Exact solution of the mean spherical model for charged hard spheres in a uniform neutralizing background

Palmer, R. G.; Weeks, John D.

doi:10.1063/1.1678973

Cited by 174 publications

(46 citation statements)

References 11 publications

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“…The MSA solution was first derived for general k by Waisman, 41 and in the limit of no screening (k = 0) also by Palmer and Weeks. 1 The original MSA solution by Waisman includes a rather complex set of algebraic equations from which the unique, physically allowed structure factor must be deduced. The MSA solution was further simplified by Blum and Hoye, 42 and Cummings and Smith.…”

Section: C(rmentioning

confidence: 99%

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Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment

Heinen

Holmqvist

Banchio

et al. 2011

The Journal of Chemical Physics

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We present a comprehensive study of the equilibrium pair structure in fluids of nonoverlapping spheres interacting by a repulsive Yukawa-like pair potential, with special focus on suspensions of charged colloidal particles. The accuracy of several integral equation schemes for the static structure factor, S(q), and radial distribution function, g(r ), is investigated in comparison to computer simulation results and static light scattering data on charge-stabilized silica spheres. In particular, we show that an improved version of the so-called penetrating-background corrected rescaled mean spherical approximation (PB-RMSA) by Snook and Hayter [Langmuir 8, 2880[Langmuir 8, (1992], referred to as the modified PB-RMSA (MPB-RMSA), gives pair structure functions which are in general in very good agreement with Monte Carlo simulations and results from the accurate but nonanalytical and therefore computationally more expensive Rogers-Young integral equation scheme. The MPB-RMSA preserves the analytic simplicity of the standard rescaled mean spherical (RMSA) solution. The combination of high accuracy and fast evaluation makes the MPB-RMSA ideally suited for extensive parameter scans and experimental data evaluation, and for providing the static input to dynamic theories. We discuss the results of extensive parameter scans probing the concentration scaling of the pair structure of strongly correlated Yukawa particles, and we determine the liquidsolid coexistence line using the Hansen-Verlet freezing rule.

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Section: C(rmentioning

confidence: 99%

“…The model system of hard spheres with Yukawa-type repulsive pair interaction, commonly referred to as the hardsphere Yukawa (HSY) fluid, has been extensively used as a reference system for a large variety of atomic systems including plasmas and liquid metals, [1][2][3] and alloys. 4,5 In the HSY model, the pair potential is taken to be…”

Section: Introductionmentioning

confidence: 99%

Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment

Heinen

Holmqvist

Banchio

et al. 2011

The Journal of Chemical Physics

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“…In conclusion, the reliability of the low-density expansion becomes worse as the coupling parameter increases, but one can always find a window of small densities within which the expansion should work. Finally, we mention that in a different calculation scheme, based on an integral-equation-procedure within the socalled mean-spherical-model (MSM) approximation, similar results for the free energy and other thermodynamic functions have been obtained [17,18,19]. Those results also reproduce the limiting laws, namely the hard-core behavior as the coupling parameter goes to zero, and the leading Debye-Hückel correction at low density, and give a quite satisfactory description even for much larger values of the density.…”

Section: The Virial Coefficientsmentioning

confidence: 78%

Virial expansion for charged colloids and electrolytes

Moreira

Netz

2002

The European Physical Journal D - Atomic, Molecular and Optical

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Abstract. Using a field-theoretic approach, we derive the first few coefficients of the exact low-density ("virial") expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters d+ and d− and charge valences q+ and q− of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically d+ ∼ d− and q+ ∼ q−, as well as colloidal suspensions, where the difference in size and valence between macroions and counterions can be very large. We show how to map the TCPHC on a one-component hardcore plasma (OCPHC) in the colloidal limit of large size and valence ratio, in which case the counterions effectively form a neutralizing background. A sizable discrepancy with the standard OCPHC with uniform, rigid background is detected, which can be traced back to the fact that the counterions cannot penetrate the colloids. For the case of electrolyte solutions, we show how to obtain the cationic and anionic radii as independent parameters from experimental data for the activity coefficient.

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“…The charged hard sphere (CHS) model is very useful to evaluate the structure factor of metals in liquid state [1][2][3][4][5][6]. Such a system of CHS in a uniform background of electrons has been solved exactly in a mean spherical approximation by Palmer and Weeks [5]. According to CHS model, the reference system consists of Coulombically interacting positively charged point charges in a uniform background of conduction electrons.…”

Section: Introductionmentioning

confidence: 99%

Structural Study of Liquid Rare Earth Metals From Charged Hard Sphere Reference Fluid

Thakor¹,

Gajjar²,

Jani³

2002

Condens. Matter Phys.

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The present article deals with the investigation of structure factor, s(q) ; radial distribution function, g(r) and interatomic distance, r 1 of liquid rare earth metals, Nd, Dy, Ho, Er and Lu by adopting Charged Hard Sphere (CHS) reference fluid. To describe electron-ion interaction, our well established model potential along with the dielectric function due to Taylor is used. Good agreement between present and experimental findings is concluded.

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Exact solution of the mean spherical model for charged hard spheres in a uniform neutralizing background

Cited by 174 publications

References 11 publications

Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment

Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment

Virial expansion for charged colloids and electrolytes

Structural Study of Liquid Rare Earth Metals From Charged Hard Sphere Reference Fluid

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