Low-Density Fluid Phase of Dipolar Hard Spheres

1996 ◽  
Vol 76 (13) ◽  
pp. 2310-2313 ◽  
Author(s):  
Richard P. Sear
Keyword(s):  
Hard Spheres ◽  
Fluid Phase ◽  
Low Density

On the pair correlation function for hard spheres at low density and temperature

1968 ◽  
Vol 46 (7) ◽  
pp. 879-888 ◽  
Author(s):  
M. S. Miller ◽  
J. D. Poll
Keyword(s):  
Correlation Function ◽  
Pair Correlation Function ◽  
Hard Spheres ◽  
Pair Correlation ◽  
Quantum Mechanical Calculation ◽  
Quantum Mechanical ◽  
Low Density ◽  
Free Particles ◽  
Low Density Limit ◽  
Hard Sphere Diameters

A quantum-mechanical calculation of the pair correlation function for hard spheres in the low-density limit has been made. This calculation is, therefore, valid at low temperatures, where quantum-mechanical diffraction and symmetry effects are important. Results are given for various temperatures and hard-sphere diameters. The pair correlation function is presented in the form g = gB + gS, where gB is the correlation function for Boltzmann particles and gS describes the symmetry effects. It is found that gS(R) for any value of the separation R is always smaller than the corresponding value for free particles.

Monte Carlo and Perturbation Calculations for a Triangular Well Fluid

1974 ◽  
Vol 52 (1) ◽  
pp. 80-88 ◽  
Author(s):  
Damon N. Card ◽  
John Walkley
Keyword(s):  
Monte Carlo ◽  
Hard Spheres ◽  
Low Density ◽  
Monte Carlo Data ◽  
Density Region ◽  
Wide Range ◽  
Model Fluid ◽  
High Density Region ◽  
Superposition Approximation ◽  
Triangular Well Potential

Monte Carlo data have been generated for a simple model fluid consisting of hard spheres with an attractive triangular well potential. The ranges spanned by the temperature and density are as follows. [Formula: see text] and [Formula: see text]. The machine data have been compared to the modern perturbation theories of (i) Barker, Henderson, and Smith and (ii) Weeks, Chandler, and Andersen. Comparison with the machine data shows that the latter theory is successful in the high density region only, but over a wide range of temperature. The Barker–Henderson approach is best in the low density region but the use of the superposition approximation limits the utility of this theory at high densities.

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

KINETIC THEORY AND HYDRODYNAMICS FOR A LOW DENSITY GRANULAR GAS

2001 ◽  
Vol 04 (04) ◽  
pp. 397-406 ◽  
Author(s):  
JAMES W. DUFTY
Keyword(s):  
Kinetic Theory ◽  
Hard Spheres ◽  
A Priori ◽  
Inelastic Collisions ◽  
Low Density ◽  
Qualitative And Quantitative ◽  
Granular Gas ◽  
Rapid Flow ◽  
Special Case ◽  
Domain Of Validity

Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to calculate properties of interest. The domain of validity for such methods is a priori uncertain due to the inelasticity, but recent systematic studies continue to support the utility of kinetic theory and hydrodynamics as both qualitative and quantitative descriptions for many physical states. The basis for kinetic theory and hydrodynamic descriptions is discussed briefly for the special case of a low density gas.

scholarly journals Bulk fluid phase behaviour of colloidal platelet–sphere and platelet–polymer mixtures

2013 ◽  
Vol 371 (1988) ◽  
pp. 20120259 ◽  
Author(s):  
Daniel de las Heras ◽  
Matthias Schmidt
Keyword(s):  
Phase Diagrams ◽  
Nematic Phase ◽  
Density Functional ◽  
Hard Spheres ◽  
Hard Core ◽  
Fluid Phase ◽  
Phase Behaviour ◽  
Size Ratio ◽  
Polymer Mixtures ◽  
Bulk Fluid

Using a geometry-based fundamental measure density functional theory, we calculate bulk fluid phase diagrams of colloidal mixtures of vanishingly thin hard circular platelets and hard spheres. We find isotropic–nematic phase separation, with strong broadening of the biphasic region, upon increasing the pressure. In mixtures with large size ratio of platelet and sphere diameters, there is also demixing between two nematic phases with differing platelet concentrations. We formulate a fundamental measure density functional for mixtures of colloidal platelets and freely overlapping spheres, which represent ideal polymers, and use it to obtain phase diagrams. We find that, for low platelet–polymer size ratio, in addition to isotropic–nematic and nematic–nematic phase coexistence, platelet–polymer mixtures also display isotropic–isotropic demixing. By contrast, we do not find isotropic–isotropic demixing in hard-core platelet–sphere mixtures for the size ratios considered.

scholarly journals Evidence of Structural Inhomogeneities in Hard-Soft Dimeric Particles without Attractive Interactions

Materials ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 84 ◽  
Author(s):  
Gianmarco Munaò ◽  
Franz Saija
Keyword(s):  
Hard Spheres ◽  
Hard Core ◽  
Fluid Phase ◽  
Colloidal Dispersion ◽  
Systematic Investigation ◽  
Distribution Functions ◽  
Structure Factors ◽  
Soft Spheres ◽  
Wide Range ◽  
Structural Inhomogeneities

We perform Monte Carlo simulations of a simple hard-soft dimeric model constituted by two tangent spheres experiencing different interactions. Specifically, two hard spheres belonging to different dimers interact via a bare hard-core repulsion, whereas two soft spheres experience a softly repulsive Hertzian interaction. The cross correlations are soft as well. By exploring a wide range of temperatures and densities we investigate the capability of this model to document the existence of structural inhomogeneities indicating the possible onset of aggregates, even if no attraction is set. The fluid phase behavior is studied by analyzing structural and thermodynamical properties of the observed structures, in particular by computing radial distribution functions, structure factors and cluster size distributions. The numerical results are supported by integral equation theories of molecular liquids which allow for a finer and faster spanning of the temperature-density diagram. Our results may serve as a framework for a more systematic investigation of self-assembled structures of functionalized hard-soft dimers able to aggregate in a variety of structures widely oberved in colloidal dispersion.

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