Equilibrium morphology of block copolymer melts

Ohta, Takao; Kawasaki, Kyozi

doi:10.1021/ma00164a028

Cited by 1,106 publications

(1,136 citation statements)

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“…In other words, the mobility of the azobenzene is constrained by an additional long-range interaction potential, which gives rise to an additional free-energy term F L . To account for the nonlocal character of this long-range interaction, we have introduced a Green's function Gðr; r′Þ that satisfies ∇ 2 Gðr; r′Þ = −δðr − r′Þ (30). As a result, the long-range interaction term F L becomes…”

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confidence: 99%

“…The formation of hexagonal arrays of cis-rich domains implies the presence of a long-range interaction between these domains. In the case of diblock copolymer blends, it has been shown that this long-range interaction results from the connectivity of the two different isomers in the polymer chain (30). As this interaction is isotropic, the domains try to maximize the distance between each other, which causes the formation of a hexagonally ordered structure in two dimensions.…”

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confidence: 99%

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Instability-induced pattern formation of photoactivated functional polymers

Galinski

Ambrosio

Maddalena

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

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Since the pioneering work of Turing on the formation principles of animal coat patterns [Turing AM (1952) Phil Trans R Soc Lond B 237(641):37-72], such as the stripes of a tiger, great effort has been made to understand and explain various phenomena of selfassembly and pattern formation. Prominent examples are the spontaneous demixing in emulsions, such as mixtures of water and oil [Herzig EM, et al. (2007) Nat Mater 6:966-971]; the distribution of matter in the universe [Kibble TWB (1976 A zobenzenes, which belong to photochromic materials, are switchable two-state systems with distinct optical, electronic, magnetic, and/or electrochemical properties that can be reversibly converted by irradiation. Since the discovery of the unique photochemical properties of azobenzene in 1937 (1), azobenzenes have been mainly used in the chemical industry. Only recently, after studies of the molecular physics of the photoisomerization of azo dyes have revealed that the photoisomerization reaction occurs on the timescale of a few picoseconds (2, 3), azobenzenes came back into focus as potential photoswitchable materials (4, 5). Azobenzenes have been investigated in terms of ultrafast spectroscopy (4, 6, 7), mechanoisomerization (8), the effect of slow photons (9), two-photon absorption (10) and laser-induced periodic surface structuring (11-17). The latter describes the phenomenon of Turing pattern formation on the surface of an azopolymer film upon exposure to UV or visible light. The outstanding feature of this photoactivated pattern formation is its dependence on both the light's intensity and polarization, which allows for the formation of a large variety of Turing patterns, such as hexagonal cells, parallel stripes, or turbulent structures. Several attempts have been made to understand the underlying physics that controls these various forms of pattern formation (18-23), but a sound picture is still lacking.In this paper, we demonstrate that the photoactivated pattern formation on azopolymer films can be entirely explained by the physical concept of phase separation of two coexistent immiscible phases in the polymer. A phase separation can be briefly characterized as follows: A (meta)stable configuration subjected to an external perturbation (temperature, light) becomes unstable. The unstable system tends to equilibrate by the formation of two immiscible phases. These two phases tend to separate leading to a spatial reorganization of the system.In the case of azopolymers, the instability is caused by the random optical excitation of the isomers in the polymer film. Excited by a photon of suitable energy (λ = 200-550 nm), the azobenzene isomer undergoes a structural transition by inversion or rotation (3), called photoisomerization, and relaxes either in the trans or cis ground state. The symmetry of the system is broken. The principle of the photoisomerization reaction for one azobenzene isomer is illustrated in Fig. 1A. The ground-state energy is characterized by an asymmetric double-well potential (Fig. 1A), containing...

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confidence: 99%

mentioning

confidence: 99%

Instability-induced pattern formation of photoactivated functional polymers

Galinski

Ambrosio

Maddalena

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

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“…The corresponding free energy was derived by Leibler [16] in the weak segregation limit (close to T ODT ), and later extended by Ohta and Kawasaki [17] to the strong segregation regime. If the temporal evolution of ψ occurs through advection by a flow field as well as through local dissipation driven by free energy reduction, ψ obeys a time dependent Ginzburg-Landau equation [18,7],…”

Section: Mesoscopic Model Equations and Lamellar Phasesmentioning

confidence: 99%

Lamellar Phase Stability in Diblock Copolymers under Oscillatory Shear Flows

Chen

Viñals

2002

Macromolecules

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A mesoscopic model of a diblock copolymer is used to study the stability of a uniform lamellar phase under a reciprocating shear flow. Approximate viscosity contrast between the microphases is allowed through a linear dependence of the (Newtonian) shear viscosity on monomer composition. We first show that viscosity contrast does not affect the composition of the base lamellar phase in an unbounded geometry, and that it only couples weakly to long wavelength perturbations. A perturbative analysis is then presented to address the stability of uniform lamellar structures under long wavelength perturbations by self-consistently solving for the composition and velocity fields of the perturbations. Stability boundaries are obtained as functions of the physical parameters of the polymer, the parameters of the flow and the initial orientation of the lamellae. We find that all orientations are linearly stable within specific ranges of parameters, but that the perpendicular orientation is generally stable within a larger range than the parallel orientation. Secondary instabilities are both of the Eckhaus type (longitudinal) and zig-zag type (transverse). The former is not expected to lead to re-orientation of the lamella, whereas in the second case the critical wavenumber is typically found to be along the perpendicular orientation.

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“…Such problem first appeared in the liquid drop model of the atomic nuclei proposed by Gamow in 1928 [13] and then developed by other researchers [3,9], and it is also relevant in some models of diblock copolymer melts [5,17]. In [15,16] (see also [6]) the authors showed that global minimizers of (1) exist if the volume m is small, and do not exist if the volume is large enough.…”

Section: Introductionmentioning

confidence: 99%

Rigidity of critical points for a nonlocal Ohta–Kawasaki energy

2017

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We investigate the shape of critical points for a free energy consisting of a nonlocal perimeter plus a nonlocal repulsive term. In particular, we prove that a volume-constrained critical point is necessarily a ball if its volume is sufficiently small with respect to its isodiametric ratio, thus extending a result previously known only for global minimizers.We also show that, at least in one-dimension, there exist critical points with arbitrarily small volume and large isodiametric ratio. This example shows that a constraint on the diameter is, in general, necessary to establish the radial symmetry of the critical points.

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Equilibrium morphology of block copolymer melts

Cited by 1,106 publications

References 4 publications

Instability-induced pattern formation of photoactivated functional polymers

Instability-induced pattern formation of photoactivated functional polymers

Lamellar Phase Stability in Diblock Copolymers under Oscillatory Shear Flows

Rigidity of critical points for a nonlocal Ohta–Kawasaki energy

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