A rough classification by
topic is shown below
Relevant graphical logos are appended to each paper
Relevant graphical logos are appended to each paper
 |
 |
 |
 |
 |
 |
| Nets Networks Embedded Graphs Tangled Patterns |
Biominerals and biomaterials "Biomorphs": living vs. dead matter |
Cellular structures, surfaces | "Hard"
framework materials: Zeolites Metallo-organic frameworks Novel carbon nanofoam etc. |
Soft
matter: Lyotropic liquid crystals microemulsions block copolymers Membranes in vivo |
Theoretical
crystallography |
PDF files are available for private use only as they are copyrighted
- T Castle, M Evans and S T Hyde, “Entanglement of embedded graphs”, to be published (2011).
Abstract:
We discuss the identification of untangled graph embeddings for finite planar and non-
planar graphs as well as infinite crystallographic nets. Two parallel approaches are discussed:
explicit 3-space embeddings and reticulations of 2-manifolds. 2D and 3D energies are pro-
posed that allow ranking of (un)tangled embedded graphs.
planar graphs as well as infinite crystallographic nets. Two parallel approaches are discussed:
explicit 3-space embeddings and reticulations of 2-manifolds. 2D and 3D energies are pro-
posed that allow ranking of (un)tangled embedded graphs.
- M. Saba, M. Thiel , M.D. Turner, S.T. Hyde, M. Gu, K. Grosse-Brauckmann, D.N. Neshev, K. Mecke, and G.E. Schröder-Turk, “Circular dichroism in biological photonic crystals and cubic chiral nets”, Phys Rev Lett, in press (2011).
Abstract:
Nature provides impressive examples of chiral photonic crystals, with the notable example of the
cubic srs network structure realized in wing-scales of several butterfly species. By a novel circular
polarization analysis of the band structure of such networks, we demonstrate strong circular dichro-
ism effects: The butterfly srs micro-structure, of cubic I 41 32 symmetry, shows significant circular
dichroism for blue to ultra-violet light, that warrants a search for biological receptors sensitive to
circular polarization. A derived synthetic structure based on four like-handed silicon srs nets ex-
hibits a large circular polarization stop band of width exceeding 30%. These findings offer design
principles for chiral photonic devices.
cubic srs network structure realized in wing-scales of several butterfly species. By a novel circular
polarization analysis of the band structure of such networks, we demonstrate strong circular dichro-
ism effects: The butterfly srs micro-structure, of cubic I 41 32 symmetry, shows significant circular
dichroism for blue to ultra-violet light, that warrants a search for biological receptors sensitive to
circular polarization. A derived synthetic structure based on four like-handed silicon srs nets ex-
hibits a large circular polarization stop band of width exceeding 30%. These findings offer design
principles for chiral photonic devices.
- G.E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J.D. Fitz Gerald, L. Poladian, M.C.J. Large and S.T. Hyde, “The chiral structure of porous chitin within the wing-scales of Callophrys rubi”, J Struct Biol, in press (2011). DOI: 10.1016/j.jsb.2011.01.004
pdf version (1.1 MB)
Abstract:
The structure of the porous
three-dimensional reticulated pattern in the wing scales of the
butterfly C. rubi (the Green Hairstreak)
is explored in detail, via scanning and transmission electron microscopy. A full 3D tomographic reconstruction of a fragment of
this material reveals that the predominantly chitin material is assembled in the wing scale to form a structure whose geometry
bears a remarkable correspondence to the srs net, well-known in solid state chemistry and soft materials science. The porous solid
is bounded to an excellent approximation by a parallel/cmc surface to the Gyroid, a three-periodic minimal surface with cubic
crystallographic symmetry I 41 32, as foreshadowed by Stavenga and Michielson. The scale of the structure is commensurate with
the wavelength of visible light, with an edge of the conventional cubic unit cell of the cmc-Gyroid of approximately 310 nm. The
genesis of this structure is discussed, and we suggest it affords a remarkable example of templating of a chiral material via soft
matter, analogous to the formation of mesoporous silica via surfactant assemblies in solution. In the butterfly, the templating is
achieved by the lipid-protein membranes within the smooth endoplasmic reticulum (while it remains in the chrysalis), that likely
form cubic membranes, folded according to the form of the Gyroid. The subsequent formation of the chiral hard chitin framework
is suggested to be driven by the gradual polymerisation of the chitin precursors, whose inherent chiral assembly in solution (during
growth) promotes the formation of a single enantiomer.
