Deep Learning Enabled Comprehensive Evaluation of Jumping-Droplet Condensation and Frosting.

Superhydrophobicity-enabled jumping-droplet condensation and frosting have great potential in various engineering applications, ranging from heat transfer processes to antifog/frost techniques. However, monitoring such droplets is challenging due to the high frequency of droplet behaviors, cross-scale distribution of droplet sizes, and diversity of surface morphologies. Leveraging deep learning, we develop a semisupervised framework that monitors the optical observable process of condensation and frosting. This system is adept at identifying transient droplet distributions and dynamic activities, such as droplet coalescence, jumping, and frosting, on a variety of superhydrophobic surfaces. Utilizing this transient and dynamic information, various physical properties, such as heat flux, jumping characteristics, and frosting rate, can be further quantified, conveying the heat transfer and antifrost performances of each surface perceptually and comprehensively. Furthermore, this framework relies on only a small amount of annotated data and can efficiently adapt to new condensation conditions with varying surface morphologies and illumination techniques. This adaptability is beneficial for optimizing surface designs to enhance condensation heat transfer and antifrosting performance.

Positive-Negative Tunable Coefficients of Friction in Superlubric Contacts.

In conventional systems, the coefficient of friction (COF) is typically positive, signifying a direct relationship between frictional and normal forces. Contrary to this, we observe that the load dependence of friction exhibits a unique bell-shaped curve when studying the frictional properties between graphite and α-Al_{2}O_{3} surfaces. As the applied normal force increases, the friction initially rises and then decreases. Finite element simulations reveal this behavior is due to edge detachment at the graphite/α-Al_{2}O_{3} interface as the normal force approaches a critical value. Because friction in superlubric contacts predominantly arises from edges, their detachment leads to a decrease in overall friction. We empirically validate these findings by varying the radii of curvature of the tips and the thicknesses of graphite flakes. This unprecedented observation offers a new paradigm for tuning COF in superlubric applications, enabling transitions from positive to negative values.

Ultrahigh Critical Current Density across Sliding Electrical Contacts in Structural Superlubric State.

In conventional sliding electrical contacts (SECs), large critical current density (CCD) requires a high ratio between actual and apparent contact area, while low friction and wear require the opposites. Structural superlubricity (SSL) has the characteristics of zero wear, near zero friction, and all-atoms in real contact between the contacting surfaces. Here, we show a measured current density up to 17.5 GA/m^{2} between microscale graphite contact surfaces while sliding under ambient conditions. This value is nearly 146 times higher than the maximum CCD of other SECs reported in literatures (0.12 GA/m^{2}). Meanwhile, the coefficient of friction for the graphite contact is less than 0.01 and the sliding interface is wear-free according to the Raman characterization, indicating the presence of the SSL state. Furthermore, we estimate the intrinsic CCD of single crystalline graphite to be 6.69 GA/m^{2} by measuring the scaling relation of CCD. Theoretical analysis reveals that the CCD is limited by thermal effect due to the Joule heat. Our results show the great potential of the SSL contacts to be used as SECs, such as micro- or nanocontact switches, conductive slip rings, or pantographs.

Uniform and Persistent Jumping Detachment of Condensed Nanodroplets.

Realizing jumping detachment of condensed droplets from solid surfaces at the smallest sizes possible is vital for applications such as antifogging/frosting and heat transfer. For instance, if droplets uniformly jump at sizes smaller than visible light wavelengths of 400-720 nm, antifogging issues could be resolved. In comparison, the smallest droplets experimentally observed so far to jump uniformly were around 16 µm in radius. Here, we show molecular dynamics (MD) simulations of persistent droplet jumping with a uniform radius down to only 3.6 nm on superhydrophobic thin-walled lattice (TWL) nanostructures integrated with superhydrophilic nanospots. The size cutoff is attributed to the preferential cross-lattice coalescence of island droplets. As an application, the MD results exhibit a 10× boost in the heat transfer coefficient (HTC), showing a -1 scaling law with the maximum droplet radius. We provide phase diagrams for jumping and wetting behaviors to guide the design of lattice structures with advanced antidew performance.

Filtering Robust Graphite without Incommensurate Interfaces by Electrical Technique.

