Inter-layer Edge Research Articles

Defect Engineering in GO Membranes - Tailoring Size and Oxidation Degree of Nanosheet for Enhanced Pore Channels.

Graphene Oxide (GO) membrane has been extensively applied in the field of water purification and membrane separation processes. While the solute molecule transport in GO membranes encompasses interlayer channels, edge defects, and in-plane crack-like holes, the significance of edge defects or crack-like pores in ultrathin membranes is often overlooked. In our study, we focused on the construction of short-range channel GO membranes with varied defect structures by modulating the transverse size of the porous nanosheets. GO nanosheets with different sizes were procured through high-energy γ-irradiation combined with centrifugation. Notably, the large-sized porous GO nanosheets (L-pGO) exhibit a consistent structure, and numerous in-plane defects. In contrast, the smaller counterparts (S-pGO) present a fewer in-plane defects. The performance metrics revealed that L-pGO exhibited a water flux of 849.25 L m-2 h-1 bar-1, while S-pGO demonstrated nearly 100 % dye rejection capacity. These findings underscore the potential of defect engineering as a powerful strategy to enhance the efficiency of two-dimensional membranes.

Alkali Containing Layered Metal Oxides as Catalysts for the Oxygen Evolution Reaction

AbstractImproving the efficiency of the oxygen evolution reaction (OER) is essential to realise energy systems based on water electrolysis. Many catalysts have been developed for the OER to date, with iridium‐based oxides being the most promising due to their relative stability towards corrosion in acidic electrolytes under oxidising potentials. In recent years, examples of catalysts adopting layered structures have been shown to have promising characteristics such as higher conductivity and higher electrochemically active surface area compared to highly crystalline metal oxides. Furthermore, such materials possess additional tuneable properties such as interlayer spacing, identity and concentration of the interlayer species, edge and interlayer active sites, and higher active surface area. Recent attention has focused on mono‐ and polymetallic lithium‐containing layered materials, where the presence of interlayer lithium cations, in situ delithiation processes and combinations of transition metal oxides result in enhanced catalytic properties towards OER. This review aims to provide a summary of the recent developments of such layered materials, in which lithium or other alkali metal ions occupy interlayer sites in oxides.

Robustness of Consensus of Two-Layer Ring Networks

The topology structure of multi-layer networks is highly correlated with the robustness of consensus. This paper investigates the influence of different interlayer edge connection patterns on the consensus of the two-layer ring networks. Two types of two-layer ring network models are first considered: one is a kind of two-layer ring network with two linked edges between layers (Networks-a), and the other is a kind of two-layer ring network with three linked edges between layers (Networks-b). Using the Laplacian spectrum, the consensus of the network model is derived. The simulation experiments are used to demonstrate the influence of different interlayer edge connection patterns on the consensus of networks. To determine the best edge connection pattern for Networks-a and Networks-b, the number of nodes in a single-layer ring network is denoted by n. The best edge connection pattern for Networks-a is 1 & [(n+2)/2]. Furthermore, n is subdivided into 3k,3k+1,3k+2, and the best edge connection patterns of Networks-b are near 1 & k+1 & 2k+1.

Smoothing of inter-layer edge artifacts in depth-map computer-generated holograms.

In the depth-map computer-generated hologram (CGH), inter-layer edge artifacts are observed in the discontinuous edges of section-wise depth-map objects. CGH synthesis, utilizing the hybrid smoothing method of silhouette masking and edge-apodization, alleviates unwanted inter-layer edge artifacts. The proposed method achieves improved de-artifact filtering that generates holographic images closer to the ground truth image of the depth-map object unattainable by the conventional CGH synthesis method.

