Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture. II. Intermediate scattering function and dynamic susceptibility

We have performed a molecular dynamics computer simulation of a supercooled binary Lennard-Jones system in order to compare the dynamical behavior of this system with the predictions of the idealized version of mode-coupling theory (MCT). By scaling the time t by the temperature dependent α-relaxation time τ(T), we find that, in the α-relaxation regime, F(q,t) and ${\mathit{F}}_{\mathit{s}}$(q,t), the coherent and incoherent intermediate scattering functions, for different temperatures each follows a q-dependent master curve as a function of scaled time. We show that during the early part of the α relaxation, which is equivalent to the late part of the β relaxation, these master curves are well approximated by the master curve predicted by MCT for the β relaxation. This part is also fitted well by a power law, the so-called von Schweidler law. We show that the effective exponent b′ of this power law depends on the wave vector q if q is varied over a large range. The early part of the β-relaxation regime does not show the critical decay predicted by MCT. The q dependence of the nonergodicity parameter for ${\mathit{F}}_{\mathit{s}}$(q,t) and F(q,t) is in qualitative agreement with MCT. On the time scale of the late α relaxation the correlation functions show a Kohlrausch-Williams-Watts behavior (KWW).

The KWW exponent β is significantly different from the effective von Schweidler exponent b′. At low temperatures the α-relaxation time τ(T) shows a power-law behavior with a critical temperature that is the same as the one found previously for the diffusion constant [Kob and Andersen, Phys. Rev. Lett. 73, 1376 (1994)]. The critical exponent of this power law and the von Schweidler exponent b′ fulfill the connection proposed by MCT between these two quantities. We also show that the q-dependent relaxation times extracted from the correlation functions are in accordance with the α-scale universality proposed by MCT. The dynamic susceptibility χ′′(ω) data for different temperatures also fall on a master curve when frequency is scaled by the location of the minimum between the microscopic peak and the α peak and χ′′ is scaled by its value at this minimum. The low frequency part of this master curve can be fitted well with a functional form predicted by MCT. However, the optimal value for the exponent parameter from this fit does not agree with the one determined from the corresponding fit in the time domain. The high frequency part of the master curve of χ′′(ω) cannot be fitted well by the functional forms predicted by MCT, in accordance with our findings from the time domain. We test various scaling laws predicted by the theory and find that they are qualitatively correct but that the exponents do not fulfill certain relations predicted by the theory if they involve the critical exponent a of MCT. This discrepancy can be rationalized by means of the strong influence of the microscopic dynamics on the β relaxation at early times. Those scaling laws that do not involve the critical exponent a are in qualitative and quantitative accordance with the theory.