is explored in detail, via scanning and transmission electron microscopy. A full 3D tomographic reconstruction of a fragment of
this material reveals that the predominantly chitin material is assembled in the wing scale to form a structure whose geometry
bears a remarkable correspondence to the srs net, well-known in solid state chemistry and soft materials science. The porous solid
is bounded to an excellent approximation by a parallel/cmc surface to the Gyroid, a three-periodic minimal surface with cubic
crystallographic symmetry I 41 32, as foreshadowed by Stavenga and Michielson. The scale of the structure is commensurate with
the wavelength of visible light, with an edge of the conventional cubic unit cell of the cmc-Gyroid of approximately 310 nm. The
genesis of this structure is discussed, and we suggest it affords a remarkable example of templating of a chiral material via soft
matter, analogous to the formation of mesoporous silica via surfactant assemblies in solution. In the butterfly, the templating is
achieved by the lipid-protein membranes within the smooth endoplasmic reticulum (while it remains in the chrysalis), that likely
form cubic membranes, folded according to the form of the Gyroid. The subsequent formation of the chiral hard chitin framework
is suggested to be driven by the gradual polymerisation of the chitin precursors, whose inherent chiral assembly in solution (during
growth) promotes the formation of a single enantiomer.
- Stephen T. Hyde and Olaf Delgado Friedrichs, “From untangled nets to tangled materials”, Solid State Sci., in press (2010). DOI 10.1016/j.solidstatesciences.2010.10.028
pdf version (1.1 MB)
Abstract:
We suggest constructive definitions for the determination of untangled finite graphs and three-periodic
nets, using barycentric embeddings in two and three dimensions. The possibility of deliberately con-
structing tangled graphs and nets is canvassed, and we conclude that tangled patterns offer a novel class
of nano- and meso-structured materials with useful features, including high internal surface area and
volume and chirality.
nets, using barycentric embeddings in two and three dimensions. The possibility of deliberately con-
structing tangled graphs and nets is canvassed, and we conclude that tangled patterns offer a novel class
of nano- and meso-structured materials with useful features, including high internal surface area and
volume and chirality.
- Liliana de Campo, Trond Varslot, Minoo J. Moghaddam, Jacob J. K. Kirkensgaard, Kell Mortensen and Stephen T. Hyde, “A Novel Lyotropic Liquid Crystal Formed by Triphilic Star-Polyphiles: Hydrophilic/Oleophilic/Fluorophilic Rods Arranged in a 12.6.4. tiling”, Phys Chem Chem Phys, DOI:10.1039/C0CP01201G (2010).
pdf version (2.4 MB)
Abstract:
Triphilic star-polyphiles are short-chain oligomeric molecules with a radial arrangement of
hydrophilic, hydrocarbon and fluorocarbon chains linked to a common centre. They form a number
of liquid crystalline structures when mixed with water. In this contribution we focus on a
hexagonal liquid crystalline mesophase found in star-polyphiles as compared to the corresponding
double chain surfactant to determine whether the hydrocarbon and fluorocarbon chains are in fact
demixed in these star-polyphile systems, or whether both hydrocarbon and fluorocarbon chains are
miscible, leading to a single hydrophobic domain, making the star-polyphile effectively
amphiphilic. We report SANS contrast variation data that is compatible only with the presence of
three distinct immiscible domains within this hexagonal mesophase, confirming that these star-
polyphile liquid crystals are indeed hydrophilic/oleophilic/fluorophilic 3-phase systems.
