Analytic solutions for Baxter's model of sticky hard sphere fluids within closures different from the Percus-Yevick approximation.

@article{Gazzillo2004AnalyticSF,
  title={Analytic solutions for Baxter's model of sticky hard sphere fluids within closures different from the Percus-Yevick approximation.},
  author={Domenico Gazzillo and Achille Giacometti},
  journal={The Journal of chemical physics},
  year={2004},
  volume={120 10},
  pages={
          4742-54
        }
}
We discuss structural and thermodynamical properties of Baxter's adhesive hard sphere model within a class of closures which includes the Percus-Yevick (PY) one. The common feature of all these closures is to have a direct correlation function vanishing beyond a certain range, each closure being identified by a different approximation within the original square-well region. This allows a common analytical solution of the Ornstein-Zernike integral equation, with the cavity function playing a… 
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The leading order effects of size polydispersity on the cloud curve delimiting the region of two-phase coexistence and on the associated shadow curve are determined and the extent of size fractionation between the coexisting phases is studied.
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We present a study of the self-consistent Ornstein–Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width δ. The main purpose of this investigation is to elucidate whether, in…
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TLDR
The optimized Baxter model works significantly better than an often used, naive method determining the stickiness parameter by equating the respective second virial coefficients based on the attractive Yukawa and Baxter potentials.
Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions.
TLDR
The main finding is that, for most of the potentials considered, the size-dependence of tij(T, sigmai,sigmaj) can be approximated by essentially the same expression, i.e., a simple polynomial in the variable sigmaisigmaj/sigmaij2, with coefficients depending on the temperature T, or--for depletion interactions--on the packing fraction eta0 of the depletant particles.
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References

SHOWING 1-10 OF 40 REFERENCES
Pathologies in the sticky limit of hard sphere Yukawa models for colloidal fluids: a possible correction
A known ‘sticky hard sphere’ model, starting from a hard sphere Yukawa potential and taking the limit of infinite amplitude and vanishing range with their product remaining constant, is shown to be…
Distribution functions and equations of state of sticky hard sphere fluids in the percus-yevick approximation
Sticky hard spheres beyond the Percus-Yevick approximation.
  • Yuste, Santos
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1993
TLDR
This paper considers the next approximation, i.e. the Pade approximant (3,4), and determine the two new parameters by imposing the values of y(r) at contact point and of the isothermal compressibility.
On the compressibility equation of state for multi-component adhesive hard sphere fluids
The compressibility equation of state (EOS) for a multi-component sticky hard sphere model alternative to Baxter's one is investigated within the mean spherical approximation (MSA). For this model…
Analysis of the hypernetted chain equation for ionic fluids
It is well known that the numerical solution of the hypernetted chain (HNC) equations yields satisfactory results for the pair correlation function of the primitive model of electrolytes and similar…
Structure factors for the simplest solvable model of polydisperse colloidal fluids with surface adhesion
Closed analytical expressions for scattering intensity and other global structure factors are derived for a new solvable model of polydisperse sticky hard spheres. The starting point is the exact…
Sticky spheres and related systems
Some properties of a system of hard-core particles with attractive wells in the Baxter sticky-sphere limit and a related limit are considered, as is the approach to these limits. A demonstration of…
Application of the adhesive sphere model to the structure of colloidal suspensions
The fluid of adhesive sphere (AS) is considered a tool for the investigation of the structure and thermodynamics of dispersed colloidal systems. We compare this model to a more realistic fluid such…
Radial distribution function for sticky hard-core fluids
Following heuristic arguments, analytic expressions for the radial distribution functiong(r) of one- and three-dimensional sticky hard-core fluids (i.e., square-well fluids in a scaled limit of…
A simple approximation for fluids with narrow attractive potentials
A simple modification of the optimized random phase approximation (ORPA) has been made, aimed at improving the performance of the theory for interactions with a narrow attractive well by taking into…
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