Analysis of time-resolved CW-EPR spectra of short-lived radicals at different times after laser excitation

Laser excitation combined with time-resolved CW-EPR spectroscopy of a carotenoid-porphyrin-diquinone tetrad (1), observes polarized spectra of the end quinone radical anion, Q·_B ^?. These spectra strongly depend on the time interval between the laser pulse and the position of the detection window of the transient magnetization profile, and may lead to misinterpretation of the radical intermediates participating in the reaction route. Spectral distortions arise from small hyperfine splittings and narrow line widths, resulting in the appearance of Torrey wiggles at off-resonance fields. The correct spectrum, however, and its line shape appear at times above 1 μs after the laser pulse, and is in complete agreement with the Fourier transform EPR spectrum. Analysis and reconstruction of the transient spectra is carried out in Fourier conjugate space. The experimental spectra are shown to be the Fourier transform of the free-induction decay (FID) multiplied by an appropriate windowing function. The changes in the spectra taken at t<1 μs are due to line distortions and not to chemical processes. This treatment is of general applicability in the spectral analysis of time-resolved CW-EPR spectra.     

One-electron oxidation and demetalation of metalloporphyrins and chlorophyll a in dichloroethane solutions as studied by pulse radiolysis

Formation of cation radicals by pulse radiolysis of metalloporphyrins and chlorophyll a in 1,2-dichloroethane is reported Demetalation of the metalloporphyrin by radiolytically produced HC1 is also observed. Rate constants for demetalation of ZnTPP and Chl a are 1 1 × 10⁸ and ≈ 3 × 10⁸ M^?1 S^?1. Oxidation of Chl a by ZnTPP⁺ has a rate constant of ≈ 4× 10⁹ M^?1S^?1.     

Magnetic field dependence of electron spin polarization generated through radical-triplet interactions

The magnetic field dependence of electron spin polarization (ESP), generated in free radicals when they encounter photoexcited triplets, was measured experimentally and analyzed theoretically. The time-resolved electron paramagnetic resonance measurements were performed with a microwave setup consisting of low-loss dielectric ring resonators with tunable microwave frequencies and the corresponding magnetic fields. The ESP of the radical was found in the magnetic field range of 170-370 mT, and the results of the calculation based on the numerical solution of the stochastic Liouville equation were found to be in line with the experimental data showing that ESP decreases when the magnetic field increases.     

TRIPLET STATE OF METALLOPORPHYCENES: ZnPCl, PdPC2, PtPC2, and NiPC2

We report on a study of the photoexcited triplet state, at low temperatures in ordered liquid crystals, and at room temperatures in the liquid phase, of some new metalloporphycenes: normal zincporphycene, ZnPCl; Pd(II), and Ni(II) complexes of 2,7,12,17-tetra- n -propylporphycene, PdPC2, PtPC2, and NiPC2, respectively. The triplet state at low temperature is obtained by selective laser excitation and its magnetization response is detected by EPR in the 250 ns time scale. From triplet EPR line shapes and triplet spin polarization directions it is concluded that the zinc cation lies above the molecular plane and the palladium cation fits into the porphycene's cavity. Such a proposed structure implies a strong spin-orbit interaction in PdPC2, thus resulting in an out-of-plane active spin state (z-axis), whereas that in ZnPCl, having a smaller spin-orbit interaction, in-plane ( x,y -axes) are the active spin states. Laser photolysis of the metalloporphycenes gives rise to detectable triplets of ZnPCl, PdPC2 and PtPC2 with triplet lifetimes of 26, 5 and 0.2 µs, respectively. The sensitization experiment, using β-acetonaphthone as a sensitizer to produce the triplet, results in detectable transients of only ZnPCl and PdPC2 with much longer triplet lifetimes of 85 and 20 µs, respectively. The short triplet lifetime of PtPC2 (and probably that of NiPC2) do not allow for triplet detection with the present sensitizer. However, the latter two metalloporphycenes quench the triplet lifetime of β-acetonaphthone from 29 to 10µs.     

