Prescribed Performance Bipartite Consensus Control for Stochastic Nonlinear Multiagent Systems Under Event-Triggered Strategy.

In this article, the event-triggered bipartite consensus problem for stochastic nonlinear multiagent systems (MASs) with unknown dead-zone input under the prescribed performance is studied. To surmount the influence of the dead-zone input, the dead-zone model is transformed into a linear term and a disturbance term. Meanwhile, the prescribed tracking performance is realized by developing a speed function, which means that all tracking errors of MASs can converge to a predefined set in a given finite time. Moreover, the unknown nonlinear dynamics are approximated by fuzzy-logic systems. By combining the dynamic surface approach and the Lyapunov stability theory, we design an adaptive event-triggered control algorithm, such that the bipartite consensus problem of stochastic nonlinear MASs can be achieved, and all signals are semiglobally uniformly ultimately bounded in probability of the closed-loop systems. Finally, simulation examples are proposed to verify the feasibility of the algorithm.

Swarm Control for Self-Organized System With Fixed and Switching Topology.

In this article, we propose the swarm control for a self-organized system with fixed and switching topology, which can realize aggregation, dispersion, or switching formation when swarm moves. The self-organized system can automatically construct the communication topology for intelligent units in swarm. Swarm control can realize aggregation and dispersion of intelligent units based on its communication topology when swarm moves. The proposed swarm control, in which distances between the related intelligent units are time varying, is different from traditional swarm consensus or swarm formation maintenance. To design swarm control, we define the normalization adjacency matrix and normalization degree matrix based on communication topology. The communication topology is automatically generated based on relation-invariable persistent formation. Depending on whether the communication topology changes or not, the swarm control can be classified as fixed topology and switching topology. Then, the swarm control with fixed and switching topology is designed and analyzed, respectively. The swarm control can realize stability asymptotically when topology is fixed and realize stability in finite time when topology is switched. The simulation results show that the proposed approaches are effective.

Size-Dependent Physical and Electrochemical Properties of Two-Dimensional MXene Flakes.

Two-dimensional (2D) particles, including transition metal carbides (MXenes), often exhibit large lateral-size polydispersity in delaminated colloidal solutions. This heterogeneity results in challenges when conducting fundamental studies, such as investigating correlations between properties and the 2D flake size. To resolve this challenge, we have developed solution-processable techniques to control and sort 2D titanium carbide (Ti3C2T x) MXene flakes after synthesis based on sonication and density gradient centrifugation, respectively. By tuning the sonication conditions, Ti3C2T x flakes with varied lateral sizes, ranging from 0.1 to ∼5 µm, can be obtained. Furthermore, density gradient centrifugation was used to sort Ti3C2T x flakes with different lateral sizes into more monodisperse fractions. These processing techniques allow for the characterization of size-dependent optical and electronic properties by measuring the absorption spectra and film conductivity, respectively. Additionally, by testing the material as electrochemical capacitor electrodes, we show the Ti3C2T x flake-size dependence of electrochemical performance. Ti3C2T x films made of flakes with lateral sizes of ∼1 µm showed the best capacitance of 290 F/g at 2 mV/s and rate performance with 200 F/g at 1000 mV/s. The work provides a general methodology which can be followed to control the size of MXenes  and other 2D materials for a variety of applications and fundamental size-dependent studies.

Metallic Ti3C2Tx MXene Gas Sensors with Ultrahigh Signal-to-Noise Ratio.

Achieving high sensitivity in solid-state gas sensors can allow the precise detection of chemical agents. In particular, detection of volatile organic compounds (VOCs) at the parts per billion (ppb) level is critical for the early diagnosis of diseases. To obtain high sensitivity, two requirements need to be simultaneously satisfied: (i) low electrical noise and (ii) strong signal, which existing sensor materials cannot meet. Here, we demonstrate that 2D metal carbide MXenes, which possess high metallic conductivity for low noise and a fully functionalized surface for a strong signal, greatly outperform the sensitivity of conventional semiconductor channel materials. Ti3C2Tx MXene gas sensors exhibited a very low limit of detection of 50-100 ppb for VOC gases at room temperature. Also, the extremely low noise led to a signal-to-noise ratio 2 orders of magnitude higher than that of other 2D materials, surpassing the best sensors known. Our results provide insight in utilizing highly functionalized metallic sensing channels for developing highly sensitive sensors.

