Modeling and Computer Simulation of Block Copolymer/Nanoparticle Composites

Abstract

Molecular dynamics computer simulation is used to explore the phase behavior and structural properties of block copolymers and block copolymer nanocomposites. Block copolymers microphase separate into ordered structures with domains on a nanometer length scale, which can then be used as a template for nanoparticles. This research provides insight into the fundamental physics that govern phase behavior and properties of these materials.

We first focus on the case of neat diblock copolymers. We performed discontinuous molecular dynamics simulation to study the phase behavior of diblock copolymers modeled as chains of tangent hard spheres with square shoulder repulsions between unlike species as a function of chain length, volume fraction (f) and interaction strength (χ). The location of the order-disorder transition for a symmetric copolymer is close to the predictions of Fredrickson and Helfand. Our simulation results for packing fractions of 0.35, 0.40 and 0.45 and chain lengths 10 and 20 are summarized in phase diagrams which display disordered, lamellae, perforated lamellae, cylindrical and BCC spherical phases in the χN vs. f plane. These phase diagrams are consistent with phase diagrams from other simulation studies. Contrary to theoretical predictions we observe the perforated lamellar phase near regions of predicted gyroid stability, and the spherical phase only in the systems with high packing fraction and long chain length. These discrepancies may be due to the short chain lengths considered, as they are less evident in the 20-bead chains than the 10-bead chains. We examine the structural spacing of the microphases and the variation of that spacing with χN. We also examine the internal energy and entropy and their variation with χN. Our results are consistent with self-consistent field theory results for the strong segregation limit.

We then extend our simulations to study the phase behavior and properties of diblock copolymer/nanoparticle composites. The nanoparticles are modeled as hard spheres with a square shoulder repulsion with one of the copolymer blocks. The resulting phase diagrams are presented for composites containing nanoparticles of various sizes and interaction strengths, and include lamellae, perforated lamellae, cylinders and disordered phases. Composites containing large nanoparticles also exhibit two-phase coexistence between different copolymer phases, or between a copolymer phase and a nanoparticle phase, depending upon the nanoparticle interaction strength. We also present concentration profiles perpendicular to the lamellar interface for nanoparticles of different sizes and interaction strengths. Neutral nanoparticles concentrate at the interface between copolymer domains while interacting nanoparticles concentrate within the favorable domain. The larger nanoparticles are more easily localized, but have less impact on the copolymer concentration profiles. The lamellar spacing increases with nanoparticle volume fraction for interacting nanoparticles, but decreases with nanoparticle size. The locations of the phase transitions are in qualitative agreement with theoretical predictions, but the concentration profiles are inconsistent with theoretical predictions. The variation of the spacing with nanoparticle volume fraction is consistent with experimental data.