Abstract: Many natural radial symmetrical shapes (e.g., sea stars) follow the Gielis equation (GE) or its twin equation (TGE). A supertriangle (three triangles arranged around a central polygon) represents such a shape, but no study has tested whether natural shapes can be represented as/are supertriangles or whether the GE or TGE can describe their shape. We collected 100 pieces of Koelreuteria paniculata fruit, which have a supertriangular shape, extracted the boundary coordinates for their vertical projections, and then fitted them with the GE and TGE. The adjusted root mean square errors (RMSEadj) of the two equations were always less than 0.08, and >70% were less than 0.05. For 57/100 fruit projections, the GE had a lower RMSEadj than the TGE, although overall differences in the goodness of fit were non-significant. However, the TGE produces more symmetrical shapes than the GE as the two parameters controlling the extent of symmetry in it are approximately equal. This work demonstrates that natural supertriangles exist, validates the use of the GE and TGE to model their shapes, and suggests that different complex radially symmetrical shapes can be generated by the same equation, implying that different types of biological symmetry may result from the same biophysical mechanisms.

Abstract: Plant leaves exhibit diverse shapes that enable them to utilize a light resource maximally. If there were a general parametric model that could be used to calculate leaf area for different leaf shapes, it would help to elucidate the adaptive evolutional link among plants with the same or similar leaf shapes. We propose a simplified version of the original Gielis equation (SGE), which was developed to describe a variety of object shapes ranging from a droplet to an arbitrary polygon. We used this equation to fit the leaf profiles of 53 species (among which, 48 bamboo plants, 5 woody plants, and 10 geographical populations of a woody plant), totaling 3310 leaves. A third parameter (namely, the floating ratio c in leaf length) was introduced to account for the case when the theoretical leaf length deviates from the observed leaf length. For most datasets, the estimates of c were greater than zero but less than 10%, indicating that the leaf length predicted by the SGE was usually smaller than the actual length. However, the predicted leaf areas approximated their actual values after considering the floating ratios in leaf length. For most datasets, the mean percent errors of leaf areas were lower than 6%, except for a pooled dataset with 42 bamboo species. For the elliptical, lanceolate, linear, obovate, and ovate shapes, although the SGE did not fit the leaf edge perfectly, after adjusting the parameter c, there were small deviations of the predicted leaf areas from the actual values. This illustrates that leaves with different shapes might have similar functional features for photosynthesis, since the leaf areas can be described by the same equation. The anisotropy expressed as a difference in leaf shape for some plants might be an adaptive response to enable them to adapt to different habitats.

Abstract: Plants have diverse leaf shapes that have evolved to adapt to the environments they have experienced over their evolutionary history. Leaf shape and leaf size can greatly influence the growth rate, competitive ability, and productivity of plants. However, researchers have long struggled to decide how to properly quantify the complexity of leaf shape. Prior studies recommended the leaf roundness index (RI = 4πA/P2) or dissection index (DI = ), where P is leaf perimeter and A is leaf area. However, these two indices merely measure the extent of the deviation of leaf shape from a circle, which is usually invalid as leaves are seldom circular. In this study, we proposed a simple measure, named the ellipticalness index (EI), for quantifying the complexity of leaf shape based on the hypothesis that the shape of any oval leaf can be regarded as a variation from a standard ellipse. 2220 leaves from nine species of Magnoliaceae were sampled to check the validity of the EI. We also tested the validity of the Montgomery equation (ME), which assumes a proportional relationship between leaf area and the product of leaf length and width, because the EI actually comes from the proportionality coefficient of the ME. We also compared the ME with five other models of leaf area. The ME was found to be the best model for calculating leaf area based on consideration of the trade-off between model fit vs. complexity, which strongly supported the robustness of the EI for describing oval leaf shape. The new index can account for both leaf shape and size, and we conclude that it is a promising method for quantifying and comparing oval leaf shapes across species in future studies.

Abstract: Active crystal facets can generate special properties for various applications. Herein, we report a (001) faceted nanosheet-constructed hierarchically porous TiO2/rGO hybrid architecture with unprecedented and highly stable lithium storage performance. Density functional theory calculations show that the (001) faceted TiO2 nanosheets enable enhanced reaction kinetics by reinforcing their contact with the electrolyte and shortening the path length of Li+ diffusion and insertion-extraction. The reduced graphene oxide (rGO) nanosheets in this TiO2/rGO hybrid largely improve charge transport, while the porous hierarchy at different length scales favors continuous electrolyte permeation and accommodates volume change. This hierarchically porous TiO2/rGO hybrid anode material demonstrates an excellent reversible capacity of 250 mAh g(-1) at 1 C (1 C = 335 mA g(-1)) at a voltage window of 1.0-3.0 V. Even after 1000 cycles at 5 C and 500 cycles at 10 C, the anode retains exceptional and stable capacities of 176 and 160 mAh g(-1), respectively. Moreover, the formed Li2Ti2O4 nanodots facilitate reversed Li+ insertion-extraction during the cycling process. The above results indicate the best performance of TiO2-based materials as anodes for lithium-ion batteries reported in the literature.

