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Conformational asymmetry has recently been shown to drive the symmetry breaking required to form Frank-Kasper mesophases in linear AB diblock copolymers. In this work, we experimentally demonstrate that this physical origin of complex spherical order is augmented through the architectural asymmetry of corresponding branched ABn miktoarm block copolymers. As previous arduous preparatory routes have limited access to these unique architectures, our preliminary efforts have concentrated on developing general synthetic methods that precisely control the number of linked arms using controlled polymerization and click chemistry and a specialized molecule that forms the junction between the blocks. Preliminary results have prepared an AB3 molecular junction through chemical modification of methyl α-D-glucopyranoside via iterative protection and deprotection steps at the primary and secondary hydroxyl groups, which allows click attachment of the A block and growth of three B-arms via Cu(0)-mediated atom transfer radical polymerization. Our current investigations focus on the block polymer system, poly(trifluoroethyl methacrylate)-block-poly(lauryl acrylate) (PTFEMA-PLAc), which anticipatedly has a high conformational asymmetry parameter due to the low statistical segment length of PLAc and high density of PTFEMA. The phase behavior of a corresponding series of compositionally asymmetric block polymers of varied molar mass and volume fraction of AB3 architecture will be studied and compared to their corresponding linear AB analogues. This strategy will also be extended to other monosaccharides to produce varied arm number diblocks in order to show that the ordered morphologies displayed are highly dependent on architecture.