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Mesoscopic structure prediction of nanoparticle assembly and coassembly: Theoretical foundation
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Image of FIG. 1.
FIG. 1.

The general schematic procedure and key equations of the present approach for a homogeneous system of molecules composed of monomers specified as .

Image of FIG. 2.
FIG. 2.

Multicomponent molecule representations with the linear configuration for (a) flexible monomers and (b) HS particles with flexible molecules.

Image of FIG. 3.
FIG. 3.

Comparison of particle density profiles in the lamellar morphology of BCP/NP self-assembly varying the excess HS free energy functional. We verify our approach by comparing with results of previous calculations (Ref. 31). Black solid lines are results applying the FMT, blue dashed lines results from the HNC approximation form of the FMT, and red dotted lines results from applying the DFT by Tarazona, see Ref. 31. (a) Large particles at the dilute condition (, ). (b) Small particles with intermediate volume fraction (, ). Compared with the FMT approach, the HS interactions of the DFT approach by Tarazona (Ref. 54) and HNC approximation are more repulsive. The discrepancy originates from different functional forms of the excess free energy for HS interactions.

Image of FIG. 4.
FIG. 4.

Density profiles of positively charged, , and negatively charged HS particles, , as a function of distance from a positively charged flat wall with different surface charge densities, , 0.42, 0.55, and (bottom to top for and top to bottom for ), where is the diameter of HS particles. Open red circles are Monte Carlo simulation results of Ballone et al. at (Ref. 55) The inset displays results from Groot (Ref. 57). The double layer formation is observed at high surface charge densities.

Image of FIG. 5.
FIG. 5.

Density profiles of NPs, , and local volume fractions of BCPs, . The solid blue lines depict of the p1-type NPs and the solid red lines show of the p2-type NPs. The dotted blue lines represent of block A and the red lines show of block B. (a) Free NPs. [(b) and (c)] NPs connected by a homopolymer molecule with size (b) and (c) .

Image of FIG. 6.
FIG. 6.

Comparison of the bead-spring model and SCFT. The bead-spring model exhibits a larger lamellar spacing due to excluded volume interactions between monomer units. (a) Illustration of the bead-spring representation of a BCP. (b) Normalized local volume fractions of block A (black) and block B (red). The solid lines are results of SCFT and the dotted lines are those of the bead-spring model.

Image of FIG. 7.
FIG. 7.

Self-assembly of BCPs, NPs with charged ligands, and CAs, illustrating the effect of NP Coulomb repulsions on enhancing the regular dispersion of NPs. (a) Illustration of NPs with charged ligands and CAs. [(b) and (c)] Red color represents block A, blue color block B, and green color NPs with ligands. Density profiles of [(d) and (e)] NPs and [(f) and (g)] CAs. Two different conditions are studied by varying the parameter : [(b), (d), and (f)] and [(c), (e), and (g)] .


Generic image for table
Table I.

Flory–Huggins parameters for the simulation of HS particle self-assembly within BCPs.

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Table II.

Flory–Huggins parameters for the simulation of self-assembly of two chemically distinct HS particles connected by a homopolymer molecule within BCPs.

Generic image for table
Table III.

Flory–Huggins parameters for the self-assembly of BCPs and NPs with charged ligands.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Mesoscopic structure prediction of nanoparticle assembly and coassembly: Theoretical foundation