Abstract: Transition metal oxides with exposed highly active facets have become of increasing interest as anode materials for lithium ion batteries, because more dangling atoms exposed at the active surface facilitate the reaction between the transition metal oxides and lithium. In this work, we probed the electrochemical behavior of hollow Cu2O microspheres with {111} and {110} active facets on the polyhedron surface as anodes for lithium storage. Compared to commercial Cu2O nanoparticles, hollow Cu2O microspheres with {111} and {110} active facets show a rising specific capacity at 30 cycles which then decreases after 110 cycles during the cycling process. Via advanced electron microscopy characterization, we reveal that this phenomenon can be attributed to the highly active {111} and {110} facets with dangling “Cu” atoms facilitating the conversion reaction of Cu2O and Li, where part of the Cu2O is oxidized to CuO during the charging process. However, as the reaction proceeds, more and more formed Cu nanoparticles cannot be converted to Cu2O or CuO. This leads to a decrease of the specific capacity. We believe that our study here sheds some light on the progress of the electrochemical behavior of transition metal oxides with respect to their increased specific capacity and the subsequent decrease via a conversion reaction mechanism. These results will be helpful to optimize the design of transition metal oxide micro/nanostructures for high performance lithium storage.

Abstract: Novel 3DOM BiVO4/TiO2 nanocomposites with intimate contact were for the first time synthesized by a hydrothermal method in order to elucidate their visible-light-driven photocatalytic performances. BiVO4 nanoparticles and 3DOM TiO2 inverse opal were fabricated respectively. These materials were characterized by XRD, XPS, SEM, TEM, N2 adsorption–desorption and UV-vis diffuse (UV-vis) and photoluminescence spectroscopies. As references for comparison, a physical mixture of BiVO4 nanoparticles and 3DOM TiO2 inverse opal powder (0.08 : 1), and a BiVO4/P25 TiO2 (0.08 : 1) nanocomposite made also by the hydrothermal method were prepared. The photocatalytic performance of all the prepared materials was evaluated by the degradation of rhodamine B (RhB) as a model pollutant molecule under visible light irradiation. The highly ordered 3D macroporous inverse opal structure can provide more active surface areas and increased mass transfer because of its highly accessible 3D porosity. The results show that 3DOM BiVO4/TiO2 nanocomposites possess a highly prolonged lifetime and increased separation of visible light generated charges and extraordinarily high photocatalytic activity. Owing to the intimate contact between BiVO4 and large surface area 3DOM TiO2, the photogenerated high energy charges can be easily transferred from BiVO4 to the 3DOM TiO2 support. BiVO4 nanoparticles in the 3DOM TiO2 inverse opal structure act thus as a sensitizer to absorb visible light and to transfer efficiently high energy electrons to TiO2 to ensure long lifetime of the photogenerated charges and keep them well separated, owing to the direct band gap of BiVO4 of 2.4 eV, favourably positioned band edges, very low recombination rate of electron–hole pairs and stability when coupled with photocatalysts, explaining the extraordinarily high photocatalytic performance of 3DOM BiVO4/TiO2 nanocomposites. It is found that larger the amount of BiVO4 in the nanocomposite, longer the duration of photogenerated charge separation and higher the photocatalytic activity. This work can shed light on the development of novel visible light responsive nanomaterials for efficient solar energy utilisation by the intimate combination of an inorganic light sensitizing nanoparticle with an inverse opal structure with high diffusion efficiency and high accessible surface area.

