On position-space renormalization group approach to percolation

In a position-space renormalization group (PSRG) approach to percolation one calculates the probabilityR(p,b) that a finite lattice of linear sizeb percolates, wherep is the occupation probability of a site or bond. A sequence of percolation thresholdsp _c (b) is then estimated fromR(p _c ,b)=p _c (b) and extrapolated to the limitb to obtainp _c =p _c (). Recently, it was shown that for a certain spanning rule and boundary condition,R(p _c ,)=R _c is universal, and sincep _c is not universal, the validity of PSRG approaches was questioned. We suggest that the equationR(p _c ,b)=, where isany number in (0,1), provides a sequence ofp _c (b)'s thatalways converges top _c asb. Thus, there is anenvelope from any point inside of which one can converge top _c . However, the convergence is optimal if =R _c . By calculating the fractal dimension of the sample-spanning cluster atp _c , we show that the same is true aboutany critical exponent of percolation that is calculated by a PSRG method. Thus PSRG methods are still a useful tool for investigating percolation properties of disordered systems.     

Pathwise rate- stability for input-output processes

An input-output processZ = {Z(t), t 0} is said to be-rate stable ifZ(t) = o((t)) for some non-negative function(t). We prove that the processZ is -rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions for-rate-stability can be verified from input data. For example, using input information, we establish-rate stability of the workload for multiserver queues, an ATM multiplexer, and-rate stability of queue-length processes for infinite server queues.     

A photochemical method for patterning the immobilization of ligands and cells to self-assembled monolayers

This work describes a chemically well defined method for patterning ligands to self-assembled monolayers (SAMs) of alkanethiolates on gold. This method begins with monolayers presenting a nitroveratryloxycarbonyl (NVOC)-protected hydroquinone which is photochemically irradiated to reveal a hydroquinone group. The resulting hydroquinone is then oxidized to the corresponding benzoquinone, providing a site for the Diels-Alder mediated immobilization of ligands. The rate constant for the photochemical deprotection is 0.032 s(-1) (with an intensity of approximately 100 mW/cm(2) between 355 and 375 nm), corresponding to a half-life of 21 s. The hydroquinone is oxidized to the benzoquinone using either electrochemical or chemical oxidation and then functionalized by reaction with a cyclopentadiene-tagged ligand. Two methods for patterning the immobilization of ligands are described. In the first, the substrate is illuminated through a mask to generate a pattern of hydroquinone groups, which are elaborated with ligands. In the second method, an optical microscope fit with a programmable translational stage is used to write patterns of deprotection which are then again elaborated with ligands. This technique is characterized by the use of well-defined chemical reactions to control the regions and densities of ligand immobilization and will be important for a range of applications that require patterned ligands for biospecific interactions.     

9,9-diphenyl-1,9,10,10a-tetrahydro-2H-phenaleno[1,9-bc]pyrans

Reaction between some naphtho[2,1-b]pyrans and 1,1-diphenylethene affords 9,9-diphenyl-1,9,10,10a-tetrahydro-2H-phenaleno[1,9-bc]pyrans.     

Retention, kinetics and thermodynamics profile of cadmium adsorption from iodide medium onto polyurethane foam and its separation from zinc bulk

The sorption behaviour of 2.5 × 10⁻⁵ M solution of Cd(II) on polyurethane foam (PUF) from iodide medium have been investigated. The conditions were optimized from aqueous solutions of different pH (1-10) and of acids of varied concentration (0.01-1.0 M). The maximum concentration of KI was found to be 0.24 M and equilibration time was established to be 20 min. The data successfully followed the Freundlich and Dubinin-Radushkevich (D-R) isotherms at low metal ion concentration while Langmuir isotherm followed at higher metal ion concentration. The Freundlich parameter 1/n = 0.66 ± 0.02 have been evaluated whereas D-R isotherm yields the sorption free energy E = 10.5 ± 0.1 kJ mol⁻¹ indicating ion exchange type chemisorption. The monolayer coverage (XL) constant of Langmuir isotherm was found to be 23.7 ± 0.4 mg g⁻¹. The numerical values of thermodynamics parameters enthalpy (ΔH), entropy (ΔS) and Gibbs free energy (ΔG) indicated the endothermic and spontaneous nature of sorption. The Scatchard plot analysis was tested to evaluate the binding sites of the PUF and stability constants of sorption were determined. On the basis of these parameters, the sorption mechanism was discussed. Among the foreign ions tested, Pb(II), Hg(II), cyanide and nitrite should be absent. The clean separation of Cd(II) from Zn(II) ions in the ratio 1:250, respectively, was achieved by column chromatography.     

