A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS

In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.

Unconventionally anisotropic growth of PbSe nanorods:Controllable fabrication under solution-solid-solid regime over Ag2Se catalysis for broadband photodetection

Broadband optoelectronic devices intrigue enormous interests on account of their promising potential in optical communications,sensors and environmental monitoring.PbSe nanocrystals are promising candidates for the construction of next-generation photodetectors due to their fascinating intrinsic properties and solution-processed compatibility with varied substrates.Here,we report the fabrication of a broadband photodetector on the basis of high-quality solution-processed PbSe nanorods in rock-salt phase grown along unconventionally anisotropic growth direction of<112>zone axis.The rock-salt PbSe nanorods are synthesized in solution phase over the catalysis of Ag2Se with relatively high-temperature body-centered cubic phase via a solution-solid-solid growth regime using oleylamine and oleic acid as solvents and stabilizer surfactants,from which the PbSe nanorods with the unconventionally anisotropic growth direction are controllably grown in size and shape in the synthetic procedure typically with about 17 nm in diameter and 58 nm in length on average.Meanwhile,the PbSe nanorods-based photodetector exhibits a broadband response from 405 to 1,064 nm with a high responsivity of 0.78 A·W^(-1)and a fast response time of 17.5μs.The response time is much faster in comparison with most of the PbSe-based photodetectors with response time in millisecond level.

Enhanced thermoelectric properties of p-type polycrystalline SnSe by regulating the anisotropic crystal growth and Sn vacancy

Thermoelectric selenides have attracted more and more attentions recently.Herein,p-type Sn Se polycrystalline bulk materials with good thermoelectric properties are presented.By using the SnSe2 nanostructures synthesized via a wetchemistry route as the precursor,polycrystalline Sn Se bulk materials were successfully obtained by a combined heattreating process under reducing atmosphere and following spark plasma sintering procedure.As a reference,the Sn Se nanostructures synthesized via a wet-chemistry route were also fabricated into polycrystalline bulk materials through the same process.The thermoelectric properties of the Sn Se polycrystalline transformed from SnSe2 nanostructures indicate that the increasing of heattreating temperature could effectively decrease the electrical resistivity,whereas the decrease in Seebeck coefficient is nearly invisible.As a result,the maximum power factor is enhanced from 5.06×10^-4W/m·K^2 to 8.08×10^-4W/m·K^2 at 612℃.On the other hand,the reference sample,which was obtained by using Sn Se nanostructures as the precursor,displays very poor power factor of only 1.30×10^-4W/m·K^2 at 537℃.The x-ray diffraction（XRD）,scanning electron microscope（SEM）,x-ray fluorescence（XRF）,and Hall effect characterizations suggest that the anisotropic crystal growth and existing Sn vacancy might be responsible for the enhanced electrical transport in the polycrystalline Sn Se prepared by using SnSe2 precursor.On the other hand,the impact of heat-treating temperature on thermal conductivity is not obvious.Owing to the boosting of power factor,a high z T value of 1.07 at 612℃ is achieved.This study provides a new method to synthesize polycrystalline Sn Se and pave a way to improve the thermoelectric properties of polycrystalline bulk materials with similar layered structure.

Anisotropic nanowire growth via a self-confined amorphous template process： A reconsideration on the role of amorphous calcium carbonate

Calcium carbonate crystals with various morphologies have been found in a variety of biospecimens and artificially synthesized structures. Usually, the diversity in morphology can be attributed to different types of interactions between the specific crystal faces and the environment or the templates used for the growth of CaCO3 crystals. On the other hand, isotropic amorphous calcium carbonate （ACC） has been recognized as the precursor of other crystalline calcium carbonate forms for both in vivo and in vitro systems. However, here we propose a self-confined amorphous template process leading to the anisotropic growth of single-crystalline calcite nanowires. Initiated by the assembly of precipitated nanoparticles, the calcite nanowires grew via the continuous precipitation of partly crystallized ACC nanodroplets onto their tips. Then, the crystalline domains in the tip, which were generated from the partly crystallized nanodroplets, coalesced in the interior of the nanowire to form a single-crystalline core. The ACC domains were left outside and spontaneously formed a protective shell to retard the precipitation of CaCO3 onto the side surface of the nanowire and thus guided the highly anisotropic growth of nanowires as a template.

