Porous GaN as a template to produce surface-enhanced Raman scattering-active surfaces

Surface-enhanced Raman spectroscopy (SERS) substrates have been prepared by depositing Au or Ag on porous GaN (PGaN). The PGaN used as the template for the metal deposition in these studies was generated by a Pt-assisted electroless etching technique. PGaN was chosen as a potential SERS template due to its nanostructured surface and high surface area, two characteristics that are important for SERS substrates. Metal films were deposited either by solution-based electroless deposition or by thermal vacuum evaporation. SERS spectra were recorded at lambda = 752.5 nm for Au films and at lambda = 514.5 nm for Ag films deposited on PGaN. The SERS signal strength across the metal coated PGaN substrates was uniform and was not plagued by "hot" or "cold" spots on the surface, a common problem with other SERS surfaces. The Ag film deposited by electroless deposition had the highest overall SERS response, with an enhancement factor (EF) relative to normal Raman spectroscopy of 10(8). A portion of the increase in EF relative to typical SERS-active substrates can be assigned to the large surface area characteristic of the PGaN-Ag structures, but some of the enhancement is intrinsic and is likely related to the specific morphology of the metal-nanopore composite structure.     

PAA/PEO comb polymer effects on rheological properties and inter-particle forces in aqueous silica suspensions

The effects of a poly(acrylic acid) (PAA)-poly(ethylene) (PEO) comb polymer dispersant on the rheological properties and inter-particle forces in aqueous silica suspensions have been studied under varying pH conditions. The comb polymer was found to adsorb more strongly under acidic than basic conditions, indicating that the PAA backbone of the copolymer preferentially adsorbs onto silica surfaces with the PEO "teeth" extending out from the surface into the solution. In the presence of low concentrations of copolymer, the silica suspensions were stable due to electrostatic repulsions between the silica surfaces. At higher copolymer concentrations and under neutral and basic conditions, where the copolymer interacted only weakly with silica, the suspensions showed a transition from a dispersed to weakly flocculated state and attractive forces were measured between silica surfaces. Under acidic conditions, the silica dispersion also destabilized at intermediate copolymer adsorbed density and then was re-stabilized at higher adsorbed coverage. The silica suspensions were stable at high copolymer coverage due to steric repulsions between the particles. The destabilization at intermediate coverage is thought to be due to polymer bridging between particles or possibly depletion forces.     

On the existence of conically self-similar free-vortex solutions to the Navier-Stokes equations

In this paper a proof of existence and non-existence of theconically self-similar free-vortex solutions to the Navier-Stokesequations, originally found by Yih et al. (1982, Phys. Fluids.25, 2147-2158), is presented. This proof clearly establishesthat these solutions do not have any kind of singularity atthe symmetry axis. This analysis gives considerably improvedexistence and non-existence bounds and it is shown that thesebounds are close to optimal in the low-swirling limit. Thisapproach links the questions of existence and non-existencefor the swirling case and for the non-swirling case. The proof,which is an extension of techniques developed by Serrin (1972,Phil. Trans. R. Soc. Lond. 271, 325-360), is based on Schauder'sFixed Point Theorem and is, therefore, non-constructive. Therefore,the paper ends with a brief discussion of the question of howto compute the conically self-similar free-vortex solutionsto the Navier-Stokes equations.     

Clustering and mechanics in dense depletion and thermal gels

We report on the microstructure and mechanical properties (elastic modulus) of concentrated depletion and thermal gels of octadecyl-coated silica particles for different values of the strength of interaction--polymer concentration for depletion gels and temperature for thermal gels. The depletion gels are composed of dense clusters and voids, while the thermal gels are devoid of clusters. Shear breaks up clusters in depletion gels while it induces clustering in the thermal gels. In both of these gels, the microstructure recovers to the presheared state upon cessation of shear. The recovery of the elastic modulus mimics the microstructure in the sense that the elastic modulus recovers to the presheared sheared state after shearing is stopped. Calculations of the gel boundary by modeling the interactions with an effective one-component square-well model reveals that suspensions with similar ranges of attraction gel at the same volume fraction at a fixed strength of attraction. Calculations of the elastic modulus using the na?ve mode coupling theory for depletion gels are in good agreement with experimental measurements provided clustering is taken into account and have the same magnitude as the elastic moduli of thermal gels with similar strengths of attraction. These calculations, in addition to the experimental observations reinforce the point that the microscopic parameter determining the elastic modulus of dense gels and its recovery is the localization length which is only a fraction of the particle diameter and not the structure on the length scale of the particle diameter and larger.     

