Solution of Ornstein-Zernike Equation for a Mixture of Hard Spheres with Yukawa Closure: the Case of Factorizable Coefficients

Ginoza, Mitsuaki

doi:10.1143/jpsj.55.95

Cited by 74 publications

(28 citation statements)

References 16 publications

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“…41,[43][44][45]55 The MSA solution is reasonably accurate for large concentrations and weak Yukawa repulsion. However, it predicts nonphysical negative values of g(x) for strong Yukawa repulsion and low concentrations.…”

Section: A Size-rescaled Msa Schemementioning

confidence: 92%

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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: A Size-rescaled Msa Schemementioning

confidence: 92%

“…The MSA solution was further simplified by Blum and Hoye, 42 and Cummings and Smith. 43,44 A particularly simple form of the MSA solution was obtained more recently by Ginoza 45 (see also Ref. 5), invoking a simple quartic algebraic equation from which the physical root is straightforwardly deduced.…”

Section: C(rmentioning

confidence: 96%

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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“…Properties of polydisperse hard-sphere fluid with factorized Yukawa potential have been studied earlier [5][6][7][8]. Our choice for the Yukawa potential enables us to study the effects due to the departure of the potential from its factorizable version.…”

Section: One-yukawa Polydisperse Hard-sphere Fluidmentioning

confidence: 99%

“…One of the possibilities in solving the problem is to use an analytical solution of the corresponding integral equation approximation. This possibility was used to describe the properties of polydisperse hard-sphere fluid utilizing Percus-Yewick (PY) approximation [1][2][3][4] and polydisperse Yukawa hard-sphere fluid using mean spherical approximation [5][6][7] (MSA). More recently the MSA was used to study the phase behavior of polydisperse hard-sphere mixtures with Yukawa [8], Coulombic [9][10][11], and sticky [12] interactions outside the hard core.…”

Section: Introductionmentioning

confidence: 99%

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions

Kalyuzhnyi

Cummings

2006

The Journal of Chemical Physics

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Препринти Iнституту фiзики конденсованих систем НАН України розповсюджуються серед наукових та iнформацiйних установ. Вони також доступнi по електроннiй комп'ютернiй мережi на WWW-сер-верi iнституту за адресою http://www.icmp.lviv.ua/ Анотацiя. У статтi узагальнено розв'язок середньо-сферичного наб-лиження для багатокомпонентної багатоюкавiвської рiдини твердих сфер для полiдисперсного випадку. Узагальнення використовує роз-клад по ортогональних полiномах, застосований у роботах Ладо (Phys. Rev. E 54, 4411(1996)). Представлено замкнутi аналiтичнi ви-рази для структурних та термодинамiчний властивостей системи, якi поданi в термiнах параметрiв, що з'являються пiдчас розв'язку. Для iлюстрацiї, з допомогою методу описуються термодинамiчнi власти-востi одно та двоюкавiвської моделi.Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions Yurij V. Kalyuzhnyi and Peter T. CummingsAbstract. The Blum-Høye solution of the MSA for multi-component multi-Yukawa hard-sphere fluid is extended to a polydisperse multiYukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado (Phys.Rev.E 54, 4411(1996)). Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters, that follow directly from the solution. By way of illustration the method of solution is applied to describe the thermodynamic properties of one-and two-Yukawa versions of the model. Подається в Журнал хiмiчної фiзики

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“…The Ornstein-Zernike direct correlation functions c~j (r), where i and j refer to the various components of the mixture, take at distances larger than contact the form ZiZj (6) cij(r) = kBTr exp [-~r] for r > ~ij (~i § Cry)/2, where zi are the ionic charges and ~i the ionic diameters. Using earlier results by Blum [15] and Ginoza [16], the excess internal energy Uex per unit volume can be cast into the form The expressions for the quantities ~IN, 2i, ~i and Vi can be found in ref. [16], while the self-consistent equation satisfied by the inverse length F has been derived in ref.…”

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confidence: 99%

A model for the metal-non-metal transition in metal-molten-salt solutions

1994

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(ricevuto il 7 Marzo 1994; approvato il 26 Aprile 1994)Summary. --We outline a theory for the metal-non-metal transition occm'ring in solutions of alkali metals in molten alkali halides as governed by a balance between the binding of ionic clusters by localized electrons and the excess free energy of an ionic assembly screened by metallic electrons. In the model the transition is driven by the composition dependence of the screening length. The theory is amenable to an analytic solution within the mean spherical approximation when Thomas-Fermi screening is used and the ions are described by charged hard spheres. Metal-molten-salt solutions and the metal-non-metal (MNM) and demixing (DM) transitions that they undergo with varying composition have attracted considerable experimental attention in recent years (for reviews see [I-3]). Related theoretical work includes evaluations of thermodynamic, structural and dynamical properties of alkali-alkali halide solutions within models which treat the valence electrons accompanying the metallic component as either forming an inert neutralizing background [4,5] or screening the ionic interactions in a linear-response approach [6][7][8], as is most appropriate in the metallic range of composition. The salt-rich end of the phase diagram has also been studied by means of first-principles computer simulations [9]. The evidence on the MNM and DM transitions has been discussed in comparison with that on metal ammonia solutions [10].In the present note we outline a liquid-structure theory of the MNM transition in these melts as arising from a balance between the free-energy gain from binding the valence electrons in localized states associated with ionic clusters and the free-energy gain from dissolving the components of such clusters into an ionic asserhbly screened by metallic electrons. We also point out a connection with the Mott criterion for MNM transitions, in which the controlling factor is the composition-dependent screening length in comparison with the size of the cluster. We consider for definiteness the case of the Kc-(KC1)I-c liquid mixture as an illustrative example, although the assumptions of the theory in its simplest formulation would probably be more appropriate to systems where the localized electronic state is more strongly bound 307

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Solution of Ornstein-Zernike Equation for a Mixture of Hard Spheres with Yukawa Closure: the Case of Factorizable Coefficients

Cited by 74 publications

References 16 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

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions

A model for the metal-non-metal transition in metal-molten-salt solutions

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