Programmable Self-Assembly of Nanoplates into Bicontinuous Nanostructures

Self-assembly is the process by which individual components arrange themselves into an ordered structure by changing the shapes, components, and interactions. It has enabled us to construct an extensive range of geometric forms on many length scales. Nevertheless, the potential of two-dimensional polygonal nanoplates to self-assemble into extended three-dimensional structures with compartments and corridors has remained unexplored. In this paper, we show coarse-grained Monte Carlo simulations demonstrating self-assembly of hexagonal/triangular nanoplates via complementary interactions into faceted, sponge-like "bicontinuous polyhedra" (or infinite polyhedra) whose flat walls partition space into a pair of mutually interpenetrating labyrinths. Two bicontinuous polyhedra can be self-assembled: the regular (or Platonic) Petrie-Coxeter infinite polyhedron (denoted {6,4|4}) and the semi-regular Hart "gyrangle". The latter structure is chiral, with both left- and right-handed versions. We show that the Petrie-Coxeter assembly is constructed from two complementary populations of hexagonal nanoplates. Furthermore, we find that the 3D chiral Hart gyrangle can be assembled from identical achiral triangular nanoplates decorated with regioselective complementary interaction sites. The assembled Petrie-Coxeter and Hart polyhedra are faceted versions of two of the simplest triply periodic minimal surfaces, namely, Schwarz's primitive and Schoen's gyroid surfaces, respectively, offering alternative routes to those bicontinuous nanostructures, which are widespread in synthetic and biological materials.

Mapping hyperbolic order in curved materials

Nature employs an impressive range of topologically complex ordered nanostructures that occur in various forms in both natural and synthetic materials. A particular class of these exhibits negative curvature and forms periodic saddle-shaped surfaces in three dimensions. Unlike pattern formation on flat or positively curved surfaces like spherical systems, the understanding of patterning on such surfaces is highly complicated due to the structures being intrinsically intertwined in three dimensions. We present a new method for visualisation and analysis of patterns on triply periodic negatively curved surfaces by mapping to two-dimensional hyperbolic space analogous to spherical projections in cartography thus effectively creating a more accessible "hyperbolic map" of the pattern. Specifically, we exemplify the method via the simplest triply periodic minimal surfaces: the Primitive, Diamond, and Gyroid in their universal cover along with decorations from a soft materials, whose structures involve decorations of soft matter on negatively curved surfaces, not necessarily minimal.

Starfish grow extraordinary crystals

Biomineralization in a starfish displays morphologically complex features.

The intrinsic group-subgroup structures of the Diamond and Gyroid minimal surfaces in their conventional unit cells

The intrinsic, hyperbolic crystallography of the Diamond and Gyroid minimal surfaces in their conventional unit cells is introduced and analysed. Tables are constructed of symmetry subgroups commensurate with the translational symmetries of the surfaces as well as group-subgroup lattice graphs.

Schwarzite nets: a wealth of 3-valent examples sharing similar topologies and symmetries

We enumerate trivalent reticulations of two- and three-periodic hyperbolic surfaces by equal-sided n -gonal faces, ( n , 3), where n  = 7, 8, 9, 10, 12. These are the simplest hyperbolic generalizations of the planar graphene net, (6, 3) and dodecahedrane, (5, 3). The enumeration proceeds by deleting isometries of regular reticulations of two-dimensional hyperbolic space until the ( n , 3) nets can be embedded in euclidean three-space via periodic hyperbolic surfaces. Those nets are then symmetrized in euclidean space retaining their net topology, leading to explicit crystallographic net embeddings whose edges are as equal as possible, affording candidtae patterns for graphitic schwarzites. The resulting schwarzites are the most symmetric examples. More than one hundred topologically distinct nets are described, most of which are novel.