Pricing vulnerable European options with stochastic default barriers

CF Lo and KC Ku Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China Email: cho-hoi_hui{at}hkma.gov.hk Received on 31 July 2006. Accepted on 15 March 2007. This paper develops a valuation model of European options incorporatinga stochastic default barrier, which extends a constant defaultbarrier proposed in the Hull–White model. The defaultbarrier is considered as an option writer's liability. Closed-formsolutions of vulnerable European option values based on themodel are derived to study the impact of the stochastic defaultbarriers on option values. The numerical results show that negativecorrelation between the firm values and the stochastic defaultbarriers of option writers gives material reductions in optionvalues where the options are written by firms with leverageratios corresponding to BBB or BB ratings.     

Determination of static microstructure of dilute and concentrated suspensions of anisotropic particles by ultra-small-angle X-ray scattering

Ultra-small-angle X-ray scattering was performed on suspensions of anisotropic polystyrene particles of varying degrees of anisotropy. The wave vector dependence of particle form factors is well described by a model developed by Debye for the scattering from fused spheres. As volume fraction is raised, all suspensions undergo a disorder/order phase transition. The scattering from disordered and ordered suspensions of anisotropic particles is the same as that of spheres up to volume fractions of 0.45, suggesting that, in the dilute crystalline phase, the anisotropic particles order into a rotator or plastic crystal phase, where the particle centers of mass are ordered, but the particle directors are randomly distributed. Further increase in particle volume fraction leads to differences in scattering between homonuclear dicolloids and spheres, implying that the homonuclear dicolloids form a body-centered tetragonal phase with both positional and directional order. This conclusion is supported by real-space imaging of dried films of the particles.     

Generalized phase behavior of small molecules and nanoparticles

Prediction and understanding of the thermodynamic properties and kinetics of phase transitions in molecular systems depends on tuning intermolecular interactions such that the desired structures are assembled. These interactions can depend on the solvent temperature and composition and are difficult to determine in an a priori manner. This is especially true for large and complex molecules and nanoparticles with functionalized surfaces. Here, we demonstrate the use of the pair contribution of the long-time self-diffusivity determined by pulsed-field gradient spin-echo nuclear magnetic resonance as a probe of these interactions. Materials with high solubilities have scaled long-time self-diffusivity, D2, values that are close to hard sphere values and decrease as the solubility decreases. We find a remarkable correlation between solubility and D2 for a wide range of hydrogen-bonding solutes that crystallize upon quenching solutions from high temperature. This generalized phase behavior can be understood in terms of the solutes' interacting with attractive forces that have an extent that is only a small fraction of their diameters.     

Multiscale structure, interfacial cohesion, adsorbed layers, and thermodynamics in dense polymer-nanoparticle mixtures

We establish the existence and size of adsorbed polymer layers in miscible dense nanocomposites and their consequences on microstructure and the bulk modulus. Using contrast-matching small-angle neutron scattering to characterize all partial collective structure factors of polymers, particles, and their interface, we demonstrate qualitative failure of the random phase approximation, accuracy of the polymer reference site interaction model theory, ability to deduce the adsorbed polymer layer thickness, and high sensitivity of the nanocomposite bulk modulus to interfacial cohesion.     

A metastable van der waals gel: transitioning from weak to strong attractions

Here we describe a method to create gels where the gel point is decoupled from gel elastic properties. Working with charge stabilized polystyrene latex particles with diameters, D, of 508-625 nm at ionic strengths of 0.1-1 M, the gel volume fraction is varied from 0.10-0.35 through the addition of less than monolayer coverage of hexaethylene glycol monododecyl ether (C6E12). At each surfactant concentration, the gel volume fraction depends on the background ionic strength. The changes in gel point with surfactant concentration suggest the strength of interparticle attraction decreases with increasing surfactant concentration. These changes are not reflected in the gel moduli, which are independent of surfactant concentration and ionic strength. We propose a model to describe this behavior based on gelation due to localization in a shallow truncated van der Waals minimum produced by the surfactant acting as a steric stabilizing layer. The surfactant remains mobile on the surface. Below the gel volume fraction, the time particles spend in the truncated well are not sufficient for the surfactant to be displaced such that the particles can only sample the shallow well. Above the gel volume fraction, particles are localized in the truncated van der Waals minima for sufficient periods of time to displace the surfactant layers with the result being that the particles fall into a primary van der Waals minimum. The result is gel points sensitive to surfactant concentration but moduli that are independent of the gel volume fraction.