Selective Molecular Separation on Ti3C2Tx-Graphene Oxide Membranes during Pressure-Driven Filtration: Comparison with Graphene Oxide and MXenes.

In this work, we prepared 90 nm thick Ti3C2Tx-graphene oxide (GO) membranes laminated on a porous support by mixing GO with Ti3C2Tx. This process was chosen to prevent the penetration of target molecules through inter-edge defects or voids with poor packing. The lattice period of the prepared membrane was 14.28 Å, as being swelled with water, resulting in an effective interlayer spacing of around 5 Å, which corresponds to two layers of water molecules. The composite membranes effectively rejected dye molecules with hydrated radii above 5 Å, as well as positively charged dye molecules, during pressure-driven filtration at 5 bar. Rejection rates were 68% for methyl red, 99.5% for methylene blue, 93.5% for rose Bengal, and 100% for brilliant blue (hydrated radii of 4.87, 5.04, 5.88, and 7.98 Å, respectively). Additionally, the rejections of composite membrane were compared with GO membrane and Ti3C2Tx membrane.

Hollow MXene Spheres and 3D Macroporous MXene Frameworks for Na-Ion Storage.

2D transition metal carbides and nitrides, named MXenes, are attracting increasing attentions and showing competitive performance in energy storage devices including electrochemical capacitors, lithium- and sodium-ion batteries, and lithium-sulfur batteries. However, similar to other 2D materials, MXene nanosheets are inclined to stack together, limiting the device performance. In order to fully utilize MXenes' electrochemical energy storage capability, here, processing of 2D MXene flakes into hollow spheres and 3D architectures via a template method is reported. The MXene hollow spheres are stable and can be easily dispersed in solvents such as water and ethanol, demonstrating their potential applications in environmental and biomedical fields as well. The 3D macroporous MXene films are free-standing, flexible, and highly conductive due to good contacts between spheres and metallic conductivity of MXenes. When used as anodes for sodium-ion storage, these 3D MXene films exhibit much improved performances compared to multilayer MXenes and MXene/carbon nanotube hybrid architectures in terms of capacity, rate capability, and cycling stability. This work demonstrates the importance of MXene electrode architecture on the electrochemical performance and can guide future work on designing high-performance MXene-based materials for energy storage, catalysis, environmental, and biomedical applications.

Two-Dimensional Titanium Carbide MXene As a Cathode Material for Hybrid Magnesium/Lithium-Ion Batteries.

As an alternative to pure lithium-ion, Li+, systems, a hybrid magnesium, Mg2+, and Li+ battery can potentially combine the high capacity, high voltage, and fast Li+ intercalation of Li-ion battery cathodes and the high capacity, low cost, and dendrite-free Mg metal anodes. Herein, we report on the use of two-dimensional titanium carbide, Ti3C2Tx (MXene), as a cathode in hybrid Mg2+/Li+ batteries, coupled with a Mg metal anode. Free-standing and flexible Ti3C2Tx/carbon nanotube composite "paper" delivered ∼100 mAh g-1 at 0.1 C and ∼50 mAh g-1 at 10 C. At 1 C the capacity was maintained for >500 cycles at 80 mAh g-1. The Mo2CTx MXene also demonstrated good performance as a cathode material in this hybrid battery. Considering the variety of available MXenes, this work opens the door for exploring a new large family of 2D materials with high electrical conductivity and large intercalation capacity as cathodes for hybrid Mg2+/Li+ batteries.

Antibacterial Activity of Ti3C2Tx MXene.

MXenes are a family of atomically thin, two-dimensional (2D) transition metal carbides and carbonitrides with many attractive properties. Two-dimensional Ti3C2Tx (MXene) has been recently explored for applications in water desalination/purification membranes. A major success indicator for any water treatment membrane is the resistance to biofouling. To validate this and to understand better the health and environmental impacts of the new 2D carbides, we investigated the antibacterial properties of single- and few-layer Ti3C2Tx MXene flakes in colloidal solution. The antibacterial properties of Ti3C2Tx were tested against Escherichia coli (E. coli) and Bacillus subtilis (B. subtilis) by using bacterial growth curves based on optical densities (OD) and colonies growth on agar nutritive plates. Ti3C2Tx shows a higher antibacterial efficiency toward both Gram-negative E. coli and Gram-positive B. subtilis compared with graphene oxide (GO), which has been widely reported as an antibacterial agent. Concentration dependent antibacterial activity was observed and more than 98% bacterial cell viability loss was found at 200 µg/mL Ti3C2Tx for both bacterial cells within 4 h of exposure, as confirmed by colony forming unit (CFU) and regrowth curve. Antibacterial mechanism investigation by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) coupled with lactate dehydrogenase (LDH) release assay indicated the damage to the cell membrane, which resulted in release of cytoplasmic materials from the bacterial cells. Reactive oxygen species (ROS) dependent and independent stress induction by Ti3C2Tx was investigated in two separate abiotic assays. MXenes are expected to be resistant to biofouling and offer bactericidal properties.

