Lattice Of Charges Research Articles

Lattice-gas model of DNA charge inversion by a positively charged polyelectrolyte

The model of DNA charge inversion by Nguyen and Shklovskii [T. T. Nguyen and B. I. Shklovskii, Phys. Rev. Lett. 89, 018101 (2002)] is extended. A single double-helix strand of DNA is represented by a lattice of negative charges at the positions of the protruding oxygens of the phosphates along the DNA backbone, and the adsorbed polyelectrolyte molecules are represented by charged dimers. A lattice-gas model is used in which dimers adsorbing either parallel or perpendicular to the lattice are treated as separate species, and the model allows for vacancies between adsorbed species. The mean field theory used is formulated as a saddle-point approximation of the exact functional integral representation of the grand canonical partition function, opening the way for the inclusion of the effects of charge fluctuation corrections.

Distribution of electric and magnetic hyperfine fields in Fe-rich gallo-germanates

The crystal field disorder in some tetragonal and trigonal Ca-gallo-germanates, i.e., A2Fe2Z07 and A2LnFe3Ge3014 with A=Ba or Sr, Ln=La or Nd and Z=Ge or Si, has been studied by 57Fe Mossbauer spectroscopy. The observed distribution of the hyperfine fields is analysed from a theoretical model based on the additive perturbation approximation of crystal fields, a rigid lattice of ionic point charges and the random substitution of Fe3+/Z4+ and A2+/Ln3+.

Black holes and the spectrum of half-BPS states in $N=4$ supersymmetric string theory

The entropy of a half-BPS black hole in N=4 supersymmetric heterotic string compactification is independent of the details of the charge vector and is a function only of the norm of the charge vector calculated using the appropriate Lorenzian metric. Thus in order for this to agree with the degeneracy of the elementary string states, the latter must also be a function of the same invariant norm. We show that this is true for generic CHL compactifications to all orders in a power series expansion in the inverse charges, but there are exponentially suppressed corrections which do depend on the details of the charge vector. This is consistent with the hypothesis that the black hole entropy reproduces the degeneracy of elementary string states to all orders in a power series expansion in the inverse charges, and helps us extend the earlier conjectured relation between black hole entropy and degeneracy of elementary string states to generic half-BPS electrically charged states in generic N=4 supersymmetric heterotic string compactification. Using this result we can also relate the black hole entropy to the statistical entropy calculated using an ensemble of elementary string states that contains all BPS states along a fixed null line in the lattice of electric charges.

Large gauge transformations in M-theory

We cast M-brane interactions including intersecting membranes and five-branes in manifestly gauge invariant form using an arrangement of higher dimensional Dirac surfaces. We show that the noncommutative gauge symmetry present in the doubled M-theory formalism involving dual 3-form and 6-form gauge fields is preserved in a form quantised over the integers. The proper context for discussing large noncommutative gauge transformations is relative cohomology, in which the 3-form transformation parameters become exact when restricted to the five-brane worldvolume. We show how this structure yields the lattice of M-theory charges and gives rise to the conjectured 7D Hopf–Wess–Zumino term.

On fields and charges in M-theory.

We consider some topological aspects of world-volume and space-time gauge fields in M-theory. In particular charge lattices and brane tensions are discussed.

Electrostatic free energy of the DNA double helix in counterion condensation theory

Polyelectrolyte theory based on counterion condensation is extended from the standard line charge model to helical and double helical charge arrays. The number of condensed counterions turns out to be the same as for a line charge with charge density equal to the axial charge density of the helix. Also, the logarithmic salt dependence of the electrostatic free energy is the same in the range of lower salt concentration, so that the limiting laws remain unchanged. However, the internal free energy of the condensed layer of counterions and the overall electrostatic free energy depend on the helical parameters. At higher salt, the free energies of both single and double helix are negative, indicating electrostatic stabilization of the helical charge lattices due to the mixing entropy of the condensed counterions. Except at very low salt, the free energy of a single helix is higher than the free energy of a double helix with twice the charge density. With B-DNA parameters and single strands modeled as single helices, the predicted salt dependence of the free energy of transition from double helix to separated single strands has a maximum at approximately 0.2 M salt, close to the location in the laboratory of this well-known feature of the DNA strand separation transition. We also calculate the electrostatic free energy for the transition of the DNA double helix from the B to the A conformation. The B form is electrostatically stable over most of the salt range, but there is a spontaneous electrostatic transition to A near 1 M salt. The electrostatic free energy values are close to the experimental values of the overall (electrostatic plus non-electrostatic) transition free energies for A-philic base pair sequences. We are led to suggest that the experimentally observed B-to- A transition for A-philic sequences near 1 M salt in water is governed by the polyelectrolyte properties of these two conformations of the DNA double helix. The effect of ethanol, however, cannot be attributed to lowering of the bulk dielectric constant.

