Relaxation time electronic polarization

Figrue BE 16.20 shows spectra of DQ m a solution of TXlOO, a neutral surfactant, as a function of delay time. The spectra are qualitatively similar to those obtained in ethanol solution. At early delay times, the polarization is largely TM while RPM increases at later delay times. The early TM indicates that the reaction involves ZnTPPS triplets while the A/E RPM at later delay times is produced by triplet excited-state electron transfer. Calculation of relaxation times from spectral data indicates that in this case the ZnTPPS porphyrin molecules are in the micelle, although some may also be in the hydrophobic mantle of the micelle. Furtlier,... 

In Debye solvents, x is tire longitudinal relaxation time. The prediction tliat solvent polarization dynamics would limit intramolecular electron transfer rates was stated tlieoretically [40] and observed experimentally [41]. 

Dicarbocyanine and trie arbo cyanine laser dyes such as stmcture (1) (n = 2 and n = 3, X = oxygen) and stmcture (34) (n = 3) are photoexcited in ethanol solution to produce relatively long-Hved photoisomers (lO " -10 s), and the absorption spectra are shifted to longer wavelength by several tens of nanometers (41,42). In polar media like ethanol, the excited state relaxation times for trie arbo cyanine (34) (n = 3) are independent of the anion, but in less polar solvent (dichloroethane) significant dependence on the anion occurs (43). The carbocyanine from stmcture (34) (n = 1) exists as a tight ion pair with borate anions, represented RB(CgH5 )g, in benzene solution photoexcitation of this dye—anion pair yields a new, transient species, presumably due to intra-ion pair electron transfer from the borate to yield the neutral dye radical (ie, the reduced state of the dye) (44). 

Although various structural models (Raff and Pohl, 1965 Natori and Watanabe, 1966 Newton, 1973) and semicontinuum models (Copeland et aL, 1970 Kestner and Jortner, 1973 Fueki et al, 1973) have been proposed for the solvated electron, the basis of the agreement or disagreement between theory and experiment is not well established. Another complication with the continuum or the semicontinuum models is the fact that in a number of polar systems the spectrum is fully developed in a time far shorter than the dielectric relaxation times (see, e.g., Bronskill et al, 1970 Baxendale and Wardman, 1973 Rentzepis et al, 1973). 

Usually, the most general nonspecific effects of dipole-orientational and electronic polarization of the medium are discussed, and the results of the theory of relaxational shifts developed under the approximation of a continuous dielectric medium may be used.(86 88) The shift of the frequency of the emitted light with time is a function of the dielectric constant e0, the refractive index n, and the relaxation time xR ... 

The relaxation time required for the charge movement of electronic polarization E to reach equilibrium is extremely short (about 10 s) and this type of polarization is related to the square of the index of refraction. The relaxation time for atomic polarization A is about 10 s. The relaxation time for induced orientation polarization P is dependent on molecular structure and it is temperature-dependent. 

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. 

The atomic polarization is rapid, and this and the electronic polarizations constitute the instantaneous polarization components. The remaining types of polarization are absorptive types with characteristic relaxation times corresponding to relaxation frequencies. 

The compound bis-(4,4 -dimethylaminophenyl)-sulfone (DMAPS) and related compounds show multiple fluorescences in polar solvents due to excited state charge transfer (Rettig and Chandross [144]). Su and Simon [84,85] have examined the intramolecular electron transfer reaction in DMAPS, in alcohol solution over the temperature range from — 50°C to + 30°C. They observe that the decay of the local excited state is nonexponential and significantly faster than the longitudinal relaxation time of the solvent. In addition, they observed that the emission spectrum of the TICT state... 