Two-dimensional (2D) van der Waals (vdW) layered materials have attracted considerable attention due to their potential applications in various fields. Among these materials, graphite is widely employed to achieve structural superlubricity (SSL), where the interfacial friction between two solids is almost negligible and the wear is zero. However, the development of integrated SSL systems using graphite flakes still faces a major obstacle stemming from the inherent delamination-induced instability in vdW layered materials. To address this issue, we propose a nondestructive filtering technique that utilizes electrical measurement to identify robust graphite flakes without delamination. Our experimental results confirm that all the filtered graphite flakes exhibit delamination-free behavior after more than 7000 cycles of sliding on a series of 2D and 3D substrates. Besides, we employ three types of characterizing methods to confirm that the filtering process does not impair the graphite flakes. Moreover, with focused ion beam (FIB) assisted slicing characterization and statistical analysis, we have discovered that all of the filtered flakes possess a graphite layer thickness below 100 nm. This is consistent with the thickness of the single crystalline graphite layer of our samples reported in the literature, suggesting the absence of incommensurate interfaces in the filtered graphite flakes. Our work contributes to a deeper understanding of the relationship between graphite conductance and incommensurate interfaces. In addition, we present a possible solution to address the delamination problem in layered materials, and this technique shows the potential to characterize the internal microstructure of grains and the distribution of grain boundaries in vdW materials on a large scale.

Fully automatic transfer and measurement system for structural superlubric materials.

Structural superlubricity, a state of nearly zero friction and no wear between two contact surfaces under relative sliding, holds immense potential for research and application prospects in micro-electro-mechanical systems devices, mechanical engineering, and energy resources. A critical step towards the practical application of structural superlubricity is the mass transfer and high throughput performance evaluation. Limited by the yield rate of material preparation, existing automated systems, such as roll printing or massive stamping, are inadequate for this task. In this paper, a machine learning-assisted system is proposed to realize fully automated selective transfer and tribological performance measurement for structural superlubricity materials. Specifically, the system has a judgment accuracy of over 98% for the selection of micro-scale graphite flakes with structural superlubricity properties and complete the 100 graphite flakes assembly array to form various pre-designed patterns within 100 mins, which is 15 times faster than manual operation. Besides, the system is capable of automatically measuring the tribological performance of over 100 selected flakes on Si3N4, delivering statistical results for new interface which is beyond the reach of traditional methods. With its high accuracy, efficiency, and robustness, this machine learning-assisted system promotes the fundamental research and practical application of structural superlubricity.

Manipulation and Characterization of Submillimeter Shearing Contacts in Graphite by the Micro-Dome Technique.

Manipulation techniques are the key to measuring fundamental properties of layered materials and their monolayers (2D materials) on the micro- and nanoscale as well as a necessity to the solution of relevant existing challenges. An example is the challenge against upscaling structural superlubricity, a phenomenon of near-zero friction and wear in solid contacts. To date, the largest single structural superlubric contact only has a size of a few tens of micrometers, which is achieved on graphite mesa, a system that has shown microscale superlubricity. The first obstacle against extending the contact size is the lack of suitable manipulation techniques. Here, a micro-dome technique is demonstrated on graphite mesas by shearing contacts 2500 times larger in area than previously possible. With this technique, submillimeter graphite mesas are opened, characterized for the first time, and compared to their microscale counterparts. Interfacial structures, which are possibly related to the failure of superlubricity, are observed: commensurate grains, external steps, and carbon aggregates. Furthermore, a proof-of-concept mechanical model is developed to understand how the micro-dome technique works and to predict its limits. Finally, a dual-axis force measuring device is developed and integrated with the micro-dome technique to measure the normal and lateral forces when shearing submillimeter mesas. These results provide a platform technique for future research on structural superlubricity on different scales and manipulation of structures of layered materials in general.

Robust microscale structural superlubricity between graphite and nanostructured surface.

