Aperiodic Networks Research Articles

Enhanced elastic stability of a topologically disordered crystalline metal–organic framework

By virtue of their open network structures and low densities, metal–organic frameworks (MOFs) are soft materials that exhibit elastic instabilities at low applied stresses. The conventional strategy for improving elastic stability is to increase the connectivity of the underlying MOF network, which necessarily increases the material density and reduces the porosity. Here we demonstrate an alternative paradigm, whereby elastic stability is enhanced in a MOF with an aperiodic network topology. We use a combination of variable-pressure single-crystal X-ray diffraction measurements and coarse-grained lattice-dynamical calculations to interrogate the high-pressure behaviour of the topologically aperiodic system TRUMOF-1, which we compare against that of its ordered congener MOF-5. We show that the topology of the former quenches the elastic instability responsible for pressure-induced framework collapse in the latter, much as irregularity in the shapes and sizes of stones acts to prevent cooperative mechanical failure in drystone walls. Our results establish aperiodicity as a counter-intuitive design motif in engineering the mechanical properties of framework structures that is relevant to MOFs and larger-scale architectures alike.

A Mathematical Theory of Heartbeat

This article develops a novel mathematical theory of pacemaker operation using complexity theory and network science ideas. Specifically, the author claims that pacing is a byproduct of emergence of a self-synchronizing electrical network in humans (and animals) based on a fundamental property of feedback networks – aperiodicity. The exceptional resilience and reliability of the ordinary heartbeat may be due to the emergence of a self-organized network in the sinoatrial node and the particular property of aperiodic networks. Clinical studies should be performed to verify the model. Using simulation, we show that aperiodic synchronization arises almost naturally in random network structures due to the presence of many feedback loops with lengths that are relatively prime to each other. Furthermore, we show that nearly any random network of sufficient density “naturally” forms an aperiodic subset of nodes that synchronize to provide a reliable and resilient “clock” for regulating biological rhythms such as heartbeat.

Construction of 2D metal-organic precursor networks with tunable porosity: A Monte Carlo simulation approach

Two-dimensional network structures comprising functional organic building blocks have been recently recognized as promising platforms for various physio-chemical processes running in confined spaces. In this study, we present theoretical results of the self-assembly of metal-organic precursor networks on a crystalline surface and provide quantitative characteristics of these planar architectures. To that end, a coarse-grained model of the adsorbed overlayer comprising halogenated polyaromatic aromatic hydrocarbon (PAH) molecules and bivalent metal atoms was used in combination with the equilibrium Monte Carlo (MC) simulation method. Our calculations focused on the effect of molecular features, such as size, shape and distribution of halogen substituents in the PAH monomer, on the quality and morphology of the networks formed on a model (111) crystalline surface. For the simulated porous assemblies, representing the precursor stage of the surface-assisted Ullmann coupling reaction, such descriptors as the unit cell parameters, radial distribution functions, pore size distributions and structure factors were determined. The obtained results demonstrated that fine-tuning of the monomeric PAH units enables the creation of periodic and aperiodic networks having diverse porous properties, ranging from monoporous to heteroporous with bi- and multimodal pore-size distributions. The findings of our theoretical investigations, apart from the potential application in the optimization of 2D polymeric networks, can also be helpful in designing real confined nanoenvironments for selective capture and immobilization/transformation of guest species.

Monte Carlo simulation of the surface-assisted self-assembly of metal-organic precursors comprising phenanthrene building blocks

Surface-assisted fabrication of carbon-based covalent architectures has been a promising pathway to low-dimensional materials with special physicochemical properties and functions. In this contribution, the Monte Carlo simulation method was used to predict the formation of metal-organic precursors preceding the covalent Ullmann coupling of halogenated phenanthrene monomers. To that end, the coarse-grained model of adsorbing (111) surface, phenanthrene molecules and linking adatoms was proposed, in which the monomers were equipped with active centers providing directional metal-linker interactions. The simulations performed for various intramolecular distributions of active centers in the phenanthrene unit (corresponding to halogen positions) resulted in diverse metal-organic superstructures, including chains, ring oligomers, triangular and windmill trimers, ladders, and periodic and aperiodic networks. For those molecules which were chiral in 2D the corresponding calculations in enantiopure and racemic overlayers were also carried out. These simulations resulted in characteristic examples of both advantageous and adverse effect of the opposite enantiomer on the ordering in racemic systems. Our theoretical findings provided some hints on how to halogenate monomeric phenanthrene units to create polymeric architectures with presumed structural features, such as topology, periodicity, connectivity, ramification and porosity.

Theoretical Modeling of the Metal-Organic Precursors of Anthracene-Based Covalent Networks on Surfaces.