These spectra, taken at variable temperatures and a small polarizing applied magnetic field, show a temperature-dependent transition for spinach ferredoxin. As the temperature is lowered, the effects of an internal magnetic field on the Mossbauer spectra become more distinct until they result at around 30 °K, in a spectrum which is characteristic of the low temperature data of the plant-type ferredoxins (Fig. 11). We attribute this transition in the spectra to spin-lattice relaxation effects. This conclusion is preferred over a spin-spin mechanism as the transition was identical for both the lyophilized and 10 mM aqueous solution samples. Thus, the variable temperature data for reduced spinach ferredoxin indicate that the electron-spin relaxation time is around 10-7 seconds at 50 °K. The temperature at which this transition in the Mossbauer spectra is half-complete is estimated to be the following spinach ferredoxin, 50 K parsley ferredoxin, 60 °K adrenodoxin, putidaredoxin, Clostridium. and Axotobacter iron-sulfur proteins, 100 °K. 

We can say that such a static device is a U( ) unipolar, set rotational axis, sampling device and the fast polarization (and rotation) modulated beam is a multipolar, multirotation axis, SU(2) beam. The reader may ask how many situations are there in which a sampling device, at set unvarying polarization, samples at a slower rate than the modulation rate of a radiated beam The answer is that there is an infinite number, because from the point of the view of the writer, nature is set up to be that way [26], For example, the period of modulation can be faster than the electronic or vibrational or dipole relaxation times of any atom or molecule. In other words, pulses or wavepackets (which, in temporal length, constitute the sampling of a continuous wave, continuously polarization and rotation modulated, but sampled only over a temporal length between arrival and departure time at the instantaneous polarization of the sampler of set polarization and rotation—in this case an electronic or vibrational state or dipole) have an internal modulation at a rate greater than that of the relaxation or absorption time of the electronic or vibrational state. 

Applied electric fields, whether static or oscillating, distort (polarize) the electron distribution and nuclear positions in molecules. Much of this volume describes effects that arise from the electronic polarization. Nuclear contributions to the overall polarization can be quite large, but occur on a slower time-scale than the electronic polarization. Electronic motion can be sufficiently rapid to follow the typical electric fields associated with incident UV to near IR radiation. This is the case if the field is sufficiently off resonance relative to electronic transitions and the nuclei are fixed (see ref 5 for contributions arising from nuclear motion). Relaxation between states need not be rapid, so... 

The existence of the solvated electron is well authenticated, then, in the radiolysis of polar liquids. The fate of the corresponding positive ions is less clear. Lea54 suggested that in liquid water the ion H20 + would decompose within the relaxation time of water (10-11 sec) on becoming hydrated... 

Second, any CIDNP based assignments concerning the sign of hfcs are valid only if the radical pair mechanism (RPM) [93-96] is operative they become invalid if the alternative triplet-Overhauser mechanism (TOM), based on electron nuclear cross relaxation [97-100] is the source of the observed effects. For effects induced via the TOM the signal directions depend on the mechanism of cross relaxation and the polarization intensities are proportional to the square of the hfc. Thus, they do not contain any information related to the signs of the hfcs. However, the TOM requires the precise timing of four consecutive reactions and, thus, is not very likely. In fact, this mechanism has been positively established in only two systems [98-100]. 

Alternating-current and frequency effects. With an AC rather than a DC voltage applied to the electrodes, the processes above reverse themselves with the period of the alternating voltage. But each process proceeds at a different rate (with a characteristic relaxation time) so that their relative contributions to energy dissipation vary with frequency. As the frequency is increased concentration-polarization can be reduced or eliminated, particularly if the electrode reaction is reversible (fast electron transfer in both directions). 

A case of solvent-driven electronic relaxation has been observed [76] for [Re(Etpy)(CO)3(bpy)]+ in ionic liquids TRIR spectra have shown at early times a weak signal due to the II. state, in addition to much stronger bands of the 3MLCT state. Although no accurate kinetic data are available, the II. state converts to MI.CT with a rate that is commensurate with the solvent relaxation time. Fluorescence up-conversion provided an evidence [10] for population of an upper II. state in MeCN, which converts to CT with a much faster lifetime of 870 fs (Table 1). The solvent dynamic effect on the 3IL—>3CT internal conversion can be rationalized by different polarities of the II. and JCT states, Fig. 11. The solvent relaxation stabilizes the 3CT state relative to II., driving the conversion. 

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