The Experts below are selected from a list of 57 Experts worldwide ranked by ideXlab platform
Gerhard Gompper - One of the best experts on this subject based on the ideXlab platform.
-
Bending frustration of lipid-water mesophases based on cubic minimal surfaces
Langmuir, 2001Co-Authors: Ulrich S Schwarz, Gerhard GompperAbstract:Inverse bicontinuous cubic phases are ubiquitous in lipid−water mixtures and consist of a lipid bilayer forming a cubic minimal surface, thereby dividing space into two cubic networks of water channels. For small hydrocarbon chain lengths, the monolayers can be modeled as parallel surfaces to a minimal midsurface. The bending energy of the cubic phases is determined by the distribution of Gaussian curvature over the minimal midsurfaces which we calculate for seven different structures (G, D, P, I-WP, C(P), S, and F-RD). We show that the free-energy densities of the structures G, D, and P are considerably lower than those of the other investigated structures due to their narrow distribution of Gaussian curvature. The Bonnet Transformation between G, D, and P implies that these phases coexist along a triple line, which also includes an excess water phase. Our model includes thermal membrane undulations. Our qualitative predictions remain unchanged when higher order terms in the curvature energy are included...
-
Bending Frustration of Lipid-Water Mesophases Based on Cubic Minimal Surfaces
arXiv: Soft Condensed Matter, 2001Co-Authors: Ulrich S Schwarz, Gerhard GompperAbstract:Inverse bicontinuous cubic phases are ubiquitous in lipid-water mixtures and consist of a lipid bilayer forming a cubic minimal surface, thereby dividing space into two cubic networks of water channels. For small hydrocarbon chain lengths, the monolayers can be modeled as parallel surfaces to a minimal midsurface. The bending energy of the cubic phases is determined by the distribution of Gaussian curvature over the minimal midsurfaces which we calculate for seven different structures (G, D, P, I-WP, C(P), S and F-RD). We show that the free-energy densities of the structures G, D and P are considerably lower than those of the other investigated structures due to their narrow distribution of Gaussian curvature. The Bonnet Transformation between G, D, and P implies that these phases coexist along a triple line, which also includes an excess water phase. Our model includes thermal membrane undulations. Our qualitative predictions remain unchanged when higher order terms in the curvature energy are included. Calculated phase diagrams agree well with the experimental results for 2:1 lauric acid/dilauroyl phosphatidylcholine and water.
-
Stability of inverse bicontinuous cubic phases in lipid-water mixtures
Physical review letters, 2000Co-Authors: Ulrich S Schwarz, Gerhard GompperAbstract:We investigate the stability of seven inverse bicontinuous cubic phases [G, D, P, CP, S, I-WP, F-RD] in lipid-water mixtures based on a curvature model of membranes. Lipid monolayers are described by parallel surfaces to triply periodic minimal surfaces. The phase behavior is determined by the distribution of the Gaussian curvature on the minimal surface and the porosity of each structure. Only G, D, and P are found to be stable, and to coexist along a triple line. The calculated phase diagram agrees very well with experimental results for 2:1 lauric acidDLPC. PACS numbers: 68.10. – m, 61.30.Cz, 87.16.Dg Most of the many mesomorphic phases formed by lipid-water mixtures are of the inverse type, with the selfassembled lipid monolayers curving towards the aqueous regions [1]. In inverse bicontinuous cubic phases, a single lipid bilayer extends throughout the whole sample, dividing it into two percolating water labyrinths. Until now, the structures G, D, and P have been identified. The only known lipid-water system in which G, D, and P coexist is 2:1 lauric acidDLPC and water [2]. The property of cubic lipid bilayer phases to divide space into interwoven polar and apolar compartments is utilized for biological function, e.g., in mitochondria and the endoplasmic reticulum [3]. Recently, they have also been used as artificial matrices which enable membrane proteins such as bacteriorhodopsin to crystallize in a three-dimensional array [4]. It was shown by Luzzati and co-workers [5] that the midsurfaces of the lipid bilayers are very close to cubic minimal surfaces, which have zero mean curvature everywhere. These surfaces occur in lipid-water systems due to the local symmetry of the lipid bilayer, which implies that the surface should curve to both sides in the same way. However, it is well known [6] that many more cubic minimal surfaces exist than the structures G, D, and P identified in lipid-water mixtures. What might be the reason why these other phases have not been observed thus far? Helfrich and Rennschuh [7] argued that, based on the curvature model for fluid