Polar-Nonpolar Interfaces of Normal Bicontinuous Cubic Phases in Nonionic Surfactant/Water Systems Are Parallel to the Gyroid Surface

We investigated the structures of normal (type I) bicontinuous cubic phases in hexa-, hepta-, and octaethylene glycol dodecyl ether/water mixtures by small-angle X-ray crystallography of single-crystal domains. Reconstructed electron densities showed that the hydrophilic chains with high electron density are confined to a film centered on the surface of the Gyroid (a triply periodic minimal surface), while hydrophobic chains with low electron density are distributed within the pair of interwoven labyrinths carved out by the Gyroid. Further, the local minimum within the high electron density region, due to bulk water, coincides precisely with the Gyroid. This minimum is less pronounced in mixtures with longer ethylene glycol chains, consistent with their decreased water content. Our analysis clearly shows that the polar-nonpolar interfaces are parallel to the Gyroid surface in all mixtures. The repulsive hydration or overlapping force between the pair of facing monolayers of ethylene glycol chains on either side of the Gyroid surface is the likely origin of the parallel interfaces.

Surface embeddings of the Klein and the Möbius-Kantor graphs

This paper describes an invariant representation for finite graphs embedded on orientable tori of arbitrary genus, with working examples of embeddings of the Möbius-Kantor graph on the torus, the genus-2 bitorus and the genus-3 tritorus, as well as the two-dimensional, 7-valent Klein graph on the tritorus (and its dual: the 3-valent Klein graph). The genus-2 and -3 embeddings describe quotient graphs of 2- and 3-periodic reticulations of hyperbolic surfaces. This invariant is used to identify infinite nets related to the Möbius-Kantor and 7-valent Klein graphs.

Optimal packings of three-arm star polyphiles: from tricontinuous to quasi-uniformly striped bicontinuous forms

Star-shaped molecules with three mutually immiscible arms self-assemble to form a variety of novel structures, with conformations that attempt to minimize interfacial area between the domains composed of the different arms. The geometric frustration caused by the joining of these arms at a common centre limits the size and shape of each domain, encouraging the creation of complex and interesting solutions. Some solutions are tricontinuous, and these solutions (and others) share aspects of bicontinuous structures with amphiphilic assemblies as similar molecular segregation factors are at work. We describe both highly symmetric and balanced structures, as well as unbalanced solutions that take the form of intricately striped amphiphilic membranes. All these patterns can result in chiral assemblies with multiple networks.

Hyperbolic crystallography of two-periodic surfaces and associated structures

This paper describes the families of the simplest, two-periodic constant mean curvature surfaces, the genus-two HCB and SQL surfaces, and their isometries. All the discrete groups that contain the translations of the genus-two surfaces embedded in Euclidean three-space modulo the translation lattice are derived and enumerated. Using this information, the subgroup lattice graphs are constructed, which contain all of the group-subgroup relations of the aforementioned quotient groups. The resulting groups represent the two-dimensional representations of subperiodic layer groups with square and hexagonal supergroups, allowing exhaustive enumeration of tilings and associated patterns on these surfaces. Two examples are given: a two-periodic [3,7]-tiling with hyperbolic orbifold symbol {\sf {2223}} and a {\sf {22222}} surface decoration.

Periodic entanglement III: tangled degree-3 finite and layer net intergrowths from rare forests

Entanglements of two-dimensional honeycomb nets are constructed from free tilings of the hyperbolic plane (H2) on triply periodic minimal surfaces. The 2-periodic nets that comprise the structures are guaranteed by considering regular, rare free tilings in H2. This paper catalogues an array of entanglements that are both beautiful and challenging for current classification techniques, including examples that are realized in metal-organic materials. The compactification of these structures to the genus-3 torus is considered as a preliminary method for generating entanglements of finite θ-graphs, potentially useful for gaining insight into the entanglement of the periodic structure. This work builds on previous structural enumerations given in Periodic entanglement Parts I and II [Evans et al. (2013). Acta Cryst. A69, 241-261; Evans et al. (2013). Acta Cryst. A69, 262-275].