Model of Inversion of DNA Charge by a Positive Polymer: Fractionalization of the Polymer Charge

We model one strand of DNA by a one-dimensional lattice (ODL) of negative charges and consider the problem of inversion of its charge by a positive polyelectrolyte (PE). In the neutral state of the ODL-PE complex, each of the ODL charges is locally compensated by a PE charge. When an additional PE molecule is adsorbed by ODL, its charge gets fractionalized into monomer charges of defects (tails and arches) on the background of the perfectly neutralized ODL. Defects spread all over the ODL, eliminating the self-energy of PE. For DNA this fractionalization mechanism leads to a substantial inversion of charge, a phenomenon which is widely used for gene delivery.

Improved embedded molecular cluster model

AbstractWe demonstrate that boundary effects (i.e., displacements of the cluster boundary atoms from their lattice sites and the difference between effective charges of the perfect crystal atoms and those of the cluster atoms in the case of a cluster with no point defect in it) in an embedded molecular cluster (EMC) model can be radically reduced. A new embedding scheme is proposed. It includes search for the structural elements (SE) of which perfect crystal is composed, use of corresponding to these SE expression for the total energy, and application of the degree of localization of equations consistent with the wave functions of the cluster. To get equations for the cluster wave functions, the problem of varied subsystem in the field of the frozen remaining part of the whole electron system” is investigated in the framework of a one‐electron approximation. The consideration is general for every task of this type. Homogeneous equations resulting directly from variation of the total energy expression are obtained and transformed to the eigenvalue problem equations. Orthogonality constraints are not imposed during variation. A particular case of the equations describing mutually orthogonal one‐electron wave functions of the cluster staying nonorthogonal to those of the remaining crystal is found. A proposed embedding scheme is realized in the CLUSTER code based on the calculation scheme of the semiempirical INDO method. Boundary effects both in the standard (cluster in the field of the infinite lattice of nonpoint spherical charges) and new embedding scheme are investigated, calculating the clusters of LiF, MgO, NaCl, KCl, and AgCl crystals. Significant reduction of the boundary effects in the new embedding scheme is achieved. Reasons for the boundary effects are discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Counterion Condensation on a Helical Charge Lattice

We extend the theory of counterion condensation from the standard representation of a locally stiff rodlike polyion as a line of discrete charges to a helical lattice of charges. The number of counterions condensing on a helix with given axial charge density is the same as on a line of the same charge density, but the electrostatic free energy is substantially less for the helix than for the line. In fact, the free energy of assembling the helical charge lattice becomes negative at higher salt concentrations, indicating electrostatic stabilization of the helix due to the mixing entropy of condensed counterions. The electrostatic persistence lengths of the line and helix subjected to locally elastic thermal bending fluctuations differ only slightly. They have the same κ -2 dependence as the Odijk-Skolnick-Fixman persistence length but a different prefactor. It is commonly believed that elastic bending models for the persistence length are applicable to double-helical DNA, but we point out that DNA apparently has unique mechanical properties that do not conform to the elastic model of bending. On the other hand, the helical model and its subsequent generalization to a double helix will serve as a basis for the electrostatic free energy of DNA conformational transitions.

M-theory/heterotic duality: a Kaluza-Klein perspective

We study the duality relationship between M-theory and heterotic string theory at the classical level, emphasising the transformations between the Kaluza-Klein reductions of these two theories on the K3 and T 3 manifolds. Particular attention is devoted to the corresponding structures of σ-model cosets and the correspondence between the p-brane charge lattices. We also present simple and detailed derivations of the global symmetries and coset structures of the toroidally compactified heterotic theory in all dimensions D ⩾ 3, making use of the formalism of solvable Lie algebras.

