Filler second virial coefficient normalized by its hard sphere value as a function of monomer-particle attraction strength in units of the thermal energy for and three values of spatial range.
(a) Spinodal phase diagram for and three values of . Numerical data points were determined by approaching the spinodal instability via incrementing (closed symbols) and (open symbols). Though some symbols appear close to the or 1 axes, all systems are, of course, miscible in these limits. Lines are a guide to the eye. (b) Alternate representation of the same spinodal phase boundary in terms of reduced temperature. The homogeneous miscible and phase separated depletion and bridging regimes are indicated.
Spinodal phase diagram for and three values of spatial range. The phase boundaries were determined in the same manner as in Fig. 2. Solid lines are a guide to the eye. Dashed lines show the spinodal predicted by the virial calculation (Ref. 25) of Eq. (8); endpoints of the dashed lines are spatial range labels.
Nanoparticle potential of mean force in the dilute two particle limit for and the four indicated values of attraction strength for (a) and (b) .
Nanoparticle potential of mean force in the dilute two particle limit (dashed lines) and at (solid lines) for , , and three values of interfacial cohesion range.
Nanoparticle potential of mean force for various volume fractions and fixed , , and . The curve is the pure hard sphere result at a total packing fraction of 0.4, computed using the HNC closure.
Monomer-filler pair correlation function for various filler volume fractions for , , and . The , 0.25, 0.5, 0.75, and 0.9 lines are labeled by a square, diamond, triangle, , and circle, respectively, and have contact values , 3.5, 3.0, 2.7, and 3.2, respectively. The inset shows the nonrandom part of the pair correlation function, , weighted by the surface area factor .
Monomer-monomer pair correlation function for various filler volume fractions and , , and . The inset shows the nonrandom part of the pair correlation function, , weighted by the surface area factor .
(a) Nanoparticle collective structure factor for various volume fractions for , , and . The curve corresponds to pure hard sphere result at a total packing fraction of 0.4. (b) Small angle regime of the monomer-monomer collective structure factor for the same systems.
(a) Inverse of the dimensionless filler osmotic compressibility as a function of volume fraction for various interfacial cohesion strengths, , and . The black solid curve corresponds to pure hard spheres at a total packing fraction of . (b) Analogous results for the inverse of the dimensionless polymer osmotic compressibility.
(a) Amplitude of the nanoparticle collective cage peak as a function of volume fraction for various interfacial strengths, , and . The smooth black curve (no data points) corresponds to the pure hard sphere fluid result at a total packing fraction of . Inset shows the peak location. (b) Analogous results for the microphase peak intensity of the collective polymer structure factor. Inset shows the peak location.
Value of the global minimum in the nanoparticle potential of mean force at the spinodal phase separation boundary for (a) , , 10, and 15 systems and (b) , , 0.5, and 1.0 systems. Open symbols correspond to the high (bridging) side of the phase diagrams in Figs. 2 and 3, and closed symbols correspond to the low (depletion) side.
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