Photoinduced Electron Transfer From Carbazole to Halomethanes in a Gas Phase

Intermolecular photoinduced electron transfer (PET) in a gas phase was studied using carbazole vapor fluorescence quenching by halomethanes (CHCl₃, CH₂Br₂, CCl₄, CHBr₃). The fluorescence quenching rate constants k _q changing from 2.3·10⁵ sec^–1·torr^–1 in mixtures with CHCl₃ to 4.6·10⁶ sec^–1·torr^–1 in mixtures with CHBr₃ at a constant temperature of 403 K were estimated. The dependence of the carbazole fluorescence decay rates in the presence of halomethanes on the free energy change G during transfer of the electron from carbazole to halomethanes is considered. It is suggested to take into account the influence of the vibrational energy of the carbazole molecule E _vib and its temperature changes in estimation of the G values. The differences between PET in the gas and liquid phases were analyzed. It is found that for mixtures with CCl₄ and CHBr₃ the negative temperature dependence of k _q is observed, when the decay rates and efficiencies of the intermolecular PET decreased with temperature increase in the range 403–573 K, i.e. these mixtures the electron transfer is not a barrier-restricted process.     

Temperature Dependence of the Triplet–Triplet Energy Transfer Efficiencies in Carbonyl Vapors

The temperature dependences of the rate constants k _TT and the efficiencies _DA of triplet–triplet transfer of the energy of electronic excitation in a gas phase for a number of donor–acceptor pairs (benzophenone–diacetyl, anthraquinone–diacetyl, carbazole–diacetyl, and naphthalene–diacetyl) were studied. It is shown that for gas phase systems the k _TT and _DA constants can both increase and decrease with increase in the temperature over the range 360–510 K. To explain the temperature changes of the k _TT values, the experimental rate constants were compared with those calculated by a classical model (Marcus' equation). In the temperature range under study, the influence of the average vibrational energy <E _vib> of the donor and acceptor molecules was taken into account to estimate the free energy change G, which varied from 0.4 to –1.2 eV. It is established that the increase in k _TT with temperature for certain gas-phase systems and decrease for others represent the typical, for a gas-phase system, transition from a normal region (increase in k _TT) to an inverted one (decrease in k _TT) with monotonic variation of G, including the temperature increase of <E _vib> of the molecules.     

Degradation in gain for a free electron laser amplifier due to electron momentum spread

A finite spread in axial momentum for the electron beam in a free electron laser amplifier is shown to decrease the small-signal gain. For millimeter and sub-millimeter wave amplifiers, where exponential growth dominates the gain, it is shown that the gain is approximately 3 db below that for a cold beam if the relative momentum spread (u/u)_1/2 = (G_o/248)^1/2 (_o/L), where G_o1 is the gain in db for the cold-beam case, _o is the magnetic wiggler period, and L is the amplifier length. Exact numerical examples are given for representative FEL amplifiers at 35 and 550 GHz.This research was sponsored by the U.S. Office of Naval Research, and by the U.S.-Israel Binational Science Foundation.     

Excited States of Magnesium Complexes of Porphin and Bacteriochlorin

Quantum-chemical calculations of magnesium complexes of porphin (D _4h , C _4v ) and bacteriochlorin (D _2h , C _2v ) have been carried out for three variants of Mg parameters used in the CNDO/S method. It is shown that the Mg parameters and z _Mg weakly influence the results of the calculations of these complexes in the excited S _i states localized on the macrocycles in contrast to the calculations for the S _i ^CT states. The G S _i ^CT transitions are transitions with intramolecular electron transfer (CT) from the macrocycles to Mg. The energies of the S _i ^CT states can be close to the energies of the B levels and differ by a value from 1600 to 6400 cm^–1 depending on the Mg parameters. A displacement of Mg (z _Mg) 0) from the midplane of the macrocycles and hydrogenation of the pyrrole rings decrease the energies of the lower G S _i ^CT transitions and enhance their CT character.     

Symmetry properties of nonlinear barrier coefficients

This paper concerns the properties of a symmetric barrier between two reservoirs. The barrier can passK conserved quantities. The current of theith quantity is assumed to satisfy the nonlinear relationJ _i=A _ijj+B_ijkljkl where the _i's are the affinity differences across the barrier andA _ij andB _ijkl are functions of the average affinities of the reserviors. It is shown thatB _ijkl is symmetric in all indices.     

