Geometric interpretation of linear viscoelasticity and characterization of chain architecture of polymers

We suggest a new interpretation on time-temperature superposition from the viewpoint of differential geometry and invented a viscoelastic function, called intrinsic phase angle, which is the arc length of the curve in plot of sinδ versus cosδ. The intrinsic phase angle gives a new master curve which is equivalent to conventional one without determination of shift factor. We also developed new plots based on the intrinsic phase angle and applied them to characterization of chain architecture of nonlinear polymers. Although new plots of intrinsic phase angle are similar to van Gurp-Palmen plot, they show the relation between structures of complex fluids and their rheology more clearly.