Anisotropic Fluctuations and Kinetics of Order-Order and Order-Disorder Phase Transitions of Diblock Copolymers

Author: Qi, Shuyan

Year: 1998

Degree: Dissertation (Ph.D.)

Advisor: Wang, Zhen-Gang

Committee Members: Wang, Zhen-Gang; Cross, Michael Clifford; Yeh, Nai-Chang; Frautschi, Steven C.

Option: Physics

DOI: 10.7907/0d3v-f420

Abstract

Diblock copolymers (DCP) represent the simplest block copolymers that can microphase separate into a variety of ordered phases. While the equilibrium properties of DCP have been studied extensively, the dynamical aspects have been relatively unexplored. In this work, we study the kinetics of order-disorder and order-order transitions in weakly segregated diblock copolymers using a time-dependent Ginzburg-Landau (TDGL) approach. In particular, we investigate the microstructural change as well as the order parameter evolution after a sudden temperature jump from one phase to another. Direct numerical simulation of the TDGL equations shows that depending on the extent of the temperature jump, these transitions often occur in several stages and can involve nontrivial intermediate states. For example, we find that transition from the lamellar phase to the hexagonal cylinder phase goes through a perforated lamellar state within a certain temperature range. A theory is developed based on the anisotropic fluctuations in the ordered phases. These fluctuations play two crucial roles: first, they determine the stability limit of the initial structure, and second, they are responsible for the emergence of new structures, whether they are the final equilibrium states or transient states during the transition. A linear stability analysis allows us to identify the largest fluctuation modes under both equilibrium and nonequilibrium conditions. By combining the order parameter of the initial structure with the largest fluctuation modes into a simplified multimode model (under the single-wavenumber approximation), we are able to describe qualitatively the full nonlinear evolution of the system after sudden temperature jumps beyond the spinodal of the initial phase. Specifically, the analysis reveals that the geometric characteristics of the free energy surface, particularly saddle points and ridge-like features, are responsible for the nontrivial intermediate states on the kinetic pathways. On the basis of this analysis, a generalized kinetic "phase diagram" is constructed, which is able to account for all the different scenarios observed in the numerical simulation. Our results are discussed in connection with available experimental observations.

A closely related problem concerns the nature, stability, and mechanism of formation of the so-called perforated lamellar structure, which generates considerable confusion of controversy in recent years. We show that this structure develops from the anisotropic fluctuations of the lamellar phase when it reaches its spinodal. It is proposed that there can be two different perforated lamellar structures, one based on a hep lattice and one based on a bee lattice, with nearly degenerate free energy. In the framework of a Leibler-type free energy functional, it is shown that the perforated lamellar structure is only pseudostable (corresponding to a saddle point in the free energy surface) in the weak-segregation limit, but can become metastable in the intermediate-segregation regime. Calculation of the fluctuation spectrum of metastable perforated lamellar structures enables us to explain in a simple and consistent manner several puzzling structural data from small-angle neutron scattering studies.

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