Despite the fact that Ta3N5 absorbs a major fraction of the visible spectrum, the rapid decrease of photocurrent encountered in water photoelectrolysis over time remains a serious hurdle for the practical application of Ta3N5 photoelectrodes. Here, by employing a Co3O4 nanoparticle water oxidation catalyst (WOC) as well as an alkaline electrolyte, the photostability of Ta3N5 electrode is significantly improved. Co3O4/Ta3N5 photoanode exhibits the best durability against photocorrosion to date, when compared with Co(OH)x/Ta3N5 and IrO2/Ta3N5 photoanodes. Specifically, about 75% of the initial stable photocurrent remains after 2 h irradiation at 1.2 V vs. RHE (reversible hydrogen electrode). Meanwhile, a photocurrent density of 3.1 mA cm−2 has been achieved on Co3O4/Ta3N5 photoanode at 1.2 V vs. RHE with backside illumination under 1 sun AM 1.5 G simulated sunlight. The reason for the relatively high stability is discussed on the basis of electron microscopic observations and photoelectrochemical measurements, and the surface nitrogen content is monitored by X‐ray photoelectron spectroscopic analysis.

In this work, we treat the Poisson-Nernst-Planck (PNP) equations as the basis for a consistent framework of the electrokinetic effects. The static limit of the PNP equations is shown to be the charge-conserving Poisson-Boltzmann (CCPB) equation, with guaranteed charge neutrality within the computational domain. We propose a surface potential trap model that attributes an energy cost to the interfacial charge dissociation. In conjunction with the CCPB, the surface potential trap can cause a surface-specific adsorbed charge layer σ. By defining a chemical potential μ that arises from the charge neutrality constraint, a reformulated CCPB can be reduced to the form of the Poisson-Boltzmann equation, whose prediction of the Debye screening layer profile is in excellent agreement with that of the Poisson-Boltzmann equation when the channel width is much larger than the Debye length. However, important differences emerge when the channel width is small, so the Debye screening layers from the opposite sides of the channel overlap with each other. In particular, the theory automatically yields a variation of σ that is generally known as the "charge regulation" behavior, attendant with predictions of force variation as a function of nanoscale separation between two charged surfaces that are in good agreement with the experiments, with no adjustable or additional parameters. We give a generalized definition of the ζ potential that reflects the strength of the electrokinetic effect; its variations with the concentration of surface-specific and surfacenonspecific salt ions are shown to be in good agreement with the experiments. To delineate the behavior of the electro-osmotic (EO) effect, the coupled PNP and Navier-Stokes equations are solved numerically under an applied electric field tangential to the fluid-solid interface. The EO effect is shown to exhibit an intrinsic time dependence that is noninertial in its origin. Under a step-function applied electric field, a pulse of fluid flow is followed by relaxation to a new ion distribution, owing to the diffusive counter current. We have numerically evaluated the Onsager coefficients associated with the EO effect, L 21 , and its reverse streaming potential effect, L 12 , and show that L 12 ¼ L 21 in accordance with the Onsager relation. We conclude by noting some of the challenges ahead.

In polycrystals, faceted grains may become round and rough at high temperatures. Such a roughening phenomenon remains poorly understood, partly because of the lack of experimental observations. Here, we directly visualize the roughening dynamics of grain boundaries inside thin-film colloidal crystals at the single-particle level using video microscopy. The thermal fluctuations of grain boundaries appear to exhibit both static and dynamic critical-like behaviors, in contrast to the Kosterlitz-Thouless transition in typical free surface roughening. The roughening point shifts towards the melting point as the grain boundary's mismatch angle θ decreases and is preempted by melting when θ < 18°. Counterintuitively, the amplitude of grain-boundary fluctuations decreases above the roughening point. This could be attributed to the observed widening of the grain boundary. The roughening strongly affects the mobility of the grain boundary but not the stiffness. These results provide new guidance for the control of microstructures in polycrystals and further development of roughening theory.

words)Branched networks are ubiquitous in nature, ranging in size from watercourses and trees to cellular organelles and the cytoskeleton [1][2][3][4][5] . Often, the branch diameters change systematically throughout the network, with the proximal branches frequently thicker than the distal ones. This variation is usually interpreted as an adaptation to, or consequence of, the flow of materials and/or information through the network. To describe the changes in diameter over branch points, scaling or allometric relations of the form = + , have been proposed where ( , ) is the mother (daughters) diameter and is the exponent. Among the most well-known laws are da Vinci's rule for trees 6 ( = ), Murray's law 7 for vascular and pulmonary systems ( = ), and Rall's law 8 in the nervous system ( = / ). While scaling laws have a strong theoretical foundation, based on optimality arguments, and there is some experimental support 9,10 , there is a dearth of critical tests and recent work in neurons, for example, finds sloppy morphology that defies optimization principles 11 . To test quantitatively scaling laws in the nervous system, we have established a new image-analysis method that allows us to resolve dendrite diameters down to 200 nm allowing us to measure the diameters of all branches in Drosophila Class IV dendritic arborization neurons, a model cell to study branching morphogenesis 12 . Unexpectedly, although the branch diameters vary systematically throughout the dendritic networks in these cells, they do not follow any of the known scaling laws. We propose a new scaling law governing dendritic morphology development. The law follows from two concepts: there is an incremental cross-sectional area needed to support each terminal branch, and there is a minimum branch diameter. The law is consistent with microtubule-based transport and tip extension in these cells. The new scaling law may also apply more generally to branching in other biological networks including the circulatory systems of animals 13,14 and plants 15,16 .