Activation energy for elastic interaction between Frank dislocation loops and glide dislocations in f.c.c. Metals

The activation energyG for the thermally activated passing of glide dislocations close to Frank dislocation loops which do not intersect the slip planes is calculated by means of the linear theory of elasticity as a function of the applied stress, of the distances loop centre-slip plane, and of the orientations and radii of the loops. The influence of anisotropy onG is investigated for some f.c.c. metals, especially for copper. For sufficiently high stresses the dependence ofG on stress is shown to approach theG-stress expression suggested by Seeger in his theory of radiation hardening.On leave fromFaculty of Mathematics and Physics, Charles University, Praha, Ke Karlovu 5, Czechoslovakia.     

Spectral duality for planar billiards

For a bounded open domain with connected complement inR ² and piecewise smooth boundary, we consider the Dirichlet Laplacian- on and the S-matrix on the complement ^c . We show that the on-shell S-matricesS _k have eigenvalues converging to 1 askk ₀ exactly when-- has an eigenvalue at energyk ₀ ² . This includes multiplicities, and proves a weak form of transparency atk=k ₀. We also show that stronger forms of transparency, such asS _{k 0} having an eigenvalue 1 are not expected to hold in general.     

Influence of gravity on surface melting

A chemical network system for use in the study of reaction cascades is described by the nonlinear rate equation , in which (x) is derived from the –G/x of Taylor's expansion of the order parameterx of the thermodynamic potential, Gibbs' functionG(T,P,x), at about the critical pointC(T _C ,P _C ) of the control variables (parameters)T andP. The behavior of the system around the stable pointx=0 is analyzed only with the sign ofk ₁(T, P), becausek ₂(T, P) is always positive. The system is not closed and is affected by physical and chemical changes in the neighbor systems. WhenT andP fluctuate ( ) through the changes andk ₁ passes zero, the system in the steady state becomes instable andk ₁ jumps at the reaction threshold. Then, the products are formed at the number of moleculesx=(|k ₁|/k ₂)^1/2. To describe such a transition,k ₁ giving theG curvature atx=0 is represented phenomenologically by an approximate function, tanh(G/RT), for a metastable state with a relatively smallk ₁(>0). The reaction takes place in a cascade in accordance with a cubic state equation obtained from tanh(G/RT), which describes a jump of the reaction energy G at the reaction threshold.     

Radiative and Nonradiative Deactivation of the 1Δ g State of Molecular Oxygen in Solutions of Saturated Hydrocarbons

The luminescence of singlet molecular oxygen (¹ _g or ¹O₂) caused by the ¹ _g ³ _g ^– transition in liquid saturated hydrocarbons from n-hexane to n-undecane is investigated. A model of quenching of the ¹ _g state of the oxygen molecule by the CH oscillations of the molecules of solvents is proposed, in which the rate constant of the nonradiative deactivation (k _nr) depends strongly on the average distance between the ¹O₂ and CH groups of the solvent. This experimental dependence can adequately be described by an exponential function with the distance parameter R ₀ = 0.15 , which indicates that the acceleration of quenching with the solvent density is a result of larger overlapping of the electron orbitals of oxygen and the CH groups. The detected increase in k _nr with temperature can also be explained qualitatively well within the framework of the model suggested. It is shown that the radiative rate constant (k _r of the ¹ _g ³ _g ^– transition does not depend on the distance between the ¹O₂ and CH groups and its change in a number of hydrocarbons is related to macroscopic parameters, in particular, the polarizability of the solvent.     

Image-potential surface states on Ag(100): A reinvestigation

Employing inverse photoemission we have remeasured the energy dispersionE(k) of the lowest-lying image state on Ag(100) with improved energy resolution (electrons and photons, E=0.35 eV) andk-resolution (k<0.1 Å^–1). In a least-square fit with the binding energyE _B atk=0 and the effective massm ^* as parameters we obtainE _B =E _vac –0.67 eV andm ^*=1.5 m in agreement with our earlier findings but differing from the two-photon photoemission values (0.53 eV and 1.15 m).     