Quantitative comparison with scattering simulations shows that the experimental data are in very
good agreement with an underlying 2D columnar (12.6.4) tiling. As in a conventional amphiphilic
hexagonal mesophase, the hexagonally packed water channels (dodecagonal prismatic domains)
are embedded in a hydrophobic matrix, but that matrix is split into oleophilic hexagonal prismatic
domains and fluorophilic quadrangular prismatic domains.
hydrophilic, hydrocarbon and fluorocarbon chains linked to a common centre. They form a number
of liquid crystalline structures when mixed with water. In this contribution we focus on a
hexagonal liquid crystalline mesophase found in star-polyphiles as compared to the corresponding
double chain surfactant to determine whether the hydrocarbon and fluorocarbon chains are in fact
demixed in these star-polyphile systems, or whether both hydrocarbon and fluorocarbon chains are
miscible, leading to a single hydrophobic domain, making the star-polyphile effectively
amphiphilic. We report SANS contrast variation data that is compatible only with the presence of
three distinct immiscible domains within this hexagonal mesophase, confirming that these star-
polyphile liquid crystals are indeed hydrophilic/oleophilic/fluorophilic 3-phase systems.
Quantitative comparison with scattering simulations shows that the experimental data are in very
good agreement with an underlying 2D columnar (12.6.4) tiling. As in a conventional amphiphilic
hexagonal mesophase, the hexagonally packed water channels (dodecagonal prismatic domains)
are embedded in a hydrophobic matrix, but that matrix is split into oleophilic hexagonal prismatic
domains and fluorophilic quadrangular prismatic domains.
- Stephen T. Hyde, “Contemporary geometry for the built design?”, Architecture Theory Review, 15(2), 2-10, (2010).
+erratum
Abstract:
I explore the terrain that lies
between architecture and geometry, from the perspective of a structural
scientist with no professional architectural expertise. The divide
between these disciplines perhaps stems from an ancient dichotomy
between the art vs. engineering schools of architecture, fertilised by
the current dogma that art and science can never meet. Architects stand
to gain much from study of the spectacular advances in geometry in
recent decades, such as the growing understanding of cellular patterns
in space, tiles, nets and curved surfaces. Some examples of those
advances are discussed in detail. I conclude that both architecture and
geometry would benefit from a renewed mutual interest.
- T. Castle, Myfanwy E. Evans and S. T. Hyde, “All toroidal embeddings of polyhedral graphs in 3-space are chiral”, New J. Chem., 2009, 33, 2107 - 2113 (2009).
pdf version (1.3 MB)
Abstract:
We investigate the possibility of forming achiral knottings of polyhedral (3-connected) graphs
whose minimal embeddings lie in the genus-one torus. Various analyses to show that all examples
are chiral. This result suggests a simple route to forming chiral molecules via templating on a
toroidal substrate.
whose minimal embeddings lie in the genus-one torus. Various analyses to show that all examples
are chiral. This result suggests a simple route to forming chiral molecules via templating on a
toroidal substrate.
- Stephen T. Hyde, Liliana de Campo and Christophe Oguey, “Tricontinuous mesophases of balanced three-arm ‘star polyphiles’ " , Soft Matter, 5, 2782–2794, (2009). DOI: 10.1039/b822814k
pdf version (11.1 MB)
Abstract:
We construct simple models to compare ordered tricontinuous patterns that are topologically
consistent with the constraints imposed by three-arm star polyphile self-assembly, analogous to steric
packing and elastic bending models used to analyse bicontinuous mesophases in amphiphilic
assemblies. We find a number of competing low-energy ordered structures, composed of threading of
three identical labyrinths, with three-fold infinite branch lines, that are likely to be of comparable
energy for polyphile shapes with moderately splayed arms. These patterns are triply-periodic analogues
of the hexagonal honeycomb, which is most favoured for unsplayed three-arm polyphile architectures.
consistent with the constraints imposed by three-arm star polyphile self-assembly, analogous to steric
packing and elastic bending models used to analyse bicontinuous mesophases in amphiphilic
assemblies. We find a number of competing low-energy ordered structures, composed of threading of
three identical labyrinths, with three-fold infinite branch lines, that are likely to be of comparable
energy for polyphile shapes with moderately splayed arms. These patterns are triply-periodic analogues
of the hexagonal honeycomb, which is most favoured for unsplayed three-arm polyphile architectures.