Spin–orbit proximity effect and topological superconductivity in graphene/transition-metal dichalcogenide nanoribbons

Spin–orbit coupling (SOC) plays a determinate role in spintronics and topological physics. Previous studies indicate that the SOC in graphene nanoribbon (GNR) can be enhanced by the proximity effect from two-dimensional transition-metal dichalcogenide (2D-TMD). However, the bulk inversion symmetry of GNR/2D-TMD restricts further increase of the proximity-induced SOC in GNR. In this view, we introduce a TMD nanoribbon (TMDNR) with finite width, and propose three methods to break the bulk inversion symmetry, i.e. defects in TMDNR, spatial interlayer edge coupling, and twist between GNR and TMDNR, which can further enhance the SOC in the GNR by roughly 30 times, 20 times and 150 times, respectively, depending on the relative energy between the Dirac point of GNR and the states of TMDNR. Furthermore, the significantly enhanced SOC can drive the GNR into a topological superconducting phase. By introducing the Zeeman splitting and s-wave superconductivity in the GNR, quasi one-dimensional topological superconductivity and Majorana zero modes (MZMs) can be achieved in the GNR. At last we propose a feasible experimental method to realize and manipulate MZMs in the GNR/TMDNR system.

Sampling Graphlets of Multiplex Networks: A Restricted Random Walk Approach

Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of effort has been devoted to calculating graphlet statistics where random walk-based approaches are commonly used to access restricted graphs through the available application programming interfaces (APIs). However, most of them merely consider individual networks while overlooking the strong coupling between different networks. In this article, we estimate the graphlet concentration in multiplex networks with real-world applications. An inter-layer edge connects two nodes in different layers if they actually belong to the same node. The access to a multiplex network is restrictive in the sense that the upper layer allows random walk sampling, whereas the nodes of lower layers can be accessed only through the inter-layer edges and only support random node or edge sampling. To cope with this new challenge, we define a suit of two-layer graphlets and propose novel random walk sampling algorithms to estimate the proportion of all the three-node graphlets. An analytical bound on the sampling steps is proved to guarantee the convergence of our unbiased estimator. We further generalize our algorithm to explore the tradeoff between the estimated accuracy of different graphlets when the sample budget is split into different layers. Experimental evaluation on real-world and synthetic multiplex networks demonstrates the accuracy and high efficiency of our unbiased estimators.

The effect of porewater ionic composition on arsenate adsorption to clay minerals

Adsorption of arsenate on clay minerals can control the partitioning and mobility of arsenic and subsequent contamination of groundwater. While the effect of ionic strength on arsenic adsorption to phyllosilicate minerals has been evaluated for various clay minerals, the specific ionic composition of the surrounding porewater can play a critical role in promoting adsorption (or desorption) of arsenate (HxAsO4x-4). We conducted a series of adsorption isotherms to evaluate the adsorption of arsenate to various phyllosilicates in the presence of monovalent (K+), divalent (Mg2+, Ca2+), and trivalent (La3+) cations while maintaining constant ionic strength and pH. Adsorption isotherms were combined with surface complexation modeling to examine retention processes of arsenate as a function of ionic composition in the surrounding solution. The higher charge density of greater valent cations results in stronger outer-sphere bridging complexes between negatively charged phyllosilicate mineral surfaces and negatively charged arsenate oxyanions. Higher valent cations thus enhance the propensity for arsenate adsorption on phyllosilicate minerals. We further deciphered surface complexation processes by conducting adsorption isotherms on various clay minerals including smectite, illite, and pyrophyllite to evaluate the role of interlayer, permanent charge, and terminal edge sites. We conclude that arsenate is most likely retained largely on the planar surface where structural negative charge emanates allowing cation bridging complexes to develop. Our findings illustrate that clay mineralogy of soils and sediments can combine with porewater ionic composition (and specifically the proportion of divalent cations) to describe arsenic transport, particularly in iron- or aluminum-oxide poor systems.

Species functional traits and abundance as drivers of multiplex ecological networks: first empirical quantification of inter-layer edge weights.

