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Andersen–Weeks–Chandler Perturbation Theory and One-Component Sticky-Hard-Spheres

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Abstract

We apply second order Andersen–Weeks–Chandler perturbation theory to the one-component sticky-hard-spheres fluid. We compare the results with the mean spherical approximation, the Percus–Yevick approximation, two generalized Percus–Yevick approximations, and the Monte Carlo simulations.

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References

  1. Baxter, R.J.: Percus–Yevick equation for hard spheres with surface adhesion. Chem. Phys. 49, 2770–2774 (1968)

    ADS  Google Scholar 

  2. Fantoni, R., Gazzillo, D., Giacometti, A.: The thermodynamic instabilities of a binary mixture of sticky hard spheres. Phys. Rev. E 72, 011503-1,14 (2005)

  3. Gazzillo, D., Giacometti, A., Fantoni, R., Sollich, P.: Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions. Phys. Rev. E 74, 051407-1,14 (2006)

  4. Gazzillo, D., Fantoni, R., Giacometti, A.: Phase behavior of polydisperse sticky hard spheres: analytical solutions and perturbation theory. Mol. Phys. 104, 3451–3459 (2006)

    Article  ADS  Google Scholar 

  5. Fantoni, R., Gazzillo, D., Giacometti, A., Sollich, P.: Phase behavior of weakly polydisperse sticky hard spheres: Perturbation theory for the Percus–Yevick solution. J. Chem. Phys. 125, 164504-1,16 (2006)

  6. Fantoni, R., Gazzillo, D., Giacometti, A., Miller, M.A., Pastore, G.: Patchy sticky hard spheres: analytical study and Monte Carlo simulations. J. Chem. Phys. 127, 234507-1,16 (2007)

  7. Gazzillo, D., Fantoni, R., Giacometti, A.: Fluids of spherical molecules with dipolarlike nonuniform adhesion: an analytically solvable anisotropic model. Phys. Rev. E 78, 021201-1,20 (2008)

  8. Gazzillo, D., Fantoni, R., Giacometti, A.: Local orientational ordering in fluids of spherical molecules with dipolar-like anisotropic adhesion. Phys. Rev. E 80, 061207-1,7 (2009)

  9. Hansen, J.P., McDonald, I.R.: Theory of Simple Liquids, 2nd edn. Academic Press, Amsterdam (1986)

    MATH  Google Scholar 

  10. Gazzilloand, D., Giacometti, A.: Analytic solutions for Baxter’s model of sticky hard sphere fluids within closures different from the Percus-Yevick approximation. J. Chem. Phys. 120, 4742–4754 (2004)

    Article  ADS  Google Scholar 

  11. Miller, M.A., Frenkel, D.: Competition of percolation and phase separation in a fluid of adhesive hard spheres. Phys. Rev. Lett. 90, 135702 1,4 (2003)

  12. Andersen, H.C., Weeks, J.D., Chandler, D.: Relationship between the hard-sphere fluid and fluids with realistic repulsive forces. Phys. Rev. A 4, 1597–1607 (1971)

    Article  ADS  Google Scholar 

  13. Kirkwood, J.G.: Statistical mechanics of fluid mixtures. J. Chem. Phys. 3, 300–313 (1935)

    Article  ADS  MATH  Google Scholar 

  14. Henderson, D., Barker, J.A.: Perturbation theories. In: H. Eyring, D. Henderson, W. Jost (eds.) Physical Chemistry: An Advanced Treatise, vol. VIIIA, chap. 6. Academic Press, New York (1971)

  15. Ashcroft, N.W., Lekner, J.: Structure and resistivity of liquid metals. Phys. Rev. 145, 83–90 (1966)

    Article  ADS  Google Scholar 

  16. Kalos, M.H., Whitlock, P.A.: Monte Carlo Methods, vol. I. Wiley, New York (1986)

    Book  MATH  Google Scholar 

  17. Fantoni, R., Gazzillo, D., Giacometti, A.: Stability boundaries, percolation threshold, and two phase coexistence for polydisperse fluids of adhesive colloidal particles. J. Chem. Phys. 122, 034,901–1,15 (2005)

  18. Maestre, M.A.G., Fantoni, R., Giacometti, A., Santos, A.: Janus fluid with fixed patch orientations: theory and simulations. J. Chem. Phys. 138, 094,904–1,19 (2013)

  19. Fantoni, R., Giacometti, A., Maestre, M.A.G., Santos, A.: Phase diagrams of Janus fluids with up-down constrained orientations. J. Chem. Phys. 139, 174,902–1,9 (2013)

  20. Fantoni, R., Pastore, G.: Wertheim and Bjerrum-Tani-Henderson theories for associating fluids: a critical assessment. J. Chem. Phys. 141, 074,108–1,10 (2014)

  21. Fantoni, R., Pastore, G.: Wertheim perturbation theory: thermodynamics and structure of patchy colloids. Mol. Phys. 113, 2593–2607 (2015)

    Article  ADS  Google Scholar 

  22. Fantoni, R., Giacometti, A., Santos, A.: Bridging and depletion mechanisms in colloid-colloid effective interactions: a reentrant phase diagram. J. Chem. Phys. 142, 224,905–1,14 (2015)

  23. Fantoni, R.: The square-shoulder-Asakura-Oosawa model. Physica A 457, 406–412 (2016)

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Trieste, strada Costiera 11, 34151, Grignano, Trieste, Italy

    Riccardo Fantoni

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  1. Riccardo Fantoni
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Correspondence to Riccardo Fantoni.

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Appendix A: Correction to Approximation (45)

Appendix A: Correction to Approximation (45)

One can understand that Eq. (45) is not an exact relation by comparing the small density expansion of the left and right hand side. For the left hand side we have [9]

(A1)

where in the Mayer graphs the filled circles are field points of weight 1 and connecting bonds are Mayer functions of the reference system \(f_0\). And using

(A2)

in the right hand side one finds,

(A3)

So that the correction term is of order \(\rho \), namely,

(A4)

The correct small density expansion for the density derivative of the two body correlation function is

$$\begin{aligned} \frac{\partial \rho _0(1,2)}{\partial \rho }= g_0(1,2)\left[ 2\rho +\rho ^2\alpha _0(1,2)+\rho ^2\alpha _1(1,2)+ \rho ^2\alpha _1^\prime (1,2)+O\left( \rho ^4\right) \right] ~,\quad \end{aligned}$$
(A5)

where the first term neglected in KSA is \(\rho ^2\alpha _1^\prime =O(\rho ^3)\).

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Fantoni, R. Andersen–Weeks–Chandler Perturbation Theory and One-Component Sticky-Hard-Spheres. J Stat Phys 168, 652–665 (2017). https://doi.org/10.1007/s10955-017-1810-2

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  • DOI: https://doi.org/10.1007/s10955-017-1810-2

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