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Real-space self-consistent mean-field theory study of ABC star triblock copolymers
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Image of FIG. 1.
FIG. 1.

Monomer density plots of typical ordered microstructures formed in ABC star triblock copolymers with . The colors of red, green, and blue, indicate the regions where the most components are A, B, and C, respectively. There are seven 2D cylindrical structures of polygon-tiling patterns with translational symmetry along the third direction: (a) [6.6.6], (b) [8.8.4], (c) [8.6.4; 8.6.6], (d) [10.6.4; 10.8.4], (e) [10.6.4; 10.6.6], (f) [12.6.4], and (j) [8.6.4; 8.6.6; 12.6.4] (these integers indicate the sequence of polygons meeting at a vortex in each pattern); and three other 2D structures, including (g) L3, (h) HL and hexagonally arranged HC, and one HHC. The basic vectors of these periodic structures are labeled as .

Image of FIG. 2.
FIG. 2.

Typical Fourier spectra of the density profiles of (a)–(f) and (j) in Fig. 1. The size of the filled circles denotes the peak intensities. For (a), the picture is for A (red), B (green), or C (blue) component; for (b), the left picture is for A or B, and the right one is for C; for others, the pictures from left to right are for A, B, and C, respectively. For each pattern, some typical diffraction peaks are labeled.

Image of FIG. 3.
FIG. 3.

(a) Free energy differences from the value of the homogeneous phase as a function of the volume fraction of A composition for ABC star triblock copolymers with symmetric B and C arms. With increasing, the phase structure sequence is from L3, through [8.8.4], [6.6.6], [8.6.4; 8.6.6], [10.6.4; 10.6.6], [12.6.4], HL, to HHC. The inset shows the transition between HL and HHC. (b) Phase stability regions as a function of the arm-length ratio of . Note that one break is applied with the x axis for the reason of clarity of the figure.

Image of FIG. 4.
FIG. 4.

The magnitudes of basic vectors in unit of the radius of gyration of these 2D structures along the phase path in Fig. 2. The unfilled (including the symbols of cross) and filled symbols denote the vector lengths of and , respectively. For the reason of clarity, the of HL is not shown.

Image of FIG. 5.
FIG. 5.

(a) Internal part and (b) entropic part of the free energy difference in Fig. 2(a) as a function of .

Image of FIG. 6.
FIG. 6.

The free energy difference as a function of for fixed . The phase of [8.6.4; 8.6.6; 12.6.4], denoted as filled squares, does not appear as stable one in this parameter region.

Image of FIG. 7.
FIG. 7.

The lengths of basic vectors as a function of along the phase path of fixed .

Image of FIG. 8.
FIG. 8.

(a) Internal energy of and (b) entropic energy of of various structures as a function on the phase path of fixed .

Image of FIG. 9.
FIG. 9.

The triangular phase diagram of ABC star triblock copolymers with equal interaction parameters of . The phase diagram is composed of a set of transition points shown as black dots.


Generic image for table
Table I.

The phase transition boundaries between the bcc and hex phases obtained by the OpS2 with discretizations and , together with the free energy difference of the bcc phase between the two discretizations in AB diblock copolymers. The transition data read from Fig. 2 in Ref. 38 is shown as a reference.

Generic image for table
Table II.

The free energies of [10.6.4; 10.6.6] and [12.6.4], as well as their free energy difference calculated with and , respectively.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Real-space self-consistent mean-field theory study of ABC star triblock copolymers