Particle-Mediated Tuning of Defect Stability in Lamellar Block Copolymer Systems

Abstract

We study how colloidal inclusions modify the formation energy of dislocation pairs in lamellar block copolymer systems. Using a hybrid particle/Ginzburg--Landau model, we calculate defect formation energies by comparing defect-free and defect-containing states with and without embedded colloids. Finite-size scaling is used to obtain formation energies in the thermodynamic limit. The effect of colloid insertion depends strongly on particle sizes and surface patterning. Homogeneous particles increasingly stabilize dislocation pairs with increasing particle sizes. Particles larger than one lamellar domain preferentially occupy the dislocation cores, where they replace strained polymer rather than deforming defect-free lamellae. The magnitude of this stabilization depends on surface affinity. Balanced Janus particles instead increase the formation energy, because their competing surface preferences cannot be satisfied simultaneously near the curved core. Varying the patch ratio interpolates between these limits. Surface patterning has little effect for particles smaller than one lamellar domain but changes the formation energy by several tens of $k_BT$ for larger particles. These results provide quantitative guidelines for controlling topological defect stability in lamellar block copolymer systems.