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Monte-Carlo simulation of ternary blends of block copolymers and homopolymers
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View: Figures


Image of FIG. 1.
FIG. 1.

Average density vs. homopolymer fraction in the lamellae for various homopolymer length. The reference state, pure homopolymers with α = 1, has an average density of ρ o .

Image of FIG. 2.
FIG. 2.

The equilibrium period, L B , of the ternary mixture increases as the volume fraction of homopolymers, ϕ H , increases. This increase is more pronounced with longer homopolymers. The inset shows a grand-canonical SCFT study with similar results. The Fourier spectral method limits the amount of metastable data attainable.

Image of FIG. 3.
FIG. 3.

The effective value of β (cf. Eq. (3)) is computed for different relative homopolymer lengths, α, as a function of the volume fraction, ϕ H . The horizontal lines are at the values indicated in the legend. These are the values of β used to create the curves in Fig. 2.

Image of FIG. 4.
FIG. 4.

The distribution of copolymers and homopolymers in a ternary system with α = 0.25 and ϕ H = 0.5 is shown through a snapshot (a) and density profiles (b). In the snapshot, copolymer beads of type A are red and type B are blue. Homopolymers of both types are green. In the density profile plot, the solid lines show the copolymer density and the dotted line shows the homopolymer density.

Image of FIG. 5.
FIG. 5.

The distribution of copolymers and homopolymers in a ternary system with α = 1.0 and ϕ H = 0.5. The conventions are the same as in Fig. 4.

Image of FIG. 6.
FIG. 6.

The number of copolymers, n AB , per interfacial area, A, as a function of the homopolymer volume fraction, ϕ H , measured for various homopolymer lengths, α. The inset is a grand-canonical SCFT calculation with a polymer density equivalent to the Monte-Carlo reference state. The SCFT values are larger due to a greater polymer density and period length.

Image of FIG. 7.
FIG. 7.

The Gibbs free energy of mixing per molecule, Δg mixing , as a function of the relative length of the homopolymers, α, as extracted from the nPT-simulations according to Eq. (7).

Image of FIG. 8.
FIG. 8.

In the Gibbs ensemble simulation, the equilibrium value of ϕ H = 0.39 is approached for α = 1.0.

Image of FIG. 9.
FIG. 9.

The boundary ϕ H of the symmetric three-phase coexistence between two homopolymer-rich phases and a lamellar phase is obtained by comparing the chemical potential of the A homopolymer, μ A , in the pure A phase and the lamellae swollen by both homopolymers.

Image of FIG. 10.
FIG. 10.

The difference in chemical potential between the lamellar and pure phase for homopolymers of length α = 0.25 is shown as a function of lamellar period, L B . The data points are the same as those used in Fig. 2, with ϕ H ranging from 0.1 to 0.9 in increments of 0.1. The curves fit the data to one or more exponentials, as noted in the text.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Monte-Carlo simulation of ternary blends of block copolymers and homopolymers