Relaxation in supercooled liquids: Similarities between projected and unprojected correlation functions

We have examined and interrelated a number of different relaxation processes in supercooled liquids by use of molecular correlation functions, some of which are newly developed and have projected dynamics. Experimentally it is found that in supercooled liquids both the projected and unprojected correlation functions yield similar Cole-Cole plots with skewed arc behavior. The similarity between the projected and unprojected correlation functions is possible only for a certain range of the parameter μJr(0) [τm /τcd]β, where μ and Jr (ω) are the shear modulus and retardational compliance, respectively, τm is the Maxwell stress relaxation time, and τcd and β are the relaxation time and spectral width parameter, respectively, which describe a Cole-Davidson representation of the skewed arc behavior of Jr (ω). The fact that this experimental parameter is found to be of order 2, independent of temperature, has been known, but the fact that values close to this are required for the projected and unprojected correlation functions to be similar, which in turn is required for the Cole-Cole plots for dielectric correlation and retardational compliance to be similar (as observed) is a feature newly explored in this article. © 1989 American Institute of Physics.