Electric fields in an electrolyte solution near a strip of fixed potential

Electrostatic fields produced by flat electrodes are often used to manipulate particles in solution. To study the field produced by such an electrode, we consider the problem of an infinite strip of width 2a with imposed constant potential immersed in an electrolyte solution. Sufficiently close to the edge of the strip, the solution is determined by classical electrostatics and results in a field singularity. We examine two limiting cases, (a) when strip width a<1k, the Debye screening length, and (b) when strip width is much greater than the Debye screening length, a>1k. We present exact results for the two cases in the limit of small potentials where the Poisson-Boltzmann equation can be linearized. By drawing on an analogy with antiplane shear deformations of solids, and by employing the path-independent J integral of solid mechanics, we present a new method for determining the strength of the edge singularity. The strength of the singularity defines an exact near-field solution. In the far field the solution goes to that of a line of charge. The accuracy of the solution is demonstrated by comparison with the numerical solutions of the Poisson-Boltzmann equation using the finite element method.     

Deformation of a sheet with coupling between elasticity and concentration

We investigate a simple model for equilibrium deformation of a sheet with concentration-dependent elasticity. The model is motivated by several physical situations where deformation of a sheet is modulated by concentration of a mobile species, for example, a quasi-2D array of carbon nanotubes. Elasticity of the sheet is modeled using a free energy functional that includes concentration-dependent potential energies, and a free energy of mixing. We show that the sheet responds to imposed distortion by rearranging its constituents and can do so in a smooth and stable manner only for sufficiently small distortion. For larger distortions, through phase plane and numerical analysis, we consider how the system can meet boundary conditions through nonsmooth solutions.     

Vibration of an infinite membrane supported by an array of posts

The vibration of an infinite membrane supported by a squareor triangular array of circular posts is studied by eigenfunctionexpansion and collocation. The fundamental frequencies are foundto be highly sensitive to both small and large relative postradii b. The singular nature of the frequency as b 0 is expressedin an asymptotic formula.     

Random sequential adsorption of line segments with a finite jamming limit

The traditional formulation for random sequential adsorption (RSA) of line segments onto a plane does not possess a jamming limit; there is always space for a 1D object on a 2D plane. We propose a qualitatively different RSA formulation for line segments which does lead to a finite jamming limit, 1.5707+/-0.0001 segments per square one segment on the side. To our knowledge, this is the first appearance of the number pi in the jamming limit of an RSA problem. This RSA formulation can be applied to adsorption of rigid, very high aspect ratio rods on a flat surface. These rods are not well modeled by the traditional RSA formulation. As an example of such a problem we describe the deposition of carbon nanotube-DNA hybrids on a surface and show that our theoretical formulation is consistent with experimental results.     

Pattern similarity study of functional sites in protein sequences: lysozymes and cystatins

Background  

Although it is generally agreed that topography is more conserved than sequences, proteins sharing the same fold can have different functions, while there are protein families with low sequence similarity. An alternative method for profile analysis of characteristic conserved positions of the motifs within the 3D structures may be needed for functional annotation of protein sequences. Using the approach of quantitative structure-activity relationships (QSAR), we have proposed a new algorithm for postulating functional mechanisms on the basis of pattern similarity and average of property values of side-chains in segments within sequences. This approach was used to search for functional sites of proteins belonging to the lysozyme and cystatin families.     

Theory of structure-based carbon nanotube separations by ion-exchange chromatography of DNA/CNT hybrids

Single-stranded DNA wrap helically around individual single-walled carbon nanotubes to form DNA/CNT hybrids, which are both stable and dispersible in aqueous solution. Subjected to ion-exchange chromatography, a hybrid elutes at an ionic strength that depends on the electronic character and diameter of the core nanotube, thus providing a mechanism for separating nanotubes by chirality. We present a theoretical model for this separation process that explains all the salient features observed experimentally to date, and provides accurate predictions for critical elution salt concentration. The competition between adsorption on the stationary phase and counterion condensation in the mobile phase is characterized by estimating the difference in free energy between the two states of the hybrid. Parametric study of the DNA wrapping geometry, SWNT dielectric properties, hybrid length, and diameter indicate that the elution is most sensitive to the hybrid's effective charge density, primarily governed by the DNA helical pitch. The model correctly predicts hybrids with metallic nanotubes are weaker binding than hybrids with semiconducting nanotubes and larger diameter nanotubes are eluted at later times.     

Evolution of DNA sequences toward recognition of metallic armchair carbon nanotubes

The armchair carbon nanotube is an ideal system to study fundamental physics in one-dimensional metals and potentially a superb material for applications such as electrical power transmission. Synthesis and purification efforts to date have failed to produce a homogeneous population of such a material. Here we report evolutionary strategies to find DNA sequences for the recognition and subsequent purification of (6,6) and (7,7) armchair species from synthetic mixtures. The new sequences were derived by single-point scanning mutation and sequence motif variation of previously identified ones for semiconducting tubes. Optical absorption spectroscopy of the purified armchair tubes revealed well-resolved first- and second-order electronic transitions accompanied by prominent sideband features that have neither been predicted nor observed previously. Resonance Raman spectroscopy showed a single Lorentzian peak for the in-plane carbon-carbon stretching mode (G band) of the armchair tubes, repudiating the common practice of using such a line shape to infer the absence of metallic species. Our work demonstrates the exquisite sensitivity of DNA to nanotube metallicity and makes the long-anticipated pure armchair tubes available as seeds for their mass amplification.     

Analysis of the M-shell spectra emitted by a short-pulse laser-created tantalum plasma

The spectrum of tantalum emitted by a subpicosecond laser-created plasma, was recorded in the regions of the 3d-5f, 3d-4f, and 3d-4p transitions. The main difference with a nanosecond laser-created plasma spectrum is a broad understructure appearing under the 3d-5f transitions. An interpretation of this feature as a density effect is proposed. The supertransition array model is used for interpreting the spectrum, assuming local thermodynamic equilibrium (LTE) at some effective temperature. An interpretation of the 3d-4f spectrum using the more detailed unresolved transition array formalism, which does not assume LTE, is also proposed. Fitted contributions of the different ionic species differ slightly from the LTE-predicted values.