Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

Abstract

A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction φJ of the polydisperse system as a simple function of M1M3/M 2 2 , where M k is the kth moment of the size distribution. An analysis of experimental and simulation data of φJ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the highdensity region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures. Due to its simplicity and versatility, the hard-sphere (HS) system is considered as a prototype model in statistical physics [1], being also essential in studies in biological systems, granular matter, colloids, engineering, and materials science [2,3]. In an equilibrium monodisperse HS system the only control parameter is the packing fraction φ ≡ π 6 ρσ 3 (ρ and σ being the number density and the diameter of the spheres, respectively), i.e., the volume occupied by the spheres, relative to the total volume V . It is well established that the equilibrium system is in a stable fluid phase from φ = 0 to the freezing packing fraction φ f ≃ 0.492 [4,5], undergoes a fluid-solid transition from φ f to the crystal melting point φ m ≃ 0.543 [5,6], and finally is in a stable solid (crystalline) phase from φ m to the close-packing fraction φ cp = π 6 √ 2 ≃ 0.7405, corresponding to face-centered-cubic close-packing [7,8]. However, beyond the freezing point φ f there is also a region of metastable fluid states that is supposed to end at the glass transition point φ g ≃ 0.58 [2,8]. At even higher densities the system becomes a metastable amorphous solid until it jams at a random close-packing value * andres@unex.es;

i-Rheo: Measuring the materials' linear viscoelastic properties “in a step”!

“…A random close packed sample was obtained by sedimenting a dilute suspension in a centrifuge. The sediment, whose volume fraction was estimated using simulation and experimental results to be / % 0:66 [60][61][62], was subsequently diluted to a volume fraction / ¼ 0:60. Rheological measurements were performed with an ARES G2 strain-controlled rheometer (TA instruments), using a cone and plate geometry of diameter D ¼ 25 mm, angle a ¼ 2 , and truncation d ¼ 0.048 mm.…”

Microstructure and macroscopic properties of polydisperse systems of hard spheres

“…All obtained equations for the jamming density have a similar form; we suggest that the jamming density for systems with arbitrary size distribution can be expressed using only two free parameters (see item 9) and a few moments of the size distribution function. This was recently supported by theory and simulations [248].…”

Equation of state of polydisperse hard-disk mixtures in the high-density regime

“…Recently, a fundamental-measure-theory (FMT) approach to link through an effective packing fraction φ eff the EoS of a monocomponent (three-dimensional) HS fluid to the EoS of a polydisperse HS mixture has been derived by application of some consistency conditions [64][65][66][67]. For completeness, the derivation is summarized in the Appendix.…”

“…In particular, computing the values of the thermodynamic variables with enough accuracy in the metastable states is quite a challenge, so, in general, the metastable fluid branch remains as a largely unexplored ground. In previous work [59][60][61][62][63][64][65][66], we have provided different approximations for linking the equation of state (EoS) of a polydisperse hard-core mixture and the EoS of the monocomponent system. Our approach has, for instance and among other things, allowed us [63,66] to infer the EoS of the (three-dimensional) hard-sphere (HS) fluid in the metastable fluid region from high-density simulation data of polydisperse HS mixtures.…”

“…In previous work [59][60][61][62][63][64][65][66], we have provided different approximations for linking the equation of state (EoS) of a polydisperse hard-core mixture and the EoS of the monocomponent system. Our approach has, for instance and among other things, allowed us [63,66] to infer the EoS of the (three-dimensional) hard-sphere (HS) fluid in the metastable fluid region from high-density simulation data of polydisperse HS mixtures. It also led us to estimate and put some order in a wealth of values for the random close-packing fraction of polydisperse HS mixtures from the knowledge of the random close-packing fraction of the monocomponent system [66].…”