Monte Carlo simulations of the morphology of ABC star polymers using the diagonal bond method

The microphase-separated morphology of ABC three-arm star-shaped copolymers with arm-length ratio 1:1:x is investigated by a recently proposed simulation method, the diagonal bond method. Five kinds of two-dimensional (cylindrical) phases, three kinds of lamellar-type phases and two kinds of continuous matrix phases are discovered. The phase diagram is presented: The progression of the morphologies as a function of x is the following: lamella + sphere; five polygonal cylinders, [8.8.4], [6.6.6], [8.6.4; 8.6.6], [10.6.4; 10.6.4; 10.6.6], [12.6.4]; perforated layer; lamella + cylinder; columnar piled disk; lamella-in-sphere. Two remarkable features of ABC star polymer systems are found: first, in all phases junction point monomers gather on lines where three interfaces meet, and second, the section of the cylindrical phase becomes the tessellation of even-numbered polygons. The free energy of the system is also calculated in the strong segregation limit for four kinds of simple phases, and the results are consistent with the simulations.