57 research outputs found
A new algorithm for computing distance matrix and Wiener index of zig-zag polyhex nanotubes
The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. In this paper an algorithm for constructing distance matrix of a zig-zag polyhex nanotube is introduced. As a consequence, the Wiener index of this nanotube is computed
Counterion Penetration and Effective Electrostatic Interactions in Solutions of Polyelectrolyte Stars and Microgels
Counterion distributions and effective electrostatic interactions between
spherical macroions in polyelectrolyte solutions are calculated via
second-order perturbation (linear response) theory. By modelling the macroions
as continuous charge distributions that are permeable to counterions,
analytical expressions are obtained for counterion profiles and effective pair
interactions in solutions of star-branched and microgel macroions. The
counterions are found to penetrate stars more easily than microgels, with
important implications for screening of bare macroion interactions. The
effective pair interactions are Yukawa in form for separated macroions, but are
softly repulsive and bounded for overlapping macroions. A one-body volume
energy, which depends on the average macroion concentration, emerges naturally
in the theory and contributes to the total free energy.Comment: 15 pages, 5 figure
Resistance distance, information centrality, node vulnerability and vibrations in complex networks
We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability.We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality
The Persistence Length of a Strongly Charged, Rod-like, Polyelectrolyte in the Presence of Salt
The persistence length of a single, intrinsically rigid polyelectrolyte
chain, above the Manning condensation threshold is investigated theoretically
in presence of added salt. Using a loop expansion method, the partition
function is consistently calculated, taking into account corrections to
mean-field theory. Within a mean-field approximation, the well-known results of
Odijk, Skolnick and Fixman are reproduced. Beyond mean-field, it is found that
density correlations between counterions and thermal fluctuations reduce the
stiffness of the chain, indicating an effective attraction between monomers for
highly charged chains and multivalent counterions. This attraction results in a
possible mechanical instability (collapse), alluding to the phenomenon of DNA
condensation. In addition, we find that more counterions condense on slightly
bent conformations of the chain than predicted by the Manning model for the
case of an infinite cylinder. Finally, our results are compared with previous
models and experiments.Comment: 13 pages, 2 ps figure
Pentagonal chains and annuli as models for designing nanostructures from cages
Carbon is the most versatile of chemical elements in combining with itself or other elements to form chains, rings, sheets, cages, and periodic 3D structures. One of the perspective trends for creating new molecules of nanotechnological interest deals with constructs which may be formed by chemically linking of cage molecules. The growing interest in fullerene polyhedra and other molecules with pentagonal rings raises also a question about geometrically consistent in (Formula presented.) nanoarchitectures which may be obtained by aggregating many such molecules. Simple examples are chains and rings assembled from pyramidal (car)borane subunits. Adequate geometrical models of such objects are a chain and an annulus built from regular pentagons wherein any two adjacent pentagons share an edge. Among arising combinatorial problems may be both analytical and constructive enumeration of such chains and annuli drawn in plane with no two edges crossing each other. This may also employ several mathematical disciplines, such as geometry, (spectral) graph theory, semigroup theory, theory of fractals, and others. We discuss some practical approaches for solving the mentioned mathematical problem.Peer Reviewe
Electrochemical Properties of N-Substituted Ī±-Diphenylphosphinoglycines
Ā© 2020, Pleiades Publishing, Ltd. Abstract: The electrochemical properties of the N-substituted Ī±-diphenylphosphinoglycines N-(2-methoxybenzyl) diphenylphosphinoglycine (1), N-(pyrazin-2-yl) diphenylphosphinoglycine (2), N-(1-adamantyl) diphenylphosphinoglycine (3), and N-(2,5-dimethoxycarbonylphenyl) diphenylphosphinoglycine (4) obtained in the three-component condensation of diphenylphosphine, glyoxylic acid hydrate, and the corresponding amine were studied by cyclic voltammetry on a glassy carbon electrode. The structure of compound 4 was confirmed by X-ray diffraction analysis. Compounds 1ā4 exhibited electrochemical activity in the anodic region of potentials due to the presence of an oxidizable diphenylphosphine fragment in the molecule. Compound 4 can also be electrochemically reduced at the cathodic potentials of the working electrode due to the ester groups in the aromatic fragment
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