Tunneling conductance of a Bi2Sr2CaCu2O8-SnO2 junction along the c-axis

fine structure was observed in the conductance curve of a tunneling junction composed of a single crystalline Bi2212 and an evaporated SnO₂ film. It is similar to those of Bi2212-GaAs mechanical junctions and there is a certain correspondence between the structure and the phonon density of states. Thus the previous conclusion that the structure is due to phonons has been complemented by this work. The energy gap 2 was 57 meV at 13 K and T _c was 78 K. 2(0)/k _B T _c is then 8.3. (T) showed the BCS-like temperature dependence.     

Commuting Operators and Separation of Variables for Laplacians of Projectively Equivalent Metrics

Let two Riemannian metrics g and g on one manifold M ⁿ have the same geodesics (considered as unparameterized curves). Then we can construct invariantly n commuting differential operators of second order. The Laplacian _g of the metric g is one of these operators. For any x M ⁿ , consider the linear transformation G of T _x M ⁿ given by the tensor g ^Ig_j . If all eigenvalues of G are different at one point of the manifold then they are different at almost every point; the operators are linearly independent and their symbols are functionally independent. If all eigenvalues of G are different at each point of a closed manifold then it can be covered by the n-torus and we can globally separate the variables in the equation _g f = f on this torus.     

Energy gaps and phonon structures in tunneling spectra of Bi2Sr2Ca1Cu2O8+x and Bi2Sr2Ca2Cu3O10+y superconductors

Polycrystalline Bi-2212 or Bi-2223 systems and single crystals of the Bi-2212 system were investigated at several temperatures by means of the break-junction and point-contact tunneling techniques, respectively. In the case of Bi-2223 we obtained an averaged gap value 2=65±4 meV. The Bi-2212 system yields 2= 45±5 meV in the case of polycrystalline samples and 2=47±5 meV in the case of single crystals. Hence there result BCS-ratios 2/k _B T _c of 7.3, 6.8 and 6.5, respectively. A dc-Josephson-type supercurrent could be observed in polycrystalline Bi-2212 samples in addition to the usual gap structure. The point-contact tunneling spectra of Bi-2212 single crystals exhibit structures in the second derivative d² I/d V ² which we interpret as inelastic tunneling processes due to electron-phonon scattering most likely in the barrier region. The phonon energies deduced from these structures are in accordance with data obtained from inelastic neutron scattering and Raman spectroscopy. Good agreement is obtained with a lattice dynamical calculation of the partial phonon densities of states of individual atoms in the unit cell.     

Dependency of control parameters on a rate coefficient giving the potential curvature in a reaction cascade model

Many chemical reactions in vivo are self-controlled by fluxes of chemical energy and matter through biological systems, so the induction of such reactions can be governed by changes in the control parameters of the rate equation. A potential of a system is assumed to be given by Gibbs' functionG(T, P, x), which is continuously differentiable, and the rate equation can be derived from the differential (–G/x) of Taylor's expansion ofG _(T,P)(x) for the order parameterx, which corresponds to the product number, at around the critical pointC(T _C, P_C). The equation is described bydx/dt=(x)–k₁x–k₂x³, andk ₂>0. In this equation,k ₁ andk ₂ are functions of the control parameters, temperatureT and pressureP, andk ₁ is allowed to have a positive or negative values as (T, P). Thenk ₁ is an important factor that decides the induction conditions of the reactions with a phase transition in the steady statex=0. Because bothk ₁ (the transition parameter) andG are the quantity of state, they are given by the total differential, and functions that decideG andk ₁ are related to a mutual inverse function. From the above relation, the rate of change ink ₁ by G, which corresponds to the reaction energy of the system, is uniquely determined by a function ofk ₁, [f(k ₁ ^± )] andf(k ₁ ^± ) is described approximately by ±₁ k ₁ ^± in the transient process thatk ₁ approaches zero, where ₁ implies 1/RT. These results indicate that internal driving forces caused by a stimulus in a system are proportional tok ₁ ^± and that the system is regulated by competition of the forces. an approximate function fork ₁ in the transient process is described by tanh (G/RT) and Arrhenius' law is elucidated from this theory.Decreased January 19, 1992     