Surface-assisted fabrication of molecular network architectures has been a promising route to low-dimensional materials with unique physicochemical properties and functionalities. One versatile way in this field is the Ullmann coupling reaction of halogenated organic monomers on catalytically active metallic surfaces. In this work, using the coarse-grained Monte Carlo simulations, we studied the on-surface self-assembly of metal-organic precursors preceding the covalent Ullman-type linkage of tetrahalogenated anthracene building blocks. To that end, a series of positional isomers was examined and classified with respect to their ability of creation of extended network structures. Our simulations focused on the identification of basic types of self-assembly scenarios distinguishing enantiopure and racemic systems and producing periodic and aperiodic networks. The calculations carried out for selected tectons demonstrated wide possibilities of controlling porosity (e. g. pore size, shape, periodicity, chirality, heterogeneity) of the networks by suitable functionalization of the monomeric unit. The findings reported herein can be helpful in rational designing of 2D polymeric networks with predefined structures and properties.

Aperiodic sleep networks promote memory consolidation.

Hierarchical synchronization of sleep oscillations establishes communication pathways to support memory reactivation, transfer, and consolidation. From an information-theoretical perspective, oscillations constitute highly structured network states that provide limited information-coding capacity. Recent findings indicate that sleep oscillations occur in transient bursts that are interleaved with aperiodic network states, which were previously considered to be random noise. We argue that aperiodic activity exhibits unique and variable spatiotemporal patterns, providing an ideal information-rich neurophysiological substrate for imprinting new mnemonic patterns onto existing circuits. We discuss novel avenues in conceptualizing and quantifying aperiodic network states during sleep to further understand their relevance and interplay with sleep oscillations in support of memory consolidation.

Halogenated Anthracenes as Building Blocks for the On-Surface Synthesis of Covalent Polymers: Structure Prediction with the Lattice Monte Carlo Method

Functionalized polycyclic aromatic hydrocarbons (PAHs) have been recently recognized as promising building blocks for surface-assisted polymerization reactions producing low-dimensional covalent structures with tailorable properties. In this work, we used the lattice Monte Carlo (MC) simulation method to predict the structure of the labile metal–(halogenated)anthracene connections preceding the formation of covalent polymers in the Ullmann-type coupling reaction occurring on catalytically active metallic surfaces. To that purpose, a coarse-grained model of mono-, di-, and trisubstituted anthracene monomers and two-coordinate metal atoms was proposed, in which these components were adsorbed on a triangular lattice. The formation of metal–organic nodes cementing the resulting superstructures was assumed to be dependent on the directionality of the short-range interactions assigned differently to PAH molecules. Our extensive MC simulations performed for the complete set of 50 positional isomers predicted various organometallic intermediates with morphologies ranging from cyclic oligomers, chains, ladders, ribbons to aperiodic networks and others. These results were compared with the analogous findings obtained for the smaller naphthalene unit. The outcome of the theoretical studies reported herein can be helpful in designing low-dimensional covalent polymers with tunable architecture and functions.

Ultrastrong extraordinary transmission and reflection in PT-symmetric Thue-Morse optical waveguide networks.

In this paper, we construct a 1D PT-symmetric Thue-Morse aperiodic optical waveguide network (PTSTMAOWN) and mainly investigate the ultrastrong extraordinary transmission and reflection. We propose an approach to study the photonic modes and solve the problem of calculating photonic modes distributions in aperiodic networks due to the lack of dispersion functions and find that in a PTSTMAOWN there exist more photonic modes and more spontaneous PT-symmetric breaking points, which are quite different from other reported PT-symmetric optical systems. Additionally, we develop a method to sort spontaneous PT-symmetric breaking point zones to seek the strongest extraordinary point and obtain that at this point the strongest extraordinary transmission and reflection arrive at 2.96316 × 105 and 1.32761 × 105, respectively, due to the PT-symmetric coupling resonance and the special symmetry pattern of TM networks. These enormous gains are several orders of magnitude larger than the previous results. This optical system may possess potential in designing optical amplifier, optical logic elements in photon computers and ultrasensitive optical switches with ultrahigh monochromatity.

Compositional dependence of the optical properties of novel Ga–Sb–S–XI (XI = PbI2, CsI, AgI) infrared chalcogenide glasses

AbstractA novel family of Ga2S3–Sb2S3–XI (XI = PbI2, CsI, AgI) was investigated to understand the role of metal halides and exploit new chalco‐halide glasses for infrared optics. The dependence of the thermal properties, infrared optical properties, and structural information of the novel family on different metal–iodines was investigated. Results showed that metal halides increase the glass stability but decrease the glass network connectivity. The compositional dependence of the short‐wave cut‐off edge is associated with the electronegativity difference between the cations and anions of the metal halides. Raman study showed that the metal–iodine modified the glass structure mainly through the iodide content, and the cations dissolved in the glass network mostly as charge compensators for the aperiodic network. For the glasses in the series Ga2S3–Sb2S3–XI–Dy3+, Dy3+ emission increased in the PbI2‐ and CsI‐doped glasses but decreased in the AgI‐doped glass due to the combined effect of dysprosium and oxygen. For all that, these novel glasses are highly promised for use in infrared optics.

Short-term activity cycles impede information transmission in ant colonies.

