Solution of the Ornstein–Zernike Equation in the Critical Region

Brader, Joseph M.

doi:10.1007/s10765-005-0002-5

Cited by 18 publications

(17 citation statements)

References 42 publications

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“…We therefore feel justified in claiming the theory developed in this work to be the first example of an Ornstein-Zernike closure sensitive to both the second-order liquid vapour transition and the first-order freezing transition. This goes a step beyond existing integral equation approaches which at best display a line in the phase diagram upon which the compressibility either diverges (spinodal) or the theory breaks down (no-solutions boundary) 10 and which show no indication of freezing. Of particular interest would be the characterization of the spinodal for the present theory and the determination of the critical exponents which, given the nature of the closure, may be non-classical 45 .…”

Section: B Short-range Attractionmentioning

confidence: 92%

Structural precursor to freezing: An integral equation study

Brader

2008

The Journal of Chemical Physics

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Recent simulation studies have drawn attention to the shoulder which forms in the second peak of the radial distribution function of hard-spheres at densities close to freezing and which is associated with local crystalline ordering in the dense fluid. We address this structural precursor to freezing using an inhomogeneous integral equation theory capable of describing local packing constraints to a high level of accuracy. The addition of a short-range attractive interaction leads to a well known broadening of the fluid-solid coexistence region as a function of attraction strength. The appearence of a shoulder in our calculated radial distribution functions is found to be consistent with the broadened coexistence region for a simple model potential, thus demonstrating that the shoulder is not exclusively a high density packing effect.

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Section: B Short-range Attractionmentioning

confidence: 92%

Structural precursor to freezing: An integral equation study

Brader

2008

The Journal of Chemical Physics

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“…In even dimensions numerical methods must be employed. Among the several existing algorithms [19] we use the classical Lado algorithm [20] for simplicity. In our numerical solution of the 2D system we use a real space cutoff r max = 50 with 4000 grid points.…”

Section: Static Structurementioning

confidence: 99%

Effect of mixing and spatial dimension on the glass transition

2009

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We study the influence of composition changes on the glass transition of binary hard disc and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this new method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard discs strongly resembles the random close packing diagram. Compared to 3D from previous studies, the extension of the glass regime due to mixing is much more pronounced in 2D where plasticization only sets in at larger size disparities. For small size disparities we find a stabilization of the glass phase quadratic in the deviation of the size disparity from unity.PACS numbers: 64.70.P-, 64.70.Q-, 82.70.Dd

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“…An advantage of our approach over existing integral equation based theories is that we provide a clear link between the macroscopic rheology and an underlying equilibrium free energy functional. The use of an explicit generating function avoids the familiar problem of thermodynamic inconsistency and no-solution regions of parameter space presented by integral equation closures [20]. This feature is of particular importance for systems exhibiting equilibrium phase transitions, as the proximity of the chosen thermodynamic state point to underlying phase boundaries may influence the rheological response.…”

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confidence: 99%

Density functional approach to nonlinear rheology

Reinhardt¹,

Weysser²,

Brader³

2013

EPL

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-We present a density functional based closure of the pair Smoluchowski equation for Brownian particles under shear flow. Given an equilibrium free energy functional as input the theory provides first-principles predictions for the flow-distorted pair correlation function and associated rheological quantities over a wide range of volume fractions and flow rates. Taking twodimensional hard-disks under shear flow as an illustrative model we calculate the pair correlation function, viscosity and normal stress difference under both steady and start-up shear.Introduction. -The addition of colloidal particles to a Newtonian liquid gives rise to a nonlinear rheological response, characterized by a rate dependent viscosity, finite normal stress differences and nontrivial transient dynamics [1]. Understanding the interplay between particle interactions and external stress or strain fields remains a major theoretical challenge and much effort has been invested in the search for tractable closure relations which capture the essential physics of systems driven out-of-equilibrium [2]. Realistic models for which the competing effects of Brownian motion, potential and hydrodynamic interactions are simultaneously active pose particular difficulties [3].

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Solution of the Ornstein–Zernike Equation in the Critical Region

Cited by 18 publications

References 42 publications

Structural precursor to freezing: An integral equation study

Structural precursor to freezing: An integral equation study

Effect of mixing and spatial dimension on the glass transition

Density functional approach to nonlinear rheology

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