Dielectric relaxation data

Glass-Forming Liquids I. Temperature Derivative Analysis of Dielectric Relaxation Data. 

For MeOH, the dielectric relaxation data used were obtained by Kindt and Schmuttenmaer (/. Phys. Chem. 1996, 100, 10373) by femtosecond terahertz pulse spectroscopy r, t2 and... 

Davidson and Ripmeester (1984) discuss the mobility of water molecules in the host lattices, on the basis of NMR and dielectric experiments. Water mobility comes from molecular reorientation and diffusion, with the former being substantially faster than the water mobility in ice. Dielectric relaxation data suggest that Bjerrum defects in the hydrate lattice, caused by guest dipoles, may enhance water diffusion rates. 

The first mention of the a(x) dependence was in experimental work [265], The dielectric relaxation data of water in mixtures of seven water-soluble polymers was presented there. It was found that in all these solutions, relaxation of water obeys the CC law, while the bulk water exhibits the well-known Debye-like pattern [270,271], Another observation was that a is dependent not only on the concentration of solute but also on the hydrophilic (or hydrophobic) properties of the polymer. The seven polymers were poly(vinylpyrrolidone) (PVP weight average molecular weight (MW) = 10,000), poly (ethylene glycol) (PEG MW = 8000), poly(ethylene imine) (PEI MW = 500,000), poly(acrylic acid) (PAA MW = 5000), poly(vinyl methyl ether) (PVME MW = 90,000), poly(allylamine) (PA1A MW = 10,000), and poly(vinyl alcohol) (PVA MW = 77,000). These polymers were mixed with different ratios (up to 50% of polymer in solution) to water and measured at a constant room temperature (25°C) [265]. 

In the previous subsection, we have provided conceptually the rationale and experimentally some data to justify the expectation that the primitive relaxation time To of the CM should correspond to the characteristic relaxation time of the Johari-Go Id stein (JG) secondary relaxation Xjg- Furthermore, it is clear from the CM relation, Ta = ( "to)1 1- , given before by Eq. 6 that To mimics Ta in behavior or vice versa. Thus, the same is expected to hold between Xjg and Ta. This expectation is confirmed in Section V from the properties of tjg- The JG relaxation exists in many glass-formers and hence there are plenty of experimental data to test the prediction, xjG T,P) xo(T,P). Broadband dielectric relaxation data collected over many decades of frequencies are best for carrying out the test. The fit of the a-loss peak by the one-sided Fourier transform of a Kohlrausch function [Eq. (1)] determines n and Ta, and together with tc 2 ps, To is calculated from Eq. 6... 

Since To or Xjg is usually much larger than tc =2 ps and n/( 1 — n) is a monotonic decreasing function with decreasing n, xa(7) of nano-confined liquids decreases on decreasing the size of the pores. Consequently, the difference between xa and To or x/c becomes smaller [298,302,303]. This trend is shown in Fig. 48 by the dielectric relaxation data of PDMS confined in silanized glass pores of various sizes. If in sufficiently small pores n —> 0, then xa —> To or Tjc, and the characteristics of the a-relaxation will not be very different from that of the JG relaxation. The location of the primitive frequency Vq corresponding to tq calculated from the bulk xa and n = 0.48... 

Fig. 4.6 Plot of Ejn against toEo t using dielectric relaxation data for water at 25°C [G5]. The straight line is drawn considering only the data obtained at frequencies below 40 GHz.

Fig. 4.7 Plot of Sin against using dielectric relaxation data for water at 25°C [G5].

Fig. 4.8 Plot of 8out against 8 using dielectric relaxation data for water in the frequency range 60 10 GHz [G5]. The solid line shows the contribution from the low-frequency relaxation process.

Other relationships which have been used to describe dielectric relaxation data include the Cole-Cole and Cole-Davidson equations [29]. These are preferred when a distribution of relaxation times rather than a single relaxation time is more appropriate to describe the data in a given frequency range. Nevertheless, the Debye model in its simple version or multiple relaxation versions works quite well for most of the solvents considered here. 

Fig. 4.9 Plot of e against WEout using dielectric relaxation data for aqueous KCl solutions ( ) 0.1 and ( ) 1 M.

