Structure and Dynamics of Micelle-Forming Asymmetric Diblock Copolymer Chains

Abstract

Experiments on micelle-forming asymmetric diblock copolymer melts have shown the existence of a liquid-like state of micelles at temperatures greater than the order-disorder transition temperature (ODT).These micelles have been hypothesized to appear at an even greater temperature called the critical micelle temperature (CMT). The regime between the CMT and ODT, called the disordered micellar regime, has been known to affect the formation of many exotic phases like the Frank-Kasper and the Laves phases due to its slow dynamics. Self-Consistent Field Theory (SCFT), one of the most commonly employed theoretical tools, only predicts the appearance of micelles in stationary and periodic configurations, and hence is incapable of capturing the disordered micellar regime. Some previous theoretical studies do provide predictions of the structural properties of the disordered micelles, however, these studies used SCFT predictions of free energies of isolated micelles to approximate the free energy of disordered micelles. We have used coarse-grained classical molecular dynamics to simulate melts of asymmetric diblock copolymer chains having a minority block volume fraction, $f = 0.125$.At high $\chi N$, where $\chi$ is the Flory-Huggins interaction parameter and $N$ is the degree of polymerization, SCFT predicts the formation of ordered micellar phases for this volume fraction. Our simulations show the existence of a disordered micellar regime for $\chi N$ above the $\cNso$, where $\cNso$ is the value of $\chi N$ corresponding to the ODT predicted from SCFT. We study melts having two significantly different invariant degree of polymerization, $\overline {N} = 960$ and $3820$, that span the disordered homogenous phase, disordered micellar regime, and the ordered body-centered cubic (BCC) phase. The first part of this thesis pertains to analyzing the evolution of the structure of these melts as a function of $\chi N$.By using a cluster identification algorithm, we show that micelle-like clusters appear at a CMT with the appearance being much more sudden for the higher $\overline {N}$ simulations. Moreover, micelles appear when $\chi N$ is near $\cNso$. We also show that the signature of the presence of disordered micelles in scattering experiments (SAXS and SANS) arises at a somewhat higher $\chi N$ as compared to $\cNso$. Comparisons of the free energy derivative, peak wavenumber, micelle aggregation number and the free chain fraction obtained from simulations with these quantities calculated from SCFT show close agreement, thus emphasizing similarities in the structure of the disordered micelles and the ordered micelles predicted by SCFT at the same $\chi N$. Analysis of the shape of the identified clusters also reveal a rapid formation/breaking of bridges between micelles present in both disordered and ordered phases. The latter part of this thesis considers the dynamics of these melts, namely single chain diffusion and structural relaxation.Signatures of the sudden appearance of micelles at the CMT is also reflected in the analysis of the dynamic properties as a sudden slowdown in the molecular relaxation and an even more significant slow down in the structural relaxation. We measure the rate at which polymers are expelled from micelles, and relate this to the polymer diffusivity.