram encompassing all simulated triblocks (all forming cubic phases with long-range order). Near the disordered transition, bcc is always favored and fcc lattices only begin to appear at lower temperatures. At even lower temperatures polymer transfer becomes negligible and MD would require prohibitively long simulations to reach equilibrium.

Tables

Generic image for table
Table I.

Summary of results obtained from initial test runs.

Generic image for table
Table II.

Summary of simulation results from testing the algorithm on .

Generic image for table
Table III.

Summary of simulation results from testing the algorithm on at .

Generic image for table
Table IV.

Summary of simulation results from testing the algorithm on at .

Generic image for table
Table V.

Summary of simulation results from testing the algorithm on after cooling to .

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/content/aip/journal/jcp/128/18/10.1063/1.2913522
2008-05-14
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Micellar crystals in solution from molecular dynamics simulations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/18/10.1063/1.2913522
10.1063/1.2913522
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