- Jacob Judas Kain Kirkensgaard and Stephen T. Hyde, “Beyond amphiphiles: Coarse-grained simulations of star-polyphile liquid crystalline assemblies”, Phys. Chem. Chem. Phys., 11, 2016 - 2022, (2009).
pdf version (1.5 MB)
Abstract:
We have simulated the self-assembly of a novel class of three-arm molecules,
ABC star-architecture polyphiles, using coarse-grained bead simulations. A number of
topologically complex liquid crystalline mesostructures arise that can be related to the
better-known bicontinuous mesophases of lyotropic amphiphilic systems. The simulations reveal
3D self-assemblies whose structural variations follow those expected assuming a simple steric
molecular packing model as a function of star polyphile splay and relative volumes of each arm
in the polyphile. The splay of each arm, characterised by the 3D wedge-shape emanating from the
core of each molecule to its exterior induces torsion of the interfaces along the triple lines,
whereas differences in the relative volumes of arms induce curvature of the triple lines. Three
distinct mesostructures are described, characterised by their micro-domain topologies, which are
unknown in simpler amphiphilic systems, but resemble in some respects bicontinuous mesophases.
These three- (or more) arm polyphilic systems offer an interesting extension to the better-known
self-assembly of (two-arm) amphiphiles in solution.
ABC star-architecture polyphiles, using coarse-grained bead simulations. A number of
topologically complex liquid crystalline mesostructures arise that can be related to the
better-known bicontinuous mesophases of lyotropic amphiphilic systems. The simulations reveal
3D self-assemblies whose structural variations follow those expected assuming a simple steric
molecular packing model as a function of star polyphile splay and relative volumes of each arm
in the polyphile. The splay of each arm, characterised by the 3D wedge-shape emanating from the
core of each molecule to its exterior induces torsion of the interfaces along the triple lines,
whereas differences in the relative volumes of arms induce curvature of the triple lines. Three
distinct mesostructures are described, characterised by their micro-domain topologies, which are
unknown in simpler amphiphilic systems, but resemble in some respects bicontinuous mesophases.
These three- (or more) arm polyphilic systems offer an interesting extension to the better-known
self-assembly of (two-arm) amphiphiles in solution.
Abstract:
Precipitation of barium or strontium carbonates in alkaline silica-rich
environments leads to crystalline aggregates that have been named
silica/carbonate biomorphs because they resemble the morphology of
primitive organisms. These aggregates are self-assembled materials of
purely inorganic origin, with an amorphous phase of silica intimately
intertwined with a carbonate nanocrystalline phase. We propose a
mechanism that explains all the morphologies described for biomorphs.
Chemically coupled co-precipitation of carbonate and silica leads to
fibrillation of the growing front and to laminar structures that experience
curling on their growing rim. These curls propagate surf-like along the rim
of the laminae. Observed morphologies with smoothly varying curvatures
can be explained by the combined growth of counter-propagating curls
and growing laminae.
Comments on this paper can be found at:
environments leads to crystalline aggregates that have been named
silica/carbonate biomorphs because they resemble the morphology of
primitive organisms. These aggregates are self-assembled materials of
purely inorganic origin, with an amorphous phase of silica intimately
intertwined with a carbonate nanocrystalline phase. We propose a
mechanism that explains all the morphologies described for biomorphs.
Chemically coupled co-precipitation of carbonate and silica leads to
fibrillation of the growing front and to laminar structures that experience
curling on their growing rim. These curls propagate surf-like along the rim
of the laminae. Observed morphologies with smoothly varying curvatures
can be explained by the combined growth of counter-propagating curls
and growing laminae.
Comments on this paper can be found at:
- “Oscillating chemistry explains complex, self-assembled crystal aggregates”,Physics Today, (cover article) March, pp. 17-18 (2009)
- Matthias Kellermeier, Fabian Glaab, Anna M. Carnerup, Markus
Drechsler, Benjamin Gossler, Stephen T. Hyde, and Werner Kunz,
“Additive-induced
morphological tuning of self-assembled silica-barium
carbonate crystal aggregates” , J Cryst Growth, 311, 2530-2541, doi:10....sgro.2009.02.044, (2009).
Abstract:
Crystallisation of barium carbonate from alkaline silica
solutions results in the
formation of extraordinary micron-scale architectures exhibiting
non-crystallographic curved shapes, such as helical filaments and worm-like braids.
