Depletion potential in hard-sphere fluids

Götzelmann, B.; Roth, Roland; Dietrich, S.; Dijkstra, Marjolein; Evans, Robert

doi:10.1209/epl/i1999-00402-x

Cited by 91 publications

(112 citation statements)

References 26 publications

(51 reference statements)

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“…But Eq. (2) performs as well as most other functionals proposed in the literature [13]; for example, depletion forces in binary fluids are well recovered by it [21]. For numerical use below we retain the original weight functions [14], although some recent modifications are known to give a better description of solid phases [22]; these modifications would not alter the conceptual structure of our analysis.…”

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confidence: 84%

Local Size Segregation in Polydisperse Hard Sphere Fluids

2000

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The structure of polydisperse hard sphere fluids, in the presence of a wall, is studied by the Rosenfeld density functional theory. Within this approach, the local excess free energy depends on only four combinations of the full set of density fields. The case of continuous polydispersity thereby becomes tractable. We predict, generically, an oscillatory size segregation close to the wall, and connect this, by a perturbation theory for narrow distributions, with the reversible work for changing the size of one particle in a monodisperse reference fluid. PACS numbers: 61.20.Gy, 05.20.Jj, 64.75. + g Understanding the behavior of polydisperse systems is relevant to many materials of practical interest. In particular, colloidal and/or polymeric fluids generally contain particles which have, in effect, a continuous distribution of sizes (and/or other parameters such as charge and chemical composition). This affects their performance in applications ranging from foodstuffs to polymer processing [1]. More fundamentally, colloidal systems also provide the closest experimental approach to the "theorists ideal fluid," namely, that of perfect hard spheres [2]. The fact that all colloids are in practice polydisperse (at least slightly) must then be taken into account in comparing theory with experiment. Only recently has experimental work started to clarify in a systematic way the generic consequences of polydispersity, such as the partitioning of sizes between coexisting phases [3].Despite the continuous interest polydisperse fluids have raised, their theoretical understanding remains far from complete, especially for inhomogeneous cases. More is known about partial structure factors in single-phase fluids [4,5] and liquid-liquid phase equilibrium [6,7] than about crystalline phases [8] or interfacial properties, for example. And, where such inhomogeneous situations have been studied [9] it has often proved necessary to assume that only the mean density, and not the size distribution, can vary in space [10]. This ignores size segregation effects, which (globally) influence the phase diagram [3,7]. A similar tendency to local segregation is implicit in treatments of binary and ternary hard sphere mixtures [11][12][13] and in polydisperse equilibrium structure factors in the homogeneous state [4].In what follows, we treat continuous polydispersity within a density functional theory (DFT) that properly allows for local size segregation. Our work is based on a choice of density functional (that of Rosenfeld [14]) that has previously been used to study finite mixtures of hard spheres. By exploiting the fact that its excess free energy density depends on only a small number of linear combinations of the particle densities (four "moment densities"), we are able to address the case of continuous polydispersity, where the underlying densities are infinite in number. This allows us to study, e.g., the effects of varying the shape of a smooth size distribution. Moreover, by a perturbative analysis of the same functional, we can di...

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confidence: 84%

Local Size Segregation in Polydisperse Hard Sphere Fluids

2000

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“…This model predicts the minimum of the interaction potential between two parallel flat plates reasonably accurately, as tested with self-avoiding random walk (SAW) computer simulations [17,18], and also predicts a significant maximum of the interaction potential. For a suspension of colloidal spheres between the plates, repulsion due to accumulation is a significant effect which is shown using analytical theory to third order in colloid concentration [19], by computer simulation [20] and recently by density functional theory [21,22]. Oscillations in the polymer concentration profile around the bulk polymer concentration (that lead to a repulsion) for a polymer solution near a wall have been found by using self-consistent mean-field calculations [23] and by SAW simulations [17,18].…”

Section: Introductionmentioning

confidence: 91%

Excluded-volume polymer-induced depletion interaction between parallel flat plates

Tuinier

Lekkerkerker

2001

The European Physical Journal E

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Abstract. The interaction between two parallel plates due to non-adsorbing polymer chains with excluded volume is calculated using the adsorption method. The adsorption is calculated from the profile of the polymer segment concentration between the plates, which is obtained from the product function of the concentration profile near a single wall, involving the correlation length. The renormalization group theory provides expressions for the osmotic pressure and consequently for the osmotic compressibility, chemical potential and correlation length of a polymer solution. Both the local polymer concentration profiles as well as the minimum of the interaction potential between the plates agree with recently published self-avoiding random walk computer simulations.

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“…it has the same range as φ AO . In reality the (hard-sphere) depletion potential exhibits exponentially damped oscillations as R ij → ∞ [26] but these should not be important for the phase behaviour. The key difference between φ dep and φ AO is the development in the former of a repulsive barrier, whose height increases with increasing η be emphasized once more that in this additive case there is no exact mapping between the partition functions of the full binary system and the effective one-component system, even for q 0.154, because the interactions between the small spheres can still mediate manybody forces.…”

Section: Phase Diagrams Obtained From the Depletion Potentialmentioning

confidence: 99%

Phase behaviour and structure of model colloid-polymer mixtures

Dijkstra

Brader

Evans

1999

J. Phys.: Condens. Matter

284

507

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Abstract. We study the phase behaviour and structure of model colloid-polymer mixtures. By integrating out the degrees of freedom of the non-adsorbing ideal polymer coils, we derive a formal expression for the effective one-component Hamiltonian of the colloids. Using the twobody (Asakura-Oosawa pair potential) approximation to this effective Hamiltonian in computer simulations, we determine the phase behaviour for size ratios q = σ p /σ c = 0.1, 0.4, 0.6, and 0.8, where σ c and σ p denote the diameters of the colloids and the polymer coils, respectively. For large q, we find both a fluid-solid and a stable fluid-fluid transition. However, the latter becomes metastable with respect to a broad fluid-solid transition for q 0.4. For q = 0.1 there is a metastable isostructural solid-solid transition which is likely to become stable for smaller values of q. We compare the phase diagrams obtained from simulation with those of perturbation theory using the same effective one-component Hamiltonian and with the results of the free-volume approach. Although both theories capture the main features of the topologies of the phase diagrams, neither provides an accurate description of the simulation results. Using simulation and the Percus-Yevick approximation we determine the radial distribution function g(r) and the structure factor S(k) of the effective one-component system along the fluid-solid and fluid-fluid phase boundaries. At state-points on the fluid-solid boundary corresponding to high colloid packing fractions (packing fractions equal to or larger