Radial Distribution Function and the Direct Correlation Function for One‐Dimensional Gas with Square‐Well Potential

1968 ◽  
Vol 48 (9) ◽  
pp. 4246-4251 ◽  
Author(s):  
Shigetoshi Katsura ◽  
Yoshio Tago
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Direct Correlation Function ◽  
One Dimensional ◽  
Square Well

SQUARE-WELL FLUID AT LOW DENSITIES

1967 ◽  
Vol 45 (12) ◽  
pp. 3959-3978 ◽  
Author(s):  
J. A. Barker ◽  
D. Henderson
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Critical Temperature ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Virial Coefficients ◽  
Hard Core ◽  
Direct Correlation Function ◽  
Virial Series ◽  
Square Well

Values for the radial distribution function and the direct correlation function at low densities and for the first five virial coefficients are obtained for a fluid of molecules interacting according to the square-well potential when the width of the attractive well is half the radius of the hard core. It is found that the higher-order coefficients are surprisingly large and, as a result, the virial series fails to converge even at temperatures and volumes significantly greater than the critical temperature and volume. Comparisons of these exact virial coefficients with those given by several approximate theories are made. Values are also given for the first five virial coefficients when the width of the attractive well is equal to the radius of the hard core.

ON THE TWO-POINT CORRELATION FUNCTION FOR DISPERSIONS OF NONOVERLAPPING SPHERES

1998 ◽  
Vol 08 (02) ◽  
pp. 359-377 ◽  
Author(s):  
KONSTANTIN Z. MARKOV ◽  
JOHN R. WILLIS
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Characteristic Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Integral Formula ◽  
Probability Densities ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Point Level

Random dispersions of spheres are useful and appropriate models for a wide class of particulate random materials. They can be described in two equivalent and alternative ways — either by the multipoint moments of the characteristic function of the region, occupied by the spheres, or by the probability densities of the spheres' centers. On the "two-point" level, a simple and convenient integral formula is derived which interconnects the radial distribution function of the spheres with the two-point correlation of the said characteristic function. As one of the possible applications of the formula, the behavior of the correlation function near the origin is studied in more detail and related to the behavior of the radial distribution function at the "touching" separation of the spheres.

On the theory of fluids

1953 ◽  
Vol 216 (1125) ◽  
pp. 203-218 ◽  
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Radial Distribution Function ◽  
Scattering Theory ◽  
Hard Spheres ◽  
Considerable Improvement ◽  
Direct Correlation Function ◽  
X Ray ◽  
X Ray Scattering ◽  
First Approximation

The theory of fluids based on the radial distribution function, g(r) , is related to the direct correlation function, f(r) , of scattering theory. The simplest form of the Born-Green theory is shown to be intimately related to the first approximation to f(r) . The second approximation to f(r) is considered in detail, and shown to effect a considerable improvement on earlier theories. It leads to a critical point at which p/ρkT =⅓. Fournet’s application of the Born-Green theory to X-ray scattering by fluids is shown to be correct only to the first power in the density ρ. The terms in ρ and ρ 2 are considered in detail for the case of hard spheres.

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