Effects of short-range attraction on Jamming transition*

Abstract

Enormous progresses to understand the jamming transition have been driven via simulating purely repulsive particles which were somehow idealized in the past two decades. While the attractive systems are both theoretical and practical compared with repulsive systems. By studying the statistics of rigid clusters, we find that the critical packing fraction ϕ c varies linearly with attraction μ for different system sizes when the range of attraction is short. While for systems with long-range attractions, however, the slope of ϕ c appears significantly different, which means that there are two distinct jamming scenarios. In this paper, we focus our main attention on short-range attractions scenario and define a new quantity named “short-range attraction susceptibility” χ p, which describes the degree of response of the probability of finding jammed states p j to short-range attraction strength μ. Our central results are that χ p diverges in the thermodynamic limit as χ p ∝ | ϕ − ϕ c ∞ | − γ p , where ϕ c ∞ is the packing fraction at the jamming transition for the infinite system in the absence of attraction. χ p obeys scaling collapse with a scaling function in both two and three dimensions, illuminating that the jamming transition can be considered as a phase transition as proposed in previous work.