Curvature Determination of Spinodal Interface in a Condensed Matter System

Jinnai, Hiroshi; Koga, Tomohiro; Nishikawa, Yukihiro; Hashimoto, Takeji; Hyde, Stephen T.

doi:10.1103/physrevlett.78.2248

Cited by 157 publications

(142 citation statements)

References 23 publications

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“…A couple of different types of 3D microscopes have been developed. 15 They are laser scanning confocal microscopy (LSCM), [16][17][18][19][20][21][22][23][24][25][26][27] X-ray tomography, [28][29][30] and transmission electron microtomography (TEMT). 15, The spatial resolution of LSCM and X-ray tomography is on the order of a micrometer, while that of TEMT approaches 1 nm or less.…”

mentioning

confidence: 99%

Three-Dimensional Imaging in Polymer Science: Its Application to Block Copolymer Morphologies and Rubber Composites

Dohi¹,

Kimura²,

Kotani³

et al. 2007

Polym J

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ABSTRACT:New methods to visualize polymer morphologies in three-dimension (3D) in polymer science are reviewed. Here we concentrate on one of such 3D imaging technique, transmission electron microtomography (TEMT), and introduce some experimental studies using this novel technique. They are block copolymer morphologies during order-order transition between the two different morphologies and block copolymer thin film morphology also during morphological change due to confinement. Direct visualization of 3D structure of silica particle/rubber composite and related morphological analyses are shown. Subsequently, as a very hot topic of the 3D imaging, we show for the first time to characterize the morphological change in a silica particle/rubber composite upon stretching. It was found that the aggregates of silica particles were broken down upon stretching and many voids were generated near and between the silica particles. Local stress upon stretching inside the composite was inferred from the image intensity of the 3D reconstructed image. The local stress was found not only near the silica particles but also near the top of the voids. The observations indicated that the local stress increases the modulus, causing voids to form along the stretching direction. The thickness of the specimen after the stretching was also estimated from the 3D volume data, which turned out to be non-uniform and thinner than what is expected from the affine deformation. These experimental findings indicate that the rubber composite does not obey the assumption of the affine deformation at the nano-scale. Polymer materials are ubiquitous in our daily life. Such materials often consist of more than one species of polymers and thus become multi-component systems, such as in polymer blends, 1,2 block copolymers, 3 and fillers/polymer composites. 4 The multi-component systems often show phase-separated structures due to immiscibility of constituents. Studies to characterize such morphologies inside the materials have been growing intensively over the past few decades. Academic interest in complex fluids (to which polymeric systems belong) as well as the ceaseless industrial need for developing new materials motivates such studies.In academia, pattern formation and self-assembling processes of multi-component polymer systems are one of the most fascinating research themes in nonlinear, non-equilibrium phenomena.1 Likewise, nanometer-scale periodic structures formed in block copolymers in their equilibrium state are interesting because their self-assembly is driven by the subtle balance between the entropic block chain conformation and enthalpic interaction between the constituents. 3In industry, phase-separated polymer systems provide an important route to achieve superior physical properties. Hence, the structure-property relationship in multi-component polymeric materials is of significant importance, basic studies on which eventually render new designs of polymer materials satisfying the diverse requirements of industry.Filler/polymer comp...

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confidence: 99%

Three-Dimensional Imaging in Polymer Science: Its Application to Block Copolymer Morphologies and Rubber Composites

Dohi¹,

Kimura²,

Kotani³

et al. 2007

Polym J

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“…Other physical systems that adopt a labyrinthine geometry as their spatial structure include self-assembly processes into bicontinuous mesophases of diblock copolymers [6,7] and linear terblock co-polymers [8], of lyotropic liquid crystals [9 -11] including lipid -water biochemical systems [12][13][14][15] and of synthetic surfactants [16], mesoporous inorganic materials synthesized in the presence of amphiphiles [17] and condensed mesoporous inorganics [18], late stage spinodal decomposition in polymer blends [19], biomineralization in crustacean shells [20], and the alveolar surface of a rabbit lung [21]. While the bulk of these labyrinthine phases are of cubic symmetry, anisotropic non-cubic TPMS have also been identified, in linear tri-block polymers [8], tri-continuous hexagonal mesoporous silica systems [22] and in non-cubic deformation modes in lung surfactants of rabbits [21].…”

Section: Introductionmentioning

confidence: 99%

Tensorial Minkowski functionals of triply periodic minimal surfaces

2012

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A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors.

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“…Most recently, laser scanning confocal microscopy (LSCM) was shown to be an excellent tool to capture the 3D interface structure of polymer blends. [16][17][18] By using LSCM, the time evolution of the interface between two coexisting phases developed via SD was quantitatively captured in 3D images. At present, high-resolution X-ray computed tomography (X-ray CT) was also developed and it will be possible to provide very useful quantitative information about the mm-scale 3D structures of polymer blend systems; the mechanism of phase separation for polymer blends has been clarified.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional observation of phase‐separated poly(methyl methacrylate)/poly(styrene‐ran‐4‐bromostylene) blends by 3D NMR microscopy with X‐ray microscopy

Koizumi

Yamane

Kuroki

et al. 2006

J of Applied Polymer Sci

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Three-dimensional (3D) image patterns of phase-separated poly(methyl methacrylate) (PMMA)/poly (styrene-ran-4-bromostyrene) (PS-Br) blends heated at 1808C for 6, 8, and 10 h were observed by 3D NMR microscopy with 3D X-ray microscopy in order to characterize the 3D structure of the polymer blends using a standard 3D reconstruction protocol program for obtaining the 3D digital array of the PS-Br/PMMA morphologies. The phase-separated structure of the polymer blends in several 10-mm scales was reasonably characterized. The phase-separated structure of polymer blends by 3D NMR images was quantitatively consistent with that by 3D X-ray images. It can be said that 3D NMR microscopy is a very useful means for analyzing the 3D structure of phase-separated polymer blends as well as 3D X-ray images.

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Curvature Determination of Spinodal Interface in a Condensed Matter System

Cited by 157 publications

References 23 publications

Three-Dimensional Imaging in Polymer Science: Its Application to Block Copolymer Morphologies and Rubber Composites

Three-Dimensional Imaging in Polymer Science: Its Application to Block Copolymer Morphologies and Rubber Composites

Tensorial Minkowski functionals of triply periodic minimal surfaces

Three‐dimensional observation of phase‐separated poly(methyl methacrylate)/poly(styrene‐ran‐4‐bromostylene) blends by 3D NMR microscopy with X‐ray microscopy

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