Extended analysis of surface scratch smoothing

Gruber, E.E.; Mullins, W. W.

doi:10.1016/0001-6160(66)90098-8

Cited by 12 publications

(8 citation statements)

References 2 publications

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“…First, the surface curvature differences modify diffusion and evaporation, such that material is transported from highly curved areas to those with smaller or negative curvature. In total the surface energy in the sample is reduced [38].…”

Section: Microstructure Of Resorcinol-formaldehyde and Corresponding mentioning

confidence: 99%

“…During pyrolysis they became smoother, as if they have a cover on their surface. This process was described by Gruber [38], treating quite generally the smoothing of rough surfaces by curvature driven mass transport. Previous investigations show that this kind of structural modifications (merging or smoothing) cause a strengthening of the aerogels [40,41].…”

Section: Microstructure Of Resorcinol-formaldehyde and Corresponding mentioning

confidence: 99%

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Flexible Carbon Aerogels

Schwan

Ratke

2016

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Carbon aerogels are highly porous materials with a large inner surface area. Due to their high electrical conductivity they are excellent electrode materials in supercapacitors. Their brittleness, however, imposes certain limitations in terms of applicability. In that context, novel carbon aerogels with varying degree of flexibility have been developed. These highly porous, light aerogels are characterized by a high surface area and possess pore structures in the micrometer range, allowing for a reversible deformation of the aerogel network. A high ratio of pore size to particle size was found to be crucial for high flexibility. For dynamic microstructural analysis, compression tests were performed in-situ within a scanning electron microscope allowing us to directly visualize the microstructural flexibility of an aerogel. The flexible carbon aerogels were found to withstand between 15% and 30% of uniaxial compression in a reversible fashion. These findings might stimulate further research and new application fields directed towards flexible supercapacitors and batteries.

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Section: Microstructure Of Resorcinol-formaldehyde and Corresponding mentioning

confidence: 99%

Section: Microstructure Of Resorcinol-formaldehyde and Corresponding mentioning

confidence: 99%

Flexible Carbon Aerogels

Schwan

Ratke

2016

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“…Further innovative work was carried out by Herring [33,34] who outlined a general procedure for calculating morphological change induced by capillarity and explicitly related chemical potential and curvature for anisotropic y. For materials with isotropic properties, Mullins, co-workers and others [29,37,40,52,55] have derived general solutions for the Cauchy problem of describing the relaxation of a nearly-planar surface for each of the transport processes. The problems were linearized by assuming the slope was everywhere small and invariant forms were calculated that characterize the profile for a point source, an antisymmetric and a symmetric scratch [55].…”

Section: Introductionmentioning

confidence: 99%

An integrable fourth-order nonlinear evolution equation applied to surface redistribution due to capillarity

Tritscher¹

1997

J. Aust. Math. Soc. Series B, Appl. Math

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Members of an hierarchy of integrable nonlinear evolution equations, related to the wellknown linearizable diffusion equation which has the diffusivity form as the reciprocal of the square of the concentration, are adapted to derive a new integrable nonlinear equation which models the surface evolution of an arbitrarily-oriented theoretical anisotropic material by the concomitant action of evaporation-condensation and surface diffusion. The constitutive relations are explicitly formulated and these show that the theoretical anisotropic material behaves like a liquid crystal. The integrable nonlinear equation may be used to advantage as test cases for numerical schemes. Its form has many attributes of the nonlinear governing equation for an isotropic material. Closed-form solutions are constructed for the evolution of a ramped surface by concomitant evaporation-condensation and surface diffusion.

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“…For materials with isotropic properties, Mullins, co-workers and others (Gruber & Mullins 1966;Jones et al . 1965;King & Mullins 1962;Mullins 1959Mullins , 1963 have derived general solutions for the Cauchy problem of describing the relaxation of a nearly planar surface for each of the transport processes.…”

Section: Introductionmentioning

confidence: 99%

Thermal grooving by surface diffusion for an extended bicrystal abutting a half–space

Tritscher

1999

Proc. R. Soc. Lond. A

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A theoretical anisotropic material implied from Mullins' linear fourth-order equation for surface diffusion is used to model redistribution by surface diffusion of a bicrystal occupying a half-space, terminated along two planar surfaces meeting at the grain boundary. Intersecting the junction of the two planes is an arbitrarily inclined grain boundary. The particular case where one of the bicrystal surfaces is initially coplanar with the grain boundary yields a configuration that is locally representative of some joints among crystalline sinter particles. Closed-form solutions for a family of orientations of either of the crystal lattices of the theoretical anisotropic material are derived. Dependent upon the initial geometry and the surface environment, the bicrystal may either sinter together or divide apart. The theoretical material may reasonably model isotropic materials by appropriate orientation of the crystal lattice.

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Extended analysis of surface scratch smoothing

Cited by 12 publications

References 2 publications

Flexible Carbon Aerogels

Flexible Carbon Aerogels

An integrable fourth-order nonlinear evolution equation applied to surface redistribution due to capillarity

Thermal grooving by surface diffusion for an extended bicrystal abutting a half–space

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