Showing papers on "Debye published in 2019"
159 citations
TL;DR: It is demonstrated that surface conductance generates a dynamical selectivity in ion transport, and this selectivity is controlled by so-called Dukhin, rather than Debye, overlap, suggesting the possibility of designing large-nanopore (10-100 nm), high-conductance membranes exhibiting significant ion selectivity.
Abstract: Traditionally, ion selectivity in nanopores and nanoporous membranes is understood to be a consequence of Debye overlap, in which the Debye screening length is comparable to the nanopore radius somewhere along the length of the nanopore(s). This criterion sets a significant limitation on the size of ion-selective nanopores, as the Debye length is on the order of 1-10 nm for typical ionic concentrations. However, the analytical results we present here demonstrate that surface conductance generates a dynamical selectivity in ion transport, and this selectivity is controlled by so-called Dukhin, rather than Debye, overlap. The Dukhin length, defined as the ratio of surface to bulk conductance, reaches values of hundreds of nanometers for typical surface charge densities and ionic concentrations, suggesting the possibility of designing large-nanopore (10-100 nm), high-conductance membranes exhibiting significant ion selectivity. Such membranes would have potentially dramatic implications for the efficiency of osmotic energy conversion and separation techniques. Furthermore, we demonstrate that this mechanism of dynamic selectivity leads ultimately to the rectification of ionic current, rationalizing previous studies, showing that Debye overlap is not a necessary condition for the occurrence of rectifying behavior in nanopores.
57 citations
TL;DR: In this paper, the SUSYQM method was used to solve the N-radial Schrodinger equation for heavy quarkonia in hot and dense media and the binding energy was analyzed.
Abstract: The N-radial Schrodinger equation is analytically solved by using the SUSYQM method, in which the heavy-quarkonia potential is introduced at finite temperature and baryon chemical potential. The energy eigenvalue is calculated in the N-dimensional space. The obtained results show that the binding energy strongly decreases with increasing temperature and is slightly sensitive for changing baryon chemical potential up to 0.6GeV at higher values of temperatures. We employed the nonperturbative corrections to the leading-order of the Debye mass at finite baryon chemical potential. We found that the binding energy is more dissociated when the nonperturbative corrections are included with the leading-order term of the Debye mass in both hot and dense media. A comparison with other works, such as the lattice parameterized of the Debye mass is discussed; thus, the present potential with the SUSYQM method provides satisfying results for the description of the dissociation of binding energy for heavy quarkonia in hot and dense media.
35 citations
16 Aug 2019
TL;DR: In this paper, the authors proposed an explanation for the linear dependence of the heat capacity with temperature in glasses, based on hydrodynamic quasi-localized diffusive modes, which is able to capture this feature at low temperature and the crossover to the Debye scaling.
Abstract: This paper proposes an explanation for the linear dependence of the heat capacity with temperature in glasses, based on hydrodynamic quasi-localized diffusive modes -- the diffusons. This framework is able to capture this feature at low temperature and the crossover to the Debye scaling, and it appears in agreement with the results from random matrix theory
30 citations
TL;DR: In this article, a drift-diffusion model that accounts for both charge transport and ion vacancy motion in perovskite solar cells has been proposed and compared with numerical solutions for a realistic cell over a wide range of operating conditions of practical interest.
Abstract: Increasing evidence suggests that the presence of mobile ions in perovskite solar cells (PSCs) can cause a current–voltage curve hysteresis. Steady state and transient current–voltage characteristics of a planar metal halide CH 3 NH 3 PbI 3 PSC are analysed with a drift-diffusion model that accounts for both charge transport and ion vacancy motion. The high ion vacancy density within the perovskite layer gives rise to narrow Debye layers (typical width ~2 nm), adjacent to the interfaces with the transport layers, over which large drops in the electric potential occur and in which significant charge is stored. Large disparities between (I) the width of the Debye layers and that of the perovskite layer (~600 nm) and (II) the ion vacancy density and the charge carrier densities motivate an asymptotic approach to solving the model, while the stiffness of the equations renders standard solution methods unreliable. We derive a simplified surface polarisation model in which the slow ion dynamics are replaced by interfacial (non-linear) capacitances at the perovskite interfaces. Favourable comparison is made between the results of the asymptotic approach and numerical solutions for a realistic cell over a wide range of operating conditions of practical interest.