Dielectric relaxation data for a 0.08 M Mg2S04 solution are shown in fig. 4.11. On the basis of an analysis of these data by Barthel and coworkers [29, 32], three relaxation processes may be discerned. The first one, involving the ion pair, occurs between permittivity values of 82.9 and 75.2 and involves a relaxation time of 181 ps. The second process, which is attributed to the slow reorientation of water clusters, takes place between the permittivity values of 75.2 and 8.4 with a relaxation time of 8.4 ps. Finally, the high-frequency process, which occurs between 8.4... 

Fig. 4.11 Plot of 8 against for dielectric relaxation data obtained with 0.08 M MgSO ...

A variety of dielectric relaxation data are now available for both aqueous and non-aqueous solutions. These results help one understand the properties of these solutions in more detail. They are complementary to information obtained from thermodynamic, spectroscopic, and conductivity experiments, and provide an important basis for understanding solution structure. 

The dielectric relaxation data for dimethylformamide (DMF) and dimethyl-acetamide (DMA) can be described by two Debye processes [9]. The low-frequency, high-amplitude process is attributed to rotational diffusion. For... 

Given the following dielectric relaxation data for methanol, find the values of the Es, , and td, assuming there is only one relaxation process. 

This estimate of 19 ps is much larger than the experimental estimate of 4 ps, which is obtained by applying the Debye model to dielectric relaxation data for the pure solvent (see table 4.2). However, an approximate relationship between td and t r is found when data for more solvents are considered, as shown... 

We would like to thank DuPont Polymer Products Department for supporting this work and allowing its publication. We thank Gerald Horack and Robert Tomczak for performing the OFV tests and Michael Panco for obtaining the dielectric relaxation data. D. A. Vassallo is acknowledged for many helpful discussions in the early days of this program. 

A particular treatment of dielectric relaxation data is quite common. This is the so-called Cole-Cole plot14 obtained by plotting s against s , each point corresponding to one frequency. From equation (7-28), we have... 

From a plot of dielectric relaxation data in Ref. 21 it was determined that molecular rotation in liquid ethyl alcohol has an activation energy of 4.6 kcal./mole. In ethyl alcohol at 20°C., t = 1.4 X 1010 sec. (21), so one can write for the unperturbed relaxation time... 

T, 2aV3D, (where a = 0.144 nm is the van dcr Waals radius of MjO) is (he time required for a diffusive step in the liquid. Ohiained from dielectric relaxation data. 

The best proof of invalidity of the confinement scenario is provided by the DSC and dielectric relaxation data from Arrese-Igor et al. (2010) on the highly asymmetric blends of polyisoprene (PI) of molecular weight Af = 2700 with poly(tert-butylstyrene) (PtBS) of two different molecular weights M = 1300 and Mn = 2300. Their DSC measurements confirm the presence of two separate glass transition temperatures of the PI and the PtBS components for blends with less than 50% of PI. The components Tgf and Tgs of PI and PtBS in 35% and 20% PI blends from DSC are indicated by arrows in Figures 5.28 and 5.29, where the dielectric relaxation times data are presented in an Arrhenius plot. Like that discussed before in the PEO/PMMA blends, the detection of Tgf of the fast component by DSC, PI in the present case has basically ruled out the confinement scenario. This is because the relaxation time of order of 100 s obtained by DSC has to be that of the a-relaxation of the PI component. 

Thus, from both the DSC and the dielectric relaxation data cited earlier, the crossover of r y of PI in the HAPB of 35% and 20% PI with PtBS from VFT to Arrhenius dependences is not found at any temperature. This is the most direct proof that the confinement scenario is unreal. Arrese-lgor et al. (2010) admitted that the crossover predicted by the confinement scenario is not observed on Xaf of PI in the HAPB, but still maintained a vestige of confined dynamics by invoking the marked decrease of the intensity and increase of width as temperature decreases of the a-loss peak of PI in the 20% PI blend. 

Stickel, F., Fischer, E. W., and Richer , R., Dynamics of glass-forming liquids 1. Temperature-derivative analysis of dielectric relaxation data, J. Chem. Phys., 102, 6251-6257 (1995). 

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