Dynamics Simulations of Microphase Separation in Block Copolymers

DYNAMICS SIMULATIONS OF MICROPHASE SEPARATION IN BLOCK COPOLYMERS 

XuEHAo He Xuejin Li, Peng Chen, and Haojun Liang  

Systematic study of the segregation behaviors of block copolymers is necessary for an in-depth understanding of the formation of new phase structures and the transition mechanism of various phase structures, besides being 

In the field of macromolecular simulation, the coarsegrained (CG) method, based on a viewpoint that the phase behaviors of various polymers depend on a few parameters and not sensitively on the details of molecular structures, is often used. The general property of phase separation only depends on the chain length and Flory interaction in the mean field. For example, the transition point of phase separation for the symmetric diblock copolymer is /A 10.5 [12]. A specific polymer chain can be represented using different CG models. For example, a polystyrene-fc-polyethyleneoxide (PS- -PEO) chain can be represented using lattice model, off-lattice model, or even string model (Fig. 15.2). 

The CG method not only provides general models for studying a class of block copolymers but also conducts efficient algorithms for simulation. In this chapter, we overview the theoretical and computational approaches toward the simulations of dynamics of microphase separation of block copolymers with the focus on the recent contributions applying Monte Carlo (MC), dissipation particle dynamics 

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MSI) that uses the same time-dependent Ginzburg Landau kinetic equation as CDS, but starts from (arbitrary) bead models for polymer chains. The methods have been summarized elsewhere. Examples of recent applications include LB simulations of viscoelastic effects in complex fluids under oscillatory shear,DPD simulations of microphase separation in block copoly-mers ° and mesophase formation in amphiphiles, and cell dynamics simulations applied to block copolymers under shear. - DPD is able to reproduce many features of analytical mean field theory but in addition it is possible to study effects such as hydrodynamic interactions. The use of cell dynamics simulations to model non-linear rheology (especially the effect of large amplitude oscillatory shear) in block copolymer miscrostructures is currently being investigated. ... 

Finally, an alternative level of coarse-graining involves the use of DPD (dissipative particle dynamics) models [35]. These have been used successfully in simulations of microphase separation for block copolymers [36, 37] and in a number of other areas [38, 39]. 

Zhang LS, Sevink A, Schmid F. Hybrid lattice Boltz-mann/dynamic self-consistent field simulations of microphase separation and vesicle formation in block copolymer systems. Macromolecules 2011 44 9434. 

The viscoelastic effects on the morphology and dynamics of microphase separation of diblock copolymers was simulated by Huo et al. [ 126] based on Tanaka s viscoelastic model [127] in the presence and absence of additional thermal noise. Their results indicate that for

bulk modulus of both blocks, the area fraction of the A-rich phase remains constant during the microphase separation process. For each block randomly oriented lamellae are preferred. 

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