27 citations
TL;DR: In this paper, a series of structural isomers of phenyl-1-propanol in comparison with 1-Propanol was studied and it was shown that the Debye relaxation becomes weaker the closer the position of the phenyl ring is to the hydroxy group, in accordance with the analysis of the Kirkwood/Frohlich correlation factor.
Abstract: Relaxation behavior of monohydroxy alcohols (monoalcohols) in broadband dielectric spectroscopy (BDS) is usually dominated by the Debye process. This process is regarded as a signature of the dynamics of transient supramolecular structures formed by H-bonding. In phenyl-propanols, the steric hindrance of the phenyl ring is assumed to influence chain formation and thereby to decrease or even suppress the intensity of the Debye process. In the present paper, we study this effect in a systematic series of structural isomers of phenyl-1-propanol in comparison with 1-propanol. It turns out that by combining BDS, photon correlation spectroscopy (PCS), and calorimetry, the dynamics of supramolecular structures can be uncovered. While light scattering spectra show the same spectral shape of the main relaxation for all investigated monoalcohols, the dielectric spectra differ in the Debye contribution. Thus, it becomes possible for the first time to unambiguously disentangle both relaxation modes in the dielectric spectra. It turns out that the Debye relaxation becomes weaker, the closer the position of the phenyl ring is to the hydroxy group, in accordance with the analysis of the Kirkwood/Frohlich correlation factor. Even in 1-phenyl-1-propanol, which has the phenyl group attached at the closest position to the hydroxy group, we can separate a Debye contribution in the dielectric spectrum. From this, we conclude that structure formation through hydrogen bonds is not generally suppressed by the increased steric hindrance of the phenyl ring, but rather an equilibrium of ring and chain-like structures is shifted toward ring-like shapes on shifting the phenyl ring closer to the hydroxy group. Moreover, the shape of the α-relaxation, as monitored by PCS, is the same as the self-part of the correlation in BDS, remains unaffected by the degree of hydrogen bonding and is the same among the investigated alcohols.
25 citations
TL;DR: In this paper, the effect of multi-doping in A and B site of the multiferroic prepared by the Sol-gel method Bi0.8Er0.1Ba 0.1Fe 0.96Co0.02O3 (BEBFCC) on the structural, morphological and electric properties was investigated.
23 citations
TL;DR: In this paper, the authors apply fluctuating hydrodynamics to strong electrolyte mixtures to compute the concentration corrections for chemical potential, diffusivity, and conductivity, in agreement with the limiting laws of Debye, Huckel, and Onsager.
22 citations
TL;DR: In this article, it was shown that the Debye length formulation for plasmas described by kappa distributions depends on the polytropic index, rather than the parameter that labels and governs these distributions, the kappa index.
Abstract: It is shown that the Debye length formulation, for plasmas described by kappa distributions, depends on the polytropic index, rather than the parameter that labels and governs these distributions, the kappa index—in contrast to what it was previously derived. As a consequence, the ratio of the Debye length over the plasma oscillation period gives exactly the sound speed, instead of being proportional to the thermal speed; this ratio is generalized to the fast magnetosonic speed when the magnetic Debye length is considered, leading also to the development of the vector Debye length. Finally, as an application, we derive the Debye length values for the solar wind plasma near 1 AU, exhibiting clear distinction between slow and fast wind modes, while we provide insights into the connection between plasma and polytropic processes.
22 citations
TL;DR: In this article, the effect of roughness on the diffracted intensities was analyzed and two different limits to the application of the DWF were found depending on whether the roughness is normally distributed or not.
Abstract: Periodic nanostructures are fundamental elements in optical instrumentation as well as basis structures in integrated electronic circuits. Decreasing sizes and increasing complexity of nanostructures have made roughness a limiting parameter to the performance. Grazing-incidence small-angle X-ray scattering is a characterization method that is sensitive to three-dimensional structures and their imperfections. To quantify line-edge roughness, a Debye-Waller factor (DWF), which is derived for binary gratings, is usually used. In this work, we systematically analyze the effect of roughness on the diffracted intensities. Two different limits to the application of the DWF are found depending on whether the roughness is normally distributed or not.
