Simulation Studies of Correlations, Dynamics and Phase Transitions in Diblock Copolymer Melts

Abstract

The limitations of approximate theories of diblock copolymers have motivated the computational study of these materials. Recent breakthroughs in the analysis of coarse-grained simulation models have led to an improved level of accuracy and consistency in the modeling of symmetric diblock copolymers. Simple bead-spring simulation models with a few parameters, f (relative volume fraction), χN (inter- action strength), and N (a measure of polymer-polymer overlap) can predict the behaviors of diblock copolymers. The work presented in thesis focuses attention on the study of asymmetric diblock copolymers and the study of dynamics of symmetric copolymers. Composition fluctuations in the disordered phase of asymmetric diblock copoly- mers have been investigated over a range of values of volume fraction, f , and fluctu- ation parameter, N . Results for the structure factor are shown to obey a principle of corresponding states, which states that equivalent results should be obtained for systems with equal values of f , χN and N . An empirical relationship is presented for the dependence of the peak in the structure factor of symmetric and moderately asymmetric diblock copolymers upon these state parameters. Coarse-grained simulation models have been used to study dynamical properties and linear viscoelastic properties of symmetric diblock copolymers. Among dynam- ical properties measured are diffusion, end-to-end autocorrelation, Van Hove relax- ation time, and stress relaxation modulus. The evolution of these properties has been studied from χN = 0 all the way up to the value (χN )ODT at the order-disorder tran- sition (ODT). A simple description is provided for the behavior of the intermediate structure factor S(q, t), and existing theoretical predictions for G(t) are compared to simulation results. Locations of order-disorder transitions have been identified for asymmetric di- block copolymers over a range of values of f and N . Simulation results for (χN )ODT for several models are shown to obey the principle of corresponding states and exceed self-consistent field (SCFT) predictions by an amount that increases systematically with decreasing N . SCFT predictions for the free energy in a hexagonal ordered phase are shown to be quite accurate, in contrast to the inaccuracy of predictions for the free energy in the disordered phase near the ODT. New methods are introduced to identify gyroid-disorder transitions, which are found to pose a particular technical challenge.