Structural relaxation and rheological response of a driven amorphous system

Abstract

The interplay between the structural relaxation and the rheological response of a binary LJ glass former is studied via MD simulations. In the quiescent state, the model is well known for its sluggish dynamics and a two step relaxation of correlation functions at low temperatures. An ideal glass transition temperature of $T_c = 0.435$ has been identified in the previous studies via the analysis of the system's dynamics in the frame work of the mode coupling theory of the glass transition [W. Kob and H.C. Andersen, PRE 51, 4626 (1995)]. Here, we test wether a signature of this ideal glass transition can also be found under shear. Indeed, the following distinction in the structural relaxation is found: In the supercooled state, the structural relaxation is dominated by the shear at relatively high shear rates, $\dotγ$, whereas at sufficiently low $\dotγ$ the (shear-independent) equilibrium relaxation is recovered. In contrast to this, the structural relaxation of a \emph{glass} is always driven by shear. This distinct behavior of the correlation functions is also reflected in the rheological response. In the supercooled state, the shear viscosity, $η$, decreases with increasing shear rate (shear thinning) at high shear rates, but then converges toward a constant as the $\dotγ$ is decreased below a (temperature-dependent) threshold value. Below $T_c$, on the other hand, the shear viscosity grows as $η\propto 1/\dotγ$ suggesting a divergence at $\dotγ =0$. Thus, within the accessible observation time window, a transition toward a non-ergodic state seems to occur in the driven glass as the driving force approaches zero.