Charge- and Size-Selective Ion Sieving Through Ti3C2Tx MXene Membranes.

Nanometer-thin sheets of 2D Ti3C2Tx (MXene) have been assembled into freestanding or supported membranes for the charge- and size-selective rejection of ions and molecules. MXene membranes with controllable thicknesses ranging from hundreds of nanometers to several micrometers exhibited flexibility, high mechanical strength, hydrophilic surfaces, and electrical conductivity that render them promising for separation applications. Micrometer-thick MXene membranes demonstrated ultrafast water flux of 37.4 L/(Bar·h·m(2)) and differential sieving of salts depending on both the hydration radius and charge of the ions. Cations with a larger charge and hydration radii smaller than the interlayer spacing of MXene (∼6 Å) demonstrate an order of magnitude slower permeation compared to single-charged cations. Our findings may open a door for developing efficient and highly selective separation membranes from 2D carbides.

Flexible MXene/carbon nanotube composite paper with high volumetric capacitance.

Free-standing and flexible sandwich-like MXene/carbon nanotube (CNT) paper, composed of alternating MXene and CNT layers, is fabricated using a simple filtration method. These sandwich-like papers exhibit high volumetric capacitances, good rate performances, and excellent cycling stability when employed as electrodes in supercapacitors.

Flexible and conductive MXene films and nanocomposites with high capacitance.

MXenes, a new family of 2D materials, combine hydrophilic surfaces with metallic conductivity. Delamination of MXene produces single-layer nanosheets with thickness of about a nanometer and lateral size of the order of micrometers. The high aspect ratio of delaminated MXene renders it promising nanofiller in multifunctional polymer nanocomposites. Herein, Ti3C2T(x) MXene was mixed with either a charged polydiallyldimethylammonium chloride (PDDA) or an electrically neutral polyvinyl alcohol (PVA) to produce Ti3C2T(x)/polymer composites. The as-fabricated composites are flexible and have electrical conductivities as high as 2.2 × 10(4) S/m in the case of the Ti3C2T(x)/PVA composite film and 2.4 × 10(5) S/m for pure Ti3C2T(x) films. The tensile strength of the Ti3C2T(x)/PVA composites was significantly enhanced compared with pure Ti3C2T(x) or PVA films. The intercalation and confinement of the polymer between the MXene flakes not only increased flexibility but also enhanced cationic intercalation, offering an impressive volumetric capacitance of ∼530 F/cm(3) for MXene/PVA-KOH composite film at 2 mV/s. To our knowledge, this study is a first, but crucial, step in exploring the potential of using MXenes in polymer-based multifunctional nanocomposites for a host of applications, such as structural components, energy storage devices, wearable electronics, electrochemical actuators, and radiofrequency shielding, to name a few.

Cation intercalation and high volumetric capacitance of two-dimensional titanium carbide.

The intercalation of ions into layered compounds has long been exploited in energy storage devices such as batteries and electrochemical capacitors. However, few host materials are known for ions much larger than lithium. We demonstrate the spontaneous intercalation of cations from aqueous salt solutions between two-dimensional (2D) Ti3C2 MXene layers. MXenes combine 2D conductive carbide layers with a hydrophilic, primarily hydroxyl-terminated surface. A variety of cations, including Na(+), K(+), NH4(+), Mg(2+), and Al(3+), can also be intercalated electrochemically, offering capacitance in excess of 300 farads per cubic centimeter (much higher than that of porous carbons). This study provides a basis for exploring a large family of 2D carbides and carbonitrides in electrochemical energy storage applications using single- and multivalent ions.