Dipole correlation function dielectric response

In order to explain the non-Debye response (134) it is possible to use the memory function approach [22,23,31,266-268]. Thus, the normalized dipole correlation function k(f) (22) corresponding to a nonexponential dielectric relaxation process obeys the equation... 

An alternative approach is to obtain information on the dynamic molecular properties of a substance directly in the time domain. Relation Eq. (13) shows that the equivalent information on the dielectric relaxation properties of a sample being tested can be obtained both in the frequency and the time domains. Indeed, the polarization fluctuations caused by thermal motion in the linear response case are the same as for the macroscopic reconstruction induced by the electric field (9, 10). This means that one can equate the relaxa tion function a(t) and the macroscopic dipole correlation function f(t) ... 

Dielectric spectroscopy is one of the earlier techniques for probing local chain dynamics as reviewed by Williams [20]. This technique measures the time-dependent complex dielectric constant e (x) which is then transformed by the use of linear response theory into the dipole-dipole correlation function 0(x), according to... 

Though not strictly functioning as resistors/conductors, carbon nanotubes have just been reported in an extraordinarily vapor-sensitive capacitive device [19]. The electric field lines emanating from the nanotubes are responsible for a localized dielectric response that can be modulated by minute quantities of adsorbate on the nanotube surface. A layer of hydrogen-bonding polymer, or even a mono-layer terminated in mildly acidic groups, increased sensitivity to parts per billion levels. Response strength was correlated with the dipole moment of the analytes. 

Examples of linear response functions (susceptibilities) include the frequency dependent electrical conductivity (the Fourier transform of an equilibrium current autocorrelation function), dielectric susceptibility, which is the transform of a dipole moment autocorrelation function, along with stress, heat flux, and an assortment of velocity correlation functions. 

P(co) is an internal field factor and A t) is a time-correlation function which represents the fluctuations of the macroscopic dipole moment of the volume V in time in the absence of an applied electric field. Equations (44) and (45) are a consequence of applying linear-response theory (Kubo-Callen-Green) to the case of dielectric relaxation, as was first described by Glarum in connexion with dipolar liquids. For the special case of flexible polymer chains of high molecular weight having intramolecular correlations between dipoles but no intermolecular correlations between dipoles of different chains we may write... 

The fluctuation-dissipation theorem (FDT) of Callen and Welton states a general relationship between the response of a given system to an external disturbance and the internal fluctuation of the system in the absence of the dismrbance. Such a response is characterized by a response function or equivalently by an admittance or an impedance. For dielectric relaxation, the complex dielectric function, e ( u), is related to the dipole moment correlation function < >( ) via Fourier transformation ... 

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