Dielectric relaxation in polymers

If a polymer material exhibits the crystalline solid phase, then on cooling of the melt a direct transition from the melt to crystalline solid is observed. However, as we mentioned above, the solid phase is not a 

Further complexity is added to the picture of molecular dynamics by the presence of side groups attached to the backbone chain which can move independently from the backbone, or by the possibility of network formation by the cross-linked chains. 

The interchain cross-correlations would show up first in bulk samples below the melting temperature, when the translational mobility of chains is severely restricted. In the rubbery, glassy or crystalline states the situation becomes somewhat similar to that encountered in mesomorphic materials and a detailed knowledge of the intermolecular organisation of the chains is important for proper construction of Fi(f). 

Since most of the polymer properties significant to technological applications must depend on molecular motions present in the material, detailed studies of molecular dynamics of the polymer chains are inevitably very important. In order to understand the molecular dynamics of polymer chains in bulk, one customarily begins with estimation of the intrinsic flexibility of the chain. This can be done best when the intramolecular effects are isolated from the interchain forces and effects. For this purpose, studies are performed on polymers dissolved in carefully chosen solvents. Apart from solvation effects, this offers the best available approximation of the free chain. Knowing the intramolecular dynamics of the isolated chain, one can move to investigate polymer mobility in a bulk sample, in particular to clarify interchain phenomena. 

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Relaxations observed in polymers show broader dispersion curves and lower loss maxima than those predicted by the Debye model, and the (s" s ) curve falls inside the semicircle. This led Cole and Cole (1941) to suggest the following semi-empirical equation for dielectric relaxations in polymers ... 

Another way of describing experimentally observed dielectric relaxation in polymers is based on an empirical function formulated by Havriliak and Negami (1967) for the frequency domain ... 

Figure 2 includes curves for and " calculated using equation 4 and the KWW function for = 0.50. The loss curve is broad and nonssrmmetrical, with a total half-width A1/2 2.2 (cf 1.14 for the SRT process). The dielectric data for glycerol conform approximately to the KWW function (fi increases from about 0.6 to 0.95 as temperature is increased). Thus dielectric relaxation in polymers and other materials is characterized by the shapes of the b and b" curves in addition to Ab and (t). 

Adachi, K. (1997), Dielectric relaxation in polymer solutions, in Dielectric Spectroscopy of Polymeric Materials—Fundamental and Applications,P. and Fitzgerald, J. I, eds., ACS, Washington, DC, pp. 261-282. 

The analysis of dielectric relaxation in polymers enables the mobility of functk>nal groups of chains and segments to be studied separately, since the regions of dielectric dispersion are manifested in different conditions for different structural elements of the chains 49,50). 

In order to understand dielectric relaxation in polymer liquid crystals and in liquid crystal polymers it is necessary to review DR phenomena in monomer liquid crystals and in polymers, and this will be done in turn in the next two sections. We begin with liquid crystals. 

Clark, M.B., Zimm,B.H. A linearized chain model for dielectric loss in polymers. ACS Polymer Preprints 12, 116-120 (1971). See also Tobolsky,A.V., DuPre,D.B. Macromolecular relaxation in the damped torsional oscillator and statistical segment models. Advan. Polymer Sci. 6,103-127 (1969). 

In general, the dielectric relaxation in a polar polymer exhibits a wide distribution of relaxation time. In this case, the real and imaginary parts of the dielectric constant are written in the form ... 

Sengwa, R.J., Solvent effects on microwave dielectric relaxation in poly(ethylene glycols), Polym. Int., 1998, 45, 43. 

Based on conceptions of work [105] the specific dielectric relaxation in PPX with M nanoparticles is supposed to be connected with reorientation of dipoles in polymer environment of M nanoparticles that accompanies the electron transfer between M nanoparticles of percolation cluster. Dipole centers in PPX are (Tv-units of polymer chains on a surface of lamellar PPX crystallites. Such centers are characteristic, in particular, for extended polymer defects (dislocations, grain boundaries, interfaces between amorphous and crystalline areas) where, most probably, M nanoparticles are formed. 

The epoxy resin data and the post-cure data, taken together, show that the dipolar relaxation is associated with the temperature dependence of the polymer chain mobility in the vicinity of the glass transition. The WLF analysis of the dipolar relaxation during cure has not been carried out. In order to complete the analysis, correlated measurements of Tg, extent of cure, and dielectric properties must be made as functions of cure time and temperature. In the absence of such definitive studies, various indirect methods have been employed to analyze dielectric relaxations in curing systems, as described below. 

Blyakhman, Ye. M., Borisova, T. I., Levitskaya, Ts. M. Dielectric relaxation in epoxide resins hardened with different anhydrides, Polym. Sci. USSR, 12, 1756 (1970)... 

At this point it is important to recall the theory of dielectric relaxation in a LC polymer having an alignment which is intermediate between H and P. In an earlier paper (11) we show that if the measuring electric field is uniform within the sample then the measured complex permittivity 0(a)) is given by... 

Comprehensive experimental material has been obtained on dielectric relaxation in solutions of polymers with various stereoregularities (e.g. PMMA) ... 

Jakob, E-, Wolarz, E., Bialecka-Florjanczyk, E., Bauman, D., and Haase, W. Dielectric relaxation in a mixture of a side-chain liquid crystalline polymer and a low molecular mass a/o dye. Mol. Cryst. Liq. Cryst. 258, 253 (1995). 

Montes, H. and Cavaille, J.Y. Secondary dielectric relaxations in dried amorphous cellulose and dextran, Polymer, 40, 2649,1999. 

Miyamoto Y, Miyaji H, Asai K (1980) Anisotropy of dielectric relaxation in crystal form II of poly(vinylidene fluoride). J. Polymer Sci., Polymer Phys. Ed. 18 597... 

Polymers that contain the amide group, such as chitin and CS, usually show a low temperature mechanical and dielectric relaxation in the vicinity of -70 °C (at 1 Hz) [43] which is commonly called water relaxation since it is sensibly affected by changes in the moisture content of the polymer. Typically the peak intensity, very low when samples are dried, increases with increasing moisture content, whereas correspondingly the peak maximum shifts to lower temperatures. This relaxation has been assigned as the f)-wet relaxation attributed to the motion of water-polymer complex in the amorphous regions [20, 21]. 

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