Kinetic description of site ensembles on catalytic surfaces.

We demonstrate that the Langmuir-Hinshelwood formalism is an incomplete kinetic description and, in particular, that the Hinshelwood assumption (i.e., that adsorbates are randomly distributed on the surface) is inappropriate even in catalytic reactions as simple as A + A → A2 The Hinshelwood assumption results in miscounting of site pairs (e.g., A*-A*) and, consequently, in erroneous rates, reaction orders, and identification of rate-determining steps. The clustering and isolation of surface species unnoticed by the Langmuir-Hinshelwood model is rigorously accounted for by derivation of higher-order rate terms containing statistical factors specific to each site ensemble. Ensemble-specific statistical rate terms arise irrespective of and couple with lateral adsorbate interactions, are distinct for each elementary step including surface diffusion events (e.g., A* + * → * + A*), and provide physical insight obscured by the nonanalytical nature of the kinetic Monte Carlo (kMC) method-with which the higher-order formalism quantitatively agrees. The limitations of the Langmuir-Hinshelwood model are attributed to the incorrect assertion that the rate of an elementary step is the same with respect to each site ensemble. In actuality, each elementary step-including adsorbate diffusion-traverses through each ensemble with unique rate, reversibility, and kinetic-relevance to the overall reaction rate. Explicit kinetic description of ensemble-specific paths is key to the improvements of the higher-order formalism; enables quantification of ensemble-specific rate, reversibility, and degree of rate control of surface diffusion; and reveals that a single elementary step can, counter intuitively, be both equilibrated and rate determining.

Directional Migration and Rapid Coalescence of Au Nanoparticles on Anisotropic ReS2.

Interfacial atomic configuration and its evolution play critical roles in the structural stability and functionality of mixed zero-dimensional (0D) metal nanoparticles (NPs) and two-dimensional (2D) semiconductors. In situ observation of the interface evolution at atomic resolution is a vital method. Herein, the directional migration and structural evolution of Au NPs on anisotropic ReS2 were investigated in situ by aberration-corrected transmission electron microscopy. Statistically, the migration of Au NPs with diameters below 3 nm on ReS2 takes priority with greater probability along the b-axis direction. Density functional theory calculations suggest that the lower diffusion energy barrier enables the directional migration. The coalescence kinetics of Au NPs is quantitatively described by the relation of neck radius (r) and time (t), expressed as r2=Kt. Our work provides an atomic-resolved dynamic analysis method to study the interfacial structural evolution of metal/2D materials, which is essential to the study of the stability of nanodevices based on mixed-dimensional nanomaterials.

Surface Adatom Diffusion-Assisted Dislocation Nucleation in Metal Nanowires.

We employ a hybrid diffusion- and nucleation-based kinetic Monte Carlo model to elucidate the significant impact of adatom diffusion on incipient surface dislocation nucleation in metal nanowires. We reveal a stress-regulated diffusion mechanism that promotes preferential accumulation of diffusing adatoms near nucleation sites, which explains the experimental observations of strong temperature but weak strain-rate dependence as well as temperature-dependent scatter of the nucleation strength. Furthermore, the model demonstrates that a decreasing rate of adatom diffusion with an increasing strain rate will lead to stress-controlled nucleation being the dominant nucleation mechanism at higher strain rates. Overall, our model offers new mechanistic insights into how surface adatom diffusion directly impacts the incipient defect nucleation process and resulting mechanical properties of metal nanowires.

Exploiting Zirconium-Based Metallic Glass Thin Films for Anode-Free Lithium-Ion Batteries and Lithium Metal Batteries With Ultra-Long Cycling Life.

Coating Zr-based metallic glass, Zr53 Cu31 Ni11 Al5 (Zr-MG), on a Cu current collector (CC) and Li metal anode (LMA) significantly improves the cycle performance of both types of Li-ion batteries, namely, anode-free Li-ion batteries (AFLBs) and Li metal batteries (LMB). The inherent isotropy and homogeneity of the Zr-MG significantly improve the surface uniformity of the CC and LMA. A 12 nm-thick Zr-MG thin film coating on the CC reduces the overpotential in the AFLB, leading to a more uniform Li plating morphology. The Li film covers almost the entire surface of the Zr-CC, whereas it only covers ≈75% of the bare CC during charging. An LFP||Zr-CC full-cell exhibits a capacity retention of 63.6% after the 100th cycle, with an average CE of 99.55% at a 0.2 C rate. In the case of the LMB, a 12 nm-thick Zr-MG thin film-coated LMA (Zr-LMA) exhibits a stable capacity of up to 1500 cycles. An LFP||Zr-LMA full-cell exhibits capacity retention and CE after 1500 cycles of 66.6% and 99.97%, respectively, at a 1 C rate. Zirconium-MG thin films with atomic-level uniformity, outstanding corrosion resistance, lithiophilic characteristics, and high diffusivity result in superior AFLB and LMB performances.

