Direct Observation of the Entropic Potential in a Binary Suspension

Kaplan, Peter D.; Faucheux, Luc P.; Libchaber, Albert

doi:10.1103/physrevlett.73.2793

Cited by 56 publications

(58 citation statements)

References 19 publications

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“…(For smaller size ratios we expect the Percus-Yevick theory of hard sphere mixtures, upon which the functional is based, to become inaccurate and there is no reason to expect that any approximate mixture functional would reproduce the exact s → 0 results for the depletion potential which are obtained by making the Derjaguin approximation at the outset [7].) This implies that our procedure can be profitably employed for some of the more complex geometries investigated in experiments [2]. We emphasize that our present procedure has a crucial advantage over the brute-force application of DFT to the calculation of depletion potentials.…”

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confidence: 99%

“…Depletion forces are of fundamental statistical mechanical interest since they are purely entropic in origin and much theoretical [4][5][6][7] and simulation [8,9] effort has been devoted to their determination. Many recent experiments, using a wide variety of techniques, have investigated depletion forces for colloidal mixtures or for colloid-polymer mixtures [2]. Much of the impetus for these studies stems from a need to understand how depletion determines phase separation and flocculation phenomena and this has stimulated a growing interest in ascertaining quantitative details of the depletion force.…”

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confidence: 99%

“…Using excluded volume arguments they calculated the force for two hard spheres of radius R b in a fluid of small hard spheres of radius R s and showed that this is attractive for all separations less than 2R s and is zero for larger separations. The hard sphere model captures the essence of the depletion phenomenon and can be mimicked experimentally by suitable choices of colloidal solutions [2,3]. Depletion forces are of fundamental statistical mechanical interest since they are purely entropic in origin and much theoretical [4][5][6][7] and simulation [8,9] effort has been devoted to their determination.…”

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Depletion potential in hard-sphere fluids

et al. 1999

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A versatile new approach for calculating the depletion potential in a hard sphere mixture is presented. This is valid for any number of components and for arbitrary densities. We describe two different routes to the depletion potential for the limit in which the density of one component goes to zero. Both routes can be implemented within density functional theory and simulation. We illustrate the approach by calculating the depletion potential for a big hard sphere in a fluid of small spheres near a planar hard wall. The density functional results are in excellent agreement with simulations.82.70. Dd, 61.20.Gy Typeset using REVT E X 1

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Depletion potential in hard-sphere fluids

et al. 1999

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“…This depletion potential is essentially attractive, and was derived by Asakura and Oosawa and independently by Vrij for the case of ideal polymers [9]. As it is generally accepted that the stability of binary mixtures is determined by these depletion potentials, several groups attempted to measure them directly in experiments [10]. Moreover, explicit theoretical expressions for f dep have been derived by several groups [11,12] and these have been tested against simulations [4,13].…”

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Direct Simulation of the Phase Behavior of Binary Hard-Sphere Mixtures: Test of the Depletion Potential Description

1999

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We study the phase behavior of additive binary hard-sphere mixtures by direct computer simulation, using a new technique which exploits an analog of the Gibbs adsorption equation. The resulting phase diagrams, for size ratios q 0.2, 0.1, and 0.05, are in remarkably good agreement with those obtained from an effective one-component Hamiltonian based on pairwise additive depletion potentials, even in regimes of high packing (solid phases) and for relatively large size ratios (q 0.2) where one might expect the approximation of pairwise additivity to fail. Our results show that the depletion potential description accounts for the key features of the phase equilibria for q # 0.2.[S0031-9007(98)08128-9] PACS numbers: 64.75. + g, 82.70.Dd Understanding the stability of colloidal mixtures is relevant for many industrial applications, e.g., paint, ink, etc., but is also interesting from a fundamental statistical physics point of view [1]. Surprisingly, the phase behavior of even the simplest model colloid mixture, i.e., large and small hard spheres, is still not established and remains a topic of much debate. For instance, it is still unclear whether a (stable) fluid-fluid demixing transition exists for any additive binary hard-sphere mixture. The celebrated Percus-Yevick approximation [2] predicts no fluid spinodal instability, while other integral equation approximations do [3,4], although at completely different statepoints. Experiments on colloidal hard-sphere mixtures suggest that the demixing transition is strongly coupled to the freezing transition, although sedimentation effects preclude definite conclusions [5]. Theoretical approaches that consider both the fluid and solid phase have also been inconclusive. First, a phenomenological free volume theory predicts a fluid-fluid demixing transition that is metastable with respect to a broad fluid-solid coexistence region [6]. Here "broad" refers to the width of this coexistence region in terms of the difference between the packing fractions of the larger species in the two coexisting phases. Another scenario is reported in Ref. [7] where a virial expansion is used for the fluid phase and a density functional approximation for the solid. This yields a narrow freezing transition for q 0.1, a broad one for q 0.2, and a fluid-fluid spinodal instability at such high pressures that it is argued to be metastable. Yet another theoretical treatment predicts a narrow fluid-solid coexistence for q ! 0 [8]. The calculated phase behavior is thus very sensitive to the details of the approximations involved in the above approaches.An alternative approach to asymmetric binary hardsphere mixtures stems from the analogy with colloidpolymer mixtures. The properties of such mixtures have been described succesfully in terms of the so-called depletion potential f dep which arises between a pair of (large) colloidal particles due to the presence of a "sea" of (small) polymers. This depletion potential is essentially attractive, and was derived by Asakura and Oosawa and independently by ...

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“…In addition to these energetic considerations for particle adsorption, another pos-sible mechanism, leading to attraction between solid bodies in a fluid, is a depletion force 48,49,50,51,52 resulting from the reduction of the excluded volume and the consequent increase in the entropy when solid particles are in close proximity. However, the results given previously show that changes in the interaction energy have a dramatic effect on adsorption, and suggest that the dominant considerations are energetic as further indicated from the following "inverse" simulations.…”

Section: Motion Of a Sphere Through A Cylindrical Nanochan-nel: Lomentioning

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Wetting and particle adsorption in nanoflows

et al. 2004

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Molecular dynamics simulations are used to study the behavior of closely-fitting spherical and ellipsoidal particles moving through a fluid-filled cylinder at nanometer scales. The particle, the cylinder wall and the fluid solvent are all treated as atomic systems, and special attention is given to the effects of varying the wetting properties of the fluid. Although the modification of the solid-fluid interaction leads to significant changes in the microstructure of the fluid, its transport properties are found to be the same as in bulk. Independently of the shape and relative size of the particle, we find two distinct regimes as a function of the degree of wetting, with a sharp transition between them. In the case of a highly-wetting suspending fluid, the particle moves through the cylinder with an average axial velocity in agreement with that obtained from the solution of the continuum Stokes equations. In contrast, in the case of less-wetting fluids, only the early-time motion of the particle is consistent with continuum dynamics. At later times, the particle is eventually adsorbed onto the wall and subsequently executes an intermittent stick-slip motion. We show that van der Walls forces are the dominant contribution to the particle adsorption phenomenon and that depletion forces are weak enough to allow, in the highly-wetting situation, an initially adsorbed particle to spontaneously desorb.

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Direct Observation of the Entropic Potential in a Binary Suspension

Cited by 56 publications

References 19 publications

Depletion potential in hard-sphere fluids

Depletion potential in hard-sphere fluids

Direct Simulation of the Phase Behavior of Binary Hard-Sphere Mixtures: Test of the Depletion Potential Description

Wetting and particle adsorption in nanoflows

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