Virial coefficients and close‐packing of hard spheres and disks

1994 ◽  
Vol 101 (8) ◽  
pp. 7003-7006 ◽  
Author(s):  
Isaac C. Sanchez
Keyword(s):  
Hard Spheres ◽  
Virial Coefficients ◽  
Close Packing

scholarly journals On the relation between virial coefficients and the close-packing of hard disks and hard spheres

2011 ◽  
Vol 134 (8) ◽  
pp. 084502 ◽  
Author(s):  
Miguel Ángel G. Maestre ◽  
Andrés Santos ◽  
Miguel Robles ◽  
Mariano López de Haro
Keyword(s):  
Hard Spheres ◽  
Virial Coefficients ◽  
Close Packing ◽  
Hard Disks

Quantum-chemical analysis of small silver clusters

1987 ◽  
Vol 52 (7) ◽  
pp. 1652-1657 ◽  
Author(s):  
Grigorii V. Gadiyak ◽  
Yurii N. Morokov ◽  
Mojmír Tomášek
Keyword(s):  
Hard Spheres ◽  
Electronic Configuration ◽  
Close Packing ◽  
Basis Sets ◽  
Silver Clusters ◽  
Quantum Chemical Analysis ◽  
Spin Distribution ◽  
Spin Polarized ◽  
Atomic Silver ◽  
Equilibrium Geometries

Total energy calculations of three- and four-atomic silver clusters have been performed by the spin-polarized version of the CNDO/2 method to get the most stable equilibrium geometries, atomization energies, and charge and spin distribution on the atoms for three different basis sets: {s}, {sp}, and {spd}. When viewed from the equilateral triangle and square geometries, the last electronic configuration, i.e. the {spd} one, appears to be most stable with respect to the geometrical deformations considered. In this case, the behaviour of the atoms of both clusters resembles that of hard spheres (i.e. close-packing).

Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

2010 ◽  
Vol 75 (3) ◽  
pp. 359-369 ◽  
Author(s):  
Mariano López De Haro ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Equation Of State ◽  
Binary Mixtures ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Fluid Mixture ◽  
Binary Fluid ◽  
Virial Series ◽  
Consolute Point ◽  
Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

scholarly journals New results for virial coefficients of hard spheres inD dimensions

Pramana ◽  
2005 ◽  
Vol 64 (5) ◽  
pp. 775-783 ◽  
Author(s):  
Nathan Clisby ◽  
Barry M. McCoy
Keyword(s):  
Hard Spheres ◽  
Virial Coefficients

New bounds on the sedimentation velocity for hard, charged and adhesive hard-sphere colloids

2011 ◽  
Vol 667 ◽  
pp. 403-425 ◽  
Author(s):  
W. TODD GILLELAND ◽  
SALVATORE TORQUATO ◽  
WILLIAM B. RUSSEL
Keyword(s):  
Brownian Motion ◽  
Upper Bound ◽  
Hard Sphere ◽  
Large Scale ◽  
Hard Spheres ◽  
Colloidal Dispersions ◽  
Sedimentation Velocity ◽  
Close Packing ◽  
Interparticle Potential ◽  
Equilibrium Microstructure

The sedimentation velocity of colloidal dispersions is known from experiment and theory at dilute concentrations to be quite sensitive to the interparticle potential with attractions/repulsions increasing/decreasing the rate significantly at intermediate volume fractions. Since the differences necessarily disappear at close packing, this implies a substantial maximum in the rate for attractions. This paper describes the derivation of a robust upper bound on the velocity that reflects these trends quantitatively and motivates wider application of a simple theory formulated for hard spheres. The treatment pertains to sedimentation velocities slow enough that Brownian motion sustains an equilibrium microstructure without large-scale inhomogeneities in density.

Exchange and Direct Second Virial Coefficients for Hard Spheres

1966 ◽  
Vol 45 (2) ◽  
pp. 499-508 ◽  
Author(s):  
Marjorie E. Boyd ◽  
Sigurd Yves Larsen ◽  
John E. Kilpatrick
Keyword(s):  
Hard Spheres ◽  
Virial Coefficients ◽  
Second Virial Coefficients
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