Recent Developments in Kramers' Theory of Reaction Rates.

In this short review, we provide an update of recent developments in Kramers' theory of reaction rates. After a brief introduction stressing the importance of this theory initially developed for chemical reactions, we briefly present the main theoretical formalism starting from the generalized Langevin equation and continue by showing the main points of the modern Pollak, Grabert and Hänggi theory. Kramers' theory is then sketched for quantum and classical surface diffusion. As an illustration the surface diffusion of Na atoms on a Cu(110) surface is discussed showing escape rates, jump distributions and diffusion coefficients as a function of reduced friction. Finally, some very recent applications of turnover theory to different fields such as nanoparticle levitation, microcavity polariton dynamics and simulation of reaction in liquids are presented. We end with several open problems and future challenges faced up by Kramers turnover theory.

Kinetics and mechanism of planar nanowire growth.

Surface-guided growth of planar nanowires offers the possibility to control their position, direction, length, and crystallographic orientation and to enable their large-scale integration into practical devices. However, understanding of and control over planar nanowire growth are still limited. Here, we study theoretically and experimentally the growth kinetics of surface-guided planar nanowires. We present a model that considers different kinetic pathways of material transport into the planar nanowires. Two limiting regimes are established by the Gibbs-Thomson effect for thinner nanowires and by surface diffusion for thicker nanowires. By fitting the experimental data for the length-diameter dependence to the kinetic model, we determine the power exponent, which represents the dimensionality of surface diffusion, and results to be different for planar vs. nonplanar nanowires. Excellent correlation between the model predictions and the data is obtained for surface-guided Au-catalyzed ZnSe and ZnS nanowires growing on both flat and faceted sapphire surfaces. These data are compared with those of nonplanar nanowire growth under similar conditions. The results indicate that, whereas nonplanar growth is usually dominated by surface diffusion of precursor adatoms over the nanowire walls, planar growth is dominated by surface diffusion over the substrate. This mechanism of planar nanowire growth can be extended to a broad range of material-substrate combinations for higher control toward large-scale integration into practical devices.

Estimating and leveraging protein diffusion on ion-exchange resin surfaces.

Protein mobility at solid-liquid interfaces can affect the performance of applications such as bioseparations and biosensors by facilitating reorganization of adsorbed protein, accelerating molecular recognition, and informing the fundamentals of adsorption. In the case of ion-exchange chromatographic beads with small, tortuous pores, where the existence of surface diffusion is often not recognized, slow mass transfer can result in lower resin capacity utilization. We demonstrate that accounting for and exploiting protein surface diffusion can alleviate the mass-transfer limitations on multiple significant length scales. Although the surface diffusivity has previously been shown to correlate with ionic strength (IS) and binding affinity, we show that the dependence is solely on the binding affinity, irrespective of pH, IS, and resin ligand density. Different surface diffusivities give rise to different protein distributions within the resin, as characterized using confocal microscopy and small-angle neutron scattering (length scales of micrometer and nanometer, respectively). The binding dependence of surface diffusion inspired a protein-loading approach in which the binding affinity, and hence the surface diffusivity, is modulated by varying IS. Such gradient loading increased the protein uptake efficiency by up to 43%, corroborating the importance of protein surface diffusion in protein transport in ion-exchange chromatography.

Self-Detachment and Subsurface Densification of Dealloyed Nanoporous Thin Films.

