Electron-phonon interaction in single-wall carbon nanotubes: A time-domain study

We investigate the electron-phonon (e-ph) interaction in single-wall carbon nanotube samples at room temperature using femtosecond time-resolved photoemission. By probing electrons from the vicinity of the Fermi level we are able to study the e-ph interaction in the metallic nanotube species only. The observed electron dynamics can be used to calculate e-ph scattering matrix elements for two likely scattering scenarios: forward scattering from twistons and backscattering by longitudinal acoustic phonons. The corresponding matrix elements reveal an intrinsically weak e-ph interaction approximately 50% smaller than predicted by tight-binding calculations.     

A new wavelet multigrid method

The standard multigrid procedure performs poorly or may break down when used to solve certain problems, such as elliptic problems with discontinuous or highly oscillatory coefficients. The method discussed in this paper solves this problem by using a wavelet transform and Schur complements to obtain the necessary coarse grid, interpolation, and restriction operators. A factorized sparse approximate inverse is used to improve the efficiency of the resulting method. Numerical examples are presented to demonstrate the versatility of the method.     

Electric field assisted charge carrier photogeneration in poly(spirobifluorene-co-benzothiadiazole)

The dynamics of charge carrier generation in poly(spirobifluorene-co-benzothiadiazole) was investigated by electric field-induced fluorescence quenching and differential absorption measurements. Three different time domains of carrier generation have been identified: an ultrafast phase, a subnanosecond phase, and an entire lifetime phase. The charge generation efficiencies during the first and second phases were found to be almost independent of temperature, being about 25% and 10%, respectively, at an applied electric field of 1.3×10(6)?V/cm, while the generation efficiency during the third phase increases from 2% at 80 K to 10% at room temperature. The results of transient spectroscopy measurements and quantum chemical calculations suggest an intramolecular charge transfer for about 1 ps from the alkoxy-substituted fluorene side group to the benzothiadiazole subunit of the main chain. The formation and evolution of the resulting charge transfer states determine the way of charge carrier generation.     

Free-carrier generation in aggregates of single-wall carbon nanotubes by photoexcitation in the ultraviolet regime

We present evidence for the generation of free carriers in aggregated single-wall carbon nanotubes by photoexcitation in the energetic range of the π→π(*) transition associated with the M saddle point of the graphene lattice. The underlying broad absorption culminating at 4.3 eV can be fit well with a Fano line shape that describes strong coupling of a saddle-point exciton to an underlying free electron-hole pair continuum. Moreover, it is demonstrated that transitions in this energetic region autoionize into the continuum by detecting features unique to the presence of free charges in the transient transmission spectra of the continuum-embedded second sub-band exciton, S(2).     

Tiling Convex Polygons with Congruent Equilateral Triangles

We study the sets $\mathcal{T}_{v}=\{m \in\{1,2,\ldots\}: \mbox{there is a convex polygon in }\mathbb{R}^{2}\mbox{ that has }v\mbox{ vertices and can be tiled with $m$ congruent equilateral triangles}\}$ , v=3,4,5,6. $\mathcal{T}_{3}$ , $\mathcal{T}_{4}$ , and $\mathcal{T}_{6}$ can be quoted completely. The complement $\{1,2,\ldots\} \setminus\mathcal{T}_{5}$ of $\mathcal{T}_{5}$ turns out to be a subset of Euler’s numeri idonei. As a consequence, $\{1,2,\ldots\} \setminus\mathcal{T}_{5}$ can be characterized with up to two exceptions, and a complete characterization is given under the assumption of the Generalized Riemann Hypothesis.     

Approximate Euclidean Steiner Trees

An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error from \(120^{\circ }\). This notion arises in numerical approximations of minimum Steiner trees. We investigate the worst-case relative error of the length of an approximate Steiner tree compared to the shortest tree with the same topology. It has been conjectured that this relative error is at most linear in the maximum error at the angles, independent of the number of terminals. We verify this conjecture for the two-dimensional case as long as the maximum angle error is sufficiently small in terms of the number of terminals. In the two-dimensional case we derive a lower bound for the relative error in length. This bound is linear in terms of the maximum angle error when the angle error is sufficiently small in terms of the number of terminals. We find improved estimates of the relative error in length for larger values of the maximum angle error and calculate exact values in the plane for three and four terminals.     

Adsorption behavior of 4-methoxypyridine on gold nanoparticles

We demonstrate a phase transfer method to create stable colloidal solutions of Au nanoparticles with 4-methoxypyridine ligands. We then investigate the adsorption behavior of 4-methoxypyridine onto gold surfaces by Raman spectroscopy, DFT calculations, and (1)H NMR. In contrast to unsubstituted pyridine and the frequently used (N,N-dimethylamino)pyridine (DMAP), a flat adsorption of 4-methoxypyridine on gold was found.     

Ultrafast dynamics in the excited hydrogen atom transfer states of ammonia clusters

Neutral ammonia clusters (NH₃)_m are photo-excited to the electronic state by a deep UV femtosecond laser pump pulse. Within a few hundred femtoseconds a significant fraction of the clusters rearrange to form an H-transfer state (NH₃)_m-2NH₄(3s)NH₂ with the subunit NH₄ in its 3s electronic ground state. This state is then electronically excited by a time-delayed infrared control pulse of variable wavelength. Finally, a third (probe) pulse in the UV ionizes the clusters for detection. The lifetime of the excited (NH₃)_m-2NH₄(3p)NH₂ states is found to vary between 2.7 and 0.13 ps depending on cluster size and excitation energy. It increases drastically upon deuteration. The corresponding cluster size-dependent photoelectron spectra allow us to disentangle the underlying energetics of the excitation and ionization process and reveal additional processes, such as nonresonant ionization or dissociative ionization. The experimental findings suggest that the excited H-transfer ammonia complexes with m > 2 are deactivated by an internal conversion process back to the electronically lowest H-transfer state followed by fast dissociation. Received 22 September 2001 and Received in final form 31 January 2002