Dielectr relaxation time

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

From the various autocorrelation times which characterized macromolecular fluctuations, those associated with the fluctuation of the electrostatic field from the protein on its reacting fragments are probably the most important (see Ref. 8). These autocorrelation times define the dielectric relaxation times for different protein sites and can be used to estimate dynamical effects on biological reactions (see Chapter 9 for more details). 

Dielectric relaxation times, 122, 216 Diffusion, in proteins, simulated by MD, 120-122... 

Proteins, 109,110, 116.Seealso Enzymes Macromolecules average thermal amplitudes, MD simulations, 119 binding of ligands to, 120 dielectric relaxation time of, 122 electrostatic energies in, 122, 123-125 flexibility of, 209,221,226-227, 227 folding, 109,227... 

FIGURE 24.10 Dielectric relaxation times from Figures 24.7 through 24.9 plotted versus 7V, with mode independent -y = 3.0 (1,4-polyisoprene), = 2.5 (polypropylene glycol), and = 2.65 (polyoxyhutylene). 

It takes 10-u s, the normal dielectric relaxation time for water, to form the hydrated electron, and -10-9 s for the electron to disappear by reacting with the water molecule (the former is an overestimate, the latter an underestimate). 

Notwithstanding Platzman s theory, most calculations of radiation-chemical yields in water and aqueous solutions were performed using the free-radical model (see Magee, 1953 Samuel and Magee, 1953 Ganguly and Magee, 1956). The hypothesis was that the recapture time of the electron would be shorter than the dielectric relaxation time. Therefore, recombination would outcompete solvation. 

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). 

Migus et al. s (1987) delineation of the formation of a primary species absorbing in the IR, which develops in -110 fs and which transforms to the well-known spectrum of the hydrated electron in -240 fs, which is consistent with the longitudinal dielectric relaxation time of water (Mozumder, 1969a, b). 

This approximation requires that cos. This behavior in fact follows from a Debye dielectric continuum model of the solvent when it is coupled to the solute nuclear motion [21,22] and then xs would be proportional to the longitudinal dielectric relaxation time of the solvent indeed, in the context of time dependent fluorescence (TDF), the Debye model leads to such an exponential dependence of the analogue... 

When a constant electric field is suddenly applied to an ensemble of polar molecules, the orientation polarization increases exponentially with a time constant td called the dielectric relaxation time or Debye relaxation time. The reciprocal of td characterizes the rate at which the dipole moments of molecules orient themselves with respect to the electric field. 

Y. T. Mazurenko and V. S. Udaltsov, Spectral relaxations of fluorescence. 3. Kinetics of spectra of polar solutions with distributed dielectric relaxation time, Opt. Spectrosc. (Engl, transl.) 45, 765-767 (1978). 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

Before leaving SD applications of the LRA, it is worth stressing that a different approach has often been taken in relating the electrostatic C i) to pine solvent dynamics. In this approach, the connection is made to solvent dielectric relaxation. Early theories made the connection through the longitudinal dielectric relaxation time," while more recent ones use as input the dielectric dispersion s or its generalization to finite wavevectors, e(k, co). 23.24.29,68,89... 

For positive lit electrodes one can register the drift of holes, and for negative ones- the drift of the electrons. The photosensitizer (for example Se) may be used for carrier photoinjection in the polymer materials if the polymer has poor photosensitivity itself. The analysis of the electrical pulse shape permits direct measurement of the effective drift mobility and photogeneration efficiency. The transit time is defined when the carriers reach the opposite electrode and the photocurrent becomes zero. The condition RC < tlr and tr > t,r should be obeyed for correct transit time measurement. Here R - the load resistance, Tr -dielectric relaxation time. Usually ttras 0, 1-100 ms, RC < 0.1 ms and rr > 1 s. Effective drift mobility may be calculated from Eq. (4). The quantum yield (photogenerated charge carriers per absorbed photon) may be obtained from the photocurrent pulse shape analysis. 

If the average lifetime x/ of excited state is greater than the dielectric relaxation time xD then excited state dipole moment p.e polarizes the solvent and the solvent molecules adjust to the new situation. A reaction... 

At high viscosities or low temperatures, dielectric relaxation time xj may be larger than the mean radiative lifetime t/ of the molecule. This may decrease the O—O separation between absorption and emission. On the other hand, at high temperatures solvent relaxation may be promoted thermally decreasing xd and O—O separation may again decrease. A maximum value for Av (O—O) is expected at some intermediate temperatures. Besides the relaxation effects, the O—O separation can also be affected by environmental modification of the potential energy surfaces. 

Dielectric relaxation measurements define an operational correlation time for the decay of the correlation function (P cosO)). For alcohols, the monomer rotation time, r2, increases from 18ps for n-propanol at 40°C to 44 ps for n-dodecanol at 40°C [83], A small measure of saturation in the dielectric relaxation time of alkyl bromides with increasing chain length has been noted by Pinnow et al. [242] and attributed to chain folding. 

In the simplest model investigated, including a single Debye mode (X(f) -exp(-t/ r, ), xL being the longitudinal dielectric relaxation time), the spectral effect was found to be small and negative -0.2 <[Pg.332]

Figure 5. Median jump frequencies (Sr ) 1 for water adsorbed on NaX to saturation, for water on charcoal at saturation, and that expected for bulk water (from NMR relaxation times) dashed curve marked diff diffusion coefficients by magnetic field gradient technique normalized to (Sr) 1 by choice of jump distance of 2.7 A + dielectric relaxation times of Jansen...

---