20 citations
TL;DR: In this paper, the defect-mediated, abnormal non-linear polarization behavior observed in centrosymmetric rutile TiO2 where less than 1 at% of sterically mismatched Mg2+ ions are introduced to create ferroelectric-like polarization hysteresis loops.
Abstract: In this work, we report the defect-mediated, abnormal non-linear polarization behavior observed in centrosymmetric rutile TiO2 where less than 1 at% of sterically mismatched Mg2+ ions are introduced to create ferroelectric-like polarization hysteresis loops. It is found that the defect cluster produces a dipole moment exceeding 6 Debye, with a rotatable component. Such a polarization is further enhanced by the displacement of neighboring Ti4+ ions. The coupling between such defect-driven symmetry-breaking regions generates a collective nonlinear electrical polarization state that persists to high temperatures. More importantly, an observation of abnormal bias shift of polarization hysteresis suggests an antiparallel alignment of certain dipoles frozen relative to the external poling electric field, which is associated with oxygen vacancy hopping. This result challenges the long-standing notion of parallel alignment of dipoles with the external electric field in ferroelectrics. This work also reveals an unexpected new form of non-linear dielectric polarization (non-ferroelectricity) in solid-state materials.
TL;DR: In this article, the scaling exponents and the form of the distribution function close to a nonthermal fixed point were derived from parametric estimates within kinetic theory indicating the dominance of small momentum transfer in the scattering processes.
Abstract: Motivated by the boost-invariant Glasma state in the initial stages in heavy-ion collisions, we perform classical-statistical simulations of SU(2) gauge theory in $2+1$ dimensional space-time both with and without a scalar field in the adjoint representation. We show that irrespective of the details of the initial condition, the far-from-equilibrium evolution of these highly occupied systems approaches a unique universal attractor at high momenta that is the same for the gauge and scalar sectors. We extract the scaling exponents and the form of the distribution function close to this nonthermal fixed point. We find that the dynamics are governed by an energy cascade to higher momenta with scaling exponents $\ensuremath{\alpha}=3\ensuremath{\beta}$ and $\ensuremath{\beta}=\ensuremath{-}1/5$. We argue that these values can be obtained from parametric estimates within kinetic theory indicating the dominance of small momentum transfer in the scattering processes. We also extract the Debye mass nonperturbatively from a longitudinally polarized correlator and observe an IR enhancement of the scalar correlation function for low momenta below the Debye mass.
TL;DR: In this paper, the dynamical structure factor of strongly coupled Yukawa liquids (SCYLs) has been reported through state-of-the-art equilibrium molecular dynamics simulations in a microcanonical ensemble (NVE).
Abstract: The dynamical structure factor has been reported for three dimensional strongly coupled Yukawa liquids (SCYLs) through state-of-the-art equilibrium molecular dynamics (EMD) simulations in a microcanonical ensemble (NVE). The effects of varying wave vectors (k = 2π/L) have been computed along with different arrangements of Coulomb coupling (Γ) and the Debye screening parameter (κ) on the dynamical structure-factor S(k,ω) using EMD simulations. Our new investigations of S(k,ω) show that the amplitude of oscillation decreases and the frequency increases with increasing Γ, respectively, for the SCYLs. Our simulations show that the decreasing behavior is noted for the frequency of plasma S(k,ω) with increasing κ and system size (N). The obtained EMD results are found to be more efficient and accurate than that of various previous simulation data, and the present EMD approach gives more satisfactory results with appropriate system sizes at high values of k, for a wide range of plasma states (Γ, κ). It has been shown that the present density S(k,ω) of SCYLs fluctuates more at intermediate to high Coulomb couplings (average to lower system temperature ≡ 1/Γ) and low values of Debye screening; however, it less fluctuates at higher N and κ.
