Dispersion response

Furuta, T., Momotake, A., Sugimoto, M., Hatayama, M., Torigai, H. and Iwamura, M. (1996) Acyloxycoumarinylmethyl-caged cAMP, the photolabile and membrane-permeable derivative of cAMP that effectively stimulates pigment-dispersion response of melanophores. Biochemical and Biophysical Research Communications, 228, 193-198. 

Figure 2 shows the spectral response functions (5,(r), Eq. 1) derived firom the spectra of Fig. 1. In order to adequately display data for these varied solvents, whose dynamics occur on very different time scales, we employ a logarithmic time axis. Such a representation is also useful because a number of solvents, especially the alcohols, show highly dispersive response functions. For example, one observes in methanol significant relaxation taking place over 3-4 decades in time. (Mdtiexponential fits to the methanol data yield roughly equal contributions from components with time constants of 0.2, 2, and 12 ps). Even in sinqrle, non-associated solvents such as acetonitrile, one seldom observes 5,(r) functions that decay exponentially in time. Most often, biexponential fits are required to describe the observed relaxation. This biexponential behavior does not reflect any clear separation between fast inertial dynamics and slower diffusive dynamics in most solvents. Rather, the observed spectral shift usually appears to sirrply be a continuous non-exponential process. That is not to say that ultrafast inertial relaxation does not occur in many solvents, just that there is no clear time scale separation observed. Of the 18 polar solvents observed to date, a number of them do show prominent fast components that are probably inertial in origin. For example, in the solvents water [16], formamide, acetoniuile, acetone, dimethylformamide, dimethylsulfoxide, and nitromethane [8], we find that more than half of the solvation response involves components with time constants of 00 fs.

The bulk average concentration and the bulk average velocity can be measured as a function of time for a charged species in an electrophoretic column. These experimental electrokinetic dispersion response curves can be analyzed using the method of moments. This technique has been used for the estimation of dispersion coefficients in packed-bed columns in the absence of an electric field (28-31). Expressions for moments in the time domain are given by (32) ... 

The angle of the ring anission is given by the Cherenkov relation, cose = Vpj ( )/Vgj.((i)L) We have calculated the dispersive response of the index or refraction in terms of the off-diagonal elements of the density matrix p (w) and have found that dn/di ) = 0. Thus, cos0 = n /nc. 

Now, as already mentioned in Section 1.3, the h of that section s Eq. (6) is of just the same form as the well-known Cole-Cole dielectric dispersion response function (Cole and Cole [1941]). In its normalized form, the same / function can thus apply at either the impedance or the complex dielectric constant level. We may generalize this result (J. R Macdonald [1985a,c,d]) by asserting that any IS response... 

Conductive-system dispersive response may be associated with a distribution of relaxation times (DRT) at the complex resistivity level, as in the work of Moynihan, Boesch, and Laberge [1973] based on the assumption of stretched-exponential response in the time domain (Eq. (118), Section 2.1.2.7), work that led to the widely used original modulus formalism (OMF) for data fitting and analysis, hi contrast, dielectric dispersive response may be characterized by a distribution of dielectric relaxation times defined at the complex dielectric constant or permittivity level (Macdonald [1995]). Its history, summarized in the monograph of Bbttcher and Bordewijk [1978], began more than a hundred years ago. Until relatively recently, however, these two types of dispersive response were not usually distinguished, and conductive-system dispersive response was often analyzed as if it were of dielectric character, even when this was not the case. In this section, material parameters will be expressed in specific form appropriate to the level concerned. 

Since conductive-system dispersive response may be transformed and shown graphically at the complex dielectric level, and dielectric dispersion may be presented at the complex resistivity level, frequency-response data alone may be insufficient to allow positive identification of which type of process is present, since there may be great similarity between the peaked dispersion curves that appear in plots of p"(co) and of e"(co) or of e"(cd) = e"((o) - (otjcoev). Here, e is the permittivity of vacuum. This quantity has usually been designated as b, as in other parts of this book. Its designation here as f avoids ambiguity and allows clear distinction between it and e(0) = e (0) = o, the usage in the present section. 

Types of Dispersive Response Models Strengths and Weaknesses... 

Conductive-system dispersive response involving mobile charge may be conceptually associated with the effects of three processes ... 

The ZC Power-law Model. Although we discuss some single dispersive-response models here, in practice they must always take account of and of possibly some other effects as well and so the overall model is always composite. A frequently used fitting model is the ZARC one of Eq. (22), Section 2.2. It is now more often designated as the ZC and, when written at the complex conductivity level, it may be expressed as o co) = ob[l -i- (t<0T 7zc], where 0 < 7zc < 1. The exponent jic has often been written as n and is the high-frequency-limiting log-log slope of the model. It has usually been found to have a value in the range 0.6 [Pg.267]

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