Structural superlubricity is a state of nearly zero friction and no wear between two contacted solid surfaces. However, such state has a certain probability of failure due to the edge defects of graphite flake. Here, we achieve robust structural superlubricity state between microscale graphite flakes and nanostructured silicon surfaces under ambient condition. We find that the friction is always less than 1 µN, the differential friction coefficient is on the order of 10-4, without observable wear. This is attributed to the edge warping of graphite flake on the nanostructured surface under concentrated force, which eliminate the edge interaction between the graphite flake and the substrate. This study not only challenges the traditional understanding in tribology and structural superlubricity that rougher surfaces lead to higher friction and lead to wear, thereby reducing roughness requirements, but also demonstrates that a graphite flake with a single crystal surface that does not come into edge contact with the substrate can consistently achieve robust structural superlubricity state with any non-van der Waals material in atmospheric conditions. Additionally, the study provides a general surface modification method that enables the widespread application of structural superlubricity technology in atmospheric environments.

Condensation droplet sieve.

Large droplets emerging during dropwise condensation impair surface properties such as anti-fogging/frosting ability and heat transfer efficiency. How to spontaneously detach massive randomly distributed droplets with controlled sizes has remained a challenge. Herein, we present a solution called condensation droplet sieve, through fabricating microscale thin-walled lattice structures coated with a superhydrophobic layer. Growing droplets were observed to jump off this surface once becoming slightly larger than the lattices. The maximum radius and residual volume of droplets were strictly confined to 16 µm and 3.2 nl/mm2 respectively. We reveal that this droplet radius cut off is attributed to the large tolerance of coalescence mismatch for jumping and effective isolation of droplets between neighboring lattices. Our work brings forth a strategy for the design and fabrication of high-performance anti-dew materials.

Anisotropic Fracture of Graphene Revealed by Surface Steps on Graphite.

The anisotropic fracture toughness G(θ) is an intrinsic feature of graphene and is fundamental for fabrication, functioning, and robustness of graphene-based devices. However, existing results show significant discrepancies on the anisotropic factor, i.e., the ratio between zigzag (ZZ) and armchair (AC) directions, G_{ZZ}/G_{AC}, both qualitatively and quantitatively. Here, we investigate the anisotropic fracture of graphene by atomic steps on cleaved graphite surfaces. Depending on the relation between the peeling direction and local lattice orientation, two categories of steps with different structures and behaviors are observed. In one category are straight steps well aligned with local ZZ directions, while in the other are steps consisting of nanoscale ZZ and AC segments. Combined with an analysis on fracture mechanics, the microscale morphology of steps and statistics of their directions provides a measurement on the anisotropic factor of G_{ZZ}/G_{AC}=0.971, suggesting that the ZZ direction has a slightly lower fracture toughness. The results provide an experimental benchmark for the widely scattered existing results, and offer constraints on future models of graphene fracture.

Polygonal non-wetting droplets on microtextured surfaces.

Understanding the interactions between liquids and solids is important for many areas of science and technology. Microtextured surfaces have been extensively studied in microfluidics, DNA technologies, and micro-manufacturing. For these applications, the ability to precisely control the shape, size and location of the liquid via textured surfaces is of particular importance for the design of fluidic-based systems. However, this has been passively realized in the wetting state thanks to the pinning of the contact line, leaving the non-wetting counterpart challenging due to the low liquid affinity. In this work, confinement is imposed on droplets located on well-designed shapes and arrangements of microtextured surfaces. An active way to shape non-wetting water and liquid metal droplets into various polygons ranging from triangles, squares, rectangles, to hexagons is developed. The results suggest that energy barriers in different directions account for the movement of the contact lines and the formation of polygonal shapes. By characterizing the curvature of the liquid-vapour meniscus, the morphology of the droplet is correlated to its volume, thickness, and contact angle. The developed liquid-based patterning strategy under active regulation with low adhesion looks promising for low-cost micromanufacturing technology, DNA microarrays, and digital lab-on-a-chip.

General orientation transform for the estimation of fiber orientations in white matter tissues.

PURPOSE: The orientation distribution function (ODF), which is obtained from the radial integral of the probability density function weighted by rn$$ {r}^n $$ ( r$$ r $$ is the radial length), has been used to estimate fiber orientations of white matter tissues. Currently, there is no general expression of the ODF that is suitable for any n value in the HARDI methods. THEORY AND METHODS: A novel methodology is proposed to calculate the ODF for any n>-1$$ n>-1 $$ through the Taylor series expansion and a generalized expression for -1

100 km wear-free sliding achieved by microscale superlubric graphite/DLC heterojunctions under ambient conditions.