TL;DR: In this article, a high-order accurate solver based on the generalized Debye source representation of time-harmonic electromagnetic fields is presented. But this solver uses a Nystrom discretization of a one-dimensional generating curve and high order integral equation methods for applying and inverting surface differentials.
TL;DR: In this article, the electrostatic Debye screening and wakefield potentials in a positively charged dusty plasma were investigated using a modified dielectric constant of the dust-acoustic waves to account for the beam electrons and protons from solar wind.
Abstract: The electrostatic Debye screening and wakefield potentials caused by a test charge are investigated in a positively charged dusty plasma. A modified dielectric constant of the dust-acoustic waves to account for the beam electrons and protons from solar wind is employed and analyzed the electrostatic potentials both analytically and numerically. This model is essentially applied to Jupiter's magnetosphere that contains positively charged dust grains, Maxwellian electrons and ions, as well as solar wind streaming electrons and protons. The normalized Debye potential decreases exponentially by variation of axial distance while the normalized wakefield potential is strongly influenced by the plasma temperatures and streaming speeds of solar wind electrons and protons.
TL;DR: In this paper, the authors designed four acceptor materials for small solar cell molecules with Naphthalene Di-Imide central unit by employing the wB97xd/6-31 G (d,p) and TD-wB97d/6 -31 G level of density functional theories.
Abstract: Herein current research work, we designed four new acceptor materials for small solar cell molecules with Naphthalene Di-Imide central unit by employing the wB97xd/6-31 G (d,p) and TD-wB97xd/6-31 G (d,p) level of density functional theories. Absorption properties of designed materials are excellent between the 400 nm to 510 nm with chloroform solvent and 340 nm to 490 nm in gas phase, small reorganization energy values 0.0163–0.0172 eV for electron (λe) and 0.0205–0.0257 eV for hole transfer (λh), large expected open circuit voltages (Voc) from 3.60 to 4.53 eV with respect to [6, 6]-phenyl-C61-butyric acid methyl ester (PCBM), high dipole moment strength ranging from 4.0199 to 8.9647 Debye in excited state and 3.3847 Debye to 7.2632 Debye in ground state which are very helpful for the further construction of organic solar cell (OSC) devices with improved and better power conversion efficiencies (PCEs).
17 Apr 2019
TL;DR: In this paper, the Schrodinger equation involving a fractal time derivative is solved and corresponding eigenvalues and eigenfunctions are given for fractal spaces with fractional dimension.
Abstract: In this paper, the Schrodinger equation involving a fractal time derivative is solved and corresponding eigenvalues and eigenfunctions are given. A partition function for fractal eigenvalues is defined. For generalizing thermodynamics, fractal temperature is considered, and adapted equations are defined. As an application, we present fractal Dulong-Petit, Debye, and Einstein solid models and corresponding fractal heat capacity. Furthermore, the density of states for fractal spaces with fractional dimension is obtained. Graphs and examples are given to show details.
TL;DR: In this paper, a two-layered model is investigated through its equivalent Debye circuit model, and the derived formulas are used to analyze the relationship between the effective electrical spectra and the electrical parameters of each layer.
Abstract: Debye formulas are widely used to describe the electrical dispersion characteristics of a uniform lossy material. Debye model uses some empirical coefficients to control the shape and position of spectroscopy curves. It can fit most of the data from experiments. A two-layered model is investigated through its equivalent Debye circuit model. A Finite Difference Method (FDM) is developed to extract the effective permittivity and conductivity of a two-layered model as the verification of the analytical derivation. The computation results indicate the results obtained from FDM and the layered Debye formulas agree very well, which shows the validity of the layered Debye formulas in terms of the original circuit parameters. The derived formulas are used to analyze the relationship between the effective electrical spectra and the electrical parameters of each layer. A few examples are given in the discussions. And it can be concluded that: (1) with the increase of the average value of the conductivity of the two layers, the spectra of effective permittivity transition area shifts to higher frequencies; while the spectra of effective conductivity transition kept the same with the values decrease; (2) with the increase of the average value of the relative permittivity of the two layers, the transition area of the spectra of effective permittivity kept the same with values increase; and the transition area of the spectra of effective conductivity shifts to the lower frequencies; (3) the effective permittivity enhances at the lower frequency region as the ratio between the conductivity of two layers increase.
