Deciphering orientational symmetry-breaking in nanoscale polymers of anisotropic building blocks

The advent of "patchy" surface-patterning on nanoscale building blocks has enabled the assembly and synthesis of a host of open structures via tuning the size and chemical properties of the patches. Unlike rigid patch-patch interactions in colloids, nanoscale patchy interactions are highly flexible, enabling deformable networks and lattices. In this work, we employ the theoretical framework of entropic bonding to quantify "shape orbitals" and their energetics in patch-connected anisotropic monomers. By explicitly accounting for monomer geometry, patch size, location, and connectivity constraints, we predict their preferred inter-monomer orientations. We bolster this theory with molecular simulation for extended polymeric systems and formulate a scaling law dependent on patch-bond architecture. Using this, we successfully explain tilted symmetry-breaking observed in experimental patchy polymers and 'bundlemers'. This integrated approach underscores the interplay of entropic interactions as a powerful handle in directing patchy assemblies.