Dielectric relaxation concentration dependence

Kakizaki, M. and Hideshima, T., Effect of distribution of free volume on concentration dependence of dielectric relaxation in water mixtures with poly(ethylene glycol) and glucose, Jpn. J. Appl. Phys., Part 1, 1998, 37, 900. 

The concentration dependence of ionic mobility at high ion concentrations and also in the melt is still an unsolved problem. A mode coupling theory of ionic mobility has recently been derived which is applicable only to low concentrations [18]. In this latter theory, the solvent was replaced by a dielectric continuum and only the ions were explicitly considered. It was shown that one can describe ion atmosphere relaxation in terms of charge density relaxation and the elctrophoretic effect in terms of charge current density relaxation. This theory could explain not only the concentration dependence of ionic conductivity but also the frequency dependence of conductivity, such as the well-known Debye-Falkenhagen effect [18]. However, because the theory does not treat the solvent molecules explicitly, the detailed coupling between the ion and solvent molecules have not been taken into account. The limitation of this approach is most evident in the calculation of the viscosity. The MCT theory is found to be valid only to very low values of the concentration. 

In the temperature interval of —70 to 0°C and in the low-frequency range, an unexpected dielectric relaxation process for polymers is detected. This process is observed clearly in the sample PPX with metal Cu nanoparticles. In sample PPX + Zn only traces of this process can be observed, and in the PPX + PbS as well as in pure PPX matrix the process completely vanishes. The amplitude of this process essentially decreases, when the frequency increases, and the maximum of dielectric losses have almost no temperature dependence [104]. This is a typical dielectric response for percolation behavior [105]. This process may relate to electron transfer between the metal nanoparticles through the polymer matrix. Data on electrical conductivity of metal containing PPX films (see above) show that at metal concentrations higher than 5 vol.% there is an essential probability for electron transfer from one particle to another and thus such particles become involved in the percolation process. The minor appearance of this peak in PPX + Zn can be explained by oxidation of Zn nanoparticles. 

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]. 

Figure 53. The dielectric loss of 2-picoline in mixtures with tri-styrene at different concentrations obtained at different temperatures but similar a-relaxation times of the 2-picoline component. For clarity, each spectrum is shifted by a concentration-dependent factor kc. Data from T. Blochowicz and E. A. Rossler, Phys. Rev. Lett. 92, 225701 (2004).

In HF doped ice, Kopp (personal communication) found exponents of 0.4 and 0.6 for the concentration dependence of the dielectric relaxation and of the nuclear magnetic relaxation, respectively. He suggests that the mass-action law does not hold for the relaxations. 

Steinemann (140) found that, at a given temperature, the dielectric relaxation time was inversely proportional to the HF concentration if the concentration was high, and inversely proportional to the square root of the concentration if it was lower. (The relations are listed in Table III.) Thus, the concentration dependence of the dielectric relaxation time does not follow a simple law. The formulation depends on the assumptions one makes about the nature of the relaxation process or processes (ion translation or molecular rotation), carrier concentration and dissociation, and the energies involved. 

Based on the dielectric and dynamic mechanical data, it appears that water and small polar molecules contribute to three dispersions in this poly(amide-imide). One is the low temperature relaxation between -100 and 0°C. This may be a hydrogen bonded relaxation since the activation enthalpy was 30 kJ/mol. This occurs at concentrations of water ranging between 0 to 4 weight percent. Two, the dielectric relaxation between 0 and 70 C can probably be attributed to conductive contaminants whose mobility is dependent upon a minimum amount of water. Three, at high water concentrations, greater than 2 weight percent, the water/NMP contributes to the beta relaxations observed between 50 and 150 C. 

Although the investigation in this paper mainly concentrated on the time evolution of the 001 reflection and the 4-point pattern in the SAXS region, the measurements of the time dependence of overall diffraction patterns in the WAXS region will be required in order to elucidate the microscopic mechanism of the structure formation in oriented PET. In particular, real-time measurement of the intensity distribution of the meridional reflections of higher order will reveal the detailed mechanism of the structure formation. Real-time relaxation measurements such as dielectric relaxation spectroscopy are also desired for this purpose. 

Mixing of fillers into a polymer containing polar groups alters mechanical, thermal, and electrical properties of the polymer matrix, to a degree determined primarily by the nature and amount of the filler and the interaction between the two components. Several dielectric studies concentrated on monitoring composition-dependent perturbations in the sidechain (noncooperative) and the segmental (cooperative) relaxation dynamics of the thermoplastic component. The relaxational response of the polymeric matrix could sometimes be modified by a competition between several factors. One of them is the looser packing of the polymer chains, due to the presence of nanoparticles and interactions with them. This factor leads to increased free volume and enhanced molecular mobility. Another factor is the formation of a layer of modified polymer around the nanoparticles, which leads to decreased molecular mobility [e.g., see Mohomed et al. (2005)]. 

The invariance of relaxation frequency with molecular wei t may not be apparent at finite concentrations of polymer, because cofl — c< interactions can effect the relaxation of internal modes as well as the first order, rotational mode. There have been a number of studies of the concentration dependence of dielectric loss processes some of which show weU the continuous trend in behawour from dilute solution to the bulk state. Temperature variation can provide useful information on the enthalpies of activation of local mode motions. Finally, since such local modes are very structure sensitive, differences in chain tacticity would be expected, and do cause changes in loss behaviour. This prediction has been authenticated for such polymers as poly(methyl methacrylate) and poly(ethyl acrylate). ... 

Experimental data by addition of 1, 3.5, 8 and 15 mol% of C to A are presented in Figs. 30 and 31 [158]. There is a clear evidence for the existence of mixed associates. A chemical variation of the components results a stronger (B/C) or weaker (B/D) increase of the dielectric increment Ay depending on the overall dipole moment in the direction of the molecular long axis (Fig. 32) [159]. The relaxation frequencies do not depend on the concentration but depend on the chemical structure of the associates (Fig. 33). 

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