GPU-ACCELERATED COMPUTATIONAL STUDY OF SELF-ASSEMBLED BLOCK COPOLYMERS

Abstract

This thesis uses GPU-accelerated theoretical calculations and molecular simulations of the dissipative particle dynamics chain (DPDC) model to study ordered phases of block copolymer melts. The DPDC model is a compressible model of discrete Gaussian chains interacting with the DPD non-bonded potential. It can be used in both particle-based simulations and self-consistent field (SCF) calculations, thus providing a stringent and quantitative assessment of the mean-field approximation inherent in the latter. This work has two parts: (1) parameter-free comparisons between Langevin dynamics (LD) and SCF results for ABC miktoarm star triblock terpolymers and (2) SCF study on the relative stability of Frank-Kasper (FK) phase of conformationally asymmetric diblock copolymers. For ABC stars, LD simulations were performed for several ordered phases including the three-layer lamellae (L3), core-shell cylinders (C3), hierarchical lamellae (HL), and two tiling patterns ([63] and [82.4]). LD simulation parameters were judiciously chosen, finite-size effects were carefully studied, and bulk periods were accurately determined from pressure-tensor analysis. The LD results were then directly compared with SCF calculations based on the same DPDC model. It is found that SCF theory overestimates the bulk periods and the changes in Helmholtz free energy, non-bonded internal energy, and chemical potential from the homopolymer melts, while underestimating the corresponding changes in entropy and pressure, for all phases solely due to the system fluctuations and correlations fully sampled in LD simulations but completely neglected in SCF theory. For diblock copolymers, 12 FK phases were considered: A15, σ, H, Z, pσ, C14, C15, zra-d, and 10-, 9-, 8-, and 6-layers. The Helmholtz free energy per chain and its energetic and entropic contributions were compared among these phases. It is found that the σ phase has the lowest free energy throughout the parameter range studied, with A15 being the closest competitor followed by H. The variations in the Helmholtz free energy and non-bonded internal energy curves of these FK phases are correlated with their average coordination number, and the relative stability of these FK phases is mainly controlled by their A−B repulsion.