Entropy-Driven Mechanics of Crystalline and Biological Membranes

Force generation by actin assembly shapes cellular membranes. An experimentally constrained multiscale model shows that a minimal branched actin network is sufficient to internalize endocytic pits against membrane tension. Around 200 activated Arp2/3 complexes are required for robust internalization. A newly developed molecule-counting method determined that ~200 Arp2/3 complexes assemble at sites of clathrin-mediated endocytosis in human cells. Simulations predict that actin self-organizes into a radial branched array with growing ends oriented toward the base of the pit. Long actin filaments bend between attachment sites in the coat and the base of the pit. Elastic energy stored in bent filaments, whose presence was confirmed by cryo-electron tomography, contributes to endocytic internalization. Elevated membrane tension directs more growing filaments toward the base of the pit, increasing actin nucleation and bending for increased force production. Thus, spatially constrained actin filament assembly utilizes an adaptive mechanism enabling endocytosis under varying physical constraints.

<sec>Two-dimensional (2D) material has atomic smooth surface, nano-scale thickness and ultra-high specific surface area, which is an important platform for studying the interface interaction between metal nanoparticles (NPs) and 2D materials, and also for observing the surface atomic migration, structural evolution and aggregation of metal NPs in real time and <i>in situ</i>. By rationally designing and constructing the interfaces of metal NPs and 2D materials, the characterization of the interface structure on an atomic scale is very important in revealing the structure-property relationship. It is expected that the investigation is helpful in understanding the mechanism of interaction between metal and 2D materials and optimizing the performance of the devices based on metal-2D material heterojunctions.</sec><sec>In this review, the recent progress of interface modulation and physical properties of the heterostructure of metal NPs and 2D materials are summarized. The nucleation, growth, structural evolution and characterization of metal NPs on the surface of 2D materials are reviewed. The effects of metal NPs on the crystal structure, electronic state and energy band of 2D materials are analyzed. The possible interfacial strain and interfacial reaction are also included. Because of the modulation of electrical and optical properties of 2D materials, the performance of metal NPs-2D material based field effect transistor devices and optoelectronic devices are improved. This review is helpful in clarifying the physical mechanism of microstructure affecting the properties of metal NPs-2D material heterostructures on an atomic scale, and also in developing the metal-2D material heterostructures and their applications in the fields of electronic devices, photoelectric devices, energy devices, etc.</sec>

Two-dimensional (2D) materials are at the heart of many novel devices due to their unique and often superior properties. For simplicity, 2D materials are often assumed to exist in their text-book form, i.e., as an ideal solid with no imperfections. However, defects are ubiquitous in macroscopic samples and play an important – if not imperative – role for the performance of any device. Thus, many independent studies have targeted the artificial introduction of defects into 2D materials by particle irradiation. In our view it would be beneficial to develop general defect engineering strategies for 2D materials based on a thorough understanding of the defect creation mechanisms, which may significantly vary from the ones relevant for 3D materials. This paper reviews the state-of-the-art in defect engineering of 2D materials by electron and ion irradiation with a clear focus on defect creation on the atomic scale and by individual impacts. Whenever possible we compile reported experimental data alongside corresponding theoretical studies. We show that, on the one hand, defect engineering by particle irradiation covers a wide range of defect types that can be fabricated with great precision in the most commonly investigated 2D materials. On the other hand, gaining a complete understanding still remains a challenge, that can be met by combining advanced theoretical methods and improved experimental set-ups, both of which only now begin to emerge. In conjunction with novel 2D materials, this challenge promises attractive future opportunities for researchers in this field.