The systematic variation of diameters in branched networks has tantalized biologists since the discovery of da Vinci’s rule for trees. Da Vinci’s rule can be formulated as a power law with exponent two: The square of the mother branch’s diameter is equal to the sum of the squares of those of the daughters. Power laws, with different exponents, have been proposed for branching in circulatory systems (Murray’s law with exponent 3) and in neurons (Rall’s law with exponent 3/2). The laws have been derived theoretically, based on optimality arguments, but, for the most part, have not been tested rigorously. Using superresolution methods to measure the diameters of dendrites in highly branched Drosophila class IV sensory neurons, we have found that these types of power laws do not hold. In their place, we have discovered a different diameter-scaling law: The cross-sectional area is proportional to the number of dendrite tips supported by the branch plus a constant, corresponding to a minimum diameter of the terminal dendrites. The area proportionality accords with a requirement for microtubules to transport materials and nutrients for dendrite tip growth. The minimum diameter may be set by the force, on the order of a few piconewtons, required to bend membrane into the highly curved surfaces of terminal dendrites. Because the observed scaling differs from Rall’s law, we propose that cell biological constraints, such as intracellular transport and protrusive forces generated by the cytoskeleton, are important in determining the branched morphology of these cells.

We measured the intrinsic electrophoretic drag coefficient of a single charged particle by optically trapping the particle and applying an AC electric field, and found it to be markedly different from that of the Stokes drag. The drag coefficient, along with the measured electrical force, yield a mobility-zeta potential relation that agrees with the literature. By using the measured mobility as input, numerical calculations based on the Poisson-Nernst-Planck equations, coupled to the Navier-Stokes equation, reveal an intriguing microscopic electroosmotic flow near the particle surface, with a well-defined transition between an inner flow field and an outer flow field in the vicinity of electric double layer's outer boundary. This distinctive interface delineates the surface that gives the correct drag coefficient and the effective electric charge. The consistency between experiments and theoretical predictions provides new insights into the classic electrophoresis problem, and can shed light on new applications of electrophoresis to investigate biological nanoparticles. † To whom correspondence should be addressed. Emails: hdo0@lehigh.edu, sheng@ust.hk PACS: 47.57.J-(colloidal systems); 82.45.-h (Electrochemistry and electrophoresis); 47.61.-k (Micro-and nano-scale flow phenomena) HDO would also like to thank Prof. Joel A. Cohen, Prof. Daan Frenkel and Dr. Alois Würger for their critical comments and helpful suggestions. AUTHOR CONTRIBUTIONS PS and HDO initiated and supervised the research. ML and MTW carried out the experiments. ML and PS contributed to theory and simulations with help from SX. ML. HDO and PS analyzed the data with help from MTW. ML, PS and HDO wrote the draft manuscript. All participated in revising the manuscript to its final form. ML and MTW contributed equally to this work.

The Poisson-Boltzmann (PB) equation is well known for its success in describing the Debye layer that arises from the charge separation phenomenon at the silica-water interface. However, by treating only the mobile ionic charges in the liquid, the PB equation essentially accounts for only half of the electrical double layer, with the other half-the surface charge layer-being beyond the PB equation's computational domain. In this work, we take a holistic approach to the charge separation phenomenon at the silica-water interface by treating, within a single computational domain, the electrical double layer that comprises both the mobile ions in the liquid and the surface charge density. The Poisson-Nernst-Planck (PNP) equations are used as the rigorous basis for our methodology. This holistic approach has the inherent advantage of being able to predict surface charge variations that arise either from the addition of salt and acid to the liquid, or from the decrease of the liquid channel width to below twice the Debye length. The latter is usually known as the charge regulation phenomenon. We enumerate the "difficulty" of the holistic approach that leads to the introduction of a surface potential trap as the single physical input to drive the charge separation within the computational domain. As the electrical double layer must be overall neutral, we use this constraint to derive both the form of the static limit of the PNP equations, as well as a global chemical potential µ that is 2 shown to replace the classical zeta potential (with a minus sign) as the boundary value for the PB equation, which can be re-derived from our formalism. In contrast to the zeta potential, however, µ is a calculated quantity whose value contains information about the surface charge density, salt concentration, etc.By using the Smoulochowski velocity, we define a generalized zeta potential that can better reflect the electrokinetic activity in nano-sized liquid channels. We also present several predictions of our theory that are beyond the framework of the PB equation alone- (1) the surface capacitance and the so-called pK and pL values that reflects the surface reactivity, (2) the isoelectronic point at which the surface charge layer is neutralized, in conjunction with the surface charge variation as a function of the solution acidity (pH), and (3) the appearance of a Donnan potential that arises from the formation of an electrical double layer at the inlet regions of a nano-channel connected to the bulk reservoir. All theory predictions are shown to be in good agreement with the experimental observations.

Quantification of molecular numbers and concentrations in living cells is critical for testing models of complex biological phenomena. Counting molecules in cells requires estimation of the fluorescence intensity of single molecules, which is generally limited to imaging near cell surfaces, in isolated cells, or where motions are diffusive. To circumvent this difficulty, we have devised a calibration technique for spinning-disk confocal (SDC) microscopy, commonly used for imaging in tissues, that uses single-step bleaching kinetics to estimate the single-fluorophore intensity. To cross-check our calibrations, we compared the brightness of fluorophores in the SDC microscope to those in the total-internal-reflection (TIRF) and epifluorescence microscopes. We applied this calibration method to quantify the number of EB1-eGFP in the comets of growing microtubule ends and to measure the cytoplasmic concentration of EB1-eGFP in sensory neurons in fly larvae. These measurements allowed us to estimate the dissociation constant of EB1-eGFP from the microtubules as wells as the GTP-tubulin cap size. Our results show the unexplored potential of single-molecule imaging using spinning disk confocal microscopy and provide a straight-forward method to count the absolute number of fluorophores in tissues which can be applied to a wide range of biological systems and imaging techniques.