Soap Froths and Crystal Structures
Abstract. We discuss the physics and mathematics of sphere packing and minimal surfaces and use these to explain the crystal symmetries found in macromolecular and supramolecular micellar materials and charged colloids. In the case of molecular assemblies, we argue that the packing entropy of the ha...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kamien, Randall D. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2003 |
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| Schlagwörter: |
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| Anmerkung: |
© Birkhäuser Verlag, Basel 2003 |
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| Übergeordnetes Werk: |
Enthalten in: Annales Henri Poincaré - Birkhäuser-Verlag, 2000, 4(2003), Suppl 2 vom: Dez., Seite 679-681 |
|---|---|
| Übergeordnetes Werk: |
volume:4 ; year:2003 ; number:Suppl 2 ; month:12 ; pages:679-681 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00023-003-0953-7 |
|---|
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OLC2058749073 |
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| 520 | |a Abstract. We discuss the physics and mathematics of sphere packing and minimal surfaces and use these to explain the crystal symmetries found in macromolecular and supramolecular micellar materials and charged colloids. In the case of molecular assemblies, we argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their brush-like coronas. The observed crystal structures correspond to the Kelvin and Weaire-Phelan minimal foams. We show that these structures are stable for reasonable areal entropy densities. | ||
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10.1007/s00023-003-0953-7 doi (DE-627)OLC2058749073 (DE-He213)s00023-003-0953-7-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kamien, Randall D. verfasserin aut Soap Froths and Crystal Structures 2003 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2003 Abstract. We discuss the physics and mathematics of sphere packing and minimal surfaces and use these to explain the crystal symmetries found in macromolecular and supramolecular micellar materials and charged colloids. In the case of molecular assemblies, we argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their brush-like coronas. The observed crystal structures correspond to the Kelvin and Weaire-Phelan minimal foams. We show that these structures are stable for reasonable areal entropy densities. Minimal Surface Hard Sphere Voronoi Cell Molecular Assembly Sphere Packing Enthalten in Annales Henri Poincaré Birkhäuser-Verlag, 2000 4(2003), Suppl 2 vom: Dez., Seite 679-681 (DE-627)313331340 (DE-600)2011018-2 (DE-576)085108839 1424-0637 nnns volume:4 year:2003 number:Suppl 2 month:12 pages:679-681 https://doi.org/10.1007/s00023-003-0953-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_285 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4029 GBV_ILN_4277 AR 4 2003 Suppl 2 12 679-681 |
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10.1007/s00023-003-0953-7 doi (DE-627)OLC2058749073 (DE-He213)s00023-003-0953-7-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kamien, Randall D. verfasserin aut Soap Froths and Crystal Structures 2003 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2003 Abstract. We discuss the physics and mathematics of sphere packing and minimal surfaces and use these to explain the crystal symmetries found in macromolecular and supramolecular micellar materials and charged colloids. In the case of molecular assemblies, we argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their brush-like coronas. The observed crystal structures correspond to the Kelvin and Weaire-Phelan minimal foams. We show that these structures are stable for reasonable areal entropy densities. Minimal Surface Hard Sphere Voronoi Cell Molecular Assembly Sphere Packing Enthalten in Annales Henri Poincaré Birkhäuser-Verlag, 2000 4(2003), Suppl 2 vom: Dez., Seite 679-681 (DE-627)313331340 (DE-600)2011018-2 (DE-576)085108839 1424-0637 nnns volume:4 year:2003 number:Suppl 2 month:12 pages:679-681 https://doi.org/10.1007/s00023-003-0953-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_285 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4029 GBV_ILN_4277 AR 4 2003 Suppl 2 12 679-681 |
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10.1007/s00023-003-0953-7 doi (DE-627)OLC2058749073 (DE-He213)s00023-003-0953-7-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kamien, Randall D. verfasserin aut Soap Froths and Crystal Structures 2003 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2003 Abstract. We discuss the physics and mathematics of sphere packing and minimal surfaces and use these to explain the crystal symmetries found in macromolecular and supramolecular micellar materials and charged colloids. In the case of molecular assemblies, we argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their brush-like coronas. The observed crystal structures correspond to the Kelvin and Weaire-Phelan minimal foams. We show that these structures are stable for reasonable areal entropy densities. Minimal Surface Hard Sphere Voronoi Cell Molecular Assembly Sphere Packing Enthalten in Annales Henri Poincaré Birkhäuser-Verlag, 2000 4(2003), Suppl 2 vom: Dez., Seite 679-681 (DE-627)313331340 (DE-600)2011018-2 (DE-576)085108839 1424-0637 nnns volume:4 year:2003 number:Suppl 2 month:12 pages:679-681 https://doi.org/10.1007/s00023-003-0953-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_285 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4029 GBV_ILN_4277 AR 4 2003 Suppl 2 12 679-681 |
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10.1007/s00023-003-0953-7 doi (DE-627)OLC2058749073 (DE-He213)s00023-003-0953-7-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kamien, Randall D. verfasserin aut Soap Froths and Crystal Structures 2003 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag, Basel 2003 Abstract. We discuss the physics and mathematics of sphere packing and minimal surfaces and use these to explain the crystal symmetries found in macromolecular and supramolecular micellar materials and charged colloids. In the case of molecular assemblies, we argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their brush-like coronas. The observed crystal structures correspond to the Kelvin and Weaire-Phelan minimal foams. We show that these structures are stable for reasonable areal entropy densities. Minimal Surface Hard Sphere Voronoi Cell Molecular Assembly Sphere Packing Enthalten in Annales Henri Poincaré Birkhäuser-Verlag, 2000 4(2003), Suppl 2 vom: Dez., Seite 679-681 (DE-627)313331340 (DE-600)2011018-2 (DE-576)085108839 1424-0637 nnns volume:4 year:2003 number:Suppl 2 month:12 pages:679-681 https://doi.org/10.1007/s00023-003-0953-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_285 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4029 GBV_ILN_4277 AR 4 2003 Suppl 2 12 679-681 |
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Abstract. We discuss the physics and mathematics of sphere packing and minimal surfaces and use these to explain the crystal symmetries found in macromolecular and supramolecular micellar materials and charged colloids. In the case of molecular assemblies, we argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their brush-like coronas. The observed crystal structures correspond to the Kelvin and Weaire-Phelan minimal foams. We show that these structures are stable for reasonable areal entropy densities. © Birkhäuser Verlag, Basel 2003 |
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