Analysis of linear viscoelasticity of aging soft glasses

Abstract

Aging soft glassy materials do not follow time-translational invariance and violate the principles of linear viscoelasticity, such as the relation between the dynamic moduli in the frequency domain and the stress relaxation modulus in the time domain. Using an aqueous suspension of hectorite clay, a model aging soft glassy material, we account for time-dependent behavior by transforming the experimentally obtained stress relaxation and dynamic moduli from the real-time domain to the effective-time domain by normalizing the real-time by a time-dependent relaxation time. We find that the two sets of experiments probe different aging and deformation timescales, and simultaneous analysis provides insights into material behavior over a wide range of timescales. Careful analysis of the dynamic moduli reveals contamination of (slow) aging α modes by (fast) nonaging β modes, which is not clearly evident in the stress relaxation modulus. On the other hand, the stress relaxation measurements probe timescales long enough to characterize the terminal relaxation of the suspension. A toy Maxwell model is used to elucidate the interaction of the slow aging and fast nonaging modes, and their effect of measurements. The synergistic relationship between the two sets of experiments offers guidelines for characterizing time-dependent materials by generalizing the principles of linear viscoelasticity.