# Studies of Dielectric Relaxation in Solid Polymers and Composites

[Doktorsavhandling]

Non-linear characteristics of homogeneous solid polymers and solid polymer-based composites have been studied both experimentally and theoretically. In particular experimental studies of non-linear dielectric response of six homogeneous solid polymeric materials and the influence of the composition on the properties of solid polymer-based composites with high dielectric permittivities have been carried out and a theoretical study of dipole-dipole interaction in solids based on a formulation due to P. Debye and W. Ramm has been made.

Time-domain measurements of the dielectric relaxation of six homogeneous polymers have been analysed using the stretched exponential function exp[-(t/.tau.).^{.beta.}] to describe the dipole relaxation component. The parameter b was found to vary from about 0.2 at low temperatures to about unity for higher temperatures. The lower value indicates strong correlation between the relaxing dipoles while .BETA. = 1 is characteristic of independently relaxing dipoles.

Frequency domain studies of epoxy matrices loaded with barium titanate with and without carbon black as well as with coated carbon or coated copper fibres were also carried out. Due to interfacial polarization, the real and imaginary parts of the permittivity, Re(e*) and Im(e*), of the composites were far higher than those of the matrix itself. In the case of the epoxy-barium titanate system addition of 4.5 vol% carbon black resulted in a great increase in both Re(e*) and Im(e*). Higher concentrations of carbon black had the effect of short-circuiting the interfacial polarization. In the case of the epoxy-carbon fibre and epoxy-copper fibre systems the fibres were coated with insulating epoxy prior to mixing with the epoxy matrix, thus drastically reducing direct electrical contact between the fibres. The resistivities of the composites thus remained high.

The concept of a spectrum of relaxation times was investigated in the context of a dipole-dipole interaction under the influence of an external field. In particular, the formulation of P. Debye and W. Ramm as embodied in their rate equation was analysed in detail. It was found that in contrast to the assumptions of Debye and Ramm the rate equation has no complete set of eigenfunctions due to the lack of self-adjointness. In fact the solutions proposed by Debye and Ramm can be shown not to satisfy their rate equation. Good approximate solutions were obtained using Fourier integral operators. Numerical analysis of those solutions showed that they are unphysical, that is, they lead to results that are contrary to experimental facts. This indicates that the original rate equation proposed by Debye and Ramm does not give a physically correct description of nature. However, in spite of some attempts "repair" of the rate equation has been unsuccessful as yet.

The main conclusion to be drawn from this work is that there are wide gaps in our knowledge of the dielectric characteristics of polymers and polymer-based composites. Further, there is still much room for experience and "Fingerspitzengefühl" in designing and developing specialized polymer-based composites.

**Nyckelord: **time-domain dielectric relaxation, poly(methyl methacrylate), nitrile butadiene rubber, polyamide 6, poly(vinyl chloride), ethylene-vinyl acetate copolymer, poly(vinylidene fluoride), composite, epoxy, carbon black, coated carbon fibre, dielectric permittivity, interfacial polarization

Denna post skapades 2006-09-19. Senast ändrad 2013-09-25.

CPL Pubid: 1355