Wear-free sliding between two contacted solid surfaces is the ultimate goal in the effort to extend the lifetime of mechanical devices, especially when it comes to inventing new types of micro-electromechanical systems where wear is often a major obstacle. Here we report experimental observations of wear-free sliding for a micrometer-sized graphite flake on a diamond-like-carbon (DLC) surface under ambient conditions with speeds up to 2.5 m/s, and over a distance of 100 km. The coefficient of friction (COF) between the microscale graphite flake, a van der Waals (vdW) layered material and DLC, a non-vdW-layered material, is measured to be of the order of [Formula: see text], which belongs to the superlubric regime. Such ultra-low COFs are also demonstrated for a microscale graphite flake sliding on six other kinds of non-vdW-layered materials with sub-nanometer roughness. With a synergistic analysis approach, we reveal the underlying mechanism to be the combination of interfacial vdW interaction, atomic-smooth interfaces and the low normal stiffness of the graphite flake. These features guarantee a persistent full contact of the interface with weak interaction, which contributes to the ultra-low COFs. Together with the extremely high in-plane strength of graphene, wear-free sliding is achieved. Our results broaden the scope of superlubricity and promote its wider application in the future.

Microscale Schottky superlubric generator with high direct-current density and ultralong life.

Miniaturized or microscale generators that can effectively convert weak and random mechanical energy into electricity have significant potential to provide solutions for the power supply problem of distributed devices. However, owing to the common occurrence of friction and wear, all such generators developed so far have failed to simultaneously achieve sufficiently high current density and sufficiently long lifetime, which are crucial for real-world applications. To address this issue, we invent a microscale Schottky superlubric generator (S-SLG), such that the sliding contact between microsized graphite flakes and n-type silicon is in a structural superlubric state (an ultra-low friction and wearless state). The S-SLG not only generates high current (~210 Am-2) and power (~7 Wm-2) densities, but also achieves a long lifetime of at least 5,000 cycles, while maintaining stable high electrical current density (~119 Am-2). No current decay and wear are observed during the experiment, indicating that the actual persistence of the S-SLG is enduring or virtually unlimited. By excluding the mechanism of friction-induced excitation in the S-SLG, we further demonstrate an electronic drift process during relative sliding using a quasi-static semiconductor finite element simulation. Our work may guide and accelerate the future use of S-SLGs in real-world applications.

Diffusion coefficient orientation distribution function for diffusion magnetic resonance imaging.

BACKGROUND: Diffusion magnetic resonance imaging (dMRI) is a popular non-invasive imaging technique applied for the study of nerve fibers in vivo, with diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI) as the commonly used dMRI methods. However, DTI cannot resolve complex fiber orientations in a local area and HARDI lacks a solid physical basis. NEW METHOD: We introduce a diffusion coefficient orientation distribution function (DCODF). It has a clear physical meaning to represent the orientation distribution of diffusion coefficients for Gaussian and non-Gaussian diffusion. Based on DCODF, we then propose a new HARDI method, termed as diffusion coefficient orientation distribution transform (DCODT), to estimate the orientation distribution of nerve fibers in voxels. RESULTS: The method is verified on the simulated data, ISMRM-2015-Tracto-challenge data, and HCP datasets. The results show the superior capability of DCODT in resolving the complex distribution of multiple fiber bundles effectively. COMPARISON WITH EXISTING METHOD(S): The method is compared to other common model-free HARDI estimators. In the numerical simulations, DCODT achieves a better trade-off between the resolution and accuracy than the counterparts for high b-values. In the comparisons based on the challenge data, the improvement of DCODT is significant in scoring. The results on the HCP datasets show that DCODT provides fewer spurious lobes in the glyphs, resulting in more coherent fiber orientations. CONCLUSIONS: We conclude that DCODT may be a reliable method to extract accurate information about fiber orientations from dMRI data and promising for the study of neural architecture.

Origin of Friction in Superlubric Graphite Contacts.