TL;DR: In this article, the authors derived analytic expressions for the velocity dependence of the photon wind in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed.
Abstract: The anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force $v B(v, T, \rho)$ on the dislocation. In early studies the drag coefficient $B$ was computed and experimentally determined only for dislocation velocities $v$ much less than transverse sound speed, $c_t$. In this paper we derive analytic expressions for the velocity dependence of $B$ up to $c_t$ in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to $B$ in the range 1%-90% $c_t$ for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as $v \rightarrow c_t$, whereas $B$ is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements.
TL;DR: The particle polarIZability is calculated from first principles for arbitrary thickness of the Debye layers in liquid and semiconductor and it is shown that the polarizability dispersion arises from the combination of two relaxation interfacial phenomena: charging of the electrical double layer and the Maxwell–Wagner relaxation.
Abstract: We study theoretically the dielectrophoresis and electrorotation of a semiconducting microsphere immersed in an aqueous electrolyte. To this end, the particle polarizability is calculated from first principles for arbitrary thickness of the Debye layers in liquid and semiconductor. We show that the polarizability dispersion arises from the combination of two relaxation interfacial phenomena: charging of the electrical double layer and the Maxwell–Wagner relaxation. We also calculate the particle polarizability in the limit of thin electrical double layers, which greatly simplifies the analytical calculations. Finally, we show the model predictions for two relevant materials (ZnO and doped silicon) and discuss the limits of validity of the thin double layer approximation.
TL;DR: In this paper, an analysis of more than one hundred large-amplitude bipolar electrostatic structures in a quasi-perpendicular supercritical Earth's bow shock crossing, measured by the Magnetospheric multiscale spacecraft, is presented.
Abstract: We present analysis of more than one hundred large-amplitude bipolar electrostatic structures in a quasi-perpendicular supercritical Earth's bow shock crossing, measured by the Magnetospheric Multiscale spacecraft. The occurrence of the bipolar structures is shown to be tightly correlated with magnetic field gradients in the shock transition region. The bipolar structures have negative electrostatic potentials and spatial scales of a few Debye lengths. The bipolar structures propagate highly oblique to the shock normal with velocities (in the plasma rest frame) of the order of the ion-acoustic velocity. We argue that the bipolar structures are ion phase space holes produced by the two-stream instability between incoming and reflected ions. This is the first identification of the ion two-stream instability in collisionless shocks. The implications for electron acceleration are discussed.
TL;DR: In this paper, a tensor expression for the Breit-Pauli Hamiltonian is proposed for the atomic structure under external confinement, where the Racah wave functions are expanded in terms of the linear combinations of the multi-Slater wave functions.
Abstract: An accurate theoretical expression is proposed for the atomic structure under external confinement. The analysis is based on the tensor expression for the Breit-Pauli Hamiltonian in which the Racah wave functions are expanded in terms of the linear combinations of the multi-Slater wave functions. The variables are separated into radial and angular parts, where the variational parameters in the trial wave functions are obtained by solving the radial Schrodinger equation and the expressions of the angular part are worked out using an irreducible theory of complex system. Relativistic corrections are derived directly, which are treated as a sum of five terms: mass correction, one-body Darwin correction, two-body Darwin correction, spin-spin contact interaction correction, and orbit-orbit interaction correction. Energies and radiative decay rates of Be-like Fe22+ and Kr32+ ions in the presence of two kinds of plasma environments are presented for demonstration purposes, one is the Debye plasma which is described by a standard Debye-Huckel potential and the other is the quantum plasma which is treated under an exponential cosine screened Coulomb potential. Independent self-consistent calculations within the fully relativistic frame by incorporating the above two potentials are also performed using the Flexible Atomic Code to verify the validity of the proposed expressions. Results are given over a wide range of screening lengths. Relativistic effects in energy spectra are studied for the first time and are found to be rather important, especially in the high-Z system. Comparisons between our two sets of results and other theoretical predictions when available are made. Some behavior of the respective properties with respect to the plasma shielding strength is discussed. The present study should be beneficial for the analysis of spectra in astrophysical and fusion plasmas.