Engineering molecular interactions at two-dimensional (2D) materials interfaces enables new technological opportunities in functional surfaces and molecular epitaxy. Understanding the wettability of 2D materials represents the crucial first step toward quantifying the interplay between the interfacial forces and electric potential of 2D materials interfaces. Here we develop the first theoretical framework to model the wettability of the doped 2D materials by properly bridging the multiscale physical phenomena at the 2D interfaces, including (i) the change of 2D materials surface energy (atomistic scale, several angstroms), (ii) the molecular reorientation of liquid molecules adjacent to the interface (molecular scale, 100-101 nm), and (iii) the electrical double layer (EDL) formed in the liquid phase (mesoscopic scales, 100-104 nm). The latter two effects are found to be the major mechanisms responsible for the contact angle change upon doping, while the surface energy change of a pure 2D material has no net effect on the wetting property. When the doping level is electrostatically tuned, we demonstrate that 2D materials with high quantum capacitances (e.g., transition metal dichalcogenides, TMDCs) possess a wider range of tunability in the interfacial tension, under the same applied gate voltage. Furthermore, practical considerations such as defects and airborne contamination are also quantitatively discussed. Our analysis implies that the doping level can be another variable to modulate the wettability at 2D materials interfaces, as well as the molecular packing behavior on a 2D material-coated surface, essentially facilitating the interfacial engineering of 2D materials.

Following the graphene isolation, strong interest in two dimensional (2D) materials has been driven by their outstanding properties. Their typical intrinsic structure, including strong in-plane covalent bonding and weak out-of-plane Van der Waals interaction, makes them highly promising in diverse areas such as electronics, catalysis, and environment. Growth of 2D materials requires a synthesis approach able to control the deposition onto a support at the atomic scale. Thanks to their simplicity, versatility and ability to control thickness at the angstrom level, atomic layer deposition (ALD) and its variant atomic layer etching (ALET) appear as ones of the most suited techniques to synthesize 2D materials. The development of ALD technique for fabricating 2D materials in the last ten years justifies reviewing its most recent groundbreaking discoveries and progresses. Particular attention will be paid to stable 2D materials especially graphene, h-BN, Mo and W dichalcogenides and few monolayered metal oxides. Specificities and outputs of ALD for 2D material as well as emerging directions and remaining technical challenges will be highlighted.

Two-dimensional (2D) materials, such as graphene and transition-metal dichalcogenide monolayers, have unique properties that are distinctly different from those of their bulk counterparts, and hopefully possess a wide range of applications in 2D semiconductor device. Structural defects are known to have profound influences on the properties of crystalline materials; thus, correlating the defect structure with local properties in 2D material is of fundamental importance. However, electron microscopy studies of 2D materials on an atomic scale have become a challenge as most of these materials are susceptible to electron beam irradiation damage under high voltage and high dose experimental conditions. The development of low voltage aberration-corrected scanning transmission electron microscopy (STEM) has made it possible to study 2D materials at a single atom level without damaging their intrinsic structures. In addition, controllable structural modification by using electron beam becomes feasible by controlling the electron beam-sample interaction. New nanostructures can be created and novel 2D materials can be fabricated in-situ by using this approach. In this article, we review some of our recent studies of graphene and transition-metal dichalcogenides to showcase the applications of low voltage aberration corrected STEM in 2D material research.

Two-dimensional (2D) materials have brought a spectacular revolution in fundamental research and industrial applications due to their unique physical properties of atomically thin thickness, strong light-matter interaction, unity valley polarization and enhanced many-body interactions. To fully explore their exotic physical properties and facilitate potential applications in electronics and optoelectronics, an effective and versatile characterization method is highly demanded. Among the many methods of characterization, optical second harmonic generation (SHG) has attracted broad attention because of its sensitivity, versatility and simplicity. The SHG technique is sufficiently sensitive at the atomic scale and therefore suitable for studies on 2D materials. More importantly, it has the capacity to acquire abundant information ranging from crystallographic, and electronic, to magnetic properties in various 2D materials due to its sensitivity to both spatial-inversion symmetry and time-reversal symmetry. These advantages accompanied by its characteristics of non-invasion and high throughput make SHG a powerful tool for 2D materials. This review summarizes recent experimental developments of SHG applications in 2D materials and also provides an outlook of potential prospects based on SHG.

