Level Surfaces of Gaussian Random Fields and Microemulsions

Teubner, Max

doi:10.1209/0295-5075/14/5/003

Cited by 165 publications

(144 citation statements)

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“…(8). 33 The GRFM prediction falls well within the range of the simulation results, but lacks the systematic dependencies of γ on κ,κ, and S/V noted above. It is also interesting to note that the topology of the ordered gyroid (G) phase is characterized by γ G = −0.271.…”

Section: Topologysupporting

confidence: 52%

“…32 Since the structure of microemulsions is dominated by the curvature elasticity of the surfactant layer, a crucial step in understanding it is to identify how the scattering peaks follow from the elastic properties of the surfactant membrane. The first theories 11,33,34 were phenomenological theories of the Ginzburg-Landau type. In them, Gaussian fluctuations of the order-parameter field determine the scattering intensity, which is given by the so-called Teubner-Strey formula for bulk scattering.…”

Section: Introductionmentioning

confidence: 99%

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Scattering intensity of bicontinuous microemulsions and sponge phases

Peltomäki

Gompper

Kroll

2012

The Journal of Chemical Physics

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Monte Carlo simulations of dynamically triangulated surfaces of variable topology are used to investigate the scattering intensities of bicontinuous microemulsions. The bulk scattering intensity is shown to follow the Teubner-Strey expression. The domain size and the correlation length are extracted from the scattering peaks as a function of the bending rigidity, saddle-splay modulus, and surfactant density. The results are compared to earlier theories based on Ginzburg-Landau and Gaussian random field models. The ratio of the two length scales is shown to be well described by a linear combination of logarithmically renormalized bending rigidity and saddle-splay modulus with universal prefactors. This is in contrast to earlier theoretical predictions in which the scattering intensity is independent of the saddle-splay modulus. The equation of state, and the asymptotics of the bulk and film scattering intensities for high and low wave vectors are determined from simulations and compared with theoretical results.

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Section: Topologysupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Scattering intensity of bicontinuous microemulsions and sponge phases

Peltomäki

Gompper

Kroll

2012

The Journal of Chemical Physics

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“…The contact pressure Π 0 depends on the binding and positioning of water and ethanol molecules at the interface. The average thickness h of water-rich slabs is obtained using the surface to volume ratio of the leveled Gaussian random field (41). Alternatively, h can be estimated by the tessellation of facetted polyhedrons (42), leading to a similar result: h is close to 1.5 nm for the sample described in Table S2.…”

Section: Hydration Vs Entropy Balancementioning

confidence: 99%

How to explain microemulsions formed by solvent mixtures without conventional surfactants

