Theory for Swap Acceleration near the Glass and Jamming Transitions for Continuously Polydisperse Particles

Abstract

Swap algorithms can shift the glass transition to lower temperatures, a recent unexplained observation constraining the nature of this phenomenon. Here we show that swap dynamic is governed by an effective potential describing both particle interactions as well as their ability to change size. Requiring its stability is more demanding than for the potential energy alone. This result implies that stable configurations appear at lower energies with swap dynamics, and thus at lower temperatures when the liquid is cooled. The magnitude of this effect is proportional to the width of the radii distribution, and decreases with compression for finite-range purely repulsive interaction potentials. We test these predictions numerically and discuss the implications of these findings for the glass transition.We extend these results to the case of hard spheres where swap is argued to destroy meta-stable states of the free energy coarse-grained on vibrational time scales. Our analysis unravels the soft elastic modes responsible for the speed up swap induces, and allows us to predict the structure and the vibrational properties of glass configurations reachable with swap. In particular for continuously poly-disperse systems we predict the jamming transition to be dramatically altered, as we confirm numerically. A surprising practical outcome of our analysis is new algorithm that generates ultra-stable glasses by simple descent in an appropriate effective potential.

Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters

“…A truncated and discretized Gaussian size distribution with the same R as, but somewhat lower polydispersity δ = 7% than measured was used. Simple particle translations combined with swap moves [30] allow the efficient sampling of phase space up to high φ [31]. Simulations were run with N = 19 991 particles in a cubic box with periodic conditions.…”

Infinitesimal asphericity changes the universality of the jamming transition

“…The theoretical understanding of the jamming of nonspherical particles is challenging because particles do not hold rotational symmetry. In the previous work [5,9], we proposed a way to bypass this difficulty by considering the mapping from nonspherical particles to the breathing particles (BP), defined as a system of spherical particles for which their diameters are allowed to fluctuate [10]. An advantage of the BP particles is that the model holds the rotational symmetry, and thus, one can apply the same technique developed for the spherical particle without any difficulty.…”

Theory for the single-particle dynamics in glassy mixtures with particle size swaps

“…First, computer simulations studies [6] showed that particle size exchanges in systems with a continuous polydispersity result in the largest speed-up of the dynamics. Second, a system with a continuous polydispersity allows one to treat the particles' diameters as additional variables that evolve according to their own equation of motion [14]. The distribution of the particles diameters is then enforced by a diameter-dependent chemical potential-like term, which plays the role of an one-particle external potential for the diameter variable.…”

“…Next, Brito et al [14], in the context of continuous distribution of particles' diameters, proposed to treat the diameters as additional variables, endowed with their own equations of motion (stochastic in the case of the Monte Carlo dynamics and deterministic continuous time equations in the case of the Newtonian-like dynamics). This allowed Brito et al to put forward some general arguments, which imply that allowing particle size swaps should lead to the decrease of the onset temperature for the glassy dynamics.…”