Hopping time

Figure 4 Left Distribution of hopping times for an adatom at a solid-liquid interface at 600 K for conventional molecular dynamics and for superstate parallel-replica dynamics. Right Temperature dependence of the hopping rate for an adatom at a dry interface and at a wet interface as obtained using superstate parallel-replica dynamics.

If, however, some correlation effect exists avoiding formation of excessive spin density in an atom (for instance making a state with aligned spins stable because of Hund s principle) this state of alignment in the atom may persist much longer than the band hopping time hAV of the electrons. The fluctuations, typical of the band, will tend to even out, and the electrons wiU stay in the atomic ground state of the core (localization). 

Mixed valency with a Xh == x tends to broaden the linewidths of the Mossbauer spectra due to the superposition of several signals having hopping times in the range 10 < Xh < lO s. Line broadening with decreasing temperature T may indicate a Xj, < x that approaches lO s at lower T. 

If a diffusional model with AHm < kT is appropriate, then the time th between electron hops must approach the period cor of the optical mode vibrations that trap or correlate the electrons. With an wj = 10" s, the hopping time Th would be short relative to the time scale of Mossbauer spectroscopy, ca. 10" s. We can therefore anticipate an isomer shift for the octahedral-site iron that is midway between the values typical for Fe ions and Fe " " ions. From Table 1 and Eq. (1), we can predict a room-temperature isomer shift of 6 0.75 mm/s wrt iron. Consistent with this prediction is the... 

Above room temperature, the mobile 3 d electrons are well described by a random mixture of Fel" and FeB ions with the mobile electrons diffusing from iron to iron, some being thermally excited to FeA ions, but the motional enthalpy on the B sites is AH < kT. As the temperature is lowered through Tc, the Seebeck coefficient shows the influence of a change in mobile-electron spin degeneracy, and at room temperature the Seebeck coefficient is enhanced by correlated multielectron jumps that provide a mobile electron access to all its nearest neighbors. The electron-hopping time xi, = coi = 10" s... 

Two different explanations have been advanced for the difference in trapping rates of GG and GGG. Berlin, Burin, and Ratner [54] base their explanation on the assumptions that (1) both traps are deep, i.e., -0.5 eV for GG and -0.7 eV for GGG, and (2) the ionization potential of guanine is lower than that of the other nucleobases by at least 0.4 eV. The different reactivities of the two traps were ascribed in [54] to different relaxation times of a hole in the trap. The GG units were taken to have a long relaxation time, so that a hole is likely to make a further hop before the trap closes on it, while the relaxation time of the GGG units was supposed to be relatively short, faster than the hopping time. 

An important advantage of the GRASSHopper device is the fact that after a complete MAH cycle of three orientations, the MAH device can be re-initialized by rotating backward to the initial orientation. For this reason, a number of flexible input and output lines to the sample chamber of the GRASSHopper device exist and allow a rotation of the fixed-bed reactor about an axis in the magic-angle while the system is gas-tight (Fig. 16). In the reported experiments 66), the 120° hop time... 

When (mn) > 1, expansion (7.18) contains a large number of waves with different m. Interference of many such waves creates a wave packet, whose group velocity is proportional to (mn). Rotation through the angle 2tt/3 then can be related to the hopping time... 

In this expression r is the inter-chain hopping time and ts is the phonon scattering time along a chain. The quantity s = (d2/a2) is the ratio of the anisotropic to isotropic contribution of the hyperfine interaction and /(cd) is the spectral density of the interaction, with coe and con being electron and nuclear precession frequencies respectively,... 

It is to be expected that the radiative rate constants for spontaneous emission of exciplexes and electroplexes will resemble those for excimer and electromers [see discussion of Eqs. (20) and (21) in Sec. 2.3.1)]. This implies that, dependent on the intermolecular configuration, the fluorescence lifetimes of exciplexes range between 10 and 200 ns, and that the emission lifetime of electroplexes is limited by the intermolecular electron hopping time. Though there are no at present direct lifetime measurements on electroplexes, the measurements on a series of donor-acceptor species in solid-state solutions of PC prove these predictions for exciplexes (Table 1). 

Material Intermolecular distance3 c (nm) Exciton spin multiplicity Lifetime T (s) Diffusion length lA (nm) Diffusion coefficient D (cm2/s) Hopping time th (s) Total distance covered l (nm) l/l a... 

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