Asymptotic properties of solutions of nonlinear difference equations

Using discrete inequalities and Schauder's fixed point theorem we study the problem of asymptotic equilibrium for difference equations.     

Minimal non-orientable matroids in a projective plane

We construct a new family of minimal non-orientable matroids of rank three. Some of these matroids embed in Desarguesian projective planes. This answers a question of Ziegler: for every prime power q, find a minimal non-orientable submatroid of the projective plane over the q-element field.     

Asymptotic behavior of a linear difference equation with continuous time

We consider a class of linear homogeneous difference equations with constant coefficients and commensurate delays. We prove an asymptotic formula for the solutions as t → ∞ under the assumption of the existence of a simple “dominant” real characteristic value. Research supported by FONDECYT Grant, Chile, No. 1.070.980.     

Fuzzy ternary particle systems by surface-initiated atom transfer radical polymerization from layer-by-layer colloidal core-shell macroinitiator particles

We report the synthesis of ternary polymer particle material systems composed of (a) a spherical colloidal particle core, coated with (b) a polyelectrolyte intermediate shell, and followed by (c) a grafted polymer brush prepared by surface-initiated polymerization as the outer shell. The layer-by-layer (LbL) deposition process was utilized to create a functional intermediate shell of poly(diallyl-dimethylammonium chloride)/poly(acrylic acid) multilayers on the colloid template with the final layer containing an atom transfer radical polymerization (ATRP) macroinitiator polyelectrolyte. The intermediate core-shell architecture was analyzed with FT-IR, electrophoretic mobililty (zeta-potential) measurements, atomic force microscopy, and transmission electron microscopy (TEM) techniques. The particles were then utilized as macroinitiators for the surface-initiated ATRP grafting process for poly(methyl methacrylate) polymer brush. The polymer grafting was confirmed with thermo gravimetric analysis, FT-IR, and TEM. The polymer brush formed the outermost shell for a ternary colloidal particle system. By combining the LbL and surface-initiated ATRP methods to produce controllable multidomain core-shell architectures, interesting functional properties should be obtainable based on independent polyelectrolyte and polymer brush behavior.     

Harmonic conjugation in harmonic matroids

We study a generalization of the concept of harmonic conjugation from projective geometry and full algebraic matroids to a larger class of matroids called harmonic matroids. We use harmonic conjugation to construct a projective plane of prime order in harmonic matroids without using the axioms of projective geometry. As a particular case we have a combinatorial construction of a projective plane of prime order in full algebraic matroids.     

Thiophene dendron jacketed poly(amidoamine) dendrimers: nanoparticle synthesis and adsorption on graphite

The peripheral functionalization of amine-terminated fourth-generation poly(amidoamine) (PAMAM) with thiophene dendrons and the preparation of dendrimer-encapsulated metal nanoparticles are described. Interesting nanoparticle stabilization and energy-transfer properties were observed with these hybrid materials. The synthesis involved imine coupling of the dendron derivatives to the peripheral amine groups of PAMAM followed by reduction. The formation of these metal-organic nanoparticle hybrid materials was monitored by UV-vis spectroscopy. The complexation of metal ions and the stabilization effect of PAMAM on metal nanoparticles were investigated by FT-IR. Energy transfer was observed between the metal surface plasmon absorption and fluorescence of the terthiophene dendrons. Noncontact magnetic-AC mode AFM imaging revealed the formation of monodispersed and very stable nanoparticles adsorbed on an HOPG flat substrate.     

Stochastic transition states: reaction geometry amidst noise

Classical transition state theory (TST) is the cornerstone of reaction-rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This no-recrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. High-accuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact no-recrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a time-dependent dividing surface that is stochastically moving in phase space, such that it is crossed once and only once by each transition path.     

A spectroscopic and computational exploration of the cybotactic region of gas-expanded liquids: methanol and acetone

Local compositions in supercritical and near-critial fluids may differ substantially from bulk compositions, and such differences have important effects on spectroscopic observations, phase equilibria, and chemical kinetics. Here, we compare such determinations around a solute probe dissolved in CO2-expanded methanol and acetone at 25 degrees C from solvatochromic experiments with molecular dynamics simulations. UV/vis and steady-state fluorescence measurements of the dye Coumarin 153 in the expanded liquid phase indicate preferential solvation in both the S0 and S1 states by the organic species. Simple dielectric continuum models are used to estimate local compositions from the spectroscopic data and are compared to molecular dynamics simulations of a single C153 molecule dissolved in the liquid phase at bubble point conditions. The simulations provide information about the local solvent structure around C153. They suggest the presence of large solvent clustering near the electron-withdrawing side of the probe. Preferential solvation exists in both the S0 and S1 states, but a large disagreement between simulation and experiment exists in the S1 state. Potential reasons for this disparity are discussed.     

Nanopatterning and fabrication of memory devices from layer-by-layer poly(3,4-ethylenedioxythiophene)-poly(styrene sulfonate) ultrathin films

A write-read-erasable memory device was fabricated on layer-by-layer (LbL) ultrathin films prepared from poly(3,4-ethylenedioxythiophene)-poly(styrene sulfonate) (PEDOT-PSS) and poly(diallyldimethylammonium chloride) (PDDA). By use of current-sensing atomic force microscopy (CS-AFM), nanopatterns were formed by applying a bias voltage between a conductive tip (Pt-coated Si3N4 cantilever) in contact with the polymer film and gold substrate. The dependence of the nanopatterns on film thickness, applied bias, and writing speed was studied. Moreover, the height of the patterns was 3-5 times higher than the original thickness of the films, opening the possibility for three-dimensional nanopatterning. The ability of the patterns to be erased after nanowriting was also investigated. By comparing the I-V characteristics under ambient conditions and under N2 environment, a joule-heating activated, water meniscus-assisted anion doping mechanism for the nanopatterning process was determined. Write-read-erase memory device capability was demonstrated on the nanopatterns.