These so-called “silica biomorphs” consist of a textured assembly of uniform
elongated witherite nanocrystallites, which is occasionally sheathed by a skin of
amorphous silica. Although great efforts have been devoted to clarifying the
physical origin of these fascinating materials, to date little is known about the
processes underlying the observed self-organisation. Herein, we describe the effect
of two selected additives, a cationic surfactant and a cationic polymer, on the
morphology of the forming crystal aggregates, and relate changes to experiments
conducted in the absence of additives. Minor amounts of both substances are shown
to exert a significant influence on the growth process, leading to the formation of
predominantly flower-like spherulitic aggregates. The observed effects are discussed
in terms of feasible morphogenesis pathways. Based on the assumption of a
template membrane steering biomorph formation, it is proposed that the two
additives are capable of performing specific bridging functions promoting the
aggregation of colloidal silica which constitutes the membrane. Morphological
changes are tentatively ascribed to varying colloid coordination effecting distinct
membrane curvatures.
formation of extraordinary micron-scale architectures exhibiting
non-crystallographic curved shapes, such as helical filaments and worm-like braids.
These so-called “silica biomorphs” consist of a textured assembly of uniform
elongated witherite nanocrystallites, which is occasionally sheathed by a skin of
amorphous silica. Although great efforts have been devoted to clarifying the
physical origin of these fascinating materials, to date little is known about the
processes underlying the observed self-organisation. Herein, we describe the effect
of two selected additives, a cationic surfactant and a cationic polymer, on the
morphology of the forming crystal aggregates, and relate changes to experiments
conducted in the absence of additives. Minor amounts of both substances are shown
to exert a significant influence on the growth process, leading to the formation of
predominantly flower-like spherulitic aggregates. The observed effects are discussed
in terms of feasible morphogenesis pathways. Based on the assumption of a
template membrane steering biomorph formation, it is proposed that the two
additives are capable of performing specific bridging functions promoting the
aggregation of colloidal silica which constitutes the membrane. Morphological
changes are tentatively ascribed to varying colloid coordination effecting distinct
membrane curvatures.
- S.J. Ramsden, V. Robins and Stephen Hyde, "3D euclidean nets from
2D hyperbolic tilings: Kaleidoscopic examples", Acta
Crystallogr. A,
A65, 81-108 (2009) [Lead Article.]
Abstract:
We present a method for geometric construction of periodic
3D Euclidean nets by
projecting 2D hyperbolic tilings onto a family of triply periodic minimal surfaces (TPMS).
Our techniques extend the combinatorial tiling theory of Dress, Huson, and
Delgado-Friedrichs to enumerate simple reticulations of these TPMS.
We include a taxonomy of all networks arising from kaleidoscopic hyperbolic
tilings with up to two distinct tile types (and dually two vertex types), mapped
to three related TPMS, namely Schwarz's Primitive (P) and Diamond (D) surfaces,
and Schoen's Gyroid (G)
projecting 2D hyperbolic tilings onto a family of triply periodic minimal surfaces (TPMS).
Our techniques extend the combinatorial tiling theory of Dress, Huson, and
Delgado-Friedrichs to enumerate simple reticulations of these TPMS.
We include a taxonomy of all networks arising from kaleidoscopic hyperbolic
tilings with up to two distinct tile types (and dually two vertex types), mapped
to three related TPMS, namely Schwarz's Primitive (P) and Diamond (D) surfaces,
and Schoen's Gyroid (G)
- Stephen T. Hyde, Michael O’Keeffe and Davide M. Proserpio, "A short history of an elusive yet
ubiquitous structure in chemistry, materials and mathematics",
Angew. Chemie Int. Ed., 47, 7996-8000 (2008).
http://dx.doi.org/10.1002/anie.200801519
Abstract:
Herein we describe some
properties and the occurrences of a beautiful geometric
figure that is ubiquitous in chemistry and materials science, however, it is not as
well-known as it should be. We call attention to the need for mathematicians to pay
more attention to the richly structured natural world, and for materials scientists to
learn a little more about mathematics. Our account is informal and eschews any
pretence of mathematical rigor, but does start with some necessary mathematics.
figure that is ubiquitous in chemistry and materials science, however, it is not as
well-known as it should be. We call attention to the need for mathematicians to pay
more attention to the richly structured natural world, and for materials scientists to
learn a little more about mathematics. Our account is informal and eschews any
pretence of mathematical rigor, but does start with some necessary mathematics.
