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Controlling crystal self-assembly using a real-time feedback scheme
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View: Figures


Image of FIG. 1.
FIG. 1.

Operation of the feedback loop on short time scales for three “With-feed” simulations with different initial bond strengths . (Top) Time-dependence of the bond strength ɛb. Measurement and relaxation stages are indicated for the run with . The shaded region indicates where “No-feed” simulations found appreciable crystallisation. The inset shows the time-dependence of the perturbation strength for the run with . (Bottom) Average number of bonds per particle, .

Image of FIG. 2.
FIG. 2.

Configurations from “No-feed” (left) and “With-feed” (right) simulations at t = 104τ0, and averaged measures of crystallinity at this time. In the snapshots, particles in fcc/hcp environments are coloured orange/purple. Particles in other environments are rendered at half their actual diameter for visual clarity. The data in the table are averaged either over 8 independent simulations (“No-feed”) or over the M = 8 systems associated with single “With-feed” simulations (see the Appendix). For , we show the standard errors on these averages as an indicator of the numerical uncertainty. For n x and n 142, these errors are small: no larger than 0.02 and 0.2, respectively. The uncertainties on are significant but it is clear that “With-feed” simulations form “higher-quality” crystals with larger close-packed domains.

Image of FIG. 3.
FIG. 3.

Behaviour of the correlation and response functions for a “With-feed” simulation with . (Other data for the same run were shown in Fig. 1 ). We show and for the first three iterations of the feedback loop. The responses are quite small when compared to , indicating that irreversible bonding is taking place, and the system is vulnerable to kinetic trapping. As a result, the feedback loop acts to reduce the bond strength ɛb (see Fig. 1 ).

Image of FIG. 4.
FIG. 4.

Behaviour of bond strength ɛb at long times, for the “With-feed” simulations of Fig. 1 . The symbols and colors indicate the values of , which are the same as those in Fig. 1 . The dashed line shows the “No-feed” protocol that gave the best yield.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Controlling crystal self-assembly using a real-time feedback scheme