The mechanical response and failure mechanism of two-dimensional (2D) materials are critical issues for enhancing device reliability and informing robust structural design strategies. Such mechanical behavior at the atomic scale requires both high spatial resolution and structural stability under external tensile loading. In this study, we present an in situ transmission electron microscopy (TEM) tensile test platform designed specifically for 2D materials. A silicon chip has a TEM observation slit covered with a 400 nm thick silicon nitride membrane and a T-shaped gap is formed at the slit by focused ion beam (FIB) processing. A target 2D material is suspended in the gap and the chip is mounted on a push-to-pull titanium plate. We could observe the fracture process of thin MoS2 nanosheets at the atomic scale.

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Entropic pressure on fluctuating solid membranes

The inherent susceptibility of low-dimensional materials to thermal fluctuations has long been expected to pose a major challenge to achieve intrinsic long-range ferromagnetic order in two-dimensional materials. The recent explosion of interest in atomically thin materials and their assembly into van der Waals heterostructures has renewed interest in two-dimensional ferromagnetism, which is interesting from a fundamental scientific point of view and also offers a missing ingredient necessary for the realization of spintronic functionality in van der Waals heterostructures. Recently, several atomically thin materials have been shown to be robust ferromagnets. Such ferromagnetism is thought to be enabled by magnetocrystalline anisotropy which suppresses thermal fluctuations. In this article, we review recent progress in two-dimensional ferromagnetism in detail and predict new possible two-dimensional ferromagnetic materials. We also discuss the prospects for applications of atomically thin ferromagnets in novel dissipationless electronics, spintronics, and other conventional magnetic technologies. Particularly, atomically thin ferromagnets are promising to realize time reversal symmetry breaking in two-dimensional topological systems, providing a platform for electronic devices based on the quantum anomalous Hall effect showing dissipationless transport. Our proposed directions will assist the scientific community to explore novel two-dimensional ferromagnetic families which can spawn new technologies and further improve the fundamental understanding of this fascinating area.

Homogenization of two-dimensional materials integrating monolayer bending and surface layer effects

Fluctuations of active membranes with nonlinear curvature elasticity

Two-dimensional (2D) materials have emerged as a versatile platform for electrocatalysis, offering tunable surface properties, high surface area, and the opportunity to tailor active sites at the atomic scale. Understanding and controlling the behavior of 2D electrocatalysts at electrified interfaces is essential for advancing energy conversion technologies. This work presents computational studies that address the complexities of catalysis on 2D layered materials, with a focus on applied potential, spectator species, and structural defects. By investigating two distinct 2D-electrocatalytic systems, the nitrogen reduction reaction (NRR) on 1T′-MoS2 and the oxygen reduction reaction (ORR) on an iron-nitrogen-doped carbon (Fe-N-C)-based catalysts, we provide new insights into how these factors shape catalytic performance. Both studies leverage grand canonical density functional theory (GC-DFT) to model the influence of applied potential.For the NRR on MoS2, GC-DFT captures the effects of applied potential on the activation of π-backbonding molecules like N₂ and CO. Unlike canonical approaches, GC-DFT reveals that reductive potentials activate N2 towards electroreduction by modulating backbonding strength, thereby lengthening the N≡N bond and decreasing its bond order. This activation is essential for promoting N2 hydrogenation, though it simultaneously destabilizes the adsorbed N2. The mechanistic parallels observed with CO suggest a broader applicability of this approach to other backbonding-mediated reactions, highlighting the importance of accounting for potential-dependent changes in catalyst design.Investigations into the oxygen reduction reaction (ORR) on Fe-N-C catalysts highlight the combined effects of active site structure, spectator species, and applied potential on reactivity. Using a combinatorial approach, we evaluate the impact of counterions and other axial ligands on FeN4 sites embedded at edge and bulk sites of graphene-like structures. Our findings reveal that axial ligands destabilize adsorbates by up to 2 eV, with desorption correlating with bond orders below 0.1. For bulk-hosted sites, intermediates are over-bound compared to ideal ORR catalyst thermodynamics, whereas axial spectators align the thermodynamics more closely with the ideal. However, achieving a balance between the favorability of *O2 and *OH steps remains challenging for both bulk- and edge-hosted sites due to scaling relationships. Moving forward, further investigations of approaches to break scaling relations, alongside experimental validation, are needed, and exploration of novel synthesis approaches will be crucial to advance the practical application of Fe-N-C catalysts in fuel cell technology.Together, these studies illuminate the multifaceted roles of applied potential, spectator species, and catalyst structure in tuning electrocatalyst performance. The methods and insights presented here provide a pathway for predictive modeling of catalytic selectivity and reactivity in 2D materials, providing a framework for designing next-generation electrocatalysts with enhanced selectivity and activity.

