Decoupling of relaxation and diffusion in random pinning glass-forming liquids

We investigate numerically the relaxation and diffusion dynamics in three-dimensional Kob-Andersen glass-forming liquids in which part of the particles are randomly chosen and pinned permanently. We find that both the relaxation dynamics and diffusion dynamics slow down as increasing the pinning concentration (cpin) at fixed temperatures that we study. For higher temperature and lower cpin, the α relaxation time τ and the diffusion coefficient D have the scaling relationship D ∼ τ(-1). However, this coupling behavior breaks down if cpin is further increased, and the scaling relationship is replaced by D ∼ τ(-ν) with ν < 1. At temperatures around the onset temperature of the bulk system, a transition from ν ∼ 0.75 to ν ∼ 0.61 with increasing cpin is found. However, at lower temperatures, ν ∼ 0.67 holds in the whole studied cpin range. By fitting the relaxation time as a function of cpin with Vogel-Fulcher-Tamman equation, we find that the change of scaling exponent ν is accompanied with the change of fragility parameter K at higher temperatures. However, at lower temperatures, pinning particles have little effect on the system's qualitative properties. Moreover, we investigate three measures of heterogeneity of dynamics and find that the relaxation and the diffusion motion of particles show different responses to the pinned particles, which may lead to the slower relaxation than diffusion and the decoupling of relaxation and diffusion. The string-like motion is found to saturate at the mode-coupling theory (MCT) crossover point, which indicates that other relaxation modes may exist below the MCT transition point.