A massively parallel electrochemical approach to the miniaturization of organic micro- and nanostructures on surfaces

This paper describes a simple and convenient strategy for reducing the dimensions of organic micro-and nanostructures on metal surfaces. By varying electrochemical desorption conditions, features patterned by dip-pen nanolithography or micro contact printing and made of linear alkanethiols or selenols can be gradually desorbed in a controlled fashion. The process is referred to as electrochemical whittling because the adsorbate desorption is initiated at the exterior of the feature and moves inward as a function of time. The whittling process and adsorbate desorption were studied as a function of substrate morphology, adsorbate head and tail groups, and electrolyte solvent and salt. Importantly, one can independently address different nanostructures made of different adsorbates and effect their miniaturization based upon ajudicious selection of adsorbate, applied potential, and supporting electrolyte. Some of the physical and chemical origins of these observations have been elucidated.     

Total synthesis of (+)-xyloketal D, a secondary metabolite from the mangrove fungus Xylaria sp.

(+)-Xyloketal D was prepared in a one-pot multistep domino reaction by heating optically active 5-hydroxy-4-methyl-3-methylenepentan-2-one (R) in toluene with 2,4-dihydroxyacetophenone. The absolute configuration of the natural product was confirmed by preparation of the starting enone from a lactone of established absolute configuration.     

Polymerization of methyl methacrylate in the presence of iron(II) complex with tetradentate nitrogen ligands under conditions of atom transfer radical polymerization

Four tetradentate nitrogen ligands, viz. dichloro{[N,N^′-diphenyl-N,N^′-di(quinoline-2-methyl)]-1,2-ethylene diamine} (1), {[N,N^′-dioctyl-N,N^′-di(quinoline-2-methyl)]-1,2-ethylene diamine} (2), {[N,N^′-dibenzyl-N,N^′-di(quinoline-2-methyl)]-1,2-ethylene diamine} (3), and (1R,2R)-(−)-N,N^′-di(quinoline-2-methyl) di-iminocyclohexane (4), were investigated as novel complexing ligands in iron-mediated atom transfer radical polymerization (ATRP) of methyl methacrylate where ethyl-2-bromoisobutyrate was the initiator in o-xylene at 90 °C. With ligands 1 and 2 the experimental molecular weights increased gradually with monomer conversion. High to moderate conversions (87%, 43%) were obtained in relatively short times (90 min for 1 and 30 min for 2), which indicates an efficient catalyst system, but after these times a dramatic increase in viscosity of the polymerization medium led to loss of control. It is noteworthy that polymerization proceeded in a controlled manner with ligand 1, which has two rather bulky substituents on the N-atom. Such bulky ligands did not work for a copper-based system, where they led to excessive terminations or other side reactions. When the bulkiness of the substituents was significantly increased, as in ligand 3, a decrease in polymerization rate and loss of control occurred. Ligand 4 was less efficient than the other ligands, probably because the ethylene bridge was replaced by cyclohexane bridge.     

Synthesis and pharmacological activity of 4-(4'-(chlorophenyl)-4-hydroxypiperidine) derivatives

A new series of 4-(4'-chlorophenyl)-4-hydroxypiperidine derivatives (2-5), substituted at nitrogen, were synthesized and tested as potential analgesic compounds as well as evaluated for their effect on hypotensive activity. Results showed that all the derivatives exhibit significant analgesic activity in male Wistar rats at a dose of 50 mg/kg of body weight after intramuscular injection, when tested by thermal stimuli (tail flick test). Pethidine was used as reference drug. Compounds 2, 3 and 5 produced reduction in blood pressure in normotensive rat.