Abstract: Reduced-dimensional perovskites are attractive light-emitting materials due to their efficient luminescence, color purity, tunable bandgap, and structural diversity. A major limitation in perovskite light-emitting diodes is their limited operational stability. Here we demonstrate that rapid photodegradation arises from edge-initiated photooxidation, wherein oxidative attack is powered by photogenerated and electrically-injected carriers that diffuse to the nanoplatelet edges and produce superoxide. We report an edge-stabilization strategy wherein phosphine oxides passivate unsaturated lead sites during perovskite crystallization. With this approach, we synthesize reduced-dimensional perovskites that exhibit 97 +/- 3% photoluminescence quantum yields and stabilities that exceed 300 h upon continuous illumination in an air ambient. We achieve green-emitting devices with a peak external quantum efficiency (EQE) of 14% at 1000 cd m(-2); their maximum luminance is 4.5 x 10(4) cd m(-2) (corresponding to an EQE of 5%); and, at 4000 cd m(-2), they achieve an operational half-lifetime of 3.5 h.

Abstract: Phase-junctions. between a cocatalyst and its semiconductor host are quite effective to enhance the photo catalytic activity and are widely studied, while reports on the phase-juncted cocatalyst are still rare. In this work, we report the deposition of the Pt/PtO phase-juncted nanodots as cocatalyst via NaOH modification of an interconnected meso-macroporous TiO2 network with high surface area and inner-particle mesopores to enhance the performance of photocatalytic H-2 production. Our results show that NaOH modification can largely influence Pt/PtO phase-juncted nanodot formation and dispersity. Compared to the TiO2 nano particles, the hierarchically meso-macroporous TiO2 network containing 0.18 wt % Pt/PtO phase-juneted cocatalyst demonstrates a highest photocatalytic H-2 rate of 13 mmol g(-1) h(-1) under simulated solar light, and possesses a stable cycling activity without obvious decrease after five cycles. Such high H-2 production performance can be attributed to both the phase-juncted Pt/PtO providing more active sites while PtO suppresses the undesirable hydrogen back reaction, and the special hierarchically porous TiO2 network with inner-particle mesopores presenting short diffusion path lengths for photogenerated electrons and enhanced light harvesting efficiency. This work suggests that Pt/PtO phase-juncted cocatalyst on hierarchically porous TiO2 nanostructures is a promising strategy for advanced photocatalytic H-2 production.

Abstract: The slow photon effect, a structural effect of photonic crystal photocatalyst, is very efficient in the enhancement of photocatalytic reactions. However, slow photons in powdered photonic crystal photocatalyst have rarely been discussed because they are usually randomly oriented when the photocatalytic reaction happens in solution under constant stirring. In this work, for the first time we design a gradient ternary TiO2-Au-CdS photonic crystal based on three-dimensionally ordered macroporous (3DOM) TiO2 as skeleton, Au as electron transfer medium and CdS as active material for photocatalytic H2 production under visible-light. As a result, this gradient ternary photocatalyst is favorable to simultaneously enhance light absorption, extend the light responsive region and reduce the recombination rate of the charge carriers. In particular, we found that slow photons at blue-edge exhibit much higher photocatalytic activity than that at red-edge. The photonic crystal photocatalyst with a macropore size of 250 nm exhibits the highest visible-light H2 production rate of 3.50 mmolh⁻¹g⁻¹ due to the slow photon energy at the blue-edge to significantly enhance the incident photons utilization. This work verifies that slow photons at the blue-edge can largely enhance light harvesting and sheds a light on designing the powdered photonic crystal photocatalyst to promote the photocatalytic H2 production via slow photon effect.

Abstract: Hexagonal boron nitride (hBN) is considered as an ideal semiconductor material for solid-state neutron detector, owing to its large neutron scattering section because of the low atomic number of B and excellent physical properties. Here we study the influence of neutron irradiation on crystal structure and on intermediate energy state (IMES) levels induced by the presence of impurities and defects in hBN. Large-size and thick pyrolytic and hot-pressed hBN (PBN and HBN) samples, which can be directly applied for neutron detector devices, are prepared and bombarded by neutrons with different irradiation fluences. The SEM and TEM are used to observe the sample difference of PBN and HBN. X-ray diffraction and Raman spectroscopy are applied to examine the influence of neutron irradiation on lattice structures along different crystal directions of PBN and HBN samples. Photoluminescence (PL) is employed to study the effect of neutron irradiation on IMESs in these samples. We find that the neutron irradiation does not alter the in-plane lattice structures of both PBN and HBN samples, but it can release the inter-layer tensions induced by sample growth of the PBN samples. Interestingly and surprisingly, the neutron irradiation does not affect the IMES levels responsible for PL generation, where PL is attributed mainly from phonon-assisted radiative electron-hole coupling for both PBN and HBN samples. Furthermore, the results indicate that the neutron irradiation can weaken the effective carrier-phonon coupling and exciton transitions in PBN and HBN samples. Overall, both PBN and HBN samples show some degree of the resistance to neutron irradiation in terms of these basic physical properties. The interesting and important findings from this work can help us to gain an in-depth understanding of the influence of neutron irradiation on basic physical properties of hBN materials. These effects can be taken into account when designing and applying the hBN materials for neutron detectors.

