Dielectric correlation time

Up to now it has been tacitly assumed that each molecular motion can be described by a single correlation time. On the other hand, it is well-known, e.g., from dielectric and mechanical relaxation studies as well as from photon correlation spectroscopy and NMR relaxation times that in polymers one often deals with a distribution of correlation times60 65), in particular in glassy systems. Although the phenomenon as such is well established, little is known about the nature of this distribution. In particular, most techniques employed in this area do not allow a distinction of a heterogeneous distribution, where spatially separed groups move with different time constants and a homogeneous distribution, where each monomer unit shows essentially the same non-exponential relaxation. Even worse, relaxation... 

D. Axelson These spectra were obtained at 57.9 MHz, but that s not the problem. We can measure correlation times regardless of the frequency. The correlation time at the glass temperature is very long. From a measurement of the correlation time we should be able to tell whether it is a true glass. In all these cases the correlation times are six to nine orders of magnitude lower than can possibly exist in a glass. For this reason I think the correlation between the NMR measurement and dielectric relaxation and dynamic mechanical do not relate one to one because of the frequency effects in the other measurements. 

It was soon realized that a distribution of exponential correlation times is required to characterize backbone motion for a successful Interpretation of both carbon-13 Ti and NOE values in many polymers (, lO). A correlation function corresponding to a distribution of exponential correlation times can be generated in two ways. First, a convenient mathematical form can serve as the basis for generating and adjusting a distribution of correlation times. Functions used earlier for the analysis of dielectric relaxation such as the Cole-Cole (U.) and Fuoss-Kirkwood (l2) descriptions can be applied to the interpretation of carbon-13 relaxation. Probably the most proficient of the mathematical form models is the log-X distribution introduced by Schaefer (lO). These models are able to account for carbon-13 Ti and NOE data although some authors have questioned the physical insight provided by the fitting parameters (], 13) ... 

At high temperatures above Tb 617 K PMN behaves Hke all other simple perovskites. The dynamics of the system is determined by the soft transverse optical (TO) phonon which exhibits a normal dispersion and is imderdamped at all wave vectors. Below Tb, in addition to the soft mode—which becomes overdamped—a new dielectric dispersion mechanism appears at lower frequencies which can be described by a correlation time distribution function /(t). 

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. 

The shape of the frequency dependence of e" has been compared in Fig. 109 in terms of reduced units s / max an(i ///max> at various temperatures. The peak is asymmetric, being broader on the high-frequency side, especially at 10 °C. A gradual narrowing occurs on both the high- and low-frequency sides with increasing temperature. These results show that the motional processes involved in the dielectric j3 relaxation have a distribution of correlation times and that this distribution becomes narrower as temperature increases. 

This section presents a fundamental development of Sections V and VI. Here a linear dielectric response of liquid H20 is investigated in terms of two processes characterized by two correlation times. One process involves reorientation of a single polar molecule, and the second one involves a cooperative process, namely, damped vibrations of H-bonded molecules. For the studies of the reorientation process the hat-curved model is employed, which was considered in detail in Section V. In this model a hat-like intermolecular potential comprises a flat bottom and parabolic walls followed by a constant potential. For the studies of vibration process two variants are employed. 

The effective correlation times for an approximately isotropic motion, tr, ranged from 40.3 ps in methanol to 100.7 ps in acetic acid for 5a, and from 61.6 ps to 180.1 ps for 5b in the same solvents. Neither solvent viscosity nor dielectric constant bore any direct relationship to the correlation times found from the overall motion, and attempts to correlate relaxation data with parameters (other than dielectric constant) that reflect solvent polarity, such as Kosover Z-values, Win-stein y-values, and the like, were unsuccessful.90 Based on the maximum allowed error of 13% in the tr values derived from the propagation of the experimental error in the measured T, values, the rate of the overall motion for either 5a or 5b in these solvents followed the order methanol N,N-dimethylformamide d2o < pyridine < dimethyl sulfoxide. This sequence appears to reflect both the solvent viscosity and the molecular weight of the solvated species. On this basis, and assuming that each hydroxyl group is hydrogen-bonded to two molecules of the solvent,137 the molecular weights of the solvated species are as follows in methanol 256, N,N-dimethylformamide 364, water 144, pyridine 496, and dimethyl sulfoxide 312. 

As emphasized elsewhere in this text, the physical act constituting an electrodynamic force is the correlated time-varying fluctuation of all component electric charges and electromagnetic fields in each material composing a system. Charge fluctuations at each point are either spontaneous or are in response to electric fields set up by fluctuations elsewhere. The dielectric permittivity is an experimental quantity that codifies not only the response of a material to an applied electric field but also the magnitude of spontaneous fluctuations. 

Winkler (144-148) has studied the proton NMR relaxation time of water on y-Al203 and found that the correlation time = 1.2 x 10 second lies between that of water (149) (3.5 x 10 second) and ice (150) (2 X second). Winkler observed two regions of behavior, one in micropores with radii less than 1000 A, and another in macropores with larger radii. A rapid exchange occurred between the various layers of water molecules in micropores. Ebert (151,152) used dielectric constant measurements to distinguish between monolayer and multilayer water coverages. 

Dielectric relaxation T2, correlation time for rotation about the dipolar axis Tc, rotational correlation time for solvation complexes Z>s, self-diffusion coefficient Ti, correlation time for rotation of the dipole... 

Much of the work in this area has been stimulated by Kosower s observation of a 1 1 correspondence between the dielectric relaxation rate of the solvent and the rate of formation of a charge transfer (or zwitterionic) state from relaxation of the singlet excited state of an amino-sulfone substituted naphthalene, and this has recently been reviewed/ In this correlation, the dielectric relaxation rate of the solvent around the ion pair is related to the bulk solvent relaxation time ( ) by equation (10), where Ds and D p are the static and optical dielectric... 

Figure 7.5 Arrhenius plot of inverse correlation times (1/tc) measured by various techniques for poly(methyl methacrylate). ( ) Mechanical ( + ) dielectric (o) NMR. Reprinted with permission from [3]. (c) (1971) American Chemical Society.

Table 1 Origins of correlation times obtained in water protein systems by dielectric measurements...

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