Experiment shows thin films of dealloyed nanoporous gold (NPG) spontaneously detaching from massive gold base layers. NPG can also densify near its external surface. This is naturally reproduced by kinetic Monte Carlo (KMC) simulation of dealloying and coarsening and so appears generic for nanoscale network materials evolving by surface diffusion. Near the porous layer's external surface and near its interface with the base layer, gradients in the depth-profile of a laterally averaged mean surface curvature provide driving forces for diffusion and cause divergences of the net fluxes of matter, leading to accretion/densification or to erosion/disconnection. As a toy model, the morphology evolution of substrate-supported nanopillars by surface diffusion illustrates and confirms our considerations. Contrary to cylindrical nanowires, the ligaments in nanoporous materials exhibit pre-existing gradients in the mean curvature. The Plateau-Rayleigh long-wavelength stability criterion is then not applicable and the disconnection accelerated.

Twin-Boundary Reduced Surface Diffusion on Electrically Stressed Copper Nanowires.

Surface diffusion is intimately correlated with crystal orientation and surface structure. Fast surface diffusion accelerates phase transformation and structural evolution of materials. Here, through in situ transmission electron microscopy observation, we show that a copper nanowire with dense nanoscale coherent twin-boundary (CTB) defects evolves into a zigzag configuration under electric-current driven surface diffusion. The hindrance at the CTB-intercepted concave triple junctions decreases the effective surface diffusivity by almost 1 order of magnitude. The energy barriers for atomic migration at the concave junctions and different faceted surfaces are computed using density functional theory. We proposed that such a stable zigzag surface is shaped not only by the high-diffusivity facets but also by the stalled atomic diffusion at the concave junctions. This finding provides a defect-engineering route to develop robust interconnect materials against electromigration-induced failures for nanoelectronic devices.

Adsorption and Diffusion of Oxygen on Pure and Partially Oxidized Metal Surfaces in Ultrahigh Resolution.

The interaction of gas molecules with metal and oxide surfaces plays a critical role in corrosion, catalysis, sensing, and heterogeneous materials. However, insights into the dynamics of O2 from picoseconds to microseconds have remained unavailable to date. We obtained 3D potential energy surfaces for adsorption of O2 on 11 common pristine and partially oxidized (hkl) surfaces of Ni and Al in picometer resolution and high accuracy of 0.1 kcal/mol, identified binding sites, and surface mobility from 25 to 300 °C. We explain relative oxidation rates and parameters for oxide growth. We employed over 150 000 molecular mechanics and molecular dynamics simulations with the interface force field (IFF) using structural data from X-ray diffraction (XRD) and low-energy electron diffraction (LEED). The methods reach 10 to 50 times higher accuracy than possible before and are suited to analyze gas interactions with metals up to the micrometer scale including defects and irregular nanostructures.

Angstrom-Scale Electrochemistry at Electrodes with Dimensions Commensurable and Smaller than Individual Reacting Species.

In nature and technologies, many chemical reactions occur at interfaces with dimensions approaching that of a single reacting species in nano- and angstrom-scale. Mechanisms governing reactions at this ultimately small spatial regime remain poorly explored because of challenges to controllably fabricate required devices and assess their performance in experiment. Here we report how efficiency of electrochemical reactions evolves for electrodes that range from just one atom in thickness to sizes comparable with and exceeding hydration diameters of reactant species. The electrodes are made by encapsulating graphene and its multilayers within insulating crystals so that only graphene edges remain exposed and partake in reactions. We find that limiting current densities characterizing electrochemical reactions exhibit a pronounced size effect if reactant's hydration diameter becomes commensurable with electrodes' thickness. An unexpected blockade effect is further revealed from electrodes smaller than reactants, where incoming reactants are blocked by those adsorbed temporarily at the atomically narrow interfaces. The demonstrated angstrom-scale electrochemistry offers a venue for studies of interfacial behaviors at the true molecular scale.

Impact of Molecular Surface Diffusion on the Physical Stability of Co-Amorphous Systems.

