Thermal oxidative degradation reactions of perfluoroalklethers

The objective of this contract was to investigate the mechanisms operative in thermal and thermal oxidative degradation of Fomblin Z and hexafluoropropene oxide derived fluids and the effect of alloys and additives upon these processes. The nature of arrangements responsible for the inherent thermal oxidative instability of the Fomblin Z fluids has not been established. It was determined that this behavior was not associated with hydrogen end-groups or peroxy linkages. The degradation rate of these fluids at elevated temperatures in oxidizing atmospheres was found to be dependent on the surface/volume ratio. Once a limiting ratio was reached, a steady rate appeared to be attained. Based on elemental analysis and oxygen consumption data, -CF2OCF2CF2O-, not -CF2CF2O-, is one of the major arrangements present. The action of the M-50 and Ti(4 Al, 4 Mn) alloys was found to be much more drastic in the case of Fomblin Z fluids than that observed for the hexalfuoropropane oxide derived materials. The effectiveness of antioxidation/anticorrosion additives, P-3 and phospha-s-triazine, in the presence of metal alloys was very limited at 316 C; at 288 C the additives arrested almost completely the fluid degradation. The phospha-s-triazine appeared to be at least twice as effective as the P-3 compound; it also protected the coupon better. The Ti(4 Al, 4 Mn) alloy degraded the fluid mainly by chain scission processes; this took place to a much lesser degree with M-50

The effects of metals and inhibitors on thermal oxidative degradation reactions of unbranched perfluoroalkylethers

Thermal oxidative degradation studies were performed on unbranched perfluoroalkylethers at 288 C in oxygen. Metals and alloys studied included Ti, Al, and Ti (4 Al, 4 Mn). The mechanism of degradation was by chain scission. Ti and Al promoted less degradation than Ti (4 Al, 4 Mn). The two inhibitors investigated (a perfluorophenyl phosphine and a phosphatriazine) reduced degradation rates by several orders of magnitude. Both inhibitors were effective for the same duration (75 to 100 hours). The phosphatriazine appeared to provide more surface protection

Ion exchange phase transitions in "doped" water--filled channels

Ion transport through narrow water--filled channels is impeded by a high electrostatic barrier. The latter originates from the large ratio of the dielectric constants of the water and a surrounding media. We show that ``doping'', i.e. immobile charges attached to the walls of the channel, substantially reduces the barrier. This explains why most of the biological ion channels are ``doped''. We show that at rather generic conditions the channels may undergo ion exchange phase transitions (typically of the first order). Upon such a transition a finite latent concentration of ions may either enter or leave the channel, or be exchanged between the ions of different valences. We discuss possible implications of these transitions for the Ca-vs.-Na selectivity of biological Ca channels. We also show that transport of divalent Ca ions is assisted by their fractionalization into two separate excitations.Comment: 16 pages, 27 figure

Measurement of the Casimir force between dissimilar metals

The first precise measurement of the Casimir force between dissimilar metals is reported. The attractive force, between a Cu layer evaporated on a microelectromechanical torsional oscillator, and an Au layer deposited on an Al$_2$O$_3$ sphere, was measured dynamically with a noise level of 6 fN/$\sqrt{\rm{Hz}}$. Measurements were performed for separations in the 0.2-2 $\mu$m range. The results agree to better than 1% in the 0.2-0.5 $\mu$m range with a theoretical model that takes into account the finite conductivity and roughness of the two metals. The observed discrepancies, which are much larger than the experimental precision, can be attributed to a lack of a complete characterization of the optical properties of the specific samples used in the experiment.Comment: 6 pages, 4 figure

On the exact electric and magnetic fields of an electric dipole

We derive from Jefimenko's equations a multipole expansion in order to obtain the exact expressions for the electric and magnetic fields of an electric dipole with an arbitrary time dependence. A few comments are also made about the usual expositions found in most common undergraduate and graduate textbooks as well as in the literature on this topic

Diffraction of light by a planar aperture in a metallic screen

We present a complete derivation of the formula of Smythe [Phys.Rev.72, 1066 (1947)] giving the electromagnetic field diffracted by an aperture created in a perfectly conducting plane surface. The reasoning, valid for any excitating field and any hole shape, makes use only of the free scalar Green function for the Helmoltz equation without any reference to a Green dyadic formalism. We compare our proof with the one previously given by Jackson and connect our reasoning to the general Huygens Fresnel theorem.Comment: J. Math. Phys. 47, 072901 (2006

Coupled-Mode Theory of Field Enhancement in Complex Metal Nanostructures

We describe a simple yet rigorous theoretical model capable of analytical estimation of plasmonic field enhancement in complex metal structures. We show that one can treat the complex structures as coupled multi-pole modes with highest enhancements obtained due to superposition of high order modes in small particles. The model allows one to optimize the structures for the largest possible field enhancements, which depends on the quality factor Q of the metal and can be as high as Q^2 for two spherical particles. The "hot spot" can occur either in the nano-gaps between the particles or near the smaller particles. We trace the optimum field enhancement mechanism to the fact that the extended dipole modes of larger particles act as the efficient antennas while the modes in the gaps or near the smaller particles act as the compact sub-wavelength cavities. We also show how easily our approach can be extended to incorporate large numbers of particles in intricate arrangements.Comment: 23 pages, 7 figure

Diffraction by a small aperture in conical geometry: Application to metal coated tips used in near-field scanning optical microscopy

Light diffraction through a subwavelength aperture located at the apex of a metallic screen with conical geometry is investigated theoretically. A method based on a multipole field expansion is developed to solve Maxwell's equations analytically using boundary conditions adapted both for the conical geometry and for the finite conductivity of a real metal. The topological properties of the diffracted field are discussed in detail and compared to those of the field diffracted through a small aperture in a flat screen, i. e. the Bethe problem. The model is applied to coated, conically tapered optical fiber tips that are used in Near-Field Scanning Optical Microscopy. It is demonstrated that such tips behave over a large portion of space like a simple combination of two effective dipoles located in the apex plane (an electric dipole and a magnetic dipole parallel to the incident fields at the apex) whose exact expressions are determined. However, the large "backward" emission in the P plane - a salient experimental fact that remained unexplained so far - is recovered in our analysis which goes beyond the two-dipole approximation.Comment: 21 pages, 6 figures, published in PRE in 200

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page