On the Concentration Fluctuations of a Binary Mixture of Hard Spheres

1988 ◽  
Vol 43 (10) ◽  
pp. 847-850 ◽  
Author(s):  
L. J. Gallego ◽  
J. A. Somoza ◽  
M. C. Blanco
Keyword(s):  
Phase Transition ◽  
Binary Mixture ◽  
Hard Sphere ◽  
Equations Of State ◽  
Hard Spheres ◽  
Fluid Phase ◽  
Packing Fraction ◽  
Concentration Fluctuations ◽  
Entropy Of Mixing ◽  
First Approximation

Abstract We have computed the concentration fluctuations, Scc(0), in a binary mixture of hard spheres on the basis of the Percus-Yevick compressibility (PYC), Percus-Yevick virial (PYV) and Mansoori- Carnahan-Starling (MCS) equations of state. We have also used the Flory-Huggins (FH) model for an athermal solution as a first approximation to the hard sphere description. At fluid packing fraction values, the PYC and MCS theories give similar Scc (0) results, whereas the differences between these and those derived from the PYV equation are more significant. The FH model appears to give rather bad results, which is consistent with the studies of other authors on the entropy of mixing of a binary mixture of hard spheres. The impossibility of a fluid-fluid phase transition in this kind of system is clearly shown by the behaviour of Scc (0) in any of the theories studied.

Solid-fluid phase transition of quantum hard spheres at finite temperatures

1988 ◽  
Vol 38 (1) ◽  
pp. 135-162 ◽  
Author(s):  
Karl J. Runge ◽  
Geoffrey V. Chester
Keyword(s):  
Phase Transition ◽  
Hard Spheres ◽  
Fluid Phase

Demixing phase transition in a mixture of hard-sphere dipoles and neutral hard spheres

1991 ◽  
Vol 67 (19) ◽  
pp. 2674-2677 ◽  
Author(s):  
X. S. Chen ◽  
M. Kasch ◽  
F. Forstmann
Keyword(s):  
Phase Transition ◽  
Hard Sphere ◽  
Hard Spheres

scholarly journals Crystallizing hard-sphere glasses by doping with active particles

Soft Matter ◽  
2014 ◽  
Vol 10 (35) ◽  
pp. 6609-6613 ◽  
Author(s):  
Ran Ni ◽  
Martien A. Cohen Stuart ◽  
Marjolein Dijkstra ◽  
Peter G. Bolhuis
Keyword(s):  
Hard Sphere ◽  
Hard Spheres ◽  
Packing Fraction ◽  
Active Particles

A large nucleated crystalline cluster in a glass of hard spheres at a packing fraction of 0.61 induced by 10% active hard spheres inside.

Equations of state for hard spheres and hard-sphere chains

2000 ◽  
Vol 167 (2) ◽  
pp. 187-206 ◽  
Author(s):  
In Ha Kim ◽  
Young Chan Bae
Keyword(s):  
Hard Sphere ◽  
Equations Of State ◽  
Hard Spheres

scholarly journals Temperature dependence of entropy of mixing of liquid alkali alloys

BIBECHANA ◽  
2016 ◽  
Vol 14 ◽  
pp. 16-29
Author(s):  
B K Singh ◽  
Sudhir Singh ◽  
Golak Kumar Mandal ◽  
Dhiraj Kumar Singh
Keyword(s):  
Temperature Dependence ◽  
Hard Sphere ◽  
Liquid Metals ◽  
Packing Fraction ◽  
Physical Parameters ◽  
Pure Liquid ◽  
Hard Sphere Model ◽  
Sphere Diameter ◽  
Entropy Of Mixing ◽  
Increasing Temperature

A semi-empirical approach has been considered to study the temperature dependence of entropy of mixing, (ΔsM), for various alkai-alkali alloys using hard-sphere model. The most important physical parameters occurring here is the hard-sphere diameter (σ) and the packing fraction (η). For pure liquid metals, this is usually determined empirically from the observed entropy as a function of temperature which in turn are utilised to compute ΔSM for Na-K, K-Rb, Na-Rb, NaCs, Rb-Cs and K-Cs alloys as a function of concentration at five different temperature ranging from 400°K-800°K. The study reveals that entropy of mixing for Na-K, Na-Rb and K-Rb systems decreases with increasing temperature. But the result for Cs-based alloys exhibit a mixed behaviour.BIBECHANA 14 (2017) 16-29

scholarly journals Bose–Einstein Condensation as a Deposition Phase Transition of Quantum Hard Spheres and New Relations between Bosonic and Fermionic Pressures

2020 ◽  
Vol 65 (11) ◽  
pp. 963
Author(s):  
К.А. Bugaev ◽  
O.I. Ivanytskyi ◽  
B.E. Grinyuk ◽  
I.P. Yakimenko
Keyword(s):  
Phase Transition ◽  
Equations Of State ◽  
Canonical Ensemble ◽  
Hard Spheres ◽  
Hard Core ◽  
Grand Canonical Ensemble ◽  
Einstein Condensation ◽  
Dirac Particles ◽  
Bose Einstein ◽  
Grand Canonical

We investigate the phase transition of Bose–Einstein particles with the hard-core repulsion in the grand canonical ensemble within the Van der Waals approximation. It is shown that the pressure of non-relativistic Bose–Einstein particles is mathematically equivalent to the pressure of simplified version of the statistical multifragmentation model of nuclei with the vanishing surface tension coefficient and the Fisher exponent тF = 5/2 , which for such parameters has the 1-st order phase transition. The found similarity of these equations of state allows us to show that within the present approach the high density phase of Bose-Einstein particles is a classical macro-cluster with vanishing entropy at any temperature which, similarly to the system of classical hard spheres, is a kind of solid state. To show this we establish new relations which allow us to identically represent the pressure of Fermi–Dirac particles in terms of pressures of Bose–Einstein particles of two sorts.

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