In this study, surface diffusion of l-aspartic acid-carvedilol (ASP-CAR) co-amorphous systems at different ASP concentrations is measured and correlated with their physical stability. ASP-CAR films at ASP concentrations of 1-5% (w/w) were prepared by a newly developed method based on a vacuum compression molding process. Surface diffusion measurements were conducted on these systems based on the surface grating decay method using atomic force microscopy (AFM). The results demonstrate that a small amount of ASP (i.e., ≤ 5% w/w) in the co-amorphous systems could significantly slow down the grating decay process compared with that of pure amorphous CAR, indicating a reduced surface diffusion of CAR molecules. The decay time gradually increased in co-amorphous systems with increasing ASP concentration from 1 to 5% (w/w), with the longest observed decay time of around 800 h for the 5%ASP-CAR system, which was more than 200 times longer compared to the decay time of pure amorphous CAR (approximately 3 h). A good correlation between the decay constants of the pure amorphous CAR and co-amorphous films at ASP concentrations of 1-5% (w/w) and the physical stability of corresponding amorphous powder samples was found. Overall, this study provides a new method to prepare co-amorphous films for surface property measurements and reveals the impact of surface diffusion on the physical stability of co-amorphous systems.

Effects of microstructure formation on the stability of vapor-deposited glasses.

Glasses formed by physical vapor deposition (PVD) are an interesting new class of materials, exhibiting properties thought to be equivalent to those of glasses aged for thousands of years. Exerting control over the structure and properties of PVD glasses formed with different types of glass-forming molecules is now an emerging challenge. In this work, we study coarse-grained models of organic glass formers containing fluorocarbon tails of increasing length, corresponding to an increased tendency to form microstructures. We use simulated PVD to examine how the presence of the microphase-separated domains in the supercooled liquid influences the ability to form stable glasses. This model suggests that increasing molecule tail length results in decreased thermodynamic stability of the molecules in PVD films. The reduced stability is further linked to the reduced ability of these molecules to equilibrate at the free surface during PVD. We find that, as the tail length is increased, the relaxation times near the surface of the supercooled equilibrium liquid films of these molecules are slowed and become essentially bulk-like, due to the segregation of the fluorocarbon tails to the free surface. Surface diffusion is also markedly reduced due to clustering of the molecules at the surface. Based on these results, we propose a trapping mechanism where tails are unable to move between local phase-separated domains on the relevant deposition time scales.

Thermodynamic Regulation of Dendrite-Free Li Plating on Li3Bi for Stable Lithium Metal Batteries.

Rechargeable batteries with metallic lithium (Li) anodes are attracting ever-increasing interests because of their high theoretical specific capacity and energy density. However, the dendrite growth of the Li anode during cycling leads to poor stability and severe safety issues. Here, Li3Bi alloy coated carbon cloth is rationally chosen as the substrate of the Li anode to suppress the dendrite growth from a thermodynamic aspect. The adsorption energy of a Li atom on Li3Bi is larger than the cohesive energy of bulk Li, enabling uniform Li nucleation and deposition, while the high diffusion barrier of the Li atom on Li3Bi blocks the migration of adatoms from adsorption sites to the regions of fast growth, which further ensures uniform Li deposition. With the dendrite-free Li deposition, the composite Li/Li3Bi anode enables over 250 cycles at an ultrahigh current density of 20 mA cm-2 in a symmetrical cell and delivers superior electrochemical performance in full batteries.

Two-Dimensional Interfacial Exchange Diffusion Has the Potential to Augment Spatiotemporal Precision of Ca2+ Signaling.

Nano-junctions between the endoplasmic reticulum and cytoplasmic surfaces of the plasma membrane and other organelles shape the spatiotemporal features of biological Ca2+ signals. Herein, we propose that 2D Ca2+ exchange diffusion on the negatively charged phospholipid surface lining nano-junctions participates in guiding Ca2+ from its source (channel or carrier) to its target (transport protein or enzyme). Evidence provided by in vitro Ca2+ flux experiments using an artificial phospholipid membrane is presented in support of the above proposed concept, and results from stochastic simulations of Ca2+ trajectories within nano-junctions are discussed in order to substantiate its possible requirements. Finally, we analyze recent literature on Ca2+ lipid interactions, which suggests that 2D interfacial Ca2+ diffusion may represent an important mechanism of signal transduction in biological systems characterized by high phospholipid surface to aqueous volume ratios.

Surface Diffusion Aided by a Chirality Change of Self-Assembled Oligomers under 2D Confinement.