Simplification of complex EPR spectra by cepstral analysis

As the Fourier transform of time-series data is known as the spectrum, the Fourier transform of the logarithm of the time-series data is called the cepstrum of the data. When cepstral analysis is applied to free induction decay signals of free radicals showing first-order EPR spectra, the identification of nuclear hyperfine coupling constants becomes simple. In a systematic manner, we have examined how the technique of cepstral analysis is affected by the presence of aliasing, noise, uncertainty in the time origin of the free induction decay, the presence of second-order hyperfine couplings, and the applications of various apodization methods. This technique was then applied to analyze the EPR spectrum of anthraquinone anion radical, and anion radicals of porphycene and tetrapropyl-porphycene, and the hyperfine coupling constants thus obtained were compared with published data. A good agreement was always found. We make a case for the usefulness of cepstral analysis in determining the hyperfine coupling constants of complex EPR spectra of organic free radicals.     

Anticipative calculus for Lévy processes and stochastic differential equations*

We develop an anticipative calculus for Lévy processes with finite second moment for analysing anticipating stochastic differential equations. The calculus is based on the chaos expansion of square-integrable random variables in terms of iterated integrals with respect to the compensated Poisson random measure. We define a space of smooth and generalized random variables in terms of such chaos expansions, and present anticipative stochastic integration, the Wick product and the so-called 𝒮-transform. These concepts serve as tools for studying general Wick type stochastic differential equations with anticipative initial conditions. We apply the 𝒮-transform to find the unique solutions to a class of linear stochastic differential equations. The solutions can be expressed in terms of the Wick product.     

Filling factor in a pulsed electron paramagnetic resonance experiment

A definition and mathematical treatment to calculate the filling factor in a pulsed electron paramagnetic resonance (EPR) experiment are presented. The differences between filling factors in traditional, continuous wave (CW)-EPR experiments (eta), and in pulsed-EPR experiments (eta(p)), are discussed. We present some examples to demonstrate how eta(p) depends upon the particular pulse sequence and sample characteristics.     

A critical analysis and a recent improvement of the two-dimensional model for solution–precipitation creep: application to silicon nitride ceramics

The step model is one of the most widely used models of solution–precipitation creep in polycrystalline ceramics with secondary glassy phases. However, it leads to unrealistic stress exponent values when two-dimensional step nucleation takes place at the grain boundaries. We present a modification of the original model of step nucleation that avoids such unreasonable values by considering in detail the precipitation (or solution) process. The modified model agrees with reported experimental results for ceramic systems in which it has been accepted that high-temperature plasticity occurs by solution–precipitation.     

Probing the photoexcited states of rhodium corroles by time-resolved Q-band EPR. Observation of strong spin-orbit coupling effects

The photoexcited states of two 5,10,15-tris(pentafluorophenyl)corroles (tpfc), hosting Rh(III) in their core, namely Rh(pyr)(PPh 3)(tpfc) and Rh(PPh 3)(tpfc), have been studied by time-resolved electron paramagnetic resonance (TREPR) combined with pulsed laser excitation. Using the transient nutation technique, the spin polarized spectra are assigned to photoexcited triplet states. The spectral widths observed for the two Rh(III) corroles crucially depend on the axial ligands at the Rh(III) metal ion. In case of Rh(PPh 3)(tpfc), the TREPR spectra are found to extend over 200 mT, which exceeds the spectral width of non-transition-metal corroles by more than a factor of 3. Moreover, the EPR lines of the Rh(III) corroles are less symmetric than those of the non-transition-metal corrroles. The peculiarities in the TREPR spectra of the Rh(III) corroles can be rationalized in terms of strong spin-orbit coupling (SOC) associated with the transition-metal character of the Rh(III) ion. It is assumed that SOC in the photoexcited Rh(III) corroles effectively admixes metal centered (3)dd-states to the corrole centered (3)pipi*-states detected in the TREPR experiments. This admixture leads to an increased zero-field splitting and a large g-tensor anisotropy as manifested by the excited Rh(III) corroles.