Docetaxel-Loaded Fluorescent Liquid-Crystalline Nanoparticles for Cancer Theranostics

Here, we describe a novel monoolein-based cubosome formulation engineered for possible theranostic applications in oncology. The Docetaxel-loaded nanoparticles were stabilized in water by a mixture of commercial Pluronic (poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer) F108 (PF108) and rhodamine- and folate-conjugated PF108 so that the nanoparticles possess targeting, therapeutic, and imaging properties. Nanoparticles were investigated by DLS, cryo-TEM, and SAXS to confirm their structural features. The fluorescent emission characterization of the proposed formulation indicated that the rhodamine conjugated to the PF108 experiences an environment less polar than water (similar to chloroform), suggesting that the fluorescent fragment is buried within the poly(ethylene oxide) corona surrounding the nanoparticle. Furthermore, these nanoparticles were successfully used to image living HeLa cells and demonstrated a significant short-term (4 h incubation) cytotoxicity effect against these cancer cells. Furthermore, given their analogy as nanocarriers for molecules of pharmaceutical interest and to better stress the singularities of these bicontinuous cubic nanoparticles, we also quantitatively evaluated the differences between cubosomes and multilamellar liposomes in terms of surface area and hydrophobic volume.

Ideal geometry of periodic entanglements

Three-dimensional entanglements, including knots, knotted graphs, periodic arrays of woven filaments and interpenetrating nets, form an integral part of structure analysis because they influence various physical properties. Ideal embeddings of these entanglements give insight into identification and classification of the geometry and physically relevant configurations in vivo . This paper introduces an algorithm for the tightening of finite, periodic and branched entanglements to a least energy form. Our algorithm draws inspiration from the Shrink-On-No-Overlaps (SONO) (Pieranski 1998 In Ideal knots (eds A Stasiak, V Katritch, LH Kauffman), vol. 19, pp. 20–41.) algorithm for the tightening of knots and links: we call it Periodic-Branched Shrink-On-No-Overlaps (PB-SONO). We reproduce published results for ideal configurations of knots using PB-SONO. We then examine ideal geometry for finite entangled graphs, including θ -graphs and entangled tetrahedron- and cube-graphs. Finally, we compute ideal conformations of periodic weavings and entangled nets. The resulting ideal geometry is intriguing: we see spontaneous symmetrisation in some cases, breaking of symmetry in others, as well as configurations reminiscent of biological and chemical structures in nature.

Crystals: animal, vegetable or mineral?

The morphologies of biological materials, from body shapes to membranes within cells, are typically curvaceous and flexible, in contrast to the angular, facetted shapes of inorganic matter. An alternative dichotomy has it that biomolecules typically assemble into aperiodic structures in vivo, in contrast to inorganic crystals. This paper explores the evolution of our understanding of structures across the spectrum of materials, from living to inanimate, driven by those naive beliefs, with particular focus on the development of crystallography in materials science and biology. The idea that there is a clear distinction between these two classes of matter has waxed and waned in popularity through past centuries. Our current understanding, driven largely by detailed exploration of biomolecular structures at the sub-cellular level initiated by Bernal and Astbury in the 1930s, and more recent explorations of sterile soft matter, makes it clear that this is a false dichotomy. For example, liquid crystals and other soft materials are common to both living and inanimate materials. The older picture of disjoint universes of forms is better understood as a continuum of forms, with significant overlap and common features unifying biological and inorganic matter. In addition to the philosophical relevance of this perspective, there are important ramifications for science. For example, the debates surrounding extra-terrestrial life, the oldest terrestrial fossils and consequent dating of the emergence of life on the Earth rests to some degree on prejudices inferred from the supposed dichotomy between life-forms and the rest.