Rhythmical activity patterns are ubiquitous in nature. We study an oscillatory biological system: collective activity cycles in ant colonies. Ant colonies have become model systems for research on biological networks because the interactions between the component parts are visible to the naked eye, and because the time-ordered contact network formed by these interactions serves as the substrate for the distribution of information and other resources throughout the colony. To understand how the collective activity cycles influence the contact network transport properties, we used an automated tracking system to record the movement of all the individuals within nine different ant colonies. From these trajectories we extracted over two million ant-to-ant interactions. Time-series analysis of the temporal fluctuations of the overall colony interaction and movement rates revealed that both the period and amplitude of the activity cycles exhibit a diurnal cycle, in which daytime cycles are faster and of greater amplitude than night cycles. Using epidemiology-derived models of transmission over networks, we compared the transmission properties of the observed periodic contact networks with those of synthetic aperiodic networks. These simulations revealed that contrary to some predictions, regularly-oscillating contact networks should impede information transmission. Further, we provide a mechanistic explanation for this effect, and present evidence in support of it.

Controlling the Sensitivity, Specificity, and Time Signature of Sensors through Architectural Design on the Nanoscale

When multifunctionality and molecular transport paths are critical, as they are in chemical sensing, architectural design enables high performance. The chemical interactions that trigger recognition (i.e., sensing) of molecules are more effective when they structured within mesoporous architectures with continuous, but aperiodic networks that wrap around the reactive solid network in 3-D.

Accurate Path Integration in Continuous Attractor Network Models of Grid Cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

Amorphization and recrystallization of covalent tetrahedral networks

In the present paper recent studies on the amorphization and recrystallization of the light covalent ceramics SiC, Si 3N 4 and SiO 2 (and in comparison Si) shall be reviewed. By combining long and short range order sensitive analysis techniques new insights into the disordering/reordering mechanisms and the structure of the disordered materials were gained. The results will be discussed in the light of a topological approach of the transition between periodic and aperiodic networks.

Network topology in aperiodic networks

Topological descriptions are an attractive alternative to conventional crystallographic formalism for describing crystals and are essential for describing aperiodic states lacking long-range translational and orientational order. In networks, topological connectivity approaches are usefully applied in making assessments of glass-forming ability and in providing a local description of network structure which can assess extendability. The structural freedom required to form aperiodic networks is directly related to connectivity, and the range of allowable structural possibilities can be enumerated using combinatorial geometry. Detailed applications to periodic and aperiodic network silicas are reviewed.

The structure of metamict zircon: A temperature-dependent EXAFS study

The thermal annealing (300–1700 K) of two metamict zircons (Ampagabe, Madagascar and Naegy, Japan) has been studied using X-Ray Diffraction (XRD) and Extended X-ray Absorption Fine Structure spectroscopy (EXAFS) at Zr K-edge. Two stages of thermal annealing within the aperiodic zircon are evidenced between 293 and 1700 K. The first stage (up to 600° C) shows a decrease of the a 0-cell parameter from 6.674 (at 300° C) to 6.610 (at 600° C)± 0.005 A. In that temperature range, the average local environment around Zr (presence of VIIZr and d(Zr-Zr) ≈ 3.3–3.6 A) shows a weak, but significant increase of the Zr-Zr correlations located at 3.3–3.4 A, undetectable by XRD. At temperatures up to 700° C (stage 2), the XRD-Bragg component arising from crystalline zircon increases in magnitude, whereas, Zr-K EXAFS analysis indicates a progressive VIIZr→VIIIZr transition, associated with a recovery of the crystalline zircon medium-range environment. For both techniques, the zircon structure is fully recovered at annealing temperatures up to 900° C. Electrostatic modelings suggest that the VIIIZr→VIIZr transition observed in zircon with increasing alpha-decay damage creates significantly overbonded oxygen atoms around Zr. With increasing temperature, those oxygen atoms are better bonded to VIIZr, due to the thermal expansion of the Zr-O bond. The congruent recovery of the zircon structure should therefore be favoured with increasing temperature. On the other hand, the metamict network can be also partially reorganized around 400–500° C, with the creation of Zr-rich domains, as measured by EXAFS. However, the growth of these domains after 3 hours annealing affects only minor portions of the aperiodic network. This model is corroborated by a similar thermal behaviour observed for a synthetic sol-gel of ZrO2 · SiO2 composition.

Superconducting phase boundary of aperiodic networks in a magnetic field.

We have used electron-beam lithography to fabricate superconducting ``wire'' arrays in a variety of patterns ranging from periodic to random and including the intermediate quasicrystalline and incommensurate configurations. Sweeping an applied magnetic field while observing the critical temperature reveals which fields are favorable or commensurate with the pattern. We find sharp dips in the ${T}_{c}$(H) curve for periodic, incommensurate (quasiperiodic), and quasicrystalline arrays reflecting a lock-in of the flux lattice with the underlying network. We find no similar fine structure for random arrays. This allows us to generalize the concept of commensurability to nonperiodic structures.

X-ray diffraction studies of glasses in the TeO 2V 2O 5 system

The short-range order in glasses of the TeO 2V 2O 5 system is studied with the aid of X-ray diffraction. It is found that the main structural units in most of the glasses are VO 5- and TeO 3-groups. The assumption is made that their structures gradually change; sheet complexes are formed close to V 2O 5; chains - around 2TeO 2V 2O 5, and a tridimensional aperiodic network in glasses from TeO 2.