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Surface-induced phase behavior of polymer/nanoparticle blends with attractions
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10.1063/1.4705308
/content/aip/journal/jcp/136/16/10.1063/1.4705308
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/16/10.1063/1.4705308

Figures

Image of FIG. 1.
FIG. 1.

Pressure for calculations at constant packing fraction (dashed blue curve, left axis) and packing fraction for calculations at constant pressure (solid brown curve, right axis), for N = 80 and σ n = 2σ p .

Image of FIG. 2.
FIG. 2.

Surface free energy as a function of nanoparticle density for a system with N = 80 and σ n = 2σ p . Open squares correspond to constant pressure and open triangles correspond to constant packing fraction calculations.

Image of FIG. 3.
FIG. 3.

Density profiles for the system with N = 80 and σ n = 2σ p for constant pressure calculations. (a) Converged from a lower density profile and (b) Converged from a higher density profile. The polymers (x) scale is along the left axis and the nanoparticle (+) scale is on the right axis.

Image of FIG. 4.
FIG. 4.

Nanoparticle density at the first phase transition as a function of chain length N for blends with σ n = 2σ p . Squares are for constant pressure and triangles are for constant packing fraction.

Image of FIG. 5.
FIG. 5.

Transition density as a function of nanoparticle diameter for blends with N = 80. Squares are for constant pressure and triangles are for constant packing fraction.

Image of FIG. 6.
FIG. 6.

Surface free energy as a function of nanoparticle density for a system with N = 80 and σ n = 3σ p . Open squares correspond to constant pressure and open triangles correspond to constant packing fraction calculations. Note: The continuation curves are cutoff to show the phase transition point more clearly.

Image of FIG. 7.
FIG. 7.

Density profiles of polymer (dotted magenta) and nanoparticles (solid brown) at constant pressure for N = 80 and σ n = 2σ p at .

Image of FIG. 8.
FIG. 8.

Surface free energy as a function of nanoparticle density for N = 80, σ np = 2σ p , and α np = 0.5σ np at ε np = 0 (blue), ε np = 0.05 (dashed brown), ε np = 0.1 (black), ε np = 0.2 (red), ε np = 0.4 (dash-dot green), and ε np = 0.5 (magenta).

Image of FIG. 9.
FIG. 9.

Nanoparticle density at the phase transition for monomer-particle attractions with N = 80 and σ n = 2σ p , as a function of ε np at α np = 0.5σ p (lower axis, blue squares) and as a function of α np at ε np = 0.05 kT (upper axis, brown circles).

Image of FIG. 10.
FIG. 10.

Density profiles for polymer (dashed curves, left axis) and nanoparticles (solid curves, right axis), for N = 80, σ np = 2σ p , α np = 0.5σ p , and ε np = 0.5, at (top), (middle), and (bottom).

Image of FIG. 11.
FIG. 11.

Density profiles for polymer (dashed curve) and nanoparticles (solid curve), for N = 80, σ np = 2σ p , α np = 0.5σ p , and ε np = 0.5, at , with periodic boundary conditions (no wall).

Image of FIG. 12.
FIG. 12.

Surface free energy as a function of nanoparticle density for N = 80, σ np = 2σ p , and ε np = 0.5 kT at α np = 0.5 (solid blue), α np = 0.7 (dashed brown), α np = 0.9 (solid black), α np = 1.0 (solid red), α np = 1.1 (dashed-dot green), and α np = 1.4 (solid magenta).

Image of FIG. 13.
FIG. 13.

Surface free energy as a function of nanoparticle density for N = 80, σ np = 2σ p , and ε np = 0.5 kT at ε wp = 0.05 (solid blue), ε wp = 0.1 (dashed brown), ε wp = 0.2 (solid black), and ε wp = 0.3 (solid magenta).

Image of FIG. 14.
FIG. 14.

Nanoparticle density at the phase transition for monomer-particle attractions with N = 80 and σ n = 2σ p , as a function of ε wp at α wp = 0.5σ p (lower axis, blue squares) and as a function of α wp at ε wp = 0.05 kT (upper axis, brown circles).

Image of FIG. 15.
FIG. 15.

Nanoparticle transition density as a function of N at constant pressure, for hard sphere systems (closed blue squares), weakly attractive particle-monomer interactions (open brown squares), and weakly attractive polymer-wall attractions (purple triangles).

Tables

Generic image for table
Table I.

Weight functions associated with various parts of the DFT. In all cases, |r| = |rr |. Here R α = σα/2 is the radius of site α, δ is the Dirac delta function and Θ is the Heaviside step function.

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/content/aip/journal/jcp/136/16/10.1063/1.4705308
2012-04-27
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Surface-induced phase behavior of polymer/nanoparticle blends with attractions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/16/10.1063/1.4705308
10.1063/1.4705308
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