membranes [8], structures with a narrow distribution of Gaussian curvature over the minimal midsurface should be most favorable. However, the relevant data was known to them only for G, D, and P, which are degenerate in this respect due to the existence of a Bonnet Transformation. Recently, we obtained numerical representations for a large number of cubic minimal surfaces in the framework of a simple Ginzburg-Landau model [9]. In this Letter we use this data to investigate seven inverse bicontinuous cubic phases (G, D, P, CP, S, I-WP, F-RD). For an illustration of the G and S surfaces, see Fig. 1. We find that the width of the different distributions of Gaussian curvature is indeed smallest for G, D, and P and larger for all other structures considered. This proves for the first time why only G, D, and P should be observed experimentally. Our detailed investigation of the stability of bicontinuous cubic phases shows that the existence of the Bonnet Transformation implies that, with increasing water concentration, G, D, and P coexist along a triple line. We show that this sequence is determined by a universal geometrical quantity, the topology index, and that higher order terms in the curvature energy and thermal membrane undulations do not lift this degeneracy. Furthermore, we calculate phase diagrams as functions of concentration and temperature, which are in good agreement with an intermediate temperature range of the experimental phase diagram for 2:1 lauric acidDLPC and water [2]. The main contributions to the free energy of an inverse bicontinuous cubic phase are the curvature energy of the lipid monolayers and the stretching energy of the hydrocarbon chains [10]. The curvature energy is described by the Canham-Helfrich Hamiltonian [8]
Kazuhiko Kuroki - One of the best experts on this subject based on the ideXlab platform.
-
Electronic structure of periodic curved surfaces: Topological band structure
Physical Review B, 2001Co-Authors: Hideo Aoki, Mikito Koshino, D. Takeda, H. Morise, Kazuhiko KurokiAbstract:The electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface characterized completely in terms of "navels") but represent the topology of real systems such as zeolites and negative-curvature fullerenes. The band structure turns out to be primarily determined by the topology of the surface, i.e., how the wave function interferes on a multiply connected surface, so that the bands are little affected by the way in which we confine the electrons on the surface (thin-slab limit or zero thickness from the outset). Another curiosity is that different minimal surfaces connected by the Bonnet Transformation (such as Schwarz's P and D surfaces) possess one-to-one correspondence in their band energies at Brillouin-zone boundaries.
A. L. Mackay - One of the best experts on this subject based on the ideXlab platform.
-
Negatively curved graphite and triply periodic minimal surfaces
Journal of Mathematical Chemistry, 1994Co-Authors: H. Terrones, A. L. MackayAbstract:The Weierstrass representation has been used to construct negatively curved graphite in which atoms rest no a perfect triply periodic minimal surface. By applying the Bonnet Transformation on a patch of the D surface decorated with graphite we have been able to construct the Gyroid and P minimal surfaces. Curvatures, densities and lattice parameters have been calculated. It has been found that the maximum Gaussian curvature for our negatively curved structures is less in magnitude than the Gaussian curvature of C _60. In addition, a new periodic graphitic set with the same topology as the I-WP minimal surface has been obtained by introducing pentagonal and octagonal rings.
-
Triply periodic minimal surfaces decorated with curved graphite
Chemical Physics Letters, 1993Co-Authors: H. Terrones, A. L. MackayAbstract:Abstract Hypothetical negatively curved structures derived from graphite are described, in which all carbon atoms rest on triply periodic minimal surfaces (TPMS). The D minimal surface was calculated using the Weierstrass representation. By applying the Bonnet Transformation to the D surface, the gyroid and P surfaces were constructed. Curvatures, densities, lattice parameters and energies have been calculated for all structures. The absolute value of the maximum Gaussian curvature is smaller than that for C 60 fullerene. A new periodic graphite net with the same topology as the I-WP minimal surface, using 5-, 6- and 8-membered rings is found possible. The stability of 11 negatively curved graphitic structures has been determined using Tersoff's three-body potential. All the structures described are more stable than C 60 ,mainly because the 120° bond angles in ordinary graphite are almost preserved in the 7- and 8-membered carbon rings. The way is now open to explore the decoration of minimal surfaces with further arrangements of atoms of different elements.