Self-organization and tunable characteristic lengths of twodimensional hexagonal superlattices of nanowires directly grown on substrates

The organization of nano-objects on macroscopic surfaces is a key challenge for the technological improvement and implementation of nanotechnologies.For achieving operational functions,it is required to assemble nano-objects as controllable building blocks in highly ordered superstructures.Herein,we demonstrate the growth and self-organization of metallic nanowires on surfaces into hexagonal superlattices with tunable characteristic lengths depending of the stabilizing surfactants employed.Starting from a reacting mixture containing a Pt(111)substrate,a Co organometallic precursor,an amine,and an acid dissolved in a solvent,we quantify the structural evolution of superlattices of vertical single-crystalline Co nanowires on Pt,using a combined analysis of small angle neutron scattering,transmission,and scanning electron microscopies.We show the concerted steps of a spontaneous growth and self-organization of the nanowires into two-dimensional(2D)hexagonal lattice on Pt,at intervals starting from a few hours of reaction to a highly ordered superlattice at longer times.Furthermore,it is shown that apart from long-chain acid and long-chain aliphatic amine pairs used as stabilizers,the combination of a long-chain aliphatic and a short-chain aromatic ligand in the synthesis can also be employed for the nanowire superlattices development.Interestingly,the possibility to employ different pairs allows quantitative modulation of the nanowire arrays,such as the interwire distance and the packing fraction.

Leaf morphogenesis:The multifaceted roles of mechanics

Plants produce a rich diversity of biological forms,and the diversity of leaves is especially notable.Mechanisms of leaf morphogenesis have been studied in the past two decades,with a growing focus on the interactive roles of mechanics in recent years.Growth of plant organs involves feedback by mechanical stress:growth induces stress,and stress affects growth and morphogenesis.Although much attention has been given to potential stress-sensing mechanisms and cellular responses,the mechanical principles guiding morphogenesis have not been well understood.Here we synthesize the overarching roles of mechanics and mechanical stress in multilevel and multiple stages of leaf morphogenesis,encompassing leaf primordium initiation,phyllotaxis and venation patterning,and the establishment of complex mature leaf shapes.Moreover,the roles of mechanics at multiscale levels,from subcellular cytoskeletal molecules to single cells to tissues at the organ scale,are articulated.By highlighting the role of mechanical buckling in the formation of three-dimensional leaf shapes,this review integrates the perspectives of mechanics and biology to provide broader insights into the mechanobiology of leaf morphogenesis.

Facet-induced coordination competition for highly ordered CsPbBr_(3) nanoplatelets with strong polarized emission

Controllable anisotropic growth of perovskite nanocrystals(NCs)is challenging since it is difficult to separate the nucleation and growth processes.Here,a two-step nucleation strategy is proposed to control the binding interaction between surface ligands and NCs,resulting in facet-induced coordination competition.Oleic acid as surface activated ligand leads to the formation of defective lead bromine octahedron,and the binding interaction between 4-dodecylbenzenesulfonic acid and lead atoms promotes the formation of two kinds of binding interactions.Based on this strategy,the anisotropic growth of CsPbBr_(3) nanoplatelet(NPLs)with adjusted length from 11.4 to 24 nm,and the evolution of NPLs from stacked to tongue-shaped have been realized.Elemental line scan reveals the sulfur atoms mainly distribute at the edge of NPLs.Furthermore,binding energy calculation and experimental results illustrate the coordination competition of different binding interaction on specific facets induces the anisotropic growth of NPLs.Importantly,strong emission anisotropy of highly ordered NPLs with polarization ratio up to 0.58 is illustrated.This work not only deepens our understanding of the controllable synthesis of perovskite NCs,but also provides a reference for the regulation of light emitting diode and soler cells.