Ren, Yongzhi

Block copolymers are amphiphilic macromolecules, which consist of multiple incompatible parts. Although block copolymers may differ in their microscopic interactions, their phase behaviors share many similarities. In equilibrium, block copolymers self-assemble into various spatially modulated phases with long-range order whose free energy may differ only a small fraction of thermal energy per molecule. 
This characteristic makes the understanding of the structure formation both interesting and challenging. In this thesis, we investigate the structure formation of block copolymers on the basis of the free-energy landscape. We develop numerical schemes to investigate two important quantities: One is the thermodynamic
forces that drive the formation of the patterns. The other is the Onsager coefficient that translates the thermodynamic forces into the flow of the particles. 
The calculation of the thermodynamic forces is indirect and computational demanding in particle-based simulations. The most efficient approach is probably the field-theoretic umbrella sampling method. We propose an equivalent approach in the framework of the self-consistent field theory (SCFT), which significantly improves the computational efficiency and accuracy.
The Onsager coefficient connects the single-chain dynamics with the co-operative movement of many molecules. An analytical form of the Onsager coefficient is difficult to obtain. We propose a numerical scheme to directly measure Onsager coefficients in particle-based simulations. To be specific, we measure the Onsager coefficient in symmetric homopolymer blends. We find that the single polymer dynamics and the kinetics of collective variables are highly correlated.
As a result, on very short time and length scales, the Onsager coefficient is a time-dependent variable, which differs from the prediction of the Rouse model.
The structure formation of block copolymers is an important and multi-faceted research topic. We focus on the structure formation process in a quasi-two-dimensional system of symmetric diblock copolymer melts. When the system is quenched far below the order-disorder transition temperature, the relaxation of the structure towards long-range order is very protracted because it
involves numerous thermally activated processes that alter the topology of the microphase-separated morphology. The free-energy landscape of the system is rugged and it has been likened to that of glass-forming systems.Using large-scale particle-based simulations we study the kinetics of structure formation in symmetric lamella-forming diblock copolymers after a quench from the disordered state. We characterize the ordering process by the correlation length of the lamellar structure and its Euler characteristics. The latter
integral-geometry morphological measure indicates changes of the structure topology and allows us to identify defects.
The density fields of snapshots of the particle-based simulations are used as starting values for SCFT calculations. The latter converge to a local, metastable minimum of the free-energy landscape. This combination of particle-based simulation
and SCFT calculations allows us to relate an instantaneous configuration of the particle-based model to a corresponding metastable free-energy minimum of SCFT, and we typically observe that a change of the metastable state is associated with a change of the Euler characteristics of the particle-based morphology, i.e., changes of free-energy basins are correlated to changes of the
domain topology.
Additionally, we employ the string method in conjunction with the SCFT to study the free-energy barriers and minimum free-energy paths (MFEP) involved in changes of the domain topology.
By a combination study of the free-energy landscape and the Onsager coefficient that connects the thermodynamic force with the polymer dynamics, we obtain a complete description of the density evolution dynamics. By a comparison to the particle-based simulations, our findings capture essential properties which allow us to predict the kinetics of structure formation in many nanostructure-forming systems

Georg-August-University Göttingen

Kinetics of structure formation in block copolymers

https://ediss.uni-goettingen.de/bitstream/11858/00-1735-0000-002E-E3CA-5/1/Thesis2.pdf

Kinetics of structure formation in block copolymers

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Georg-August-University Göttingen