Electronic structure of lithium tetraborate Li2B4O7 crystals. Cluster calculations and x-ray photoelectron spectroscopy

The results of an investigation of the electronic structure of lithium tetraborate crystals using experimental (x-ray photoelectron spectroscopy) and theoretical (quantum-chemical modeling) methods are reported. The experimental spectrum of the valence-band states of the crystal lies 2–15 eV below the Fermi level and is due primarily to boron-oxygen groups (B4O9). The quantum-chemical calculations were performed self-consistently, using the standard variant of the scattered-wave method in the model of a cluster embedded in a lattice of point charges. The data obtained on the partial contribution of the model densities to the one-electron spectrum of the [B4O9]6 cluster make it possible to interpret the fine structure of the experimental spectrum of the valence-band states.

A fast and simple method for calculating electrostatic potentials

A fast and simple method for calculating the electrostatic potential of an electrically neutral lattice of point charges has been developed. It is applicable to orthogonal and non-orthogonal unit cells with the rate of convergence independent of the degree of non-orthogonality. Results from the method has been compared to values obtained from the Ewald method with good agreement obtained for a number of structures including ZnS, CsCl, NaCl, CaF 2, Rutile and a general triclinic lattice.

Subpicosecond vibronic dynamics in KBrFcenters

Based on a symmetry analysis of recent results of femtosecond pump-probe optical-absorption experiments on KBr $F$ centers, we present a twofold theoretical analysis. The first part is concerned with a density-matrix calculation of the experimentally observed beating pattern of two modes of ${A}_{1g}$ symmetry in the sample transmission. This allows us to assign the observed frequencies to the breathing modes of the surrounding octahedron of cations in the electronic ground and excited state. The stiffening of the ${A}_{1g}$ mode in the unrelaxed excited state is consistent with simple arguments based on a lattice of point charges. In the second part, the observed ultrafast loss of initial orientation of the excited $p$ state is analyzed using a real-time integration of the wave function in the Hilbert space spanned by the vibrations of lower symmetries ${(E}_{1g}$ and ${T}_{2g})$ and the three degenerate $p$ states. The resulting reorientation of the $p$ state can be regarded as the transient analogue of the Jahn-Teller effect, and it turns out that the total wave function loses its initial orientation on a very fast time scale. This phenomenon is interpreted as a loss of coherence, so that the breathing mode oscillation becomes observable only if the pulse length is of the order of the so-defined coherence time of ${\ensuremath{\tau}}_{c}=12$ fs.

The polarizabilities of halide ions in crystals

The polarizabilities of the , and ions in their solid lithium and sodium salts in the four-coordinated B3 and eight-coordinated B2 phases are predicted from ab initio electronic structure computations. These results plus those for the experimentally observed B1 structures yield insights into the mechanisms by which the in-crystal environment modifies halide polarizabilities. The anion polarizability in each B2 phase having the cation - anion separation of the B1 structure is reduced compared with that in the B1 phase by the overlap with eight cation neighbours rather than six, these polarizabilities being essentially identical in the corresponding point charge lattices. The greater equilibrium cation - anion separation in the B2 compared with the B1 phase causes each halide polarizability at its to be greater in the B2 phase than in the B1 material. These B2 phase polarizabilities can be accurately predicted from the same function, which describes the dependence of the polarizability on for different salts having the B1 structure. This supplements previous evidence from the caesium halides that these anion polarizabilities are determined solely by , being insensitive to the precise disposition of the cation neighbours. The halide polarizabilities in the B3 phase are larger than those predicted by the above function describing the dependence of polarizability on . This phase thus differs from B1 or B2 materials, fluorite structured alkaline earth fluorides or in that the halide polarizabilities in the four latter are all essentially determined by through the same function. The halide polarizabilities in the B3 phase differ by exhibiting a specific structural dependence in addition to their variation. A new function describes the dependence of halide polarizabilities in the B3 phase.

The calculation of electrostatic potentials for periodic charge distributions

A method for obtaining the Coulomb energy of a lattice of charges is presented. The method is used here to find the Madelung constant of a number of crystals. The method is simpler than the Ewald summation method. It is based on the use of a basis set of lattices. Any lattice may be represented by a linear combination of these basis lattices.