Many vertebrate species act as both plant pollinators and seed-dispersers, thus interconnecting these processes, particularly on islands. Ecological multilayer networks are a powerful tool to explore interdependencies between processes; however, quantifying the links between species engaging in different types of interactions (i.e. inter-layer edges) remains a great challenge. Here, we empirically measured inter-layer edge weights by quantifying the role of individually marked birds as both pollinators and seed-dispersers of Galápagos plant species over an entire year. Although most species (80%) engaged in both functions, we show that only a small proportion of individuals actually linked the two processes, highlighting the need to further consider intra-specific variability in individuals' functional roles. Furthermore, we found a high variation among species in linking both processes, i.e. some species contribute more than others to the modular organization of the multilayer network. Small and abundant species are particularly important for the cohesion of pollinator seed-dispersal networks, demonstrating the interplay between species traits and neutral processes structuring natural communities.

Optimal percolation in correlated multilayer networks with overlap

Multilayer networks have been found to be prone to abrupt cascading failures under random and targeted attacks, but most of the targeting algorithms proposed so far have been mainly tested on uncorrelated systems. Here we show that the size of the critical percolation set of a multilayer network is substantially affected by the presence of inter-layer degree correlations and edge overlap. We provide extensive numerical evidence which confirms that the state-of-the-art optimal percolation strategies consistently fail to identify minimal percolation sets in synthetic and real-world correlated multilayer networks, thus overestimating their robustness. We propose two new targeting algorithms, based on the local estimation of path disruptions away from a given node, and a family of Pareto-efficient strategies that take into account both intra-layer and inter-layer heuristics, and can be easily extended to multiplex networks with an arbitrary number of layers. We show that these strategies consistently outperform existing attacking algorithms, on both synthetic and real-world multiplex networks, and provide some interesting insights about the interplay of correlations and overlap in determining the hyperfragility of real-world multilayer networks. Overall, the results presented in the paper suggest that we are still far from having fully identified the salient ingredients determining the robustness of multiplex networks to targeted attacks.

Molecular mechanisms of per- and polyfluoroalkyl substances on a modified clay: a combined experimental and molecular simulation study

Repeated application of aqueous film-forming foams (AFFF) in designated firefighting training areas has caused severe groundwater contamination by per- and polyfluoroalkyl substances (PFASs). Many research efforts are currently engaged for the effective removal of these chemicals from environmental waters. In this study, we demonstrate that modified clay produced by intercalating quaternary ammonium cations in the exchangeable interlayer sites of smectite clay can effectively remove PFAS pollutants in real groundwater via strong adsorption. The performance of the modified clay (with removal efficiencies 95~99%) is superior to those of granular activated carbon or hard-wood biochar and comparable to an ion exchange resin. Removal efficiency is not impacted by potential organic co-contaminants (e.g., diesel, BTEX, TCE, and 1,4 dioxane) or water chemistry (Ca2+ and Na+) at environmentally relevant concentrations. Furthermore, piecewise isotherms are identified to represent the uptake of PFASs by the modified clay. Based on molecular dynamics simulations, the anionic PFASs first occupy the highly polarized bare interlayer edge sites leading to a linear isotherm and then the interlayer surface sites resulting in a Langmuir isotherm. The ionic interactions between the cationic intercalant (N+) and the terminal oxygen atoms of carboxylate or sulfonate groups of PFASs play a dominant role in adsorption, and the lateral interaction in particular fluorophilic attraction among PFASs accelerate the adsorption. The strength of these interactions is quantified using Density Functional Theory calculations. Simulation results match reasonably well with the experimentally determined basal spacing and Fourier transform infrared spectroscopy of the modified clay loaded with PFASs. Overall, the combined experimental and molecular simulation studies elucidate the adsorption mechanism of PFASs on the modified clay and provide critical information to guide the use of modified clays for PFAS water treatment in the field.