-
Micelles and Foams: 2-D Manifolds Arising from Local Interactions
Growth Patterns in Physical Sciences and Biology, 1993Co-Authors: H. Terrones, A. L. MackayAbstract:Surfaces as 2-D manifolds play an important role in the description of structures, from inorganic materials to biological systems. These surfaces which can be planar, spherical or hyperbolic (saddle-shaped), arise as a consequence of interatomic forces. We are concerned with the generation and application of 2-D manifolds, in particular, periodic minimal surfaces. We show that surfaces can be decorated with atoms to obtain structures with different curvatures, related to the mean coordination number CN. When CN = 6 a planar surface or a cylinder can be obtained, if CN 6, an infinite structure, periodic or otherwise, can be generated. Regarding the case CN > 6, we have found that the existence of ordered graphite foams with topologies similar to periodic minimal surfaces is quite possible, various Transformations of surfaces, such as the Bonnet Transformation, the Goursat Transformation and a new combination of both, are analysed, since they might be useful in the description of physical and biological processes.
Ulrich S Schwarz - One of the best experts on this subject based on the ideXlab platform.
-
Bending frustration of lipid-water mesophases based on cubic minimal surfaces
Langmuir, 2001Co-Authors: Ulrich S Schwarz, Gerhard GompperAbstract:Inverse bicontinuous cubic phases are ubiquitous in lipid−water mixtures and consist of a lipid bilayer forming a cubic minimal surface, thereby dividing space into two cubic networks of water channels. For small hydrocarbon chain lengths, the monolayers can be modeled as parallel surfaces to a minimal midsurface. The bending energy of the cubic phases is determined by the distribution of Gaussian curvature over the minimal midsurfaces which we calculate for seven different structures (G, D, P, I-WP, C(P), S, and F-RD). We show that the free-energy densities of the structures G, D, and P are considerably lower than those of the other investigated structures due to their narrow distribution of Gaussian curvature. The Bonnet Transformation between G, D, and P implies that these phases coexist along a triple line, which also includes an excess water phase. Our model includes thermal membrane undulations. Our qualitative predictions remain unchanged when higher order terms in the curvature energy are included...
-
Bending Frustration of Lipid-Water Mesophases Based on Cubic Minimal Surfaces
arXiv: Soft Condensed Matter, 2001Co-Authors: Ulrich S Schwarz, Gerhard GompperAbstract:Inverse bicontinuous cubic phases are ubiquitous in lipid-water mixtures and consist of a lipid bilayer forming a cubic minimal surface, thereby dividing space into two cubic networks of water channels. For small hydrocarbon chain lengths, the monolayers can be modeled as parallel surfaces to a minimal midsurface. The bending energy of the cubic phases is determined by the distribution of Gaussian curvature over the minimal midsurfaces which we calculate for seven different structures (G, D, P, I-WP, C(P), S and F-RD). We show that the free-energy densities of the structures G, D and P are considerably lower than those of the other investigated structures due to their narrow distribution of Gaussian curvature. The Bonnet Transformation between G, D, and P implies that these phases coexist along a triple line, which also includes an excess water phase. Our model includes thermal membrane undulations. Our qualitative predictions remain unchanged when higher order terms in the curvature energy are included. Calculated phase diagrams agree well with the experimental results for 2:1 lauric acid/dilauroyl phosphatidylcholine and water.
