Carbon Dot−NaCl Crystals for White-Light Generation and Fabry-Perot Lasing

Phosphor materials with broad spectral range and an average emission lifetime (20 μs) have been achieved from carbon dots (CDs)−NaCl crystals. A one-pot synthesis pathway has been developed for CDs−NaCl crystals formation at room temperature. Precursor for CDs materials was screened at room temperature by oxidation methodology from different simple sugar molecules. CDs (size less than 10 nm) prepared from the fructose sugar exhibit most intense emission. Utilizing ripe banana peel (contains ∼27% of fructose) as a precursor for the carbon dot formation, white-light emission with a CIE index of (0.29, 0.34) has been achieved from the single source with CDs−NaCl crystals upon excitation at 430 nm. The crystals also function as Fabry-Perot (F−P) mode resonator for lasing, with a laser threshold value of 0.9 mW and a resonating Q-factor of 207. These results outline a new approach for realizing F−P lasing and white light emission from a non-toxic green source with a quick, facile and low-cost synthesis procedure.     

An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions

We prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of semi-algebraically connected components of the realizations of all realizable sign conditions of a family of real polynomials. More precisely, we prove that the number of semi-algebraically connected components of the realizations of all realizable sign conditions of a family of s polynomials in R[X ₁, …,X _k ] whose degrees are at most d is bounded by

Synthesis and crystal structure of three new copper(II) complexes with a tridentate amine and its Schiff bases

Three new mononuclear complexes of copper(II), viz. [Cu(L)(N₃)Cl] (1), [Cu(L′)(H₂O)]ClO₄ (2) and [Cu(L″)] (3) where L = N-(3-aminopropyl)-N-methylpropane-1,3-diamine, L′ = 2-(N-{3-[(3-aminopropyl)(methyl)amino]propyl}ethanimidoyl)phenolate ion and L″ = 2,2′-{(methylimino)bis[propane-3,1-diylnitrilo(1E)eth-1-yl-1-ylidene]}diphenolate ion, have been prepared. The synthesis of complex 1 has been achieved by reacting copper chloride with the triamine (L) and sodium azide in a 1:1:1 M ratio. The other two compounds have been synthesized by the reaction of copper perchlorate with the same triamine, L, plus 2-hydroxyacetophenone in a molar ratio of 1:1:1 (for 2) and 1:1:2 (for 3), so that the respective tetradentate and pentadentate Schiff bases HL′ and H₂L″ are formed in situ to bind the copper(II) ions. The complexes have been characterized by microanalytical, spectroscopic and single crystal X-ray diffraction studies. Structural studies reveal that the mononuclear units of all the three complexes adopt a distorted square pyramidal geometry and are held together by either intermolecular H-bonding (in 1 and 2) or C-H?π interactions (in 3) to form supramolecular networks in the solid state.     

Syntheses, crystal structures and magnetic properties of two dicopper(II) complexes and a zigzag 1-D Cu(II) complex of a bidentate pyridyl-pyrazole ligand

Two new dinuclear copper compounds, [Cu₂(pypz)₂(N₃)₂(NO₃)₂] (1) and [Cu₂(pypz)₂(OH)₂(NO₃)₂] (2), and one 1-D polymeric Cu(II) complex, [Cu(pypz)(dca)₃]_n (3) [‘pypz’ = (3,5dimethyl-1-(2′-pyridyl)pyrazole) and dca = (dicyanamide)], have been synthesized and characterized crystallographically and spectroscopically. Complex 1 is pseudo-octahedral, adjacent Cu atoms are connected by a pair of μ(1,1) azido groups and the structure is stabilized by π-π interactions between two pyridyl moieties from two different neighboring complex molecules. Complexes 2 and 3 are square pyramidal. The hydroxo bridged complex 2 is further stabilized through H-bonding. The 1-D polymeric chain of 3 is bridged by an end-to-end dicyanamide bridge and it propagates along the crystallographic b axis, whilst the polymer chains are stacked one upon another along the crystallographic c axis. Low temperature magnetic measurement shows that complexes 1 and 2 are ferromagnetic (J values are 30.81 and 14.79 cm⁻¹, respectively), whereas due to larger Cu-Cu distances, complex 3 shows weak ferromagnetism.     

Sensitivity of protein adsorption to architectural variations in a protein-resistant polymer brush containing engineered nanoscale adhesive sites

Patchy polymer brushes contain nanoscale (5-15 nm) adhesive elements, such as polymer coils or nanoparticles, embedded at their base at random positions on the surface. The competition between the brush's steric (protein resistant) repulsions and the attractions from the discrete adhesive elements provides a precise means to control bioadhesion. This differs from the classical approach, where functionality is placed on the brush's periphery. The current study demonstrates the impact of poly(etheylene glycol) (PEG) brush architecture and ionic strength on fibrinogen adsorption on brushes containing embedded poly-l-lysine (PLL, 20K MW) coils or "patches". The consistent appearance of a fibrinogen adsorption threshold, a minimum loading of patches on the surface, below which protein adsorption does not occur, suggests multivalent protein capture: Adsorbing proteins simultaneously engage several patches. The surface composition (patch loading) at the threshold is extremely sensitive to the brush height and ionic strength, varying up to a factor of 5 in the surface loading of the PLL patches (~50% of the range of possible surfaces). Variations in ionic strength have a similar effect, with the smallest thresholds seen for the largest Debye lengths. While trends with brush height were the clearest and most dominant, consideration of the PEG loading within the brush or its persistence length did not reveal a critical brush parameter for the onset of adsorption. The lack of straightforward correlation on brush physics was likely a result of multivalent binding, (producing an additional dependence on patch loading), and might be resolved for univalent adsorption onto more strongly binding patches. While studies with similar brushes placed uniformly on a surface revealed that the PEG loading within the brush is the best indicator of protein resistance, the current results suggest that brush height is more important for patchy brushes. Likely the interactions producing brush extension normal to the interface act similarly to drive lateral tether extension to obstruct patches.     