- Toen Castle, Myfanwy E. Evans and S.T Hyde, “Ravels: Knot-free but not free.
Novel entanglements of graphs in 3-space”, New J Chem, 32,
1484-1492 (2008).
doi:10.1039/b719665b
Abstract:
Molecular and extended framework
materials, from proteins to catenanes and metal–organic
frameworks, can assume knotted configurations in their bonding networks (the chemical graph).
Indeed, knot theory and structural chemistry have remained closely allied, due to those
connections. Here we introduce a new class of graph entanglement: ‘‘ravels’’. These ravels—often
chiral—tangle a graph without the presence of knots. Just as knots lie within cycles in the graph,
ravels lie in the vicinity of a vertex. We introduce various species of ravels, including fragile
ravels, composite ravels and shelled ravels. The role of ravels is examined in the context of finite
and infinite graphs—analogous to molecular and extended framework nets—related to the
diamond net.
frameworks, can assume knotted configurations in their bonding networks (the chemical graph).
Indeed, knot theory and structural chemistry have remained closely allied, due to those
connections. Here we introduce a new class of graph entanglement: ‘‘ravels’’. These ravels—often
chiral—tangle a graph without the presence of knots. Just as knots lie within cycles in the graph,
ravels lie in the vicinity of a vertex. We introduce various species of ravels, including fragile
ravels, composite ravels and shelled ravels. The role of ravels is examined in the context of finite
and infinite graphs—analogous to molecular and extended framework nets—related to the
diamond net.
-
Zakaria A. Almsherqi, Stephen T. Hyde, Malarmathy Ramachandran, Yuru Deng, “Cubic membranes: a structure-based design for DNA uptake”, J. R. Soc. Interface, 5, 1023-1029 (2008).
doi:10.1098/rsif.2007.1351
Abstract:
Cubic membranes are soft
three-dimensional crystals found within cell organelles in a variety
of living systems, despite the aphorism of Fedorov: ‘crystallization is death’. They consist of
multi-bilayer lipid–protein stacks, folded onto anticlastic surfaces that resemble triply
periodic minimal surfaces, forming highly swollen crystalline sponges. Although cubic
membranes have been observed in numerous cell types and under different pathophysiolo-
gical conditions, knowledge about the formation and potential function(s) of non-lamellar,
cubic structures in biological systems is scarce. We report that mitochondria with this cubic
membrane organization isolated from starved amoeba Chaos carolinense interact sufficiently
with short segments of phosphorothioate oligonucleotides ( PS-ODNs) to give significant
ODNs uptake. ODNs condensed within the convoluted channels of cubic membrane by an
unknown passive targeting mechanism. Moreover, the interaction between ODNs and cubic
membrane is sufficient to retard electrophoretic mobility of the ODN component in the gel
matrix. These ODN–cubic membrane complexes are readily internalized within the
cytoplasm of cultured mammalian cells. Transmission electron microscopic analysis confirms
ODNs uptake by cubic membranes and internalization of ODN–cubic membrane complexes
into the culture cells. Cubic membranes thus may offer a new, potentially benign medium for
gene transfection.
of living systems, despite the aphorism of Fedorov: ‘crystallization is death’. They consist of
multi-bilayer lipid–protein stacks, folded onto anticlastic surfaces that resemble triply
periodic minimal surfaces, forming highly swollen crystalline sponges. Although cubic
membranes have been observed in numerous cell types and under different pathophysiolo-
gical conditions, knowledge about the formation and potential function(s) of non-lamellar,
cubic structures in biological systems is scarce. We report that mitochondria with this cubic
membrane organization isolated from starved amoeba Chaos carolinense interact sufficiently
with short segments of phosphorothioate oligonucleotides ( PS-ODNs) to give significant
ODNs uptake. ODNs condensed within the convoluted channels of cubic membrane by an
unknown passive targeting mechanism. Moreover, the interaction between ODNs and cubic
membrane is sufficient to retard electrophoretic mobility of the ODN component in the gel
matrix. These ODN–cubic membrane complexes are readily internalized within the
cytoplasm of cultured mammalian cells. Transmission electron microscopic analysis confirms
ODNs uptake by cubic membranes and internalization of ODN–cubic membrane complexes
into the culture cells. Cubic membranes thus may offer a new, potentially benign medium for
gene transfection.