Comment on "Discovery of a tetracontinuous, aqueous lyotropic network phase with unusual 3D-hexagonal symmetry" by M. Mahanthappa, G. Sorenson and A. Schmitt

The article by Sorenson et al. (Soft Matter10, 8229, 2014) reports a novel phase formed by gemini surfactants in water, of symmetry P63/mcm and based on a triple intergrowth of three identical degree-three networks, known as 3etc(193). This phase is the first lyotropic liquid crystalline phase based on the intergrowth of a triplet of network- or labyrinth-like hydrophobic domains. We provide here results from self-consistent field theory that demonstrate that the same morphology is almost stable in standard AB diblock copolymer melts; at the phase transition between the double gyroid phase and the hexagonal columnar phase, the 3etc(193) morphology only incurs a marginal free energy penalty compared to the equilibrium phases. Interestingly, the ratio of lattice parameters c/a = 0.955 of the 3etc(193) as a diblock morphology is very close to that of the gemini surfactant phase and of the related IBN-9 mesoporous silicate phase (Han et al., Nat. Chem.1, 123, 2009). Based on the combination of these results, we hypothesise that the 3etc(193) morphology is likely a generic phase in soft materials, rather than an oddity.

Structural directing roles of isomeric phenylenediacetate ligands in the formation of coordination networks based on flexible N,N′-di(3-pyridyl)suberoamide

A 5-fold cds net and 1D network with a new mode of entanglement were formed from N,N′-di(3-pyridyl)suberoamide with Cu(ii) salts.

Tiling patterns from ABC star molecules: 3-colored foams?

We present coarse-grained simulations of the self-assembly of 3-armed ABC star polyphiles. In systems of star polyphiles with two arms of equal length the simulations corroborate and expand previous findings from related miktoarm star terpolymer systems on the formation of patterns containing columnar domains whose sections are 2D planar tilings. However, the systematic variation of face topologies as the length of the third (unequal) arm is varied differs from earlier findings regarding the compositional dependence. We explore 2D 3-colored foams to establish the optimal patterns based on interfacial energy alone. A generic construction algorithm is described that accounts for all observed 2D tiling patterns and suggests other patterns likely to be found beyond the range of the simulations reported here. Patterns resulting from this algorithm are relaxed using Surface Evolver calculations to form 2D foams with minimal interfacial length as a function of composition. This allows us to estimate the interfacial enthalpic contributions to the free energy of related star molecular assemblies assuming strong segregation. We compare the resulting phase sequence with a number of theoretical results from particle-based simulations and field theory, allowing us to tease out relative enthalpic and entropic contributions as a function of the chain lengths making up the star molecules. Our results indicate that a richer polymorphism is to be expected in systems not dominated by chain entropy. Further, analysis of corresponding planar tiling patterns suggests that related two-periodic columnar structures are unlikely hypothetical phases in 4-arm star polyphile melts in the absence of sufficient arm configurational freedom for minor domains to form lens-shaped di-gons, which require higher molecular weight polymeric arms. Finally, we discuss the possibility of forming a complex tiling pattern that is a quasi-crystalline approximant for 3-arm star polyphiles with unequal arm lengths.

Experimental investigation of the mechanical stiffness of periodic framework-patterned elastomers

Recent advances in the cataloguing of three-dimensional nets mean a systematic search for framework structures with specific properties is now feasible. Theoretical arguments about the elastic deformation of frameworks suggest characteristics of mechanically isotropic networks. We explore these concepts on both isotropic and anisotropic networks by manufacturing porous elastomers with three different periodic net geometries. The blocks of patterned elastomers are subjected to a range of mechanical tests to determine the dependence of elastic moduli on geometric and topological parameters. We report results from axial compression experiments, three-dimensional X-ray computed tomography imaging and image-based finite-element simulations of elastic properties of framework-patterned elastomers.