With the ever-growing global energy demands and environmental pollution issues, developing high-performance energy storage and conversion materials has become a hot topic in the material science community. In this regard, substantial progress has been made in theoretically predicting new materials for energy-related fields, experimentally synthesizing these materials, and further improving their properties for high performance in energy storage and conversion devices. In particular, two-dimensional (2D) materials have shown great potential in the field of energy storage and conversion. However, it remains challenging to explore 2D materials that render high efficiency of energy storage and conversion while guarantee long-term stability and safety. Over the past decades, theoretical calculations based on density functional theory (DFT) have become a practical toolkit to address this issue by revealing the reaction mechanism at an atomic scale and screening high-performance energy storage and conversion materials on a large scale. In particular, DFT calculations enable us to establish the relationships between the intrinsic properties of materials and their performance for energy storage and conversion, and provide theoretical guidance for screening and experimentally synthesizing the promising materials. In this review, we summarize the DFT calculations’ applications in recent studies of developing high-performance and reliable energy-related 2D materials for Li-ion battery (LIB), water splitting, fuel cells, and electrochemical carbon dioxide reduction (CRR). First, we introduce the reaction mechanism of LIB, hydrogen evolution reaction (HER), oxygen evolution reaction/oxygen reduction reaction (OER/ORR), and CRR in detail and the application of 2D material in these fields. Then, we highlight the role of DFT calculations in unveiling the intrinsic relationships between the electronic structure and the performance of 2D materials by comprehensively discussing the descriptors in predicting the performance of 2D materials. For example, the occupancy of d orbital and energy required to fill empty states serve as descriptors to predict the electrochemical performance of the electrode in ion intercalation battery. The d orbital center, lowest unoccupied states, and oxygen vacancy formation energy serve as descriptors to predict the catalytic performance of electrode in HER. The energy difference between the lowest valance electron orbital center and Fermi level, occupancy of p z orbital, and the energy difference between p z and p x /p y orbital center serve as descriptors to predict the catalytic performance of electrode in ORR. Even though these descriptors can help to further understand the relationships between the electronic structure and the performance of the electrochemical electrode, they are only reliable to specific materials and inapplicable to the electrode with a complex structure or complex reaction path, such as the electrode in CRR. Newly developed machine learning methods may bring a breakthrough to the exploration of a universal descriptor, which is a key factor in the large-scale screening of potential electrode materials with excellent performance and the dependable guidance to experimental synthesis. Finally, we summarize the disadvantage of DFT calculation, such as the underestimation of bandgap and incorrect description of van der Waals interaction, and give a perspective of DFT calculations in the study of new energy-related materials. The method to simulate the ambient environment of the electrode (including the electrolyte, external electric field, and non-cooperative transfer of proton and electron) based on DFT calculation is needed to be developed, which is vital to reflect the actual working condition of the electrode. The universal descriptor applicable to the electrode with a complex structure is also needed to explore to overcome the poor versatility of single intrinsic property of the material in predicting the performance of the electrochemical electrode.