Alexander Zhbanov

Van der Waals Interaction between Two Crossed Carbon Nanotubes

The analytical expressions for the van der Waals potential energy and force between two crossed carbon nanotubes are presented. The Lennard-Jones potential between pairs of carbon atoms and the smeared-out approximation suggested by L. A. Girifalco (J. Phys. Chem. 1992, 96, 858) were used. The exact formula is expressed in terms of rational and elliptical functions. The potential and force for carbon nanotubes were calculated. The uniform potential curves for single- and multiwall nanotubes were plotted. The equilibrium distance, maximal attractive force, and potential energy have been evaluated.

Universal curves for the van der Waals interaction between single-walled carbon nanotubes.

We report very simple and accurate algebraic expressions for the van der Waals (VDW) potentials and the forces between two parallel and crossed carbon nanotubes. The Lennard-Jones potential for two carbon atoms and the method of the smeared-out approximation suggested by Girifalco were used. It is found that the interaction between parallel and crossed tubes is described by two universal curves for parallel and crossed configurations that do not depend on the van der Waals constants, the angle between tubes, and the surface density of atoms and their nature but only on the dimensionless distance. The explicit functions for equilibrium VDW distances, well depths, and maximal attractive forces have been given. These results may be used as a guide for the analysis of experimental data to investigate the interaction between nanotubes of various natures.

Effects of Aggregation on Blood Sedimentation and Conductivity.

The erythrocyte sedimentation rate (ESR) test has been used for over a century. The Westergren method is routinely used in a variety of clinics. However, the mechanism of erythrocyte sedimentation remains unclear, and the 60 min required for the test seems excessive. We investigated the effects of cell aggregation during blood sedimentation and electrical conductivity at different hematocrits. A sample of blood was drop cast into a small chamber with two planar electrodes placed on the bottom. The measured blood conductivity increased slightly during the first minute and decreased thereafter. We explored various methods of enhancing or retarding the erythrocyte aggregation. Using experimental measurements and theoretical calculations, we show that the initial increase in blood conductivity was indeed caused by aggregation, while the subsequent decrease in conductivity resulted from the deposition of erythrocytes. We present a method for calculating blood conductivity based on effective medium theory. Erythrocytes are modeled as conducting spheroids surrounded by a thin insulating membrane. A digital camera was used to investigate the erythrocyte sedimentation behavior and the distribution of the cell volume fraction in a capillary tube. Experimental observations and theoretical estimations of the settling velocity are provided. We experimentally demonstrate that the disaggregated cells settle much slower than the aggregated cells. We show that our method of measuring the electrical conductivity credibly reflected the ESR. The method was very sensitive to the initial stage of aggregation and sedimentation, while the sedimentation curve for the Westergren ESR test has a very mild slope in the initial time. We tested our method for rapid estimation of the Westergren ESR. We show a correlation between our method of measuring changes in blood conductivity and standard Westergren ESR method. In the future, our method could be examined as a potential means of accelerating ESR tests in clinical practice.

Corrected field enhancement factor for the floating sphere model of carbon nanotube emitter

We have corrected the field enhancement factor for the “floating sphere at emitter-plane potential” model with the finite anode-cathode distance. If ρ is the radius of sphere, h is the distance from cathode to the center of sphere, and l is the distance from the center to the anode, then the field enhancement factor is given as the following expression βsph=(2+7η−η2)(λ2−2λ+2)/[2η(1−λ)(2−λ)], where η=ρ/h, λ=ρ/l. This expression demonstrates reasonable behavior for three limiting cases: if h→ρ, if l→∞, and if l→ρ. We have compared our factor βsph with the field enhancement factor βtube for the “hemisphere on a post” model and the factor βell for the “hemiellipsoid on plane” model. We have shown realization of the approximate evaluation βtube≈(βsph+βell)/2.

Screened field enhancement factor for the floating sphere model of a carbon nanotube array

The screened field enhancement factor for a carbon nanotube (CNT) placed in a CNT array (which is reduced due to the screening effect) is derived based on the “floating sphere” model. We obtain an expression for the field enhancement factor for a CNT in the array as γ=3+2(1+η)/{(2+η)[2πα(2+η)δ2+η]}, where ρ is the radius of sphere, h is the distance from cathode to the center of sphere, and D is the distance between the nearest spheres, η=ρ/h, δ=ρ/D, and α=1 for square or 2/3 for hexagonal lattice made of CNTs. Explicit algebraic formulas for optimizing the distance between tubes, areal density of emitters, and the anode current are also obtained.

Carbon Nanotube Field Emitters

Application of various one-dimensional nanostructure materials as field emission sources has attracted extensive scientific efforts. Elongated structures are suitable for achieving high field-emission-current density at a low electric field because of their high aspect ratio. Area of its application includes a wide range of field-emission-based devices such as flat-panel displays, electron microscopes, vacuum microwave amplifiers, X-ray tube sources, cathode-ray lamps, nanolithography systems, gas detectors, mass spectrometers etc. Since the discovery of carbon nanotubes (CNTs) (Iijima, 1991; Iijima & Ichihashi, 1993; Bethune et al., 1993) and experimental observations of their remarkable field emission characteristics (Rinzler et al., 1995; de Heer et al., 1995; Chernazatonskii et al., 1995), significant efforts have been devoted to the application of using CNTs for electron sources. One of the main problems for design such field emission emitter is the difficulties in estimation of the electric field on the apex of nanotubes. Only a few works considered forces acting on nanoemitters under electric field. Thus far, there is no analytical formula which provides a good approximation to the total current generated by the nanoscale field emitter. In this chapter, we theoretically consider the electric field strength, field enhancement factor, ponderomotive forces, and total current of a metallic elliptical needle in the form of hemi- ellipsoid in the presence of a flat anode. Also we shortly review the history CNT cold emitters and technology of their fabrication. Furthermore we consider the application areas of CNT electron sources.

Field enhancement factor for the floating sphere model of the nanotube array in parallel-plate geometry

Excellent electron-field emission properties of carbon nanotubes (CNTs) attract essential scientific and practical interests. The small gap between top of the emitter and the anode essentially increases the field enhancement factor. The screening effect reduces the field emission current of a CNT placed in an array of CNTs. We have derived explicit analytical expression of the field enhancement factor for the “floating sphere” model of CNT array in parallel-plate geometry. Comparison with other theoretical calculations is shown. We have generalized the published experimental data.

Comment on ‘Model calculation of the scanned field enhancement factor of CNTs’

The model proposed by Ahmad and Tripathi (2006 Nanotechnology 17 3798) demonstrates that the field enhancement factor of carbon nanotubes (CNTs) reaches a maximum at a certain length. Here, we show that this behavior should not occur and suggest our correction to this model.