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

Abstract

A proposal to link the equation of state of a monocomponent hard-disk fluid to the equation of state of a polydisperse hard-disk mixture is presented. Event-driven molecular dynamics simulations are performed to obtain data for the compressibility factor of the monocomponent fluid and of 26 polydisperse mixtures with different size distributions. Those data are used to assess the proposal and to infer the values of the compressibility factor of the monocomponent hard-disk fluid in the metastable region from those of mixtures in the high-density region. The collapse of the curves for the different mixtures is excellent in the stable region. In the metastable regime, except for two mixtures in which crystallization is present, the outcome of the approach exhibits a rather good performance. The simulation results indicate that a (reduced) variance of the size distribution larger than about 0.01 is sufficient to avoid crystallization and explore the metastable fluid branch.

Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures

“…Additionally, in previous work [ 63 , 64 , 93 ], we have adopted an approach to relate the EOS of the polydisperse mixture of d -dimensional hard spheres to the one of the monocomponent fluid which differs from the e1 and e2 approaches in that it does not make use of Equation ( 1 ). This involves expressing the excess free energy per particle ( ) of a polydisperse mixture of packing fraction in terms of the one of the corresponding monocomponent fluid ( ) of an effective packing fraction as …”

“…In Equation (21), and are related through while the parameters and are determined by imposing consistency with the (exact) second and third virial coefficients of the mixture, Equations ( 9 ) and (16). More specifically [ 63 , 64 ], …”

“…Thus, according to Equation (22), the effective monocomponent fluid associated with a given mixture has a rescaled packing fraction that is times smaller than that of the mixture. Moreover, in the case of three-dimensional hard-sphere mixtures, Equations (21)–(23) can be derived in the context of consistent fundamental-measure theories [ 63 , 64 , 97 , 98 ].…”

“…While of course real experiments cannot be performed in these systems, they are amenable to computer simulations and theoretical developments. Many aspects concerning hard hyperspheres have been already dealt with, such as thermodynamic and structural properties [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , …”

“…As shown below, extensions of these EOS (denoted as “ 1” and “ 2”) complying with the requirement that the third virial coefficient computed from them is the exact one, may be introduced with little difficulty. More recently, we have developed yet another approximate EOS (henceforth denoted with the label “sp”) for d -dimensional hard-sphere fluid mixtures [ 63 , 64 , 93 ], and newer simulation results for hard hypersphere mixtures have also been obtained [ 57 , 58 , 59 ]. It is the aim of this paper to carry out a comparison between available simulation data for binary additive four- and five-dimensional hypersphere fluid mixtures and our theoretical proposals.…”