TL;DR: In this paper, a many-body approach to the behavior of exciton bound states and the conduction electron band edge in a surrounding electron-hole plasma with a focus on the absorption spectrum of Rydberg excitons in cuprous oxide was developed.
Abstract: We develop a many-body approach to the behavior of exciton bound states and the conduction electron band edge in a surrounding electron-hole plasma with a focus on the absorption spectrum of Rydberg excitons in cuprous oxide. The interplay of band edge and exciton levels is analyzed numerically, whereby the self-consistent solution is compared to the semiclassical Debye approximation. Our results provide criteria which allow to verify or rule out the different band edge models against future experimental data.
TL;DR: In this paper, measurements of the low-temperature heat capacity performed for polycrystalline Tb1-xDyxNi2 intermetallic compounds with x = 0.25, 0.5 and 0.75 enable us to determine their Debye temperatures and estimate the lattice, electron and magnetic contributions to the heat capacity.
TL;DR: In this paper, the structural, electronic, elastic, thermodynamic, and thermoelectric properties of ternary XHfGe (X = Ni and Pd) Half-Heusler alloys were investigated using the full potential linearized augmented plane wave (FP-LAPW) method to the density functional theory (DFT) as part of the Generalized Gradient Approximation (GGA).
TL;DR: The enhancement of conductivity of a composite polymer as a dielectric material is an essential requirement for electrostatic storage devices as discussed by the authors, where the microstructure of the polymer mat has been modified.
Abstract: The enhancement of conductivity of a composite polymer as a dielectric material is an essential requirement for electrostatic storage devices. We have modified the microstructure of the polymer mat...
TL;DR: In this article, a generalized anharmonic correlated Einstein model (GACEM) was proposed for all material structures including complex systems and separated for each structure by its anharmonics effective potential parameters contained in the derived analytical expressions of three first EXAFS cumulants and thermal coefficient.
TL;DR: DebyeFit as mentioned in this paper is a simple tool to calculate the Debye or Einstein characteristic temperature of thermal vibrations in crystals from the equivalent atomic displacement parameters (ADPs) of any atom obtained at several temperatures.
Abstract: DebyeFit is a simple tool to calculate the Debye or Einstein characteristic temperature of thermal vibrations in crystals from the equivalent atomic displacement parameters (ADPs) of any atom obtained at several temperatures. The ADP values are separated into static and dynamic components to get a best fit to the Debye, Einstein or mixed model. The static term is added to account for possible static disorder. A nonlinear least-squares technique is used to refine the parameters of the model for sets of ADPs observed in multi-temperature structural studies. The program provides a good fit between theoretical and observed ADP values.
TL;DR: The notion that the transiently bound chain structures lead to a strong cross-correlation contribution in macroscopic dielectric experiments, to which both light scattering and TSD are insensitive, is supported due to its local character and the former due to the molecular optical anisotropy being largely independent of the OH bonded suprastructures.
Abstract: The dielectric Debye relaxation in monohydroxy alcohols has been subject of long-standing scientific interest and is presently believed to arise from the relaxation of transiently H-bonded supramolecular structures. Therefore, its manifestation in a measurement with a local dielectric probe might be expected to be different from the standard macroscopic dielectric experiment. In this work we present such local dielectric measurements obtained by triplet state solvation dynamics (TSD) and compare the results with macroscopic dielectric and light scattering data. In particular, with data from an improved TSD setup, a detailed quantitative comparison reveals that the Debye process does not significantly contribute to the local Stokes shift response function, while α- and β-relaxations are clearly resolved. Furthermore, this comparison reveals that the structural relaxation has almost identical time constants and shape parameters in all three measurement techniques. Altogether our findings support the notion that the transiently bound chain structures lead to a strong cross-correlation contribution in macroscopic dielectric experiments, to which both light scattering and TSD are insensitive, the latter due to its local character and the former due to the molecular optical anisotropy being largely independent of the OH bonded suprastructures.
TL;DR: In this article, the inversion barriers of curved aromatics (cPAH) 0.9-1.2nm in diameter are found to be persistently polar at flame temperatures.