Classification of the reversible–irreversible transitions in particle trajectories across the jamming transition point

Abstract

The reversible-irreversible (RI) transition of particle trajectories in athermal colloidal suspensions under cyclic shear deformation is an archetypal nonequilibrium phase transition which attracts much attention recently. In the low-density limit, the RI transition is predicted to belong to a universality class of the absorbing state transitions, whereas at the high densities well above the jamming transition density, ϕJ, the transition is discontinuous and is closely related to the yielding transition. The transition between the two limiting cases is largely unexplored. In this paper, we study the RI transition of athermal frictionless colloidal particles over a wide range of densities, with emphasis on the region below ϕJ, by using oscillatory sheared molecular dynamics simulation. We reveal that the nature of the RI transitions in the intermediate densities is very rich. As demonstrated by the previous work by Schreck et al.[Phys. Rev. E. 88, 052205 (2013)], there exist the point-reversible and the loop-reversible phases depending on the density and the shear strain amplitude. We find that, between the two reversible phases, a quasi-irreversible phase where the particles' trajectories are highly non-affine and diffusive. The averaged number of contacts of particles is found to characterize the phase boundaries. We also find that the system undergoes the yielding transition below but in the vicinity of ϕJ when the strain with a small but finite strain rate is applied. This yielding transition line matches with the RI transition line separating the loop-reversible from the irreversible phases. Surprisingly, the nonlinear rheological response called "softening" has been observed even below ϕJ. These findings imply that geometrical properties encoded in the sheared configurations control the dynamical transitions.

Absorbing-State Transitions in Granular Materials Close to Jamming

“…An important open question is the extent to which more detailed aspects of this scenario are universal. In particular, comprehensive reconciliation of recent findings [20,23] with the non-equilibrium phase diagram proposed here may require the inclusion in our model of spatially nonlocal effects such as elastoplasticity and long-range hydrodynamic interactions [32], perhaps guiding the development of new mean-field theories for amorphous materials. Further work is warranted on the AbI-D and D-AbII boundaries which correspond to conditions of maximal data compressibility [45] and mechanical memory storage [46,47] respectively, while fundamental understanding of driven transitions between contact-free, diffusive and jammed states is relevant to suspension flow control [48] and soil liquefaction [49].…”

“…Setting this aside, and the differing governing forces on either side of φ J (hydrodynamic vs. elastic), the two transitions between absorbing and diffusive states share a number of features including a diverging timescale for reaching the steady state [3,4,24,25] and self-organisation [26,27] (including into hyperuniform states [7,8,28,29]). An important question thus emerges about whether, how and where the absorbing-state transitions that mark the absorbingdiffusive boundary meet as φ J is approached from either side.Recent computational studies of soft spheres under cyclic shear address this question [20,23], revealing a convoluted non-equilibrium phase diagram whose interpretation within the context of absorbing-state transitions is hampered by complexities including point vs. loop reversibility [30,31], elasticity [32], and history dependence in φ J [23]. To make progress near φ J , simplified models building upon those of Refs [6,8,21] are warranted.Here we present such a model for driven particulate matter in which particles cease to be alive when they are either contact-free or jammed.…”

“…The nonconserved order parameter A carried by a conserved total number of particles, and the existence of multiple symmetry-unrelated absorbing states, should place these systems in the Manna class of non-equilibrium second order phase transitions [17][18][19]. This is borne out below φ J in experiments [6], molecular dynamics simulations [20] and in simplified models in which shear is mimicked by displacing overlapping particles [6,8,21]. Above φ J , however, experimentalists have reported both second [4] and first [22] order behaviour, with simulations [20,22,23] consistently predicting the latter.…”

“…This is borne out below φ J in experiments [6], molecular dynamics simulations [20] and in simplified models in which shear is mimicked by displacing overlapping particles [6,8,21]. Above φ J , however, experimentalists have reported both second [4] and first [22] order behaviour, with simulations [20,22,23] consistently predicting the latter. First order behaviour could be due to long-range elastoplastic effects present only above φ J and not included in our model introduced below.…”

“…Recent computational studies of soft spheres under cyclic shear address this question [20,23], revealing a convoluted non-equilibrium phase diagram whose interpretation within the context of absorbing-state transitions is hampered by complexities including point vs. loop reversibility [30,31], elasticity [32], and history dependence in φ J [23]. To make progress near φ J , simplified models building upon those of Refs [6,8,21] are warranted.…”