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Phase behavior of a blend of polymer-tethered nanoparticles with diblock copolymers
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View: Figures


Image of FIG. 1.
FIG. 1.

Illustration of the model and notations.

Image of FIG. 2.
FIG. 2.

Phase diagram for . For and a narrow lamellar region appears for small densities and a big two-phase region for larger densities. Shortening and increasing the number of arms leads to an unbinding transition at large densities and a two phase region for higher densities at higher . The diamond symbol corresponds to the density profiles of Fig. 8, and the square to those of Fig. 9.

Image of FIG. 3.
FIG. 3.

Lamellar spacing in units of as a function of particle density for . The symbols are results of the SCFT calculations for the given parameters and . The solid lines are the expected results if the interfaces are not influenced by increasing the particle density.

Image of FIG. 4.
FIG. 4.

Density profiles of the monomers of the diblocks , of the monomers , of the monomers of the stars and the particles in the lamellar phase for . Note that the particle volume fraction has been devided by . In the top panel and , in the bottom panel and . Particles arrange in the middle of the lamella. has to therefore be decreased in the middle of the lamella and is enriched close to the interface.

Image of FIG. 5.
FIG. 5.

Phase diagram for . Increasing the arm length leads to a narrower lamellar region. The circular symbol indicates the point in the phase diagram corresponding to the densities of Fig. 10.

Image of FIG. 6.
FIG. 6.

Phase diagram for . For this low number of segments in the particle shell, an extended lamellar phase is found. The star symbol indicates the parameters leading to the profiles of Fig. 11.

Image of FIG. 7.
FIG. 7.

Ratio of star to diblock mean-square size as a function of . The solid lines are ideal chain predictions for the indicated numbers of arms . The solid dots represent estimates based on the parameters used in the phase diagrams of this paper.

Image of FIG. 8.
FIG. 8.

Annealed density profiles for , , , and . The diamond symbol in Fig. 2 represents the corresponding point in the phase diagram. From top left to bottom right across rows the graphs display, , , , and , respectively. Note that the particle density has again been devided by . The expected lamellar phase is found.

Image of FIG. 9.
FIG. 9.

Similar to Fig. 8, but with , , , and . The location in the phase diagram is displayed with a square symbol in Fig. 2.

Image of FIG. 10.
FIG. 10.

Density profiles for , , , and . The point symbolized by a circle in Fig. 5 corresponds to this parameter set. Instead of a swollen lamellar phase, our annealing scheme leads to coexistence of a lamellar and a disordered phase.

Image of FIG. 11.
FIG. 11.

Density profiles for , , , and . The corresponding point in Fig. 6 is symbolized by a star. The system size leads to a confinement that results in a circular structure being formed.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Phase behavior of a blend of polymer-tethered nanoparticles with diblock copolymers