The influence of third-order interactions on the density profile of associating hard spheres

1997 ◽  
Vol 91 (4) ◽  
pp. 761-767 ◽  
Author(s):  
D. HENDERSON ◽  
S. SOKOŁOWSKI ◽  
R. ZAGORSKI ◽  
A. TROKHYMCHUK
Keyword(s):  
Density Profile ◽  
Hard Spheres ◽  
Third Order

The nonuniform Percus–Yevick equation for the density profile of associating hard spheres

1995 ◽  
Vol 103 (11) ◽  
pp. 4693-4696 ◽  
Author(s):  
D. Henderson ◽  
S. Sokol/owski ◽  
A. Trokhymchuk
Keyword(s):  
Density Profile ◽  
Hard Spheres

Density profile of hard spheres interacting with a hard wall

1978 ◽  
Vol 35 (5) ◽  
pp. 1483-1494 ◽  
Author(s):  
S. Sokołowski ◽  
J. Stecki
Keyword(s):  
Density Profile ◽  
Hard Spheres ◽  
Hard Wall

scholarly journals BEHAVIOR OF THE CONFINED HARD-SPHERE FLUID WITHIN NANOSLITS: A FUNDAMENTAL-MEASURE DENSITY-FUNCTIONAL THEORY STUDY

2008 ◽  
Vol 07 (04n05) ◽  
pp. 245-253 ◽  
Author(s):  
MOHAMMAD KAMALVAND ◽  
TAHMINEH (EZZAT) KESHAVARZI ◽  
G. ALI MANSOORI
Keyword(s):  
Density Functional Theory ◽  
Density Profile ◽  
Hard Sphere ◽  
Density Functional ◽  
Hard Spheres ◽  
Calculated Data ◽  
Computational Procedure ◽  
Functional Theory ◽  
Hard Sphere Fluid ◽  
Wide Range

A property of central interest for theoretical study of nanoconfined fluids is the density distribution of molecules. The density profile of the hard-sphere fluids confined within nanoslit pores is a key quantity for understanding the configurational behavior of confined real molecules. In this report, we produce the density profile of the hard-sphere fluid confined within nanoslit pores using the fundamental-measure density-functional theory (FM-DFT). FM-DFT is a powerful approach to studying the structure and the phase behavior of nanoconfined fluids. We report the computational procedure and the calculated data for nanoslits with different widths and for a wide range of hard-sphere fluid densities. The high accuracy of the resulting density profiles and optimum grid-size values in numerical integration are verified. The data reveal a number of interesting features of hard spheres in nanoslits, which are different from the bulk hard-sphere systems. These data are also useful for a variety of purposes, including obtaining the shear stress, thermal conductivity, adsorption, solvation forces, free volume and prediction of phase transitions.

An approximation for the radial distribution function

1957 ◽  
Vol 239 (1218) ◽  
pp. 373-381 ◽  
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Distribution Functions ◽  
Rigid Spheres ◽  
Third Order ◽  
Alternative Assumption ◽  
Better Than

The present paper is concerned with a new approximation for the distribution function of third order. This approximation may be regarded as an improved form of the well-known superposition assumption of Kirkwood. The idea is to add to Kirkwood’s expression a linear combination of distribution functions of the same type, the coefficients of which can be easily determined. The new approximation is introduced in the Bom—Green integral equation for the radial distribution function, for which an expansion into powers of the density is used. From this the terms proportional to the first and second power of the density are calculated. The first four virial coefficients can be expressed as functions of these terms, whether the pressure equation or the compressibility equation is used. Numerical evaluation is performed for the ideal case of a gas of rigid spheres. The value obtained for the fourth virial coefficient is compared with the exact one and those given by naing Kirkwood’s assumption by Rushbrooke & Scoins, and Nijboer & van Hove. It is seen to be more nearly exact and internally consistent. The term proportional to the square of the density, in the expansion of the radial distribution function, appears to be very similar to the exact one as calculated by Nijboer & van Hove. It can be seen to be better than the corresponding term when Kirkwood’s assumption or one proposed by Nijboer & van Hove is used. Finally, an alternative assumption is suggested, and applied to the case of hard spheres.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Sign in / Sign up

Export Citation Format

Share Document