Exploring the color of transition metal ions in irregular coordination geometries: new colored inorganic oxides based on the spiroffite structure, Zn2-xMxTe3O8 (M = Co, Ni, Cu)

We describe the synthesis, crystal structures, and optical absorption spectra of transition metal substituted spiroffite derivatives, Zn2-xMxTe3O8 (M-II = Co, Ni, Cu; 0 < x <= 1.0). The oxides are readily synthesized by solid state reaction of stoichiometric mixtures of the constituent binaries at 620 degrees C. Reitveld refinement of the crystal structures from powder X-ray diffraction (XRD) data shows that the Zn/MO6 octahedra are strongly distorted, as in the parent Zn2Te3O8 structure, consisting of five relatively short Zn/M-II-O bonds (1.898-2.236 angstrom) and one longer Zn/M-II-O bond (2.356-2.519 angstrom). We have interpreted the unique colors and the optical absorption/diffuse reflectance spectra of Zn2-xMxTe3O8 in the visible, in terms of the observed/irregular coordination geometry of the Zn/M-II-O chromophores. We could not however prepare the fully substituted M2Te3O8 (M-II = Co, Ni, Cu) by the direct solid state reaction method. Density Functional Theory (DFT) modeling of the electronic structure of both the parent and the transition metal substituted derivatives provides new insights into the bonding and the role of transition metals toward the origin of color in these materials. We believe that transition metal substituted spiroffites Zn2-xMxTe3O8 reported here suggest new directions for the development of colored inorganic materials/pigments featuring irregular/distorted oxygen coordination polyhedra around transition metal ions.

Green colored nano-pigments derived from Y2BaCuO5: NIR reflective coatings

A green colored nano-pigment Y2BaCuO5 with impressive near infra-red (NIR) reflectance (61% at 1100 nm) was synthesized by a nano-emulsion method. The developed nano-crystalline powders were characterized by X-ray diffraction (XRD), Transmission electron microscopy (TEM), UV-vis-NIR diffuse reflectance spectroscopy and CIE-L*a*b* 1976 color scales. The XRD and Rietveld analyses of the designed pigment powders reveal the orthorhombic crystal structure for Y2BaCuO5, where yttrium is coordinated by seven oxygen atoms with the local symmetry of a distorted trigonal prism, barium is coordinated by eleven oxygen atoms, and the coordination polyhedron of copper is a distorted square pyramid CuO5]. The UV-vis spectrum of the nano-pigment exhibits an intense d-d transition associated with CuO5 chromophore between 2.1 and 2.5 eV in the visible domain. Therefore, a green color has been displayed by the developed nano-pigment. The potential utility of the nano-pigments as ``Cool Pigments'' was demonstrated by coating on to a building roofing material like cement slab and PVC coatings. (C) 2014 Elsevier Ltd. All rights reserved.

Colored polydimethylsiloxane micropillar arrays for high throughput measurements of forces applied by genetic model organisms

Measuring forces applied by multi-cellular organisms is valuable in investigating biomechanics of their locomotion. Several technologies have been developed to measure such forces, for example, strain gauges, micro-machined sensors, and calibrated cantilevers. We introduce an innovative combination of techniques as a high throughput screening tool to assess forces applied by multiple genetic model organisms. First, we fabricated colored Polydimethylsiloxane (PDMS) micropillars where the color enhances contrast making it easier to detect and track pillar displacement driven by the organism. Second, we developed a semiautomated graphical user interface to analyze the images for pillar displacement, thus reducing the analysis time for each animal to minutes. The addition of color reduced the Young's modulus of PDMS. Therefore, the dye-PDMS composite was characterized using Yeoh's hyperelastic model and the pillars were calibrated using a silicon based force sensor. We used our device to measure forces exerted by wild type and mutant Caenorhabditis elegans moving on an agarose surface. Wild type C. elegans exert an average force of similar to 1 mu N on an individual pillar and a total average force of similar to 7.68 mu N. We show that the middle of C. elegans exerts more force than its extremities. We find that C. elegans mutants with defective body wall muscles apply significantly lower force on individual pillars, while mutants defective in sensing externally applied mechanical forces still apply the same average force per pillar compared to wild type animals. Average forces applied per pillar are independent of the length, diameter, or cuticle stiffness of the animal. We also used the device to measure, for the first time, forces applied by Drosophila melanogaster larvae. Peristaltic waves occurred at 0.4Hz applying an average force of similar to 1.58 mu N on a single pillar. Our colored microfluidic device along with its displacement tracking software allows us to measure forces applied by multiple model organisms that crawl or slither to travel through their environment. (C) 2015 AIP Publishing LLC.

Rainbow matchings in strongly edge-colored graphs

A rainbow matching of an edge-colored graph G is a matching in which no two edges have the same color. There have been several studies regarding the maximum size of a rainbow matching in a properly edge-colored graph G in terms of its minimum degree 3(G). Wang (2011) asked whether there exists a function f such that a properly edge-colored graph G with at least f (delta(G)) vertices is guaranteed to contain a rainbow matching of size delta(G). This was answered in the affirmative later: the best currently known function Lo and Tan (2014) is f(k) = 4k - 4, for k >= 4 and f (k) = 4k - 3, for k <= 3. Afterwards, the research was focused on finding lower bounds for the size of maximum rainbow matchings in properly edge-colored graphs with fewer than 4 delta(G) - 4 vertices. Strong edge-coloring of a graph G is a restriction of proper edge-coloring where every color class is required to be an induced matching, instead of just being a matching. In this paper, we give lower bounds for the size of a maximum rainbow matching in a strongly edge-colored graph Gin terms of delta(G). We show that for a strongly edge-colored graph G, if |V(G)| >= 2 |3 delta(G)/4|, then G has a rainbow matching of size |3 delta(G)/4|, and if |V(G)| < 2 |3 delta(G)/4|, then G has a rainbow matching of size |V(G)|/2] In addition, we prove that if G is a strongly edge-colored graph that is triangle-free, then it contains a rainbow matching of size at least delta(G). (C) 2015 Elsevier B.V. All rights reserved.

Heterochromatic paths in edge colored graphs without small cycles and heterochromatic-triangle-free graphs

Conditions for the existence of heterochromatic Hamiltonian paths and cycles in edge colored graphs are well investigated in literature. A related problem in this domain is to obtain good lower bounds for the length of a maximum heterochromatic path in an edge colored graph G. This problem is also well explored by now and the lower bounds are often specified as functions of the minimum color degree of G - the minimum number of distinct colors occurring at edges incident to any vertex of G - denoted by v(G). Initially, it was conjectured that the lower bound for the length of a maximum heterochromatic path for an edge colored graph G would be 2v(G)/3]. Chen and Li (2005) showed that the length of a maximum heterochromatic path in an edge colored graph G is at least v(G) - 1, if 1 <= v(G) <= 7, and at least 3v(G)/5] + 1 if v(G) >= 8. They conjectured that the tight lower bound would be v(G) - 1 and demonstrated some examples which achieve this bound. An unpublished manuscript from the same authors (Chen, Li) reported to show that if v(G) >= 8, then G contains a heterochromatic path of length at least 120 + 1. In this paper, we give lower bounds for the length of a maximum heterochromatic path in edge colored graphs without small cycles. We show that if G has no four cycles, then it contains a heterochromatic path of length at least v(G) - o(v(G)) and if the girth of G is at least 4 log(2)(v(G)) + 2, then it contains a heterochromatic path of length at least v(G) - 2, which is only one less than the bound conjectured by Chen and Li (2005). Other special cases considered include lower bounds for the length of a maximum heterochromatic path in edge colored bipartite graphs and triangle-free graphs: for triangle-free graphs we obtain a lower bound of 5v(G)/6] and for bipartite graphs we obtain a lower bound of 6v(G)-3/7]. In this paper, it is also shown that if the coloring is such that G has no heterochromatic triangles, then G contains a heterochromatic path of length at least 13v(G)/17)]. This improves the previously known 3v(G)/4] bound obtained by Chen and Li (2011). We also give a relatively shorter and simpler proof showing that any edge colored graph G contains a heterochromatic path of length at least (C) 2015 Elsevier Ltd. All rights reserved.

Stabilization of a Tetrahedral (Mn5+O4) Chromophore in Ternary Barium Oxides as a Strategy toward Development of New Turquoise/Green-Colored Pigments

An experimental investigation of the stabilization of the turquoise-colored chrornophore (Mn5+O4) in various oxide hosts, viz., A(3)(VO4)(2) (A = Ba, Sr, Ca), YVO4, and Ba2MO4 (M = Ti, Si), has been carried out. The results reveal that substitution of Mn5+O4 occurs in Ba-3(VO4)(2) forming the entire solid solution series Ba-3(V1-x MnxO4)(2) (0 < x <= 1.0), while with the corresponding strontium derivative, only up to about 10% of Mn5+O4 substitution is possible. Ca-3(VO4)(2) and YVO4 do not stabilize Mn5+O4 at all. With Ba2MO4 (M = Ti, Si), we could prepare only partially substituted materials, Ba2M1-xMn5+O4+x/2 for x up to 0.15, that are turquoise-colored. We rationalize the results that a large stabilization of the O 2p-valence band states occurs in the presence of the electropositive barium that renders the Mn5+ oxidation state accessible in oxoanion compounds containing PO43-, VO43-, etc. By way of proof-of-concept, we synthesized new turquoise-colored Mn5+O4 materials, Ba-5(BO3)(MnO4)(2)Cl and Ba-5(BO3)(PO4)(MnO4)Cl, based on the apatite-Ba-5(PO4)(3)Cl-structure.