Dispersion equations which model high-frequency linear viscoelastic behavior as described by fractional derivative models

Within the conceptual framework of linear response theory, the real and ima ginary parts of the memory function are related through the so-called Krame rs-Kronig dispersion equations (DE). In the field of linear viscoelasticity , the high-frequency asymptotic behavior predicted by these DE is that the real part converges to a constant, i.e. the glassy modulus, and the imagina ry part vanishes. However, experimental results in the high-frequency regio n on glassy polymers illustrate that both real and imaginary parts weakly i ncrease with increasing frequency. Such behavior contradicts the usual DE a symptotic pattern. In this paper DE are obtained which correctly describe t he experimental high-frequency power-law behavior, i.e, both real and imagi nary parts scale like omega(alpha), for omega --> + infinity, where alpha i s an element of(0, 1). The analytical derivation uses as starting point the linear viscoelastic behavior as predicted by the Maxwell fractional deriva tive model. A different DE pair possibly describing the behavior of elastom ers is also presented. (C) 2000 Elsevier Science Ltd, All rights reserved.