Ordering Dynamics of Directed Self-Assembly of Block Copolymers in Periodic Two-Dimensional Fields

Abstract

The ordering dynamics of directed self-assembly of cylinder-forming diblock copolymers is studied by cell dynamics simulations. The directing field, mimicking chemically or topologically patterned substrates, is in the form of hexagonally arranged potential wells attractive to minority blocks. Time evolution of the defect concentration is used to characterize the ordering dynamics of the self-assembled cylindrical structures of the block copolymers. When the period of the external potential, L s , is a small integer multiple of the cylinder-to-cylinder distance, L 0 , of the block copolymer microphase, the defect concentration decays exponentially. The defect annihilation becomes slower as L s is increased, and eventually, the exponential decay law is broken. When the ratio L s /L 0 is a square root of an integer, large polycrystalline grains with different orientations are observed. The results are consistent with available experimental and theoretical results.

Perfectly Ordered Patterns via Corner-Induced Heterogeneous Nucleation of Self-Assembling Block Copolymers Confined in Hexagonal Potential Wells

“…Specifically the defects are identified by the Delaunay triangular algorithm. 9 The corresponding Delaunay triangular plots are given for the three morphologies in Figure 1. Consequently, the defect concentrations, defined as f DF = n DF /n MD × 100% where n DF and n MD are the total numbers of defects and microdomains, respectively, are determined as 18.65%, 0.70%, and 0 for the three samples of ϕ̅ C = 0.100, 0.050, and 0.035 at the late stage, respectively.…”

“…8 The presence of this efficiency limit can be attributed to the characteristics of the dislocation pairs, as demonstrated in the dynamic simulations of time-dependent Ginzburg−Landau (TDGL) theory. 9,10 In addition, the TDGL simulations reveal that the underlying mechanism for the presence of the limit of directing efficiency is the spontaneous ordering of the system via spontaneous nucleation or spinodal kinetics.…”

Pattern formation mechanisms in sphere-forming diblock copolymer thin films

“…The process of phase separation and the kinetics of ordering in different two-dimensional systems have been studied through different phase field models [17][18][19][20]. In particular, simulations of hexagonal systems with a Cahn-Hilliard model were found to be in good agreement with experimental data for block copolymer thin films.…”

“…In recent years, such models have been used to study a variety of systems under different conditions, including shear and other external fields, curvature and patterned substrates, and pattern formation in 3D [20,33,[36][37][38][39][40]. In this work, the free energy parameters were selected to capture the desired symmetry and segregation strength of the block copolymer hexagonal phase [20,34,35]. More details about the equilibrium phase diagram and the different spinodals can be found elsewhere [34,35,[41][42][43][44].…”

Hexagonal phase ordering in strongly segregated copolymer films

“…Li et al [43] also performed cell dynamics simulations with and without a prescribed driving potential. Without the driving force, they see a two stage process characterized by rapid t −1/3 defect coarsening initially followed by slower t −1/5 coarsening at late stages.…”