On the role of hydrodynamic interactions in block copolymer microphase separation

Abstract

A melt of linear diblock copolymers (AnBm) can form a diverse range of microphase separated structures. The detailed morphology of the microstructure depends on the length of the polymer blocks An and Bm and their mutual solubility. In this paper, the role of hydrodynamic forces in microphase formation is studied. The microphase separation of block copolymer melts is simulated using two continuum methods: dissipative particle dynamics (DPD) and Brownian dynamics (BD). Although both methods produce the correct equilibrium distribution of polymer chains, the BD simulation does not include hydrodynamic interactions, whereas the DPD method correctly simulates the (compressible) Navier Stokes behavior of the melt. To quantify the mesophase structure, we introduce a new order parameter that goes beyond the usual local segregation parameter and is sensitive to the morphology of the system. In the DPD simulation, a melt of asymmetric block copolymers rapidly evolves towards the hexagonal structure that is predicted by mean-field theory, and that is observed in experiments. In contrast, the BD simulation remains in a metastable state consisting of interconnected tubes, and fails to reach equilibrium on a reasonable time scale. This demonstrates that the hydrodynamic forces play a critical part in the kinetics of microphase separation into the hexagonal phase. For symmetric block copolymers, hydrodynamics appears not to be crucial for the evolution. Consequently, the lamellar phase forms an order of magnitude faster than the hexagonal phase does, and thus it would be reasonable to infer a higher viscosity for the hexagonal phase than for the lamellar phase. The simulations suggest that the underlying cause of this difference is that the hexagonal phase forms via a metastable gyroid-like structure, and therefore forms via a nucleation-and-growth mechanism, whereas the lamellar phase is formed via spinodal decomposition.

Communication: Molecular-level insights into asymmetric triblock copolymers: Network and phase development

“…26, whereas the SCFT employed here is based on the framework developed 22 to predict the bridging fraction in molecularly symmetric A 1 BA 2 triblock copolymers with N A1 = N A2 (τ = 1/2). While DPD simulations have also focused on such copolymers, [33][34][35] we extend such simulations to molecularly asymmetric triblock systems varying in τ and containing 1000 molecules ranging in length up to 224 connected beads (each bead is ∼0.33 kDa) by using the parameterization described in Ref. 36 and the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software suite.…”

A theoretical and simulation study of the self-assembly of a binary blend of diblock copolymers

“…To achieve this, the potential of interaction between particles is modified and coupled with a thermostat that consists of dissipative and random forces. It has been applied successfully 19,20 to model microphase assembly of copolymer systems. Each macromolecule is modeled as a chain of beads (particles) linked by harmonic springs with the spring force given by F S ij = −k S r ij , where bead i is connected to bead j and spring constant k S = 4 in our calculations.…”

Phase behavior of monomeric mixtures and polymer solutions with soft interaction potentials

“…Because of the coarse-grained character of the simulation model, in which several molecular groups can be incorporated into one simulation particle, this technique is well suited for simulations on a mesoscopic scale. For example, Groot et al 8,9 used this method to study block copolymer mesophase formation. Jury et al 10 used DPD simulations of a minimal amphiphile model to study amphiphilic mesophases, and Venturoli and Smit 11 simulated the selfassembly of membranes with more realistic molecular parameters.…”