Abstract: The introduction of Na+ is considered as an effective way to improve the performance of Ni-rich cathode materials. However, the direct structure-property correlation for Na+ doped NCM-based cathode materials remain unclear, due to the difficulty of local and accurate structural characterization for light elements such as Li and Na. Moreover, there is the complexity of the modeling for the whole Li ion battery (LIB) system. To tackle the above-mentioned issues, we prepared Na+-doped LiNi0.6Co0.2Mn0.2O2 (Na-NCM622) material. The crystal structure change and the lattice distortion with picometers precision of the Na+-doped material is revealed by Cs-corrected scanning transmission electron microscopy (STEM). Density functional theory (DFT) and the recently proposed electrochemical model, i.e., modified Planck-Nernst-Poisson coupled Frumkin-Butler-Volmer (MPNP-FBV), has been applied to reveal correlations between the activation energy and the charge transfer resistance at multiscale. It is shown that Na+ doping can reduce the activation energy barrier from. G = 1.10 eV to 1.05 eV, resulting in a reduction of the interfacial resistance from 297 O to 134 Omega. Consequently, the Na-NCM622 cathode delivers a superior capacity retention of 90.8 % (159 mAh.g(-1)) after 100 cycles compared to the pristine NCM622 (67.5 %, 108 mAh.g(-1)). Our results demonstrate that the kinetics of Li+ diffusion and the electrochemical reaction can be enhanced by Na+ doping the cathode material.

Abstract: A series of BiVO4/3DOM TiO2 nanocomposites have been synthesized and their photocatalytic activity was investigated under visible light irradiation using the RhB dye as model pollutant molecule in an aqueous solution. The effect of the amount of BiVO4 as visible light sensitizer on the photocatalytic activity of BiVO4/3DOM TiO2 nanocomposites was highlighted. The heterostructured composite system leads to much higher photocatalytic efficiencies than bare 3DOM TiO2 and BiVO4 nanoparticles. As the proportion of BiVO4 in BiVO4/3DOM TiO2 nanocomposites increases from 0.04 to 0.6, the photocatalytic performance of the BiVO4/3DOM TiO2 nanocomposites increases and then decreases after reaching a maximum at 0.2. This improvement in photocatalytic perfomance is related to 1) the interfacial electron transfer efficiency between the coupled materials, 2) the 3DOM TiO2 inverse opal structure with interconnected pores providing an easy mass transfer of the reactant molecules and high accessibility to the active sites and large surface area and 3) the effect of light sensitizer of BiVO4. Intensive studies on structural, textural, optical and surface properties reveal that the electronic interactions between BiVO4 and TiO2 lead to an improved charge separation of the coupled BiVO4/TiO2 system. The photogenerated charge carrier densities increase with increasing the BiVO4 content, which acts as visible light sensitizer to the TiO2 and is responsible for the enhancement in the rate of photocatalytic degradation. However, the photocatalytic activity is reduced when the BiVO4 amount is much higher than that of 3DOM TiO2. Two reasons could account for this behavior. First, with increasing BiVO4 content, the photogenerated electron/hole pairs are accumulated at the surface of the BiVO4 nanoparticles and the recombination rate increases as shown by the PL results. Second, decreasing the amount of 3DOM TiO2 in the nanocomposite decreases the surface area as shown by the BET results. Moreover, the poor adsorptive properties of the BiVO4 photocatalyst also affect the photocatalytic performance, in particular at higher BiVO4 content. The present work demonstrates that BiVO4/3DOM TiO2 is a very promising heterojunction system for visible light photocatalytic applications.

Abstract: The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)2 + (y/b)2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., |x/a|n +|y/b|n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance.

Abstract: The angular and radial melting properties of two-dimensional classical systems consisting of different types of particles confined in a parabolic trap are studied through modified Monte Carlo simulations. A universal behavior of the angular melting process is found, which occurs in multiple steps due to shell depended melting temperatures. The melting sequence of the different shells is determined by two major factors: (1) the confinement strength which each shell is subjected to, and (2) the specific structure of each shell. Further, a continuous radial disordering of the particle types forming a single circular shell is found and analyzed. This phenomenon has never been observed before in two-dimensional mono-dispersive systems. This continuous radial disordering results from the high energy barrier between different particle types in multi-species systems.