Partial Schauder estimates for second-order elliptic and parabolic equations

We establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the independent variables.Comment: CVPDE, accepted (2010)

Etching and Narrowing of Graphene from the Edges

Large scale graphene electronics desires lithographic patterning of narrow graphene nanoribbons (GNRs) for device integration. However, conventional lithography can only reliably pattern ~20nm wide GNR arrays limited by lithography resolution, while sub-5nm GNRs are desirable for high on/off ratio field-effect transistors (FETs) at room temperature. Here, we devised a gas phase chemical approach to etch graphene from the edges without damaging its basal plane. The reaction involved high temperature oxidation of graphene in a slightly reducing environment to afford controlled etch rate (\leq ~1nm/min). We fabricated ~20-30nm wide GNR arrays lithographically, and used the gas phase etching chemistry to narrow the ribbons down to <10nm. For the first time, high on/off ratio up to ~10^4 was achieved at room temperature for FETs built with sub-5nm wide GNR semiconductors derived from lithographic patterning and narrowing. Our controlled etching method opens up a chemical way to control the size of various graphene nano-structures beyond the capability of top-down lithography.Comment: 18 pages, 4 figures, to appear in Nature Chemistr

Rotation Symmetry Spontaneous Breaking of Edge States in Zigzag Carbon Nanotubes

Analytical solutions of the edge states were obtained for the (N, 0) type carbon nanotubes with distorted ending bonds. It was found that the edge states are mixed via the distortion. The total energies for N=5 and N>=7 are lower in the asymmetric configurations of ending bonds than those having axial rotation symmetry. Thereby the symmetry is breaking spontaneously. The results imply that the symmetry of electronic states at the apex depends on the occupation; the electron density pattern at the apex could change dramatically and could be controlled by applying an external field.Comment: 19 pages, 3 figure

Experimentally Engineering the Edge Termination of Graphene Nanoribbons

The edges of graphene nanoribbons (GNRs) have attracted much interest due to their potentially strong influence on GNR electronic and magnetic properties. Here we report the ability to engineer the microscopic edge termination of high quality GNRs via hydrogen plasma etching. Using a combination of high-resolution scanning tunneling microscopy and first-principles calculations, we have determined the exact atomic structure of plasma-etched GNR edges and established the chemical nature of terminating functional groups for zigzag, armchair and chiral edge orientations. We find that the edges of hydrogen-plasma-etched GNRs are generally flat, free of structural reconstructions and are terminated by hydrogen atoms with no rehybridization of the outermost carbon edge atoms. Both zigzag and chiral edges show the presence of edge states.Comment: 16+9 pages, 3+4 figure

Graphene-Wrapped Sulfur Particles as a Rechargeable Lithium-Sulfur-Battery Cathode Material with High Capacity and Cycling Stability

We report the synthesis of a graphene-sulfur composite material by wrapping polyethyleneglycol (PEG) coated submicron sulfur particles with mildly oxidized graphene oxide sheets decorated by carbon black nanoparticles. The PEG and graphene coating layers are important to accommodating volume expansion of the coated sulfur particles during discharge, trapping soluble polysulfide intermediates and rendering the sulfur particles electrically conducting. The resulting graphene-sulfur composite showed high and stable specific capacities up to ~600mAh/g over more than 100 cycles, representing a promising cathode material for rechargeable lithium batteries with high energy density.Comment: published in Nano Letter

Spatially Resolving Spin-split Edge States of Chiral Graphene Nanoribbons

A central question in the field of graphene-related research is how graphene behaves when it is patterned at the nanometer scale with different edge geometries. Perhaps the most fundamental shape relevant to this question is the graphene nanoribbon (GNR), a narrow strip of graphene that can have different chirality depending on the angle at which it is cut. Such GNRs have been predicted to exhibit a wide range of behaviour (depending on their chirality and width) that includes tunable energy gaps and the presence of unique one-dimensional (1D) edge states with unusual magnetic structure. Most GNRs explored experimentally up to now have been characterized via electrical conductivity, leaving the critical relationship between electronic structure and local atomic geometry unclear (especially at edges). Here we present a sub-nm-resolved scanning tunnelling microscopy (STM) and spectroscopy (STS) study of GNRs that allows us to examine how GNR electronic structure depends on the chirality of atomically well-defined GNR edges. The GNRs used here were chemically synthesized via carbon nanotube (CNT) unzipping methods that allow flexible variation of GNR width, length, chirality, and substrate. Our STS measurements reveal the presence of 1D GNR edge states whose spatial characteristics closely match theoretical expectations for GNR's of similar width and chirality. We observe width-dependent splitting in the GNR edge state energy bands, providing compelling evidence of their magnetic nature. These results confirm the novel electronic behaviour predicted for GNRs with atomically clean edges, and thus open the door to a whole new area of applications exploiting the unique magnetoelectronic properties of chiral GNRs

Multiplexed five-color molecular imaging of cancer cells and tumor tissues with carbon nanotube Raman tags in the near-infrared

Single-walled carbon nanotubes (SWNTs) with five different C13/C12 isotope compositions and well-separated Raman peaks have been synthesized and conjugated to five targeting ligands in order to impart molecular specificity. Multiplexed Raman imaging of live cells has been carried out by highly specific staining of cells with a five-color mixture of SWNTs. Ex vivo multiplexed Raman imaging of tumor samples uncovers a surprising up-regulation of epidermal growth factor receptor (EGFR) on LS174T colon cancer cells from cell culture to in vivo tumor growth. This is the first time five-color multiplexed molecular imaging has been performed in the near-infrared (NIR) region under a single laser excitation. Near zero interfering background of imaging is achieved due to the sharp Raman peaks unique to nanotubes over the low, smooth autofluorescence background of biological species.Comment: Published in Nano Researc

Enteric Microbiome Metabolites Correlate with Response to Simvastatin Treatment

Although statins are widely prescribed medications, there remains considerable variability in therapeutic response. Genetics can explain only part of this variability. Metabolomics is a global biochemical approach that provides powerful tools for mapping pathways implicated in disease and in response to treatment. Metabolomics captures net interactions between genome, microbiome and the environment. In this study, we used a targeted GC-MS metabolomics platform to measure a panel of metabolites within cholesterol synthesis, dietary sterol absorption, and bile acid formation to determine metabolite signatures that may predict variation in statin LDL-C lowering efficacy. Measurements were performed in two subsets of the total study population in the Cholesterol and Pharmacogenetics (CAP) study: Full Range of Response (FR), and Good and Poor Responders (GPR) were 100 individuals randomly selected from across the entire range of LDL-C responses in CAP. GPR were 48 individuals, 24 each from the top and bottom 10% of the LDL-C response distribution matched for body mass index, race, and gender. We identified three secondary, bacterial-derived bile acids that contribute to predicting the magnitude of statin-induced LDL-C lowering in good responders. Bile acids and statins share transporters in the liver and intestine; we observed that increased plasma concentration of simvastatin positively correlates with higher levels of several secondary bile acids. Genetic analysis of these subjects identified associations between levels of seven bile acids and a single nucleotide polymorphism (SNP), rs4149056, in the gene encoding the organic anion transporter SLCO1B1. These findings, along with recently published results that the gut microbiome plays an important role in cardiovascular disease, indicate that interactions between genome, gut microbiome and environmental influences should be considered in the study and management of cardiovascular disease. Metabolic profiles could provide valuable information about treatment outcomes and could contribute to a more personalized approach to therapy

Erythroid Promoter Confines FGF2 Expression to the Marrow after Hematopoietic Stem Cell Gene Therapy and Leads to Enhanced Endosteal Bone Formation

Fibroblast growth factor-2 (FGF2) has been demonstrated to be a promising osteogenic factor for treating osteoporosis. Our earlier study shows that transplantation of mouse Sca-1+ hematopoietic stem/progenitor cells that are engineered to express a modified FGF2 leads to considerable endosteal/trabecular bone formation, but it also induces adverse effects like hypocalemia and osteomalacia. Here we report that the use of an erythroid specific promoter, β-globin, leads to a 5-fold decrease in the ratio of serum FGF2 to the FGF2 expression in the marrow cavity when compared to the use of a ubiquitous promoter spleen focus-forming virus (SFFV). The confined FGF2 expression promotes considerable trabeculae bone formation in endosteum and does not yield anemia and osteomalacia. The avoidance of anemia in the mice that received Sca1+ cells transduced with FGF2 driven by the β-globin promoter is likely due to attenuation of high-level serum FGF2-mediated stem cell mobilization observed in the SFFV-FGF2 animals. The prevention of osteomalacia is associated with substantially reduced serum Fgf23/hypophosphatemia, and less pronounced secondary hyperparathyroidism. Our improved stem cell gene therapy strategy represents one step closer to FGF2-based clinical therapy for systemic skeletal augmentation

High Performance In Vivo Near-IR (>1 {\mu}m) Imaging and Photothermal Cancer Therapy with Carbon Nanotubes

Short single-walled carbon nanotubes (SWNTs) functionalized by PEGylated phospholipids are biologically non-toxic and long-circulating nanomaterials with intrinsic near infrared photoluminescence (NIR PL), characteristic Raman spectra, and strong optical absorbance in the near infrared (NIR). This work demonstrates the first dual application of intravenously injected SWNTs as photoluminescent agents for in vivo tumor imaging in the 1.0-1.4 {\mu}m emission region and as NIR absorbers and heaters at 808 nm for photothermal tumor elimination at the lowest injected dose (70 {\mu}g of SWNT/mouse, equivalent to 3.6 mg/kg) and laser irradiation power (0.6 W/cm2) reported to date. Ex vivo resonance Raman imaging revealed the SWNT distribution within tumors at a high spatial resolution. Complete tumor elimination was achieved for large numbers of photothermally treated mice without any toxic side effects after more than six months post-treatment. Further, side-by-side experiments were carried out to compare the performance of SWNTs and gold nanorods (AuNRs) at an injected dose of 700 {\mu}g of AuNR/mouse (equivalent to 35 mg/kg) in NIR photothermal ablation of tumors in vivo. Highly effective tumor elimination with SWNTs was achieved at 10 times lower injected doses and lower irradiation powers than for AuNRs. These results suggest there are significant benefits of utilizing the intrinsic properties of biocompatible SWNTs for combined cancer imaging and therapy.Comment: Nanoresearch, in pres