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Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories.
- Source :
-
Journal of Chemical Physics . 2/21/2006, Vol. 124 Issue 7, p074508. 17p. 4 Charts, 11 Graphs. - Publication Year :
- 2006
-
Abstract
- Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as the dilute solutions of polymer chains in good solvents. The simplest bounded potential is that of penetrable spheres, which takes a positive finite value if the two spheres are overlapped, being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model is far from trivial, since interactions are not restricted to nearest neighbors and so its exact solution is not known. In this paper the structural properties of one-dimensional penetrable rods are studied. We first derive the exact correlation functions of the penetrable-rod fluids to second order in density at any temperature, as well as in the high-temperature and zero-temperature limits at any density. It is seen that, in contrast to what is generally believed, the Percus-Yevick equation does not yield the exact cavity function in the hard-rod limit. Next, two simple analytic theories are constructed: a high-temperature approximation based on the exact asymptotic behavior in the limit T→∞ and a low-temperature approximation inspired by the exact result in the opposite limit T→0. Finally, we perform Monte Carlo simulations for a wide range of temperatures and densities to assess the validity of both theories. It is found that they complement each other quite well, exhibiting a good agreement with the simulation data within their respective domains of applicability and becoming practically equivalent on the borderline of those domains. A comparison with numerical solutions of the Percus-Yevick and the hypernetted-chain approximations is also carried out. Finally, a perspective on the extension of our two heuristic theories to the more realistic three-dimensional case is provided. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00219606
- Volume :
- 124
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Journal of Chemical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 19876171
- Full Text :
- https://doi.org/10.1063/1.2166385