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A comparison of implicit- and explicit-solvent simulations of self-assembly in block copolymer and solute systems
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10.1063/1.3580293
/content/aip/journal/jcp/134/16/10.1063/1.3580293
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/16/10.1063/1.3580293

Figures

Image of FIG. 1.
FIG. 1.

Number of nanoparticles, weight-averaged number of solute molecules per nanoparticle, and weight-averaged number of diblock molecules per nanoparticle vs time. Results shown are an average of three randomly initialized simulations, with the error bars showing standard deviations at a few points during the simulation. Solid symbols are for DPD simulations and open symbols are for BD simulations. Triangles are for favorable solute–PS interaction and circles for unfavorable solute–PS interaction.

Image of FIG. 2.
FIG. 2.

Distribution of solutes in clusters of different sizes after 30 ns (top) and 70 ns (bottom). Clusters containing 20 or more solutes were included in the calculation but are not shown in this figure. The solid line represents a theoretical prediction based upon a diffusion-limited Smoluchowski approach (Ref. 56). The dashed line represents the same theoretical prediction, but with the time rescaled by a factor of 0.75. Symbols are as in Fig. 1.

Image of FIG. 3.
FIG. 3.

Number of diblocks per nanoparticle vs number of solutes per nanoparticle (both weight-averaged) at various points in time during in the simulations. The solid line represents the ratio between the total number of polymers and solutes present in the simulations. Symbols are as in Fig. 1.

Image of FIG. 4.
FIG. 4.

Snapshot of nanoparticles formed in a DPD simulation (top) and BD simulation (bottom) with favorable solute–PS interactions. The solute beads are shown in blue, PS beads in red, and PEG beads as transparent gray. Note the uniform coverage of PS beads on the nanoparticle surface and the uniform distribution of PEG chains around the outside of the nanoparticles. Movie files of a DPD simulation (movie 1) and a BD simulation (movie 2) are available (Ref. 58).

Image of FIG. 5.
FIG. 5.

Snapshot of nanoparticles formed in a DPD simulation (top) and BD simulation (bottom) with unfavorable solute–PS interactions. The color scheme for the beads is the same as in Fig. 4. Note the clustering of PS beads on the nanoparticle surface, which leaves large areas of the core exposed. Movie files of a DPD simulation (movie 3) and a BD simulation (movie 4) are available (Ref. 58).

Image of FIG. 6.
FIG. 6.

Radius of gyration of solute beads vs the number of solute molecules in a nanoparticle. The statistical uncertainty of each data point is no larger than the symbol size. Symbols are as in Fig. 1.

Image of FIG. 7.
FIG. 7.

Mean distance between all PS beads in a nanoparticle and the nanoparticle center of mass vs the maximum solute radius. The statistical uncertainty of each data point is no larger than the symbol size. Symbols are as in Fig. 1. The solid black line of unit slope is a guide to the eye.

Image of FIG. 8.
FIG. 8.

Overall nanoparticle radius vs number of solutes in the nanoparticle. The overall nanoparticle radius is the distance between the terminal bead in a PEG block and the nanoparticle center of mass, averaged over all diblocks in the nanoparticle. The statistical uncertainty of each data point is no larger than the symbol size. Symbols are as in Fig. 1.

Image of FIG. 9.
FIG. 9.

Diffusion coefficient vs overall nanoparticle radius for the nanoparticles in the BD and DPD simulations. The solid line shows the Stokes–Einstein relation. Error bars show statistical uncertainties for a few representative data points. Symbols are as in Fig. 1.

Image of FIG. 10.
FIG. 10.

Diffusion coefficients for nanoparticles from BD simulations, along with the curve D = kM −1. The constant k was chosen so that the curve passes through the infinite dilution diffusion coefficient of the solute for the implicit-solvent model. Error bars show statistical uncertainties for a few representative data points. Symbols are as in Fig. 1.

Image of FIG. 11.
FIG. 11.

Surface area per polymer vs number of solutes in nanoparticle for simulations with favorable solute–PS interactions. Symbols are as in Fig. 1. The solid line represents the surface area occupied by a randomly coiled diblock (Ref. 16).

Tables

Generic image for table
Table I.

Pairwise interaction parameters for the implicit-solvent model studied with BD simulations. Energies are given as multiples of ε BD , where ε BD /k B = 372.5 K.

Generic image for table
Table II.

Repulsion parameters used in the explicit-solvent DPD simulations, in units of ε DPD , where ε DPD /k B = 298 K.

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/content/aip/journal/jcp/134/16/10.1063/1.3580293
2011-04-28
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A comparison of implicit- and explicit-solvent simulations of self-assembly in block copolymer and solute systems
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/16/10.1063/1.3580293
10.1063/1.3580293
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