Theory of supermolecular structures in polydisperse block copolymers: 3. Cylindrical layers of bidisperse chains

Mixed Supercrystalline Structures in Mixtures of ABC Triblock and ab(bc) Diblock Copolymers, 3. Lamellar and Cylindrical Structures in Bicomponent Mixtures

“…Such a hybrid structure requires special consideration within a self-consistent field approach: for the B-domain of a mixed lamellar (mLAM) superstructure, this problem was solved in; [24] the B-domains of CC(C), and C(A, C) morphologies are specially considered in Appendices A and B; the B-domain in the CC(A) superstructure can be conceived as a bidisperse convex cylindrical brush within a fixed ends approximation. [23] In A-and B-brushes the chains are grafted at the A/B interface with the grafting area per chain equal to r A/B . In the C-brush there is the r B/C area of the B/C interface per chain.…”

“…In the C-brush there is the r B/C area of the B/C interface per chain. The grafting area r B/C as well as the size of the [22] hybrid planar [6,24] monodisperse planar [21] mCC(C) bidisperse convex cylindrical [23] hybrid concave cylindrical a) monodisperse concave cylindrical [23] mCC(A) bidisperse concave cylindrical [23] hybrid convex cylindrical [23] monodisperse convex cylindrical [23] mC(A, C) bidisperse concave cylindrical [23] hybrid bi-convex cylindrical b) mon odisperse concave cylindrical [23] a) See Appendix A. b) See Appendix B.…”

“…Note that decreasing q à with a decrease in a and b reflects a general property of the polymer brush (and hybrid brushes): a gain in the conformational free energy when chains with different contour lengths are mixed in the brush. [22,23] As follows from Equation (20), the limited capacity of a mixed "host-guest" superstructure depends on the morphologies of this mixed superstructure, as well as on the morphology of the ab diblock copolymer superstructure (l 0 ab ). Unfortunately, it was possible to obtain analytical expressions for q à appr only for certain of the investigated morphologies.…”

“…To calculate the free energy, analytical self-consistent field theories of cylindrical brushes [23] and the approach of the planar "bridging brush" theory [6,24] will be applied. The structure will be divided into two parts with respect to the presence of free ends.…”

“…According to, [23] we have for these brushes: If b a x, the B-domain can be treated as a convex monodisperse polymer brush xN B , grafted onto a cylinder with radius R 1 at a density of 1/r A/B and the hybrid brushlike structure considered in Appendix A in which short "bridges" with (x -b)N B units and long "tails" with (1 -b)N B units are grafted onto the inner side of a cylinder with radius R 4 at a density of 1/r à . Hence, according to [23] and Appendix A: The interfacial free energy of the mC(A, C) superstructure is expressed as follows:…”