Nonvibrating granular model for a glass-forming liquid: Equilibration and aging

Abstract

We studied experimentally a model of a glass-forming liquid on the basis of a nonvibrating magnetic granular system under an unsteady magnetic field. A sudden quenching was produced that drove the system from a liquid state to a different final state with lower temperature; the latter could be a liquid state or a solid state. We determined the mean-squared displacement in temporal windows to obtain the dynamic evolution of the system, and we determined the radial distribution function to obtain its structural characteristics. The results were analyzed using the intermediate scattering function and the effective potential between two particles. We observed that when quenching drives the system to a final state in the liquid phase far from the glass-transition temperature, equilibration occurs very quickly. When the final state has a temperature far below the glass-transition temperature, the system reaches its equilibrium state very quickly. In contrast, when the final state has an intermediate temperature but is below that corresponding to the glass transition, the system falls into a state that evolves slowly, presenting aging. The system evolves by an aging process toward more ordered states. However, after a waiting time, the dynamic behavior changes. It was observed that some particles get close enough to overpass the repulsive interactions and form small stable aggregates. In the effective potential curves, it was observed that the emergence of a second effective well due to the attraction quickly evolves and results in a deeper well than the initial effective well due to the repulsion. With the increase in time, more particles fall in the attractive well forming inhomogeneities, which produce a frustration in the aging process.

Scale invariance in a nonvibrating magnetic granular system

“…The effective temperature can also be determined from the Maxwell-Boltzmann velocity distribution. For a wide range of temperatures, we observed that T E is proportional to B o 16 . In this work we used B o to characterize the energy of the particles.…”

“…We studied two cases of the constant magnetic field, B c = 0 G and B c = 36 G, in both cases ν = 9.25 Hz, and B o takes values from 0 to 63 G. The case with B c = 36 G was already considered in Refs. 16,19,20 . The two-dimensional packing fraction (particle concentration) is defined by φ s = Nπσ 2…”

“…The relation between energy input and the randomization of particle motion is described elsewhere 16 . Briefly, when a vertical sinusoidal magnetic field is turned on, each particle tends to align with the magnetic field to reach a minimum potential magnetic energy.…”

“…Usually, a granular system is vibrated vertically to provide energy to the particles [8][9][10][11][12][13] , although several mechanisms have been used to fluidize particle motions 14,15 . One of the advantages of such systems, for instance, is that the interparticle interactions can be modulated by active controls [15][16][17][18] . Another advantage is that their dynamics and structural properties can be studied directly from the positions of the particles, in a straightforward way.…”

Brownian motion in non-equilibrium systems and the Ornstein-Uhlenbeck stochastic process

“…The system is open at the top but gravitation maintains the system two dimensional. Instead of mechanically vibrating the system or injecting an upflow of gas as in other works 18 , 20 – 25 , here we provide kinetic energy to the particles by applying a vertical time dependent sinusoidal magnetic field 26 . The interaction of the varying magnetic field with induced magnetic dipole on the particles, produces a time dependent net force on each particle keeping them in motion.…”