Zemb

Klossek

Lopian

et al. 2016

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

181

200

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Ternary solutions containing one hydrotrope (such as ethanol) and two immiscible fluids, both being soluble in the hydrotrope at any proportion, show unexpected solubilization power and allow strange but yet unexplained membrane enzyme activity. We study the system ethanol-water-octanol as a simple model of such kinds of ternary solutions. The stability of "detergentless" micelles or microemulsions in such mixtures was proposed in the pioneering works of Barden and coworkers [Smith GD, Donelan CE, Barden RE (1977) J Colloid Interface Sci 60(3):488-496 and Keiser BA, Varie D, Barden RE, Holt SL (1979) J Phys Chem 83(10):1276-1281] in the 1970s and then, neglected, because no general explanation for the observations was available. Recent direct microstructural evidence by light, X-ray, and neutron scattering using contrast variation reopened the debate. We propose here a general principle for solubilization without conventional surfactants: the balance between hydration force and entropy. This balance explains the stability of microemulsions in homogeneous ternary mixtures based on cosolvents.A dding slightly hydrophobic compounds to water can lead to structureless solutions, aggregate formation, or even, formation of defined structures, such as micelles, in the case where the added compound is a surfactant. In ternary or quaternary mixtures containing at least one type of surfactant, the formation of microemulsions usually occurs in specific parts of the phase diagram. These macroscopically homogeneous, transparent liquids are composed of well-defined microstructures with specific signatures in scattering experiments (1). It was only recently that similar structures, designated as "pre-Ouzo," were found and characterized in ternary mixtures of two partly miscible solvents and one hydrotropic cosolvent (2). In this paper, we present a theory that explains and even predicts the existence of such structures in "detergentless" formulations.Ouzo, Limoncello, and Pommeau liquors are popular in several European countries and produced by maceration of plants with a specific amount of ethanolic solutions containing some waterinsoluble compounds (3). Adding water to those solutions leads to spontaneous formation of fine emulsions with a remarkable stability, a phenomenon that is called the "Ouzo effect" (4). Even common mouthwash products show a similar phenomenon. In common, they entirely clear up on addition of ethanol and get milky with the addition of water (5).Ternary surfactant-free model systems, such as decane-waterisobutoxyethanol [as studied by Shinoda and Kunieda (6)], however, show this Ouzo effect only for specific points in the composition diagram. The precondition for such behavior seems to be the mixture of two miscible (either completely or at least to a large degree) solvents 1 and 2 with a solute that can also be a liquid (7) (e.g., anethole in the case of Ouzo; component 3). This component 3 must be highly soluble in one solvent (e.g., ethanol) but poorly soluble in the other one (e.g., water) (8).Where...

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“…In the case of level-cut Gaussian random fields, the ACF of the bi-continuous medium is determined (Teubner, 1991) by the covariance C ψ (r) of an underlying zeromean, unit-variance Gaussian random field ψ from which a two-phase microstructure is obtained by "segmentation" of the continuous field values with threshold β (cut-level parameter), which is in one-to-one correspondence with the volume fraction f 2 . Our particular choice of the field correlation function C ψ in Eq.…”

Section: Microstructure Representationsmentioning

confidence: 99%

SMRT: an active–passive microwave radiative transfer model for snow with multiple microstructure and scattering formulations (v1.0)

Picard

Sandells²,

Löwe³

2018

Geosci. Model Dev.

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Abstract. The Snow Microwave Radiative Transfer (SMRT) thermal emission and backscatter model was developed to determine uncertainties in forward modeling through intercomparison of different model ingredients. The model differs from established models by the high degree of flexibility in switching between different electromagnetic theories, representations of snow microstructure, and other modules involved in various calculation steps. SMRT v1.0 includes the dense media radiative transfer theory (DMRT), the improved Born approximation (IBA), and independent Rayleigh scatterers to compute the intrinsic electromagnetic properties of a snow layer. In the case of IBA, five different formulations of the autocorrelation function to describe the snow microstructure characteristics are available, including the sticky hard sphere model, for which close equivalence between the IBA and DMRT theories has been shown here. Validation is demonstrated against established theories and models. SMRT was used to identify that several former studies conducting simulations with in situ measured snow properties are now comparable and moreover appear to be quantitatively nearly equivalent. This study also proves that a third parameter is needed in addition to density and specific surface area to characterize the microstructure. The paper provides a comprehensive description of the mathematical basis of SMRT and its numerical implementation in Python. Modularity supports model extensions foreseen in future versions comprising other media (e.g., sea ice, frozen lakes), different scattering theories, rough surface models, or new microstructure models.

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Level Surfaces of Gaussian Random Fields and Microemulsions

Abstract: PACS. 05.40 -Fluctuation phenomena, random processes, and Brownian motion. PACS. 68.10 -Fluid surfaces and interfaces with fluids (inc. surface tension, capillarity, PACS. 87.20C -General theory of interfaces (inc. practical models).wetting and related phenomena).

Cited by 165 publications

References 10 publications

Scattering intensity of bicontinuous microemulsions and sponge phases

Scattering intensity of bicontinuous microemulsions and sponge phases

How to explain microemulsions formed by solvent mixtures without conventional surfactants

SMRT: an active–passive microwave radiative transfer model for snow with multiple microstructure and scattering formulations (v1.0)

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