Hierarchical self-assembly of a striped gyroid formed by threaded chiral mesoscale networks

Numerical simulations reveal a family of hierarchical and chiral multicontinuous network structures self-assembled from a melt blend of Y-shaped ABC and ABD three-miktoarm star terpolymers, constrained to have equal-sized A/B and C/D chains, respectively. The C and D majority domains within these patterns form a pair of chiral enantiomeric gyroid labyrinths (srs nets) over a broad range of compositions. The minority A and B components together define a hyperbolic film whose midsurface follows the gyroid minimal surface. A second level of assembly is found within the film, with the minority components also forming labyrinthine domains whose geometry and topology changes systematically as a function of composition. These smaller labyrinths are well described by a family of patterns that tile the hyperbolic plane by regular degree-three trees mapped onto the gyroid. The labyrinths within the gyroid film are densely packed and contain either graphitic hcb nets (chicken wire) or srs nets, forming convoluted intergrowths of multiple nets. Furthermore, each net is ideally a single chiral enantiomer, induced by the gyroid architecture. However, the numerical simulations result in defect-ridden achiral patterns, containing domains of either hand, due to the achiral terpolymeric starting molecules. These mesostructures are among the most topologically complex morphologies identified to date and represent an example of hierarchical ordering within a hyperbolic pattern, a unique mode of soft-matter self-assembly.

Nets with collisions (unstable nets) and crystal chemistry

Nets in which different vertices have identical barycentric coordinates (i.e.have collisions) are called unstable. Some such nets have automorphisms that do not correspond to crystallographic symmetries and are called non-crystallographic. Examples are given of nets taken from real crystal structures which have embeddings with crystallographic symmetry in which colliding nodes either are, or are not, topological neighbors (linked) and in which some links coincide. An example is also given of a crystallographic net of exceptional girth (16), which has collisions in barycentric coordinates but which also has embeddings without collisions with the same symmetry. In this last case the collisions are termedunforced.

Trading spaces: building three-dimensional nets from two-dimensional tilings

We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic (S (2)), Euclidean (E (2)) and hyperbolic (H (2)) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions.

From three-dimensional weavings to swollen corneocytes

A novel technique to generate three-dimensional Euclidean weavings, composed of close-packed, periodic arrays of one-dimensional fibres, is described. Some of these weavings are shown to dilate by simple shape changes of the constituent fibres (such as fibre straightening). The free volume within a chiral cubic example of a dilatant weaving, the ideal conformation of the G(129) weaving related to the Σ(+) rod packing, expands more than fivefold on filament straightening. This remarkable three-dimensional weaving, therefore, allows an unprecedented variation of packing density without loss of structural rigidity and is an attractive design target for materials. We propose that the G(129) weaving (ideal Σ(+) weaving) is formed by keratin fibres in the outermost layer of mammalian skin, probably templated by a folded membrane.

Circular dichroism in biological photonic crystals and cubic chiral nets

Nature provides impressive examples of chiral photonic crystals, with the notable example of the cubic so-called srs network (the label for the chiral degree-three network modeled on SrSi2) or gyroid structure realized in wing scales of several butterfly species. By a circular polarization analysis of the band structure of such networks, we demonstrate strong circular dichroism effects: The butterfly srs microstructure, of cubic I4(1)32 symmetry, shows significant circular dichroism for blue to ultraviolet light, that warrants a search for biological receptors sensitive to circular polarization. A derived synthetic structure based on four like-handed silicon srs nets exhibits a large circular polarization stop band of a width exceeding 30%. These findings offer design principles for chiral photonic devices.

The chiral structure of porous chitin within the wing-scales of Callophrys rubi

The structure of the porous three-dimensional reticulated pattern in the wing scales of the butterfly Callophrys rubi (the Green Hairstreak) is explored in detail, via scanning and transmission electron microscopy. A full 3D tomographic reconstruction of a section 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 surface to the Gyroid, a three-periodic minimal surface with cubic crystallographic symmetry I4₁32, 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 parallel-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.

Morphogenesis of self-assembled nanocrystalline materials of barium carbonate and silica

The precipitation of barium or strontium carbonates in alkaline silica-rich environments leads to crystalline aggregates that have been named silica/carbonate biomorphs because their morphology resembles that 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 coprecipitation of carbonate and silica leads to fibrillation of the growing front and to laminar structures that experience curling at their growing rim. These curls propagate in a surflike way along the rim of the laminae. We show that all observed morphologies with smoothly varying positive or negative Gaussian curvatures can be explained by the combined growth of counterpropagating curls and growing laminae.

Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples

We present a method for geometric construction of periodic three-dimensional Euclidean nets by projecting two-dimensional hyperbolic tilings onto a family of triply periodic minimal surfaces (TPMSs). Our techniques extend the combinatorial tiling theory of Dress, Huson & Delgado-Friedrichs to enumerate simple reticulations of these TPMSs. We include a taxonomy of all networks arising from kaleidoscopic hyperbolic tilings with up to two distinct tile types (and their duals, with two distinct vertices), mapped to three related TPMSs, namely Schwarz's primitive (P) and diamond (D) surfaces, and Schoen's gyroid (G).

Tangled (up in) cubes

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].

Self-Assembled Silica-Carbonate Structures and Detection of Ancient Microfossils

We have synthesized inorganic micron-sized filaments, whose microstucture consists of silica-coated nanometer-sized carbonate crystals, arranged with strong orientational order. They exhibit noncrystallographic, curved, helical morphologies, reminiscent of biological forms. The filaments are similar to supposed cyanobacterial microfossils from the Precambrian Warrawoona chert formation in Western Australia, reputed to be the oldest terrestrial microfossils. Simple organic hydrocarbons, whose sources may also be abiotic and indeed inorganic, readily condense onto these filaments and subsequently polymerize under gentle heating to yield kerogenous products. Our results demonstrate that abiotic and morphologically complex microstructures that are identical to currently accepted biogenic materials can be synthesized inorganically.

Meditation on an Engraving of Fricke and Klein (The Modular Group and Geometrical Chemistry)

A non-technical account of the links between two-dimensional (2D) hyperbolic and three-dimensional (3D) euclidean symmetric patterns is presented, with a number of examples from both spaces. A simple working hypothesis is used throughout the survey: simple, highly symmetric patterns traced in hyperbolic space lead to chemically relevant structures in euclidean space. The prime examples in the former space are derived from Felix Klein's engraving of the modular group structure within the hyperbolic plane; these include various tilings, networks and trees. Disc packings are also derived. The euclidean examples are relevant to condensed atomic and molecular materials in solid-state chemistry and soft-matter structural science. They include extended nets of relevance to covalent frameworks, simple (lattice) sphere packings, and interpenetrating extended frameworks (related to novel coordination polymers). Limited discussion of the projection process from 2D hyperbolic to 3D euclidean space via mapping onto triply periodic minimal surfaces is presented.

Morphology: an ambiguous indicator of biogenicity

This paper deals with the difficulty of decoding the origins of natural structures through the study of their morphological features. We focus on the case of primitive life detection, where it is clear that the principles of comparative anatomy cannot be applied. A range of inorganic processes are described that result in morphologies emulating biological shapes, with particular emphasis on geochemically plausible processes. In particular, the formation of inorganic biomorphs in alkaline silica-rich environments are described in detail.

Interwoven metal-organic framework on a periodic minimal surface with extra-large pores

Interpenetration (catenation) has long been considered a major impediment in the achievement of stable and porous crystalline structures. A strategy for the design of highly porous and structurally stable networks makes use of metal-organic building blocks that can be assembled on a triply periodic P-minimal geometric surface to produce structures that are interpenetrating-more accurately considered as interwoven. We used 4,4',4"-benzene-1,3,5-triyl-tribenzoic acid (H(3)BTB), copper(II) nitrate, and N,N'-dimethylformamide (DMF) to prepare Cu(3)(BTB)(2)(H(2)O)(3).(DMF)(9)(H(2)O)(2) (MOF-14), whose structure reveals a pair of interwoven metal-organic frameworks that are mutually reinforced. The structure contains remarkably large pores, 16.4 angstroms in diameter, in which voluminous amounts of gases and organic solvents can be reversibly sorbed.