Theory of block copolymer interfaces in the strong segregation limit

Семенов, А. Н.

doi:10.1021/ma00076a047

Cited by 212 publications

(297 citation statements)

References 4 publications

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“…Semenov [38] carefully compares this prediction with experiments and develops corrections to their theory, which underestimates the interface width by a factor of about 1.7. When required, we will use the value ξ = 3.4/ √ χN so that a ≈ 2.3.…”

Section: Calibration Of the Density Functionalmentioning

confidence: 98%

“…(c) The marginally stable wavenumber q * (f ) is also reproduced according to a prescribed benchmark. For criterion (a), it has been noted elsewhere [31,38] that the interfacial energy for strong segregation χN 1 should not depend on the composition f and should scale as (χN ) −1/2 . In the large χN limit, a one-dimensional interface is described by the Euler-Lagrange equation…”

Section: Calibration Of the Density Functionalmentioning

confidence: 99%

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Spatially Localized Structures in Diblock Copolymer Mixtures

Glasner¹

2010

SIAM J. Appl. Math.

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Abstract. Above the critical temperature for the order-disorder transition, diblock copolymer melts have been observed to exhibit localized structures that exist within the homogeneous mixture. This paper uses an Ohta-Kawasaki-type density functional to explore this regime. Spatially localized peak-shaped equilibria are studied in one, two, and three dimensions, corresponding to amphiphilic bilayers, cylindrical micelles, and spherical micelles, respectively. A combination of rigorous estimates, asymptotic analysis, and numerical computation is used to characterize solutions and the regime where they exist. The interaction of superpositions of these solutions is studied by a perturbation analysis and shows how steady multipeak configurations can be achieved. Evidence is found for a secondary bifurcation slightly below the spinodal instability threshold, beyond which self-replication phenomena are observed. Dynamics in two dimensions are also illustrated, suggesting other mechanisms for instability and growth.Key words. diblock copolymer, micelle, density functional theory, self-replication AMS subject classifications. 82D60, 35K55DOI. 10.1137/080743913 1. Introduction. Diblock copolymers are linear chain molecules composed of two distinct subchains. At low temperatures, repulsion between subchains can result in phase segregation, but macroscopic segregation cannot occur because of covalent bonding between subchains. This incomplete segregation can give rise to a variety of stable microstructures (see, e.g., [1,11,14,24]), which are typically characterized as spatially periodic patterns whose domain boundaries closely resemble minimal surfaces, such as spheres, cylinders, and gyroids [39].Outside of the regime where mixtures are unstable to spinodal decomposition, the situation for copolymers is more complicated than simple binary systems, such as those described by the Cahn-Hilliard theory [5]. In addition to a stable homogeneous state, there are other observed behaviors. Physical experiments have identified inhomogeneous states above the critical temperature, such as sparse arrangements of micellar structures [35,36,43] and anisotropic lamellar grains [15]. This paper seeks to investigate this regime and its dynamics using density functional theory and the corresponding gradient flow dynamics.Theoretical work on the disordered regime has focused on spherical micelles. Dormidontova and Lodge [9] use Semenov's strong segregation theory [37] to predict the concentration of micelle assemblies. Their theory predicts that the number of micelles increases rapidly below a "critical micelle temperature" (CMT), which is greater than the temperature at which a homogeneous mixture is spinodally unstable. Wang, Wang, and Yang [42] use self-consistent field theory calculations to find the density profile of individual spherical micelles and evaluate their excess free energy. They find that micelles exist (within the mean field approximation) for volume frac-

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Section: Calibration Of the Density Functionalmentioning

confidence: 98%

Section: Calibration Of the Density Functionalmentioning

confidence: 99%

Spatially Localized Structures in Diblock Copolymer Mixtures

Glasner¹

2010

SIAM J. Appl. Math.

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“…Dans le but de comparer les résultats expérimentaux aux prédictions théoriques, la contribution des ondes capillaires doit être prise en compte. Le produit w I a été utilisé comme borne supérieure pour les vecteurs d'onde avec de petites longueurs d'onde [32]. Donc la contribution des ondes capillaires à l'interface est donnée par :…”

Section: Dépendance De L'interface Par Rapport à La Distance Au Pointunclassified

Interfaces de polymères en couche minces : la réflectivité des neutrons

Sferrazza

Béziel

2010

Journées de la Neutronique

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Résumé. La réflectivité des neutrons est utilisée pour l'étude de la structure de l'interface entre couches minces de polymères afin de sonder les fluctuations thermiques et les effets de confinement dans ces systèmes. Des exemples d'étude sont illustrés dans ce chapitre: l'interface entre deux films minces de polymères est étudiée en fonction du degré d'immiscibilité, de l'épaisseur des films et du temps, i.e de la cinétique de formation de l'interface.

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“…As isotermas das monocamadas das moléculas maiores não apresentam nenhuma transição de fase, sendo, portanto, mais fáceis de serem reproduzidas. Outros modelos empregaram formulações similares e obtiveram boa concordância com os resultados experimentais para a descrição das fases gasosas das isotermas de substâncias surfactantes [58,59,60]. Fainerman et al [61,62] empregaram uma versão generalizada da Equação de Volmer, a qual inclui um termo que considera a agregação entre as diferentes moléculas da monocamada e conseguiram reproduzir uma transição de fase fluido-fluido.…”

Section: 2-emprego De Modelos De Simulação Molecular Para Descriçãounclassified

Emprego de modelos de campo médio para descrição termodinâmica de monocamadas de Langmuir

Robazzi¹

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Theory of block copolymer interfaces in the strong segregation limit

Cited by 212 publications

References 4 publications

Spatially Localized Structures in Diblock Copolymer Mixtures

Spatially Localized Structures in Diblock Copolymer Mixtures

Interfaces de polymères en couche minces : la réflectivité des neutrons

Emprego de modelos de campo médio para descrição termodinâmica de monocamadas de Langmuir

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