Elastic moduli of simple fluids with steeply repulsive potentials

Heyes, D. M.; Aston, Philip J.

doi:10.1063/1.466511

Cited by 22 publications

(22 citation statements)

References 17 publications

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“…As indicated, the symbol y is conventionally used for the left-hand side of (5). For the SRP potential in the large n limit it will also be entirely adequate to obtain the pressure, which we shall need shortly, from (5) with ¹ replaced by ¹ HS ² …º=6 †»¼ 3 HS , with ¼ HS given by (3). We then use the symbol y HS .…”

Section: …5 †mentioning

confidence: 99%

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Viscoelastic behaviour of fluids with steeply repulsive potentials

Powles

Heyes

2000

Molecular Physics

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We analyse the shear stress, C s …t † and pressure or`bulk', C b …t † time-correlation functions for steeply repulsive inverse power¯uids (SRP) in which the particles interact via a pair potential with the analytic form, ¿…r †ˆ°…¼=r † n , in a new approach to the understanding of their viscoelastic properties. We show analytically, and con® rm by molecular dynamics simulations, that close to the hard-sphere limit both these time-correlation functions have the analyticThis leads to an alternative and much simpler derivation of formulae for the shear and bulk viscosities which for the limiting case of hard spheres are numerically very close to the traditional Enskog relations. These simple relations for the ® nite and continuous SRP interaction are in satisfactory agreement with the essentially exact molecular dynamics simulation results for ca. n ¶ 18.

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Section: …5 †mentioning

confidence: 99%

“…These predictions have been con® rmed using molecular dynamics (MD) calculations for the speci® c case of the steeply repulsive potential given in (1) [3,4].…”

Section: Introductionmentioning

confidence: 94%

Viscoelastic behaviour of fluids with steeply repulsive potentials

Powles

Heyes

2000

Molecular Physics

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“…Heyes and Aston [15] demonstrate that the integral in Eq. (4) (and therefore G ∞ ) is infinite for a hard sphere potential with n → ∞.…”

Section: Shear Modulus For the Inverse Power Potentialmentioning

confidence: 97%

High-Frequency Shear Modulus and Relaxation Time of Soft-Sphere and Lennard–Jones Fluids

Keshavarzi

Vahedpour

Alavi

et al. 2004

International Journal of Thermophysics

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The high-frequency shear modulus, G ∞ , and shear relaxation time, τ shear , are obtained using the Zwanzig-Mountain equation for soft-sphere and LennardJones potentials. The Hansen and Weis soft-sphere radial distribution function and the Matteoli-Mansoori Lennard-Jones radial distribution function are used in the equation. The shear relaxation times of different isotherms for both of these fluids pass through a minimum at a reduced density of about 0.7, which indicates a change from fluid-like behavior to viscoelastic behavior. The origins of this common density point are discussed. It is also shown that for the Lennard-Jones fluid, if the ratio of the reduced relaxation time to a power of the reduced temperature is plotted as a function of the reduced density, all isotherms become superimposed on a single curve.

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“…5 ͑Note that the limit n Ϫ1 →0 refers to the hard-sphere potential.͒ A recent application of this procedure to the elastic moduli of steeply repulsive colloidal liquids was given by Heyes and Aston. 3 Using Eq. ͑7͒ we have,…”

Section: ͑36͒mentioning

confidence: 99%

“…2 Theoretical and simulation studies have recently demonstrated that for certain physical properties it is not acceptable that these systems are in fact hard spheres and treat all other properties of the system ͑including thermodynamic properties͒ as being those of a hard-sphere fluid with the same effective diameter, HS . For example, the elastic moduli of hard-sphere systems are infinite, 3 as is the viscosity of true hard-sphere suspensions. 4 Clearly all real colloidal systems have finite elastic moduli and shear viscosities, so the hard-sphere limit in itself has severe limitations as a physical model.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics and elastic moduli of fluids with steeply repulsive potentials

Heyes

1997

The Journal of Chemical Physics

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Analytic expressions for the thermodynamic properties and elastic moduli of molecular fluids interacting with steeply repulsive potentials are derived using Rowlinson's hard-sphere perturbation treatment which employs a softness parameter, specifying the deviation from the hard-sphere potential. Generic potentials of this form might be used to represent the interactions between near-hard-sphere stabilized colloids. Analytic expressions for the equivalent hard-sphere diameter of inverse power ͓⑀(/r) n where ⑀ sets the energy scale and the distance scale͔ exponential and logarithmic potential forms are derived using the Barker-Henderson formula. The internal energies in the hard-sphere limit are predicted essentially exactly by the perturbation approach when compared against molecular dynamics simulation data using the same potentials. The elastic moduli are similarly accurately predicted in the hard-sphere limit, as they are trivially related to the internal energy. The compressibility factors from the perturbation expansion do not compare as favorably with simulation data, and in this case the Carnahan-Starling equation of state prediction using the analytic effective hard-sphere diameter would appear to be a preferable route for this thermodynamic property. A more refined state point dependent definition for the effective hard-sphere diameter is probably required for this property.

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Elastic moduli of simple fluids with steeply repulsive potentials

Cited by 22 publications

References 17 publications

Viscoelastic behaviour of fluids with steeply repulsive potentials

Viscoelastic behaviour of fluids with steeply repulsive potentials

High-Frequency Shear Modulus and Relaxation Time of Soft-Sphere and Lennard–Jones Fluids

Thermodynamics and elastic moduli of fluids with steeply repulsive potentials

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