Derivation of a modified paraxial formalism for two-dimensional trajectories in electron and ion sources of non-simple geometries

A modified paraxial formalism has been developed which describes two-dimensional charged particle beam dynamics in electron and ion sources with pointed or needle-type geometries. A Hamiltonian formalism, and a more exact treatment of energy conservation is used to derive the modified paraxial equation for two-dimensional trajectories in systems with axially symmetric prolate-spheroidal beams. Calculations have been done for a gallium field emission liquid metal ion source modeled by a hyperboloid of revolution and planar extractor. Two important conclusions emerge from these calculations: i) The dominant effect of space-charge, for source geometries with small radii of curvature, occurs in the region close to the apex (<0.05 n) and ii) beam divergence has a strong dependence on geometry. This latter effect is a consequence of large two-dimensional field gradients near the apex of sources with needle-type or pointed geometry.This work was supported in part by the Division of Materials Research, National Science Foundation, Grant No. DMR-8108829     

Reply to comment on “variational formulation for the equilibrium condition of a conducting fluid in an electric field”

In this comment we respond to the several criticisms of the paper by Sujatha et al. raised by Kingham and Bell. In particular, we demonstrate that, contrary to their assertion, Taylor's solution for the electrostatic fields can never satisfy the boundary conditions for the actual experimental configurations involving field emission liquid metal ion sources and other experiments on electrostatically stressed conducting fluids. It is further argued that a careful analysis of Taylor's experimental procedure and observations suggests that although the observed static structures have a macroscopic axial-symmetry they have not the idealized conical shapes of prescribed angle. Furthermore, the formation of the Taylor cone structure is shown to be inconsistent with the principle of energy minimization.It is concluded that none of the criticism raised by Kingham and Bell invalidate any of the analysis or conclusions presented in the paper by Sujatha et al.This work has been supported in part by the Division of Materials Research, National Science Foundation, Grant No. DMR-81008829     

Adsorption mechanism and acidic behavior of naphthazarin on Ag nanoparticles studied by Raman spectroscopy

Surface-enhanced Raman scattering (SERS) spectroscopy is applied in this work to the study of the adsorption of naphthazarin (NZ) on Ag nanoparticles. Spectra recorded at different excitation wavelengths and pHs revealed that this molecule is adsorbed on the metal through several mechanisms. Two main types of adsorbed molecules can be identified that correspond to neutral and ionized NZ, which may be physisorbed or chemisorbed on the metal. The existence of these different forms can be due to different binding sites on the surface or to the formation of a multilayer architecture on the metal surface giving rise to different adsorbate states. Although the amount of the ionized molecule attached on the surface is higher at neutral pH, the neutral molecule may also exist even at very high pH. The amount of neutral NZ increases with the time and also as the NZ concentration is raised or as the dimethylsulfoxide (DMSO) concentration existing in the medium is increased.     

Variational formulation for the equilibrium condition of a conducting fluid in an electric field

In this paper the variational formalism is used to derive a set of equations describing the equilibrium configuration of a conducting fluid in an applied electric field. The validity of the variational equations is confirmed by application to the well-defined problem of concentric spherical electrodes. It is further shown that a cone, including the so-called Taylor cone used to model the equilibrium configuration of liquid metal ion sources, is inconsistent with the general equations. An analysis of the Taylor derivation suggests that reasons for the disagreement are the omission of the pressure difference term in the Laplace formula and use of only an approximate solution to the electrostatic cone problem. Finally a quasi-empirical method is suggested for the self-consistent solution of the variational equations.     

Photophysics of Hypericin and Hypocrellin A in Complex with Subcellular Components: Interactions with Human Serum Albumin

Time-resolved fluorescence and absorption measurements are performed on hypericin complexed with human serum albumin, HSA (1:4, 1:1 and approximately 5:1 hypericin: HSA complexes). Detailed comparisons with hypocrellin A/HSA complexes (1:4 and 1:1) are made. Our results are consistent with the conclusions of previous studies indicating that hypericin binds to HSA by means of a specific hydrogen-bonded interaction between its carbonyl oxygen and the N1-H of the tryptophan residue in the IIA subdomain of HSA. (They also indicate that some hypericin binds nonspecifically to the surface of the protein.) A single-exponential rotational diffusion time of 31 ns is measured for hypericin bound to HSA, indicating that it is very rigidly held. Energy transfer from the tryptophan residue of HSA to hypericin is very efficient and is characterized by a critical distance of 94 A, from which we estimate a time constant for energy transfer of approximately 3 x 10(-15) s. Although it is tightly bound to HSA, hypericin is still capable of executing excited-state intramolecular proton (or hydrogen atom) transfer in the approximately 5:1 complex, albeit to a lesser extent than when it is free in solution. It appears that the proton transfer process is completely impeded in the 1:1 complex. The implications of these results for hypericin (and hypocrellin A) are discussed in terms of the mechanism of intramolecular excited-state proton transfer, the mode of binding to HSA and the light-induced antiviral and antitumor activity.     

Comment on the validity of first-order paraxial theory for electron and ion sources with needle-type or pointed geometry

An essential feature of first-order paraxial theory is the assumption that if the potential along the axis of an axially symmetric system is known, then the potential (fields) near the axis can be obtained by a power-series expansion about points lying on axis. However, in traditional first-order theory, which commonly assumes systems with cylindrical symmetry, only terms up to second-order in the coordinate transverse to the beam axis are retained. In this letter we argue that a consequence of this restriction is that traditional first-order paraxial theory should not be applicable to electron and ion sources with pointed or needle-type geometries. In order to treat non-parallel trajectories which occur in the pointed geometries present, say, in field emission liquid metal ion sources, a modified paraxial theory is suggested which describes two-dimensional particle dynamics.This work has been supported in part by the Division of Materials Research, National Science Foundation, Grant No. DMR-81008829     

Characterization of the interaction of hypericin with protein kinase C in U-87 MG human glioma cells

A fluorescence imaging technique was used to monitor intracellular localization of protein kinase C (PKC) in U-87 MG human glioma cells in the presence of hypericin (Hyp) and phorbol 12-myristate-13-acetate (PMA). It is shown that PKC localization, which reflects its activity, is influenced by Hyp and this influence is different from that observed for PMA which acts as PKC activator. Fluorescence binding experiments were used to determine the binding constants of Hyp to several isoforms of PKC. The obtained values of K(d)s (approximately 100 nM) suggest that Hyp binds with high affinity to PKC. Finally, molecular modeling was used to compare structural models of the interaction of C1B domain of PKC (PKC isoforms alpha, delta, gamma) with Hyp and our previously published model of the (C1B domain PKCgamma)/PMA complex. The influence of Hyp on PKC translocation in U-87 MG cells in comparison with PMA, colocalization fluorescence pattern of Hyp and PKC, the higher binding affinity of Hyp to PKC in comparison with known binding constants of phorbol esters, as well as the binding mode of Hyp and PMA to the C1B domain of PKC suggested by molecular modeling, support the idea that Hyp and PMA might competitively bind to the regulatory domain of PKC.     

Theory of electron emission in high fields from atomically sharp emitters: Validity of the Fowler-Nordheim equation

Field emission from metallic emitters is generally described by the Fowler-Nordheim [F-N] theory, which is based on a planar model of the tip with a classical image correction. Within the free electron model and the WKB approximation, the planar tip model leads to the well-known Fowler-Nordheim equation, which predicts that a plot of log J/F² versus 1/F, where J is the current density and F, the field, should be a straight line within the narrow range of field strengths of typical field emission experiments, 3 - 5V/nm. This has been experimentally confirmed for conventional emitters, (i.e., electrolytically etched tips with radii 50 nm). Field emitters fabricated with today's new techniques are much sharper with radii of curvature of the order of nm's or even the size of a single atom. Hence, the local geometry of the tip may become an important factor in the electron emission process. To investigate the effects of the shape and/or size on emission, the authors, in a recent series of papers, studied the dependence of the current-voltage characteristics on the local geometry of pointed emitters. It was found that the calculated results, plotted as log J/V² vs. 1/V, do not exhibit the straight line behavior predicted by the Fowler-Nordheim theory. In addition, there is a dramatic increase in the tunneling current for a fixed external bias, V, relative to the Fowler-Nordheim result for a planar model of the tip with the same bias voltage. Using the exact current integral additional results have been obtained exhibiting the effects of emitter curvature on field electron energy distributions and on electron emission in high fields and temperatures. These results continue to differ with the predictions of the Fowler-Nordheim equation for the same emitter models. Therefore, the adequacy of a β-factor in the conventional planar model Fowler-Nordheim equation to account for emitter curvature is examined. It is demonstrated that even a β-modified Fowler-Nordheim equation is not valid when applied to sharp emitters (r_t 10nm) and will lead to spurious results when extracting information such as work function, field values or emitting area from experimental F-N curves. The explanation for this is discussed, and an approximate analytic expression for the J(V) characteristics of a prototype sharp emitter is derived which exhibits explicitly the dependence of the current density on field, tip geometry andmaterial parameters.     

The multiple-image interactions and the mean-barrier approximation in MOM and MVM tunneling junctions

The effect of the multiple image interactions on theI–V characteristics and the reliability of the mean barrier approximation in calculating the current in MOM and MVM tunneling junctions are critically examined. It is demonstrated that the continued use of the uncorrected form of Simmons' original multiple-image force interaction in the analysis of tunneling junctions can lead to serious errors in both the current and the dynamic resistance. An extensive numerical analysis of planar junctions including the image potential suggests that the basic mean barrier approximation formulated by Simmons is essentially a thick barrier approximation. It also is shown that the conventional mean barrier approximation is a relatively poor approximation for the tunneling barriers of interest, and that it is not possible to establish a reliable a priori estimate of its range of validity.This research was supported in part by the NATO Research Grants Program, Grant No. 1902, Scientific Affairs Division, Brussels, Belgium