Microphase separation of diblock copolymer induced by directional quenching

Zhang, Hongdong; Zhang, Jianwen; Yang, Yuliang; Zhou, Xuedong

doi:10.1063/1.473165

Cited by 38 publications

(40 citation statements)

References 25 publications

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“…14 Equations ͑1͒ and ͑2͒ have been the basis for several theoretical studies of dynamic issues in block copolymers. [15][16][17][18][19][20] In the ordered state, it is convenient to separate the order parameter into an average part and a fluctuating part,…”

Section: ͑3͒mentioning

confidence: 99%

Transient instability upon temperature quench in weakly ordered block copolymers

Wang

1999

The Journal of Chemical Physics

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We report a novel transient instability upon temperature quench in weakly ordered block copolymer microphases possessing a soft direction or directions, such as the lamellar and hexagonal cylinder ͑HEX͒ phases. We show that reequilibration of the order parameter is accompanied by transient long wavelength undulation of the layers or cylinders-with an initial wavelength that depends on the depth of the temperature quench-that eventually disappears as the structure reaches its equilibrium at the new temperature. Such undulation leads to a transient transverse broadening of the scattering peaks near the Bragg positions. We argue that this instability might be responsible for the experimentally observed unusual ordering dynamics of the HEX phase of a diblock copolymer after quenching from the disordered state.

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Section: ͑3͒mentioning

confidence: 99%

Transient instability upon temperature quench in weakly ordered block copolymers

Wang

1999

The Journal of Chemical Physics

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“…A great deal of simulation work on copolymer melts has been done with timedependent Ginzburg-Landau approaches [364][365][366][367][368][369][370][371][372][373][374][375][376][377][378]. These studies have mostly addressed dynamical questions, i.e., the kinetics of ordering, disordering processes in pure melts [366][367][368][369][370][371][372][373][374] and in mixtures containing copolymers [375][376][377][378].…”

Section: 25)mentioning

confidence: 99%

Theory and Simulation of Multiphase Polymer Systems

Schmid

2011

Handbook of Multiphase Polymer Systems

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The theory of multiphase polymer systems has a venerable tradition. The 'classical' theory of polymer demixing, the Flory-Huggins theory, was developed in the 1940s [1,2]. It is still the starting point for most current approaches -be they improved theories for polymer (im)miscibility that take into account the microscopic structure of blends more accurately, or sophisticated field theories that allow to study inhomogeneous multicomponent systems of polymers with arbitrary architectures in arbitrary geometries. In contrast, simulations of multiphase polymer systems are quite young. They are still limited by the fact that one must simulate a large number of large molecules in order to obtain meaningful results. Both powerful computers and smart modeling and simulation approaches are necessary to overcome this problem.In the limited space of this chapter, we can only give a taste of the state-of-the-art in both areas, theory and simulation. Since the theory has reached a fairly mature stage by now, many aspects of it are covered in textbooks on polymer physics [3][4][5][6][7][8][9]. The information on the state-of-the art of simulations is much more scattered. This is why we have put some effort into putting together a representative list of references in this area -which is of course still far from complete.The chapter is organized as follows. In Section II, we briefly introduce some basic concepts of polymer theory. The purpose of this part is to make the chapter accessible to readers who are not very familiar with polymer physics; it can safely be skipped by the others. Section III is devoted to the theory of multiphase polymer systems. We recapitulate the Flory-Huggins theory and introduce in particular the concept of the Flory interaction parameter (the χ parameter), which is a central ingredient in most theoretical descriptions of multicomponent polymer systems. Then we focus on one of the most successful mean-field theories for inhomogeneous (co)polymer blends, the self-consistent field theory. We sketch the main idea, discuss various Handbook of Multiphase Polymer Systems, First Edition. Edited by Abderrahim Boudenne, Laurent Ibos, Yves Candau, and Sabu Thomas.

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“…Such a phase separation can be regarded as local polarization of the order parameter and it is consistent with the conservation of the order parameter, i.e., Eq. (8). Moreover, the complexity of patterns increases as the control parameter R increases, and a careful examination reveals that the ordered state patterns can be regularly classified by a pair of integers [l, m] (l = 1-4), as shown in Fig.…”

Section: Numerical Aspectsmentioning

confidence: 99%

“…The occurrence of mirror images is due to the conservation of the order parameter, i.e., Eq. (8). Because of such a constraint, the phase separation can only occur as the order parameter polarization with respect to the (r, θ ) plane.…”

Section: Controlled Pattern Selection and Competitionmentioning

confidence: 99%

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Geometry and boundary control of pattern formation and competition

Guan

Lai

Wei

2003

Physica D: Nonlinear Phenomena

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This paper presents the effective control of the formation and competition of cellular patterns. Simulation and theoretical analyses are carried out for pattern formation in a confined circular domain. The Cahn-Hilliard equation is solved with the zero-flux boundary condition to describe the phase separation of binary mixtures. A wavelet-based discrete singular convolution algorithm is employed to provide high-precision numerical solutions. By extensive numerical experiments, a set of cellular ordered state patterns are generated. Theoretical analysis is carried out by using the Fourier-Bessel series. Modal decomposition shows that the pattern morphology of an ordered state pattern is dominated by a principal Fourier-Bessel mode, which has the largest Fourier-Bessel decomposition amplitude. Interesting modal competition is also observed. It is found that the formation and competition of cellular patterns are effectively controlled by the confined geometry and boundary condition.

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Microphase separation of diblock copolymer induced by directional quenching

Cited by 38 publications

References 25 publications

Transient instability upon temperature quench in weakly ordered block copolymers

Transient instability upon temperature quench in weakly ordered block copolymers

Theory and Simulation of Multiphase Polymer Systems

Geometry and boundary control of pattern formation and competition

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