-
Stability of inverse bicontinuous cubic phases in lipid-water mixtures
Physical review letters, 2000Co-Authors: Ulrich S Schwarz, Gerhard GompperAbstract:We investigate the stability of seven inverse bicontinuous cubic phases [G, D, P, CP, S, I-WP, F-RD] in lipid-water mixtures based on a curvature model of membranes. Lipid monolayers are described by parallel surfaces to triply periodic minimal surfaces. The phase behavior is determined by the distribution of the Gaussian curvature on the minimal surface and the porosity of each structure. Only G, D, and P are found to be stable, and to coexist along a triple line. The calculated phase diagram agrees very well with experimental results for 2:1 lauric acidDLPC. PACS numbers: 68.10. – m, 61.30.Cz, 87.16.Dg Most of the many mesomorphic phases formed by lipid-water mixtures are of the inverse type, with the selfassembled lipid monolayers curving towards the aqueous regions [1]. In inverse bicontinuous cubic phases, a single lipid bilayer extends throughout the whole sample, dividing it into two percolating water labyrinths. Until now, the structures G, D, and P have been identified. The only known lipid-water system in which G, D, and P coexist is 2:1 lauric acidDLPC and water [2]. The property of cubic lipid bilayer phases to divide space into interwoven polar and apolar compartments is utilized for biological function, e.g., in mitochondria and the endoplasmic reticulum [3]. Recently, they have also been used as artificial matrices which enable membrane proteins such as bacteriorhodopsin to crystallize in a three-dimensional array [4]. It was shown by Luzzati and co-workers [5] that the midsurfaces of the lipid bilayers are very close to cubic minimal surfaces, which have zero mean curvature everywhere. These surfaces occur in lipid-water systems due to the local symmetry of the lipid bilayer, which implies that the surface should curve to both sides in the same way. However, it is well known [6] that many more cubic minimal surfaces exist than the structures G, D, and P identified in lipid-water mixtures. What might be the reason why these other phases have not been observed thus far? Helfrich and Rennschuh [7] argued that, based on the curvature model for fluid membranes [8], structures with a narrow distribution of Gaussian curvature over the minimal midsurface should be most favorable. However, the relevant data was known to them only for G, D, and P, which are degenerate in this respect due to the existence of a Bonnet Transformation. Recently, we obtained numerical representations for a large number of cubic minimal surfaces in the framework of a simple Ginzburg-Landau model [9]. In this Letter we use this data to investigate seven inverse bicontinuous cubic phases (G, D, P, CP, S, I-WP, F-RD). For an illustration of the G and S surfaces, see Fig. 1. We find that the width of the different distributions of Gaussian curvature is indeed smallest for G, D, and P and larger for all other structures considered. This proves for the first time why only G, D, and P should be observed experimentally. Our detailed investigation of the stability of bicontinuous cubic phases shows that the existence of the Bonnet Transformation implies that, with increasing water concentration, G, D, and P coexist along a triple line. We show that this sequence is determined by a universal geometrical quantity, the topology index, and that higher order terms in the curvature energy and thermal membrane undulations do not lift this degeneracy. Furthermore, we calculate phase diagrams as functions of concentration and temperature, which are in good agreement with an intermediate temperature range of the experimental phase diagram for 2:1 lauric acidDLPC and water [2]. The main contributions to the free energy of an inverse bicontinuous cubic phase are the curvature energy of the lipid monolayers and the stretching energy of the hydrocarbon chains [10]. The curvature energy is described by the Canham-Helfrich Hamiltonian [8]
Hideo Aoki - One of the best experts on this subject based on the ideXlab platform.
-
Electronic structure of periodic curved surfaces: Topological band structure
Physical Review B, 2001Co-Authors: Hideo Aoki, Mikito Koshino, D. Takeda, H. Morise, Kazuhiko KurokiAbstract:The electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface characterized completely in terms of "navels") but represent the topology of real systems such as zeolites and negative-curvature fullerenes. The band structure turns out to be primarily determined by the topology of the surface, i.e., how the wave function interferes on a multiply connected surface, so that the bands are little affected by the way in which we confine the electrons on the surface (thin-slab limit or zero thickness from the outset). Another curiosity is that different minimal surfaces connected by the Bonnet Transformation (such as Schwarz's P and D surfaces) possess one-to-one correspondence in their band energies at Brillouin-zone boundaries.