Interpenetration of homogeneous sphere packings and of two-periodic layers of spheres

M, Rawat P, Singh RN, Shahid M, Trivedi S, Gautam A, Zeeshan M. A new Zn(ii) MOF assembled from metal–organic cubes (MOCs) as a highly efficient adsorbent for cationic dyes

A new MOC [Zn₃(Tz)₂(tpa)₂(DMSO)₄] was synthesized. The cluster representation reveals an interwoven pcu 6/4/c1 sqc1 topological type. The MOC exhibits excellent water stability, recyclability, adsorption and separation abilities toward selected dyes.

Isotopy classes for 3-periodic net embeddings

Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. Periodic isotopy classifications are obtained for various families of embedded nets with small quotient graphs. The 25 periodic isotopy classes of depth-1 embedded nets with a single-vertex quotient graph are enumerated. Additionally, a classification is given of embeddings of n-fold copies of pcu with all connected components in a parallel orientation and n vertices in a repeat unit, as well as demonstrations of their maximal symmetry periodic isotopes. The methodology of linear graph knots on the flat 3-torus [0,1)3 is introduced. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.

A novel sustainable metal organic framework as the ultimate aqueous phase sensor for natural hazards: detection of nitrobenzene and F− at the ppb level and rapid and selective adsorption of methylene blue

A novel metal organic framework (MOF) exhibits good aqueous phase sensing properties towards nitrobenzene and fluoride anions and selective adsorption/separation ability for methylene blue.

A new cubic Ia3̅d crystal structure observed in a model single component system by molecular dynamics simulation

In our molecular dynamics simulations of the system of identical particles interacting through the harmonic-repulsive pair potential, we observed the formation of a cubic crystal structure that belongs to the Ia3̅d (#230) crystallographic space group. This crystal structure has not been previously seen either in experiments or in computer simulations, though its framework topology has been known from theoretical crystallographic considerations. Its unit cell contains 16 atoms, occupying only (16b) Wyckoff site, and arranged as two mutually intertwined unconnected networks with packing fraction of 0.37. The appearance of this structure is explained by the soft repulsive nature of the interaction potential. The observed Ia3̅d structure extends the small number of cubic structures formed in single component systems with spherically symmetric pair potentials in MD simulations. We speculate that materials with such structure could be found in soft matter systems or in selected crystals under high pressure.

On the group-theoretical approach to the study of interpenetrating nets

Using group–subgroup and group–supergroup relations, a general theoretical framework is developed to describe and derive interpenetrating 3-periodic nets. The generation of interpenetration patterns is readily accomplished by replicating a single net with a supergroupGof its space groupHunder the condition that site symmetries of vertices and edges are the same in bothHandG. It is shown that interpenetrating nets cannot be mapped onto each other by mirror reflections because otherwise edge crossings would necessarily occur in the embedding. For the same reason any other rotation or roto-inversion axes fromG \ Hare not allowed to intersect vertices or edges of the nets. This property significantly narrows the set of supergroups to be included in the derivation of interpenetrating nets. A procedure is described based on the automorphism group of aHopf ring net[Alexandrovet al.(2012).Acta Cryst.A68, 484–493] to determine maximal symmetries compatible with interpenetration patterns. The proposed approach is illustrated by examples of twofold interpenetratedutp,diaandpcunets, as well as multiple copies of enantiomorphic quartz (qtz) networks. Some applications to polycatenated 2-periodic layers are also discussed.

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].

High-symmetry embeddings of interpenetrating periodic nets. Essential rings and patterns of catenation

Symmetrical embeddings are given for multiply intergrown sets of some commonly occurring nets such asdia(diamond),qtz(quartz),pcu(net of primitive cubic lattice) andsrs(labyrinth net of theGminimal surface). Data are also given for all known pairs of nets which have edge-transitive self-dual tilings. Examples are given for symmetrical polycatenation of the 2-periodic netssql(square lattice) andhcb(honeycomb). The idea that the rings that are the faces of natural tilings form a complete basis set (essential rings) is explored and patterns of catenation of such rings described.