- Alina E. Voinescu, Matthias Kellermeier, Anna M. Carnerup, Ann-Kristin Larsson, Didier Touraud, Werner Kunz, Lorenz Kienle, Arno Pfitzner and Stephen T. Hyde and, “Inorganic Self-organized silica aragonite biomorphic composites”, Cryst Growth Design, 8, 1515-1521 (2008).
Abstract:
The precipitation of calcium
carbonate in alkaline silica solutions results in the formation of
complex curvilinear
forms if aragonite formation is encouraged by growth at an elevated temperature (80 °C). The resulting coralline self-assembled
silica-calcium carbonate particles are “biomorphs”, bearing a striking resemblance to natural coral forms. These materials, comprised
of calcium carbonate nanocrystals and an amorphous silica matrix, have a complex ultrastructure, made of clusters of gathered
sheets of variable curvatures formed by successive curling. The nanocrystals within these “ruled surfaces” are thin, elongated,
densely packed needles of aragonite. These clusters are outgrowths from central saddlelike cores that resemble developable petaloid
surfaces. The size, shape, crystallography, and chemical composition of the resulting biomorphs were examined by optical microscopy,
field emission scanning electron microscopy (FE-SEM), powder X-ray diffractometry (XRD), Fourier transform infrared spectroscopy
(FT-IR), transmission electron microscopy (TEM and HRTEM), and energy dispersive X-ray analysis (EDX).
forms if aragonite formation is encouraged by growth at an elevated temperature (80 °C). The resulting coralline self-assembled
silica-calcium carbonate particles are “biomorphs”, bearing a striking resemblance to natural coral forms. These materials, comprised
of calcium carbonate nanocrystals and an amorphous silica matrix, have a complex ultrastructure, made of clusters of gathered
sheets of variable curvatures formed by successive curling. The nanocrystals within these “ruled surfaces” are thin, elongated,
densely packed needles of aragonite. These clusters are outgrowths from central saddlelike cores that resemble developable petaloid
surfaces. The size, shape, crystallography, and chemical composition of the resulting biomorphs were examined by optical microscopy,
field emission scanning electron microscopy (FE-SEM), powder X-ray diffractometry (XRD), Fourier transform infrared spectroscopy
(FT-IR), transmission electron microscopy (TEM and HRTEM), and energy dispersive X-ray analysis (EDX).
- G.E. Schröder-Turk, A. Fogden and S.T.Hyde, ” Local v/a variations as a measure of structural packing frustration in bicontinuous mesophases, and geometric arguments for an alternating Im3m (I-WP) phase in block-copolymers with polydispersity”, Eur. Phys. J., B59, 115-126 (2007).
Abstract:
This article explores global
geometric features of bicontinuous space-partitions and their rele-
vance to self-assembly of block-copolymers. Using a robust definition of ‘local channel radius’, based on the
concept of a medial surface [1], we relate radius variations of the space-partition to polymolecular chain
stretching in bicontinuous diblock- and terblock copolymer assemblies. We associate local surface patches
with corresponding cellular volume elements, to define local volume-to-surface ratios. The distribution of
these v/a ratios and of the channel radii are used to quantify the degree of packing frustration of molecular
chains as a function of the specific bicontinuous geometry, modelled by triply-periodic minimal surfaces
and related parallel interfaces. The Gyroid geometry emerges as the most nearly homogeneous bicontinu-
ous form, with the smallest heterogeneity of channel radii, compared to the cubic Primitive and Diamond
surfaces. We clarify a geometric feature of the Gyroid geometry: the three-coordinated nodes of the graph
are not the widest points of the labyrinths; the widest points are at the midpoints of the edges. We also ex-
plore a more complex cubic triply-periodic surface, the I-WP surface, containing two geometrically distinct
channel subdomains. One of the two channel systems is nearly as homogeneous in local channel diameters
as the Gyroid, the other is more heterogeneous than the Primitive surface. Its hybrid nature suggests the
possibility of an “alternating I-WP” phase in polydisperse linear ABC-terpolymer blends, with monodis-
perse molecular weight distributions (MWD) in the A and B blocks and a more polydisperse C block.
