Interfaces and grain boundaries of lamellar phases

Villain-Guillot, Simon; Netz, Roland R.; Andelman, David; Schick, M.

doi:10.1016/s0378-4371(97)00476-7

Cited by 14 publications

(21 citation statements)

References 10 publications

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“…Twist grain boundaries in the lamellar phase have been investigated within self-consistent field theory for diblock copolymers 28 and observed experimentally 29 to have a structure similar to Scherk's minimal surface. Tilt grain boundaries in the lamellar phase, where the normals of the lamellae of the two grains define a plane perpendicular to the boundary, have been shown within a Ginzburg-Landau theory to be chevron-shaped at small tilt angles and omega-shaped at large tilt angles, 22,27 in agreement with experimental results. 30 The nucleation of defects in the gyroid cubic mesophase has recently been observed in Lattice-Boltzmann simulations.…”

Section: Introductionsupporting

confidence: 77%

“…In amphiphilic systems many kinds of interfaces occur: between two ordered phases, between ordered and disordered phases, and between two grains of the same ordered phase which differ by their spacial orientation. Recently, interfaces between coexisting lamellar, hexagonal, and disordered phases, [21][22][23] interfaces between lamellar and gyroid phases, 24,25 dislocations in cubic phases, 26 and grain boundaries in the lamellar phase 22,27,28 have been studied. Twist grain boundaries are interfaces between two grains of the same phase which differ only by a rotation around an axis perpendicular to the grain boundary.…”

Section: Introductionmentioning

confidence: 99%

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Twist grain boundaries in cubic surfactant phases

Belushkin

Gompper

2009

The Journal of Chemical Physics

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Twist grain boundaries in bicontinuous cubic surfactant phases are studied by employing a Ginzburg-Landau model of ternary amphiphilic systems. Calculations are performed on a discrete real-space lattice with periodic boundary conditions for the lamellar L ␣ , gyroid G, diamond D, and the Schwarz P phases for various twist angles. An isosurface analysis of the scalar order parameter reveals the structure of the surfactant monolayer at the interfaces between the oil-rich and water-rich regions. The curvature distributions show that the grain boundaries are minimal surfaces. The interfacial free energy per unit area is determined as a function of the twist angle for the G, D, P, and lamellar phases using two complementary approaches: the Ginzburg-Landau free-energy functional and a geometrical approach based on the curvature energy of a monolayer. For the L ␣ , G, and D phases the interfacial free energy per unit area is very small, has the same order of magnitude, and exhibits a nonmonotonic dependence on the twist angle. The P phase is found to be unstable with respect to the nucleation of grain boundaries.

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Section: Introductionsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Twist grain boundaries in cubic surfactant phases

Belushkin

Gompper

2009

The Journal of Chemical Physics

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“…Assuming for simplicity 1d lamellar modulations that are symmetric around φ 0 = 0, we use for φ the single-mode ansatz φ(x) = φ 0 + φ q cos(q 0 x), where the spatial average of φ(x) for the symmetric case is φ 0 = φ = 0, and φ q is its modulation amplitude, while ρ(x) is taken without any spatial modulations and is equal to its spatial average, ρ 0 = ρ [43][44][45][46]. Taking a variation with respect φ q , it can be shown that for the most dominant mode, q = q 0 , its amplitude φ q satisfies:…”

Section: Bulk Propertiesmentioning

confidence: 99%

Interfacial Phenomena of Solvent-Diluted Block Copolymers

Cohen

Andelman

2013

Macromolecules

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A phenomenological mean-field theory is used to investigate the properties of solvent-diluted diblock copolymers (BCP), in which the two BCP components (A and B) form a variety of phases that are diluted by a solvent (S). Using this approach, we model mixtures of di-block copolymers and a solvent and obtained the corresponding critical behavior. In the low solvent limit, we find how the critical point depends on the solvent density. Due to the non-linear nature of the coupling between the A/B and BCP/solvent concentrations, the A/B modulation induces modulations in the polymer-solvent relative concentration with a double wavenumber. The free boundary separating the polymer-rich phase from the solvent-rich one is studied in two situations. First, we show how the presence of a chemically patterned substrate leads to deformations of the BCP film/solvent interface, creation of terraces in lamellar BCP film and even formation of multi-domain droplets as induced by the patterned substrate. Our results are in agreement with previous self-consistent field theory calculations. Second, we compare the surface tension between parallel lamellae coexisting with a solvent phase with that of a perpendicular one, and show that the surface tension has a nonmonotonic dependence on temperature. The anisotropic surface tension can lead to deformation of spherical BCP droplets into lens-shaped ones, together with re-orientation of the lamellae inside the droplet during the polymer/solvent phase separation process in agreement with experiment.

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“…[21] Furthermore, interfacial properties between different coexisting phases have been investigated using a similar model. [22][23][24] In the above expression for the free energy F, the f-leaflet has a dominant wavenumber q* 0 ¼ 1= ffiffi ffi 2 p , and so has the y-leaflet with q* y ¼ ffiffiffiffiffiffiffiffiffiffiffi C=2D p . The modulation wavenumbers and amplitudes of the two monolayers coincide when D = C = 1 and the average compositions are the same.…”

Section: Modelmentioning

confidence: 99%

Coupled Modulated Bilayers: A Phenomenological Model

2009

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We propose a model addressing the coupling mechanism between two spatially modulated monolayers. We obtain the mean-field phase diagrams of coupled bilayers when the two monolayers have the same preferred modulation wavelength. Various combinations of the monolayer modulated phases are obtained and their relative stability is calculated. Due to the coupling, a spatial modulation in one of the monolayers induces a similar periodic structure in the second one. We have also performed numerical simulations for the case when the two monolayers have different modulation wavelengths. Complex patterns may arise from the frustration between the two incommensurate but annealed structures.

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Interfaces and grain boundaries of lamellar phases

Cited by 14 publications

References 10 publications

Twist grain boundaries in cubic surfactant phases

Twist grain boundaries in cubic surfactant phases

Interfacial Phenomena of Solvent-Diluted Block Copolymers

Coupled Modulated Bilayers: A Phenomenological Model

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