The lamellar-disorder interface: one-dimensional modulated profiles

Villain-Guillot, Simon; Andelman, David

doi:10.1007/s100510050355

Cited by 18 publications

(12 citation statements)

References 8 publications

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“…Moreover, the phase diagrams for µ + = 0 are analogous to those describing the phase separation of two-component mixtures in fluid bilayers which also exhibits tricritical behavior [42] and other related amphiphilic systems [43][44][45][46][47]. However, in the former case of two-component bilayers the concentration difference between the two leaflets of the membrane is linearly coupled to the curvature of the bilayer and the difference in the chemical potential is not taken into account.…”

Section: Relation To Other Modelsmentioning

confidence: 88%

Adhesion-induced lateral phase separation in membranes

Komura

Andelman²

2000

The European Physical Journal E

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Adhesion between membranes is studied using a phenomenological model, where the intermembrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both adhesion of two flexible membranes and to adhesion of one flexible membrane onto a second membrane supported on a solid substrate. We mainly consider the case where the sticker molecules form bridges and adhere directly to both membranes. The calculated mean-field phase diagrams show an upward shift of the transition temperature indicating that the lateral phase separation in the membrane is enhanced due to the coupling effect. Hence the possibility of adhesion-induced lateral phase separation is predicted. For a particular choice of the parameters, the model exhibits a tricritical behavior. We also discuss the non-monotonous shape of the inter-membrane distance occurring when the lateral phase separation takes place. The inter-membrane distance relaxes to the bulk values with two symmetric overshoots. Adhesion mediated by other types of stickers is also considered. PACS. 87.16.-b Subcellular structure and processes -68.10.-m Fluid surfaces and fluid-fluid interfaces -82.70.-y Disperse systems

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Section: Relation To Other Modelsmentioning

confidence: 88%

Adhesion-induced lateral phase separation in membranes

Komura

Andelman²

2000

The European Physical Journal E

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“…In contrast to the complete minimization of the free energy functional which requires a numerical calculation, we shall employ here a simple ansatz for the form of the grain boundary in order to obtain analytic results. Recently, similar methods were employed to obtain analytically the interface between the lamellar and disordered phases of diblock copolymers [9]. Our motivation is to demonstrate that the essence of these interesting morphologies does not depend on strong segregation conditions or a large number of Fourier components, and so should be observable in all systems with modulated phases.…”

Section: Introductionmentioning

confidence: 99%

Defects in lamellar diblock copolymers: Chevron- and Ω-shaped tilt boundaries

2000

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The lamellar phase in diblock copolymer systems appears as a result of a competition between molecular and entropic forces which select a preferred periodicity of the lamellae. Grain boundaries are formed when two grains of different orientations meet. We investigate the case where the lamellae meet symmetrically with respect to the interface. The form of the interface strongly depends on the angle, θ, between the normals of the grains. When this angle is small, the lamellae transform smoothly from one orientation to the other, creating the chevron morphology. As θ increases, a gradual transition is observed to an omega morphology characterized by a protrusion of the lamellae along the interface between the two phases. We present a theoretical approach to find these tilt boundaries in two-dimensional systems, based on a Ginzburg-Landau expansion of the free energy which describes the appearance of lamellae. Close to the tips at which lamellae from different grains meet, these lamellae are distorted. To find this distortion for small angles, we use a phase variation ansatz in which one assumes that the wave vector of the bulk lamellar phase depends on the distance from the interface. Minimization of the free energy gives an expression for the order parameter φ(x, y). The results describe the chevron morphology very well. For larger angles, a different approach is used. We linearize φ around its bulk value φL and expand the free energy to second order in their difference. Minimization of the free energy results in a linear fourth order differential equation for the distortion field, with proper constraints, similar to the Mathieu equation. The calculated monomer profile and line tension agree qualitatively with transmission electron microscope experiments, and with full numerical solution of the same problem.

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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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The lamellar-disorder interface: one-dimensional modulated profiles

Cited by 18 publications

References 8 publications

Adhesion-induced lateral phase separation in membranes

Adhesion-induced lateral phase separation in membranes

Defects in lamellar diblock copolymers: Chevron- and Ω-shaped tilt boundaries

Coupled Modulated Bilayers: A Phenomenological Model

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