More than thirty years ago, it was theoretically predicted that friction for incommensurate contacts between atomically smooth, infinite, crystalline materials (e.g., graphite, MoS_{2}) is vanishing in the low speed limit, and this corresponding state was called structural superlubricity (SSL). However, experimental validation of this prediction has met challenges, since real contacts always have a finite size, and the overall friction arises not only from the atoms located within the contact area, but also from those at the contact edges which can contribute a finite amount of friction even when the incommensurate area does not. Here, we report, using a novel method, the decoupling of these contributions for the first time. The results obtained from nanoscale to microscale incommensurate contacts of graphite under ambient conditions verify that the average frictional contribution of an inner atom is no more than 10^{-4} that of an atom at the edge. Correspondingly, the total friction force is dominated by friction between the contact edges for contacts up to 10 µm in lateral size. We discuss the physical mechanisms of friction observed in SSL contacts, and provide guidelines for the rational design of large-scale SSL contacts.

Superlubricity between Graphite Layers in Ultrahigh Vacuum.

Graphite has been conventionally believed to exhibit an inferior lubricating performance with significantly larger friction coefficient and wear rate in a vacuum environment than in ambient air. Dangling bonds at the edge planes of graphite, accounting for the high friction in inert atmosphere are saturated by chemisorbed vapor molecules in air, which contributes to low surface adhesion and low friction. However, there is still a lack of direct experimental evidence whether basal planes of graphite excluding the negative effects of edges or dangling bonds shows intrinsic lubricity when sliding under ultrahigh vacuum (UHV) conditions. By the interlayer friction measurement enabled by graphite flake-wrapped atomic force microscope tips in UHV, we show a record-low friction coefficient of 4 × 10-5 (slope of friction vs normal force curve) when sliding between graphite layers, which is much lower than that in ambient air. This discrepancy manifests the intrinsic sliding frictional behavior between the graphite basal planes when the tribo-materials and experimental conditions are well-designed and strictly controlled. In addition, the temperature dependence of the kinetic friction between the graphite layers has been investigated under UHV conditions over the temperature range of 125-448 K, which is consistent with the thermally activated process.

Characterization of a Microscale Superlubric Graphite Interface.

Direct characterizations of the two component surfaces of a solid-solid interface are essential for understanding its various interfacial mechanical, physical, and electrical behaviors. Particularly, the fascinating phenomenon termed structural superlubricity, a state of nearly zero friction and wear, is sensitively dependent on the interface structure. Here we report a controllable pick-and-flip technique to separate a microscale contact pair for the characterization of its two component surfaces for van der Waals layered materials. With this technique, the interface of a graphite superlubric contact is characterized with resolution from microscale down to the atomic level. Imaging of the graphite lattice provides direct proof that this superlubric interface consists of two monocrystalline surfaces incommensurate with each other. More importantly, the structure-property relationship for this contact is investigated. Friction measurements combined with fully atomistic molecular dynamics reveal that internal structures [internals steps, pits, and bulges buried underneath the topmost graphene sheet(s)] have negligible contribution to the total friction; in contrast, external defects lead to a high friction. These results help us to better understand the structure of highly oriented pyrolytic graphite and the fundamental mechanisms of structural superlubricity, as well as to guide the design of superlubricity-based devices.

Temperature-regulated adhesion of impacting drops on nano/microtextured monostable superrepellent surfaces.

The monostable Cassie state is a favorable wetting state for superhydrophobic materials, in which water drops can automatically transfer from the Wenzel wetting state to the Cassie wetting state, such that as a consequence the water repellency can be maintained. Drop impact phenomena are ubiquitous in nature and of critical importance in industry, and previous works show that the efficiency of self-cleaning and dropwise condensation could benefit from drop impact on monostable surfaces. However, whether such a feature is sufficiently robust remains unclear when the temperature of the surface is taken into consideration. Here, we report that there exists a lower bound of the temperature of the surface, under which a transition from the Cassie wetting state to the Wenzel wetting state arises. By varying the temperature of the surface, it is found that the solid-liquid wetting region could be regulated. Based on thermodynamics, we propose a model to predict the controllable wetting region, and we show that the gradual transition of the wetting state is a result of the accumulation of droplets on the nanoscale. Connections between the dynamics occurring at the solid-liquid interfaces on the microscale and the condensation occurring in the nanotextures are constructed. These results deepen our understanding of the breakdown of superhydrophobicity under dynamic impinging in high humidity. Moreover, this study will shed new light on the applications for controllable liquid deposition and surface decoration, such as catalysts on the superhydrophobic surfaces.