Chirality switching of self-assembled molecular structures is of potential interest for designing functional materials but is restricted by the strong interaction between the embedded molecules. Here, we report on an unusual approach based on reversible chirality changes of self-assembled oligomers using variable-temperature scanning tunneling microscopy supported by quantum mechanical calculations. Six functionalized diazomethanes each self-assemble into chiral wheel-shaped oligomers on Ag(111). At 130 K, a temperature far lower than expected, the oligomers change their chirality even though the molecules reside in an embedded self-assembled structure. Each chirality change is accompanied by a slight center-of-mass shift. We show how the identical activation energies of the two processes result from the interplay of the chirality change with surface diffusion, findings that open the possibility of implementing various functional materials from self-assembled supramolecular structures.

The structural symmetry of nanoholes upon droplet epitaxy.

Nanoholes obtained by droplet epitaxy has been intensively investigated as an important material platform for the fabrication of nanodevices due to their unique topology. However, the final fabricated nanoholes are very difficult to achieve a highly symmetric circular structure, and usually have two or four gaps in the sidewall of the holes. Here we have presented a developed model to inquire into the reasons for the formation of the gaps at the periphery of nanoholes and discuss how to improve the structural symmetry of the nanoholes. It is found that the anisotropic interface diffusion of As atoms decomposed by substrate can result in the formation of the gaps. In order to improve the symmetry of final nanostructures, we can minimize the interval time between deposition of Ga droplets and open operation of As flux, and set up a multistep growth procedure by changing the intensity of As flux or growth temperature.

Self-Healing of Nanoporous Gold Under Ambient Conditions.

Failure of a material is an irreversible process since the material loses its original characteristics and properties. The catastrophic brittle failure under tensile stress of nanoporous gold (np-Au) with a bicontinuous open-cell structure makes impossible otherwise attractive applications. Here, we first demonstrate a self-healing process in tensile-fractured np-Au to overcome the limit of fragility via mechanically assisted cold-welding under ambient conditions. The self-healing ability of np-Au in terms of mechanical properties shows strength recovery up to 64.4% and fully recovered elastic modulus compared with initial tensile properties. Topological parameters obtained by three-dimensional reconstruction of self-healed np-Au clarify the strength, elastic modulus, and strain distribution. The self-healing process in np-Au is attributed to surface diffusion expedited by local compressive stress in the ultrasmall dimension of ligaments formed by ductile failures of individual ligaments.

Stability Analysis of a Bulk-Surface Reaction Model for Membrane Protein Clustering.

Protein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on the surface of the PM plays an important role in governing their heterogeneous surface distribution. However, the stability behavior of the surface distribution of protein aggregates remains poorly understood. Therefore, understanding the spatial patterns that can emerge on the PM solely through protein-protein interaction, lateral diffusion, and feedback is an important step toward a complete description of the mechanisms behind protein clustering on the cell surface. In this work, we investigate the pattern formation of a reaction-diffusion model that describes the dynamics of a system of ligand-receptor complexes. The purely diffusive ligand in the cytosol can bind receptors in the PM and the resultant ligand-receptor complexes not only diffuse laterally but can also form clusters resulting in different oligomers. Finally, the largest oligomers recruit ligands from the cytosol using positive feedback. From a methodological viewpoint, we provide theoretical estimates for diffusion-driven instabilities of the protein aggregates based on the Turing mechanism. Our main result is a threshold phenomenon, in which a sufficiently high recruitment of ligands promotes the input of new monomeric components and consequently drives the formation of a single-patch spatially heterogeneous steady state.

Decoupling of surface diffusion and relaxation dynamics of molecular glasses.

Tobacco mosaic virus is used as a probe to measure surface diffusion of ultrathin films of N,N'-Bis(3-methylphenyl)-N,N'-diphenylbenzidine (TPD) (12 nm [Formula: see text] 53 nm, where [Formula: see text] is the film thickness) at various temperatures below the glass transition temperature, [Formula: see text], of all films. As the film thickness is decreased, [Formula: see text] decreases rapidly and the average film dynamics are enhanced by 6-14 orders of magnitude. We show that the surface diffusion is invariant of the film thickness decrease and the resulting enhanced overall mobility. The values of the surface diffusion coefficient and its temperature dependence are invariant of film thickness and are the same as the corresponding bulk values ([Formula: see text]400 nm). For the thinnest films ([Formula: see text]20 nm), the effective activation energy for rearrangement (temperature dependence of relaxation times) becomes smaller than the activation energy for surface diffusion. These results suggest that the fast surface diffusion is decoupled from film relaxation dynamics and is a solely free surface property.