vance to self-assembly of block-copolymers. Using a robust definition of ‘local channel radius’, based on the
concept of a medial surface [1], we relate radius variations of the space-partition to polymolecular chain
stretching in bicontinuous diblock- and terblock copolymer assemblies. We associate local surface patches
with corresponding cellular volume elements, to define local volume-to-surface ratios. The distribution of
these v/a ratios and of the channel radii are used to quantify the degree of packing frustration of molecular
chains as a function of the specific bicontinuous geometry, modelled by triply-periodic minimal surfaces
and related parallel interfaces. The Gyroid geometry emerges as the most nearly homogeneous bicontinu-
ous form, with the smallest heterogeneity of channel radii, compared to the cubic Primitive and Diamond
surfaces. We clarify a geometric feature of the Gyroid geometry: the three-coordinated nodes of the graph
are not the widest points of the labyrinths; the widest points are at the midpoints of the edges. We also ex-
plore a more complex cubic triply-periodic surface, the I-WP surface, containing two geometrically distinct
channel subdomains. One of the two channel systems is nearly as homogeneous in local channel diameters
as the Gyroid, the other is more heterogeneous than the Primitive surface. Its hybrid nature suggests the
possibility of an “alternating I-WP” phase in polydisperse linear ABC-terpolymer blends, with monodis-
perse molecular weight distributions (MWD) in the A and B blocks and a more polydisperse C block.
- Alina E. Voinescu, Matthias Kellermeier, Anna M. Carnerup,
Ann-Kristin Larsson, Didier Touraud, Stephen T. Hyde and W. Kunz,
“Co-precipitation of silica
and alkaline-earth carbonates using TEOS as silica source”, J
Cryst Growth, 306 152-158 (2007).
Abstract:
We explore the use of
tetraethoxysilane (TEOS) as a silica source for the formation of
carbonate-silica composite materials known as ‘biomorphs’. The basic hydrolysis of
TEOS furnishes silica in a controllable fashion, allowing a significantly higher reproducibility
of the obtained silica–barium and silica–strontium carbonate co-precipitates compared to
commercial water glass silica used so far. We further discuss the influence of ethanol used
as a co-solvent on the morphologies of biomorphs, which are examined by optical microscopy,
field emission scanning electron microscopy (FESEM) and energy dispersive X-ray analysis (EDX).
carbonate-silica composite materials known as ‘biomorphs’. The basic hydrolysis of
TEOS furnishes silica in a controllable fashion, allowing a significantly higher reproducibility
of the obtained silica–barium and silica–strontium carbonate co-precipitates compared to
commercial water glass silica used so far. We further discuss the influence of ethanol used
as a co-solvent on the morphologies of biomorphs, which are examined by optical microscopy,
field emission scanning electron microscopy (FESEM) and energy dispersive X-ray analysis (EDX).
- S.T. Hyde and G.E. Schröder-Turk, “Tangled (up in) Cubes”, Acta
Cryst A63 186-197 (2007).
Abstract:
The ‘simplest’ entanglements of
the graph of edges of the cube are enumerated,
forming two-cell {6, 3} (hexagonal mesh) complexes on the genus-one two-
dimensional torus. Five chiral pairs of knotted graphs are found. The examples
contain non-trivial knotted and/or linked subgraphs [(2, 2), (2, 4) torus links and
(3, 2), (4, 3) torus knots].
forming two-cell {6, 3} (hexagonal mesh) complexes on the genus-one two-
dimensional torus. Five chiral pairs of knotted graphs are found. The examples
contain non-trivial knotted and/or linked subgraphs [(2, 2), (2, 4) torus links and
(3, 2), (4, 3) torus knots].