Electrical and optical properties of amorphous Te40As38Ge10Si12 thin films

Electrical, optical and structural, properties, of Te₄₀As₃₈Ge₁₀Si₁₀ thin films were studied. X-ray diffraction patterns indicate that these films are in an amorphous state. The dark electrical resistivity of Te₄₀As₃₈Ge₁₀Si₁₂ films was measured at room temperature and at elevated temperature. The thermal activation energy E was determined. The optical constants (refractive index n and absorption index k) of such films were determined in the spectral range of 0.5–2.0 m. The absorption coefficient () of this system was also determined using the known equation =4k/. The refractive index n has anomalous behaviour near the absorption edge. Analysis of the absorption spectrum reveals indirect optical transitions. The corresponding forbidden-band width was determined. Its value is approximately twice the thermal activation energy.     

Relationship between field shift and phase constant change in two-dimensional three-layered dielectric or hollow waveguides due to uniform bends

It is shown theoretically that the field shift x and phase constant change in two-dimensional three-layered dielectric or hollow waveguides bent uniformly with large bending radiusR are related by x = 2R/ ₀, where ₀ is the axial phase constant. The relationship predicts that the field distributions of the TE₀ or TM₀ mode shift toward the outward direction of bending, whereas those of other TE _n or TM _n (n=1,2,...) modes shift inward in a hollow waveguide. Characteristic features in dielectric waveguides are also described.     

Wavevector scaling,surface critical behavior,and wetting in the 2-d, 3-state chiral clock model

The controversial 2-d, 3-state chiral Potts model is studied using transfer matrix finite size scaling. at =0, we find dq _N/dN ^–4/5, whereq is the wavevector, the chiral field, andN the strip width (N=4–10). The result is consistent with den Nijs's crossover exponent =1/6. With surface fields on the infinite free boundaries, exponents associated with bulk magnetizationy _H, surface magnetizationy _H, and surface susceptibility are computed vs. ; results are similar for or to the infinite direction. Preliminary results are given for the bulk specific heat critical amplitudes, to test the universality of amplitude ratios. The interface wetting line is located for 01/4 using simple transfer matrix calculations of surface tensions in the solid-on-solid approximation. Overhangs or bubbles seem relatively unimportant at all temperatures.     

Scaling of the energy gap withT c in Bi2Sr2CaCu2O8+δ

The results of a high-resolution photoemission study using synchrotron radiation of two single crystals of Bi₂Sr₂CaCu₂O₈₊, with different critical temperaturesT _c due to a variation in oxygen stoichiometry are reported. Within experimental accuracy, the energy gap 2 is found to scale withT _c , amounting to a reduced gap parameter of 2/k _BT_c7.4. Employing resonant photoemission at the O–2s and Cu–3p thresholds, two spectral peaks at binding energies of 180 meV and 320 meV were identified as predominantly O–2p-and Cu–3d 4s-derived states, respectively.     

The Experimental Evaluation of Decay Rate Variations of 57Co by the Δλ/λ Method

The measurement of the relative changes / of the radioactive decay by the electron capture process is a direct experimental way to determine the relative changes of the electron charge density on the nucleus. Here we present the results of the experiment with ⁵⁷Co, where the differences of the decay rate were determined for different chemical states of ⁵⁷Co. We analyzed the experimental time dependences of the activity of ⁵⁷Co by means of the direct approximation method and the specialized optimization tool – a genetic algorithm. Using these methods improved the accuracy of the final / values between ⁵⁷Co and ⁵⁷Co(Pd), ⁵⁷CoCl₂,⁵⁷CoS, ⁵⁷CoSO₄7H₂O, which are in good agreement with theoretical considerations reflecting the electron charge rearrangement and screening effects.     

Spatio-temporal Fourier components and soft modes in thermal convection: A neutron scattering study

In a nematic liquid crystal subjected to a vertical temperature difference T in a vertical slab container, we find, using real-time and real-space neutron scattering, that the spatiotemporal pattern can be indexed on a two-dimensional lattice with selection rule (h+k)=2n. Higher index modes are sequentially activated as T increases from the convection threshold T _c . The frequency softening as TT _c and asTT ₀, the super-cooling limit of the nematic, is discussed.