Cesium removal using acid- and base-activated biotite and illite

Biotite and illite have excellent cesium (Cs) adsorption capacity due to their negative charges in addition to adsorption sites of the planar, interlayer, and frayed edge sites (FES). The aim of this study is to investigate the Cs adsorption capacity using acid- and base-activated biotite and illite based on their mineralogical characteristics. The acid-activated biotite and base-activated illite exhibited high Cs removal efficiency from the low-level Cs-containing DI water (97.5 % and 97.3 %, respectively). The acid-activation of biotite increased the specific surface area (SSA, 12.08 → 43.04 m2/g), Fe(III)/Fe(II) ratio (0.56 → 0.76), and wedge zone d-spacing (1.017 → 1.065 nm), while the zeta potential (-4.06 → -4.82 mV) decreased. The base-activation of illite resulted to a decrease in the SSA (22.14 → 18.49 m2/g), zeta potential (-7.68 → -31.64 mV), and Fe(III)/Fe(II) ratio (0.92 → 0.79). However, only acid-activated biotite appeared to have a high capacity of Cs removal from Cs-containing seawater (73.9 %; base-activated illite: 26.1 %). These results indicate that the FES of biotite owing to acid-activation showed better results in regards to Cs adsorption as compared to the pH-dependent negative charges of the base-activated illite.

Edge-terminated MoS2 nanosheets with an expanded interlayer spacing on graphene to boost supercapacitive performance

The supercapacitive performance of two-dimensional (2D) MoS2 nanomaterials strongly depends on the interlayer spacing and edge orientation, which remains a formidable challenge. Herein, we demonstrate a sheet-on-sheet 2D heterostructure with edge-terminated and interlayer-expanded MoS2 few-layered nanosheets on graphene. The preferential (0 0 2) edge orientation with an expanded interlayer spacing of 0.98 nm enables easy insertion of ions into the MoS2 nanosheets. The intimate connection with conductive graphene further expedites the electrochemical kinetics by promoting electron/ion transport and structural stability. As a result, the MoS2@graphene nanoarchitecture can deliver a high specific capacitance of 428 F g−1 at 1 A g−1 along with superior rate and long-term durability, which is among the best performance reported so far. The present work highlights the importance of engineering edge-oriented and interlayer-expanded 2D materials for their promising use toward high-performance supercapacitors.

Robustness in Multilayer Networks Under Strategical and Random Attacks

Many real-world complex systems are modelled by multilayer networks (MLNs) which are inter-connected and inter-dependent in nature. For example, Transport networks, Power grid networks, Biological networks etc. In these networks, damage to any network layer may affect the functionality of other network layers or the entire system of multilayer network. For example, in the Transport networks, damage to Road networks may affect the Railway network as well as Air-Transport networks. Therefore, the robustness of these networks is not only an important characteristics, but also it is a challenging area of research. In the present research work, we study the robustness behavior of synthetic MLNs under random attacks as well as targeted attack by removing the specified fraction of nodes from each network layer and compare the results with single layer networks. For both kinds of attacks, it is revealed that the single layer networks are more vulnerable towards failure as compared to the MLNs. We also study the robustness in the case of MLN where network layers contain more than one connected components. By keeping the network layers intact (not removing the nodes), we remove the inter-layer edges sequentially. It is found that before the removal of last inter-layer edge, MLN contains approximately 95% of nodes in largest connected component (LCC)in the best case and approximately 73% of nodes in (LCC) in the worst case under strategical attacks.

Consensus dynamics on weighted multiplex networks: a long-range interaction perspective

Real-world multiplex networks are weighted in nature, e.g. transports networks (variation in traffic loads over links), social networks (variation in communication between individuals), etc. In addition, the dynamical behavior of multiplex networks is influenced by the contribution of both local as well as global neighbors to individual network layers and the corresponding neighbors in other network layers. In the present work, we propose a method to compute the intra-layer and inter-layer edge weights of multiplex networks and study the consensus dynamics by analyzing the Laplacian spectra from the perspective of long-range interactions (LRIs) in each network layer. To this end, we extend the Kuramoto model for multiplex networks, consider synthetic multiplex networks with different topological characteristics and an empirical data-set. Our analysis reveals that in the case of LRIs, there is an improvement in the stability of the consensus process in the independent network layers as well as in the multiplex networks. However, depending upon the topology of the network layers being added to the existing multiplex network, the behavior of stability is different. In addition, we study the level of synchronization (R) by analyzing the Laplacian spectra and order parameter () of the Kuramoto model. We find that by adding more layers to the existing multiplex network, the value of R increases at the given timestamps in the case of Laplacian spectra analysis. In the case of the Kuramoto model, the order parameter shows different behavior depending upon the topological characteristics of the network layers being added to the existing multiplex network.

Characterizing interlayer edge placement with SEM contours

Background: The continuous scaling of integrated circuit requires not only a very good control of the device critical dimensions but also a very accurate control of the device overlay between layers to achieve satisfactory yields. These two critical factors can be combined to a single metric called interlayer edge placement error (EPEinterlayer) that quantifies the process margin necessary to keep a safe separation, extension, or overlap between the edges of a pattern in one layer with respect to another pattern in a second layer. Aim: The purpose of this work is to characterize with scanning electron microscopy (SEM), the EPEinterlayer and overlay variances of complex contact shapes relative to a poly layer to assess the contributions of the systematic and random EPEinterlayer. Approach: SEM images of a few etched patterns were recorded sequentially for both contact and poly features at the same locations on the wafer. Then, SEM contours were extracted, aligned, and overlapped to derive EPEinterlayer. One experiment was focusing on intrawafer EPEinterlayer characterization whereas another was studying more specifically intrafield overlay variations. For the latter experiment, systematic overlay errors were added to facilitate the comparison of the SEM-based method with respect to a reference image-based overlay (IBO) method. Results: The earliest direct metrology of EPEinterlayer and overlay in device enabled by this work shows a very high variability of EPEinterlayer and overlay errors across wafer and across field. Conclusions: By directly measuring the EPEinterlayer on devices that are not accessible by the standard method (optical IBO on OL structures), we showed the feasibility of this metrology and observed more dimensional variance in devices than recognized with IBO, thereby enabling better control of device pattern variation.

Frequency-based brain networks: From a multiplex framework to a full multilayer description.

We explore how to study dynamical interactions between brain regions by using functional multilayer networks whose layers represent different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as (i) a multilayer network, in which all brain regions can interact with each other at different frequency bands; and as (ii) a multiplex network, in which interactions between different frequency bands are allowed only within each brain region and not between them. We study the second-smallest eigenvalue λ2 of the combinatorial supra-Laplacian matrix of both the multiplex and multilayer networks, as λ2 has been used previously as an indicator of network synchronizability and as a biomarker for several brain diseases. We show that the heterogeneity of interlayer edge weights and, especially, the fraction of missing edges crucially modify the value of λ2, and we illustrate our results with both synthetic network models and real data obtained from resting-state magnetoencephalography. Our work highlights the differences between using a multiplex approach and a full multilayer approach when studying frequency-based multilayer brain networks.

Double-edged sword effect of edge overlap on asymmetrically interacting spreading dynamics

There is a close interplay between the disease spreading on contact network and corresponding information propagation on communication network. Especially, it will be of much interest when there are certain overlaps between the topological edges of communication network and contact network. In this paper, we study the effect of inter-layer edge overlap on the asymmetrically interacting spreading dynamics of disease and information, mainly including the final fraction of infected nodes and the epidemic threshold Though extensive simulations, we find that there is a so called double-edged sword effect on epidemic spreading and information propagation. Namely, when the disease spreads faster than information, a smaller amount of overlapping edges is able to effectively inhibit the epidemic spreading. On the contrary, when the information propagates more quickly than disease spreads, the more overlapping edges are, the better the epidemic spreading is suppressed. In further, we show that the epidemic threshold is improved when the overlapping edges increase. These results can provide a significant guidance to make optimal strategies for suppressing epidemic spreading.

Topologically biased random walk for diffusions on multiplex networks

Random walks constitute a basic mechanism for diffusion processes occurring on multiplex networks composed by different layers describing interactions of different nature. However, existing random walk diffusions focus only on network topology, leading to randomly traverse both intralayer and interlayer edges with certain equal probability. In order to efficiently explore diffusions on multiplex networks, topologically biased random walks whose movement is forcedly biased toward certain topological properties of a neighboring node are introduced to such systems, depending both upon multiplex topology and upon diffusion processes (the class of bias in the walker). Here, we introduce topologically biased random walks on multiplex networks and derive analytical expressions for their long-term diffusion properties such as entropy rate and stationary probability distribution. In particular, according to the dependence of the biased function's parameters on the layer number, we propose topologically biased additive, multiplicative and multiplex random walks. Then, we study the impact of different topologies of synthetic multiplex networks on the steady-state diffusion behaviors of these walks and find that interlayer coupling strength, edge overlapping, the sign and presence of interlayer degree–degree correlations and the layer number capture the extent to which the diffusions on a multiplex network are efficiently explored by a biased walk. Experimentally we conduct diffusion processes on four real-world multiplex networks. Our results show that a better trade-off between efficient diffusion exploration and homogeneity sampling of network nodes by opportunely tuning the biased exponents toward intrinsically multiplex nodes.

Void reduction of high-performance thermoplastic composites via oven vacuum bag processing

In this study, void reduction mechanisms during oven vacuum bag processing of high-performance carbon fiber thermoplastic composites are investigated. Entrapped air exists within the prepreg tape and between layers during lay-up and must be removed during processing to achieve aerospace quality (<1% void content) Key void reduction mechanisms during oven vacuum bag processing include through-thickness air diffusion and in-plane flow to the laminate edges through the permeable interlayer regions created by the prepreg surface roughness. Interlayer permeability between unidirectional and cross-ply laminates is measured experimentally and is sufficiently high for effective air removal during oven vacuum bag processing. Thick 72-layer carbon fiber/PEEK (poly (ether ether ketone)) laminates were fabricated with oven vacuum bag process under different edge sealing conditions. Void reduction in the laminate with sealed perimeter is dominated by air diffusion through the entire laminate thickness, and the laminate exhibits very high void content levels after oven vacuum bag processing. In the laminates with edges open to vacuum, air diffusion through a single layer and flow through the permeable interlayer lead to essentially void-free laminates. The findings show the importance of the interlayer permeability and edge conditions on the void reduction, and demonstrate that low void content can be achieved in thick section thermoplastic composite laminates via cost effective oven vacuum bag processing.

Efficient exploration of multiplex networks

Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on properties of neighbouring nodes, have been largely exploited to design smart local strategies to explore a network, for instance by constructing maximally mixing trajectories or by allowing an almost uniform sampling of the nodes. Here we introduce and study biased random walks on multiplex networks, graphs where the nodes are related through different types of links organised in distinct and interacting layers, and we provide analytical solutions for their long-time properties, including the stationary occupation probability distribution and the entropy rate. We focus on degree-biased random walks and distinguish between two classes of walks, namely those whose transition probability depends on a number of parameters which is extensive in the number of layers, and those whose motion depends on intrinsically multiplex properties of the neighbouring nodes. We analyse the effect of the structure of the multiplex network on the steady-state behaviour of the walkers, and we find that heterogeneous degree distributions as well as the presence of inter-layer degree correlations and edge overlap determine the extent to which a multiplex can be efficiently explored by a biased walk. Finally we show that, in real-world multiplex transportation networks, the trade-off between efficient navigation and resilience to link failure has resulted into systems whose diffusion properties are qualitatively different from those of appropriately randomised multiplex graphs. This fact suggests that multiplexity is an important ingredient to include in the modelling of real-world systems.