MECHANICAL SPECTROMETRY OF THE BETA-RELAXATION IN POLY(METHYL METHACRYLATE)

Shear modulus and loss spectra of poly(methyl methacrylate) (PMMA) have been measured over a frequency range from 2 x 10(-4) to 1 Hz and under isothermal conditions at temperatures from 200 to 300 K, and similar measurements have been made for fixed frequencies of 0.1 and 1 Hz in the temperature range of its beta-relaxation. The height of the beta-relaxation peak increases with increase in the temperature, and its rate is described according to the Arrhenius and Eyring equations. The spectra of mechanical loss are asymmetric and broader at the high-frequency side despite the contributions, which are significant at the low-frequency side or at high temperatures, from the alpha-relaxation process. The shape of the spectra has been analyzed in terms of (i) a stretched exponential or Kohlrausch-Williams-Watts relaxation function and (ii) a Gaussian distribution function modified to introduce asymmetry in a relaxation spectrum. A procedure for the analysis of the real and imaginary components of the elastic modulus has been developed for both functions and used to obtain the strength of the beta-relaxation process. The modified Gaussian distribution allows an interpretation in terms of the distribution of activation entropies and enthalpies and a self-consistent description of the isothermal spectra and of the mechanical relaxation data measured for a fixed frequency but at different temperatures. The dielectric relaxation rate for the beta-process is the same as the mechanical relaxation rate over a wide range of temperature. Theoretical implications of these observations of the mechanical spectra for our concepts of localized relaxation in amorphous materials have been discussed, and it is argued that the frequency-independent background loss in PMMA is negligible or zero.