Size-related stabilization of diamond nanoparticles

Abstract Boundaries of stability regions (of particles sizes) of diamond and graphite at low pressure and various temperatures have been established by modeling and computation of free energies of the crystal phases. The results indicate that diamond is the stable modification of carbon, and graphite is the metastable one at small particle sizes. The diamond charge lattice is presented by ion-electron lattice of negative bond charges and positive ions. The graphite charge lattice consists of hexagonal ion-electron nets and collectivized conduction electrons located between the nets. The consideration of conduction electrons in the graphite model provides the stable graphite structure, since the attraction between the conduction electrons and hexagonal nets compensates the repulsive forces acting between the nets. The intersection of size dependencies of free energies of diamond and graphite indicates the size-related stabilization of small diamond particles. The established boundaries of stability regions of diamond and graphite are: 10.2 nm at room temperature, 6.1 nm at 525 °C, 4.8 nm at 800 °C and 4.3 nm at 1100 °C.

Energetical preference of diamond nanoparticles.

The energetical advantage of diamond in comparison with graphite caused by small particle sizes is established by modeling and computation of free energy. The results, obtained for low external pressure, P\ensuremath{\simeq}0, and for temperatures up to 1100 \ifmmode^\circ\else\textdegree\fi{}C, indicate that diamond is the stable modification of carbon, and graphite is the metastable one at small particle sizes which are less than the boundary of stability regions of these phases. The models of crystal charge lattices have been determined to compute lattice energies by summation of pair interaction potentials acting between elements (ions, electrons) of the charge lattices. The diamond charge lattice is presented by an ion-electron lattice of negative bond charges and positive ions. The graphite charge lattice consists of hexagonal ion-electron nets and collectivized conduction electrons located between the nets. The consideration of conduction electrons in the graphite model provides the stable graphite structure because the attraction between the conduction electrons and hexagonal nets compensates for the repulsive forces acting between the nets. Mechanisms of the nucleation of diamond and graphite have been considered to determine the structure of clusters forming these phases. The considered mechanism of nucleation of diamond clusters consists in the forming of octagonal carbon clusters with the following transformation of the octagonal clusters to the ten-atomic-diamond clusters. The octagonal clusters consist of the same fragments of carbon atoms as the fragments forming the graphite nets. But the difference is that diamond crystals are generated from an octagon of atoms and the graphite clusters are formed from hexagons. The intersection of size dependences of free energies of diamond and graphite indicates the size-related stabilization of diamond nanoparticles. The established boundaries of the stability regions of diamond and graphite are 10.2 nm at room temperature, 6.1 nm at 525 \ifmmode^\circ\else\textdegree\fi{}C, 4.8 nm at 800 \ifmmode^\circ\else\textdegree\fi{}C, and 4.3 nm at 1100 \ifmmode^\circ\else\textdegree\fi{}C. \textcopyright{} 1996 The American Physical Society.

The coupling between ripplons and the motion of ion pools trapped beneath the surface of4 He

It is well known that the motion of positive or negative ions close to the surface of superfluid4 He can excite ripplons in the helium surface. We consider a simple toy model in which a lattice of point charges couples to the4 He surface via electrostatic forces. We calculate the coupled mode spectrum of this system and present detailed information on the mode splitting which occurs when the ripplons and the normal modes of the ion pool are degenerate. Such energy gaps should, we believe, be experimentally observable.

Surface stress of point charge lattices

An expression for the Coulomb component of the stress tensor of a point charge lattice cast in the Parry-Ewald formulation is given. Also, an expansion is presented of the surface potential for charges separated by a small out-of-plane distance compared with the periodicity length parallel to the surface. This latter formula is suitable for incorporation in molecular dynamics or Monte Carlo computer simulations of thin ionic films, such as Langmuir or Langmuir-Blodgett films.

Surface stress of point charge lattices

An expression for the Coulomb component of the stress tensor of a point charge lattice cast in the Parry-Ewald formulation is given. Also, an expansion is presented of the surface potential for charges separated by a small out-of-plane distance compared with the periodicity length parallel to the surface. This latter formula is suitable for incorporation in molecular dynamics or Monte Carlo computer simulations of thin ionic films, such as Langmuir or Langmuir-Blodgett films.