Phase behavior of polydisperse spheres: Simulation strategies and an application to the freezing transition

Abstract

The statistical mechanics of phase transitions in dense systems of polydisperse particles presents distinctive challenges to computer simulation and analytical theory alike. The core difficulty, namely, dealing correctly with particle size fractionation between coexisting phases, is set out in the context of a critique of previous simulation work on such systems. Specialized Monte Carlo simulation techniques and moment free energy method calculations, capable of treating fractionation exactly, are then described and deployed to study the fluid-solid transition of an assembly of repulsive spherical particles described by a top-hat "parent" distribution of particle sizes. The cloud curve delineating the solid-fluid coexistence region is mapped as a function of the degree of polydispersity δ, and the properties of the incipient "shadow" phases are presented. The coexistence region is found to shift to higher densities as δ increases, but does not exhibit the sharp narrowing predicted by many theories and some simulations.

Effect of size polydispersity on the crystal-fluid and crystal-glass transition in hard-core repulsive Yukawa systems

“…Later, solid-fluid coexistence with fractionation was found in more realistic theory and simulation work for the experimentally relevant situation of a fixed overall size distribution. 18,22 Also, in theoretical and computational studies the coexistence of multiple solid phases was found, each with a narrow size distribution, in a system with a large overall polydispersity and a fixed overall size distribution. 18,21,23 It should be noted here that, when given enough time, a system can of course always divide itself up in less polydisperse subsystems that then may form crystal phases.…”

“…In experimental systems the charge on the particles is affected by the local chemical potential of the charge-determining ions; the two limiting cases are described by assuming constant-charge or constant-potential boundary conditions on the particle surface. 12 For the case of hard spheres (or approximations thereof), phenomena arising from the presence of polydispersity have been investigated theoretically, [13][14][15][16][17][18][19][20][21][22][23] computationally 15,[21][22][23][24][25] and experimentally [26][27][28][29] (for a review see Ref. 11).…”

Soft matrix and fixed point of Lennard-Jones potentials for different hard-clusters in size at glass transition

“…Note that the second balance point 0' (1/2, -17/16) only occur on a part of thawed domains, which corresponding to the abnormal heat capacity and can be called as the abnormal or additional balance point at the GT. The additional attractive potential on point 0' comes from the self-similar fluctuation limit equation (14), or the recursion equation (6). …”

“…4, none of the potential curves, except for those who have passed, correspond with the stability condition of Eq. (14).…”

“…Lennard -Jones (L-J) potential is widely used to describe molecule-cluster interactions and glass transition (GT), [1][2][3][4][5][6] However, the fundamental theory to unify the mechanisms for the truncated L-J potential, 7-9 the presence of long-ranged interparticle potentials, 10 the density or cluster size fluctuation stability, 11 and the two kinds of relaxations: fast and slow in current Mode-Coupling Theory, 12 the distribution of particle sizes, 13 or the core difficulty of particle size fractionation 14 in simulation are still not simply and fully established. The relationship between GT and general displacement transitions in condensed matter physics has remained obscure.…”