Polynomial Hierarchy, Betti Numbers, and a Real Analogue of Toda’s Theorem

Toda (in SIAM J. Comput. 20(5):865–877, 1991) proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the class P ^#P , namely the class of languages that can be decided by a Turing machine in polynomial time given access to an oracle with the power to compute a function in the counting complexity class #P. This result, which illustrates the power of counting, is considered to be a seminal result in computational complexity theory. An analogous result in the complexity theory over the reals (in the sense of Blum–Shub–Smale real machines in Bull. Am. Math. Soc. (NS) 21(1): 1–46, 1989) has been missing so far. In this paper we formulate and prove a real analogue of Toda’s theorem. Unlike Toda’s proof in the discrete case, which relied on sophisticated combinatorial arguments, our proof is topological in nature. As a consequence of our techniques, we are also able to relate the computational hardness of two extremely well-studied problems in algorithmic semi-algebraic geometry: the problem of deciding sentences in the first-order theory of the reals with a constant number of quantifier alternations, and that of computing Betti numbers of semi-algebraic sets. We obtain a polynomial time reduction of the compact version of the first problem to the second. This latter result may be of independent interest to researchers in algorithmic semi-algebraic geometry.     

Magneto-structural xorrelations in 2D and 3D extended structures of manganese(II)-malonate systems

Two polymeric malonato-bridged manganese(II) complexes of formula [Mn(mal)(H(2)O)(2)](n)() (1) and [Mn(2)(mal)(2)(4,4'-bipy)(H(2)O)(2)](n)() (2) have been synthesized and characterized (mal = malonate dianion; 4,4'-bipy = 4,4'-bipyridine). The crystal structure of complex 1 was already known. Complex 2 crystallizes in monoclinic space group P2(1)/n, Z = 2, with unit cell parameters of a = 7.2974(10) A, b = 18.7715(10) A, c = 7.514(3) A, and beta = 91.743(12) degrees. The structure determination reveals that the complex [Mn(2)(mal)(2)(4,4'-bipy)(H(2)O)(2)](n)() (2) is a 3D network being composed of Mn-malonate sheets which are pillared by bidentate 4,4'-bipy spacer forming small voids. The Mn-Mn distances through Mn-mu-(O3-C8-O4)-Mn, Mn-mu(O1-C6-O2)-Mn, and Mn-mu-4,4'-bipy-Mn bridges are 5.561, 5.410, and 11.723 A, respectively. The magnetic behaviors of complexes 1 and 2 in the temperature range 300-2 K are very close, corresponding to a weak antiferromagnetic coupling. The magnetic pathways of complex 1 are through two Mn-O-C-O-Mn with anti-anti conformation and two Mn-O-C-O-Mn with syn-anti conformations and in complex 2 through all Mn-O-C-O-Mn with syn-anti conformations. Both syn-anti and anti-anti conformations create weak antiferromagnetic coupling, and the susceptibility data are fitted by the expansion series of Lines and the Curély formula for an S = 5/2 antiferromagnetic quadratic layer, based on the exchange Hamiltonian H = -Sigma(nn)()JS(i)()S(j)(). The best fit is given by the superexchange parameters J = -0.32 cm(-)(1) and g = 2.00 for complex 1 and J = -0.14 cm(-)(1), J(inter) = -0.031 cm(-)(1), and g = 2.00 for complex 2. Finally, in both the complexes there is a magnetic pathway Mn-O-C-C-C-O-Mn, and this pathway through the three carbon atoms of the malonato-bridging ligand could be considered negligible.     

Polymeric networks of copper(II) using succinate and aromatic N-N donor ligands: synthesis, crystal structure, magnetic behaviour and the effect of weak interactions on their crystal packing

Four succinato-bridged complexes of copper(II) have been synthesized. Complex 1, [Cu(2)(mu-OH(2))(2)L(bpy)(2)(NO(3))(2)](n) and 2, [Cu(2)(mu-OH(2))(2)L(phen)(2)(NO(3))(2)](n)(bpy = 2,2[prime or minute]-bipyridine; phen = 1,10-phenanthroline and LH(2)= succinic acid) exhibit 1D coordination polymer structures where both the nitrate ions are directly linked to the copper(ii) producing synthons in a 2D sheet. A novel 2D grid-like network, ([Cu(4)L(2)(bpy)(4)(H(2)O)(2)](ClO(4))(4)(H(2)O))n3, is obtained upon changing the nitrate by perchlorate anion in complex 1, where the channels are occupied by the anions. On changing the nitrate by tetrafluoroborate anion in complex 2, a novel octanuclear complex, [Cu(8)L(4)(phen)(12)](BF(4))(8).8H(2)O 4, is isolated. The coligand bpy and phen in these complexes show face-to-face (in 1,2,3,4) or edge-to-face (in 4 )pi-pi interactions forming the multidimensional supramolecular architectures. Interestingly, the appearance of edge-to-face pi-pi interactions in complex facilitates the formation of discrete octanuclear entities. Variable-temperature (300-2 K) magnetic measurements of complexes have been done. Complexes 1 and 2 show very weak antiferromagnetic (OOC-CH(2)-CH(2)-COO) and ferromagnetic coupling (mu-H(2)O). Complex 3 also shows antiferromagnetic (syn-syn mu-OCO), and ferromagnetic coupling (mu-O of the -COO group). Complex 4 with two types (syn-syn and syn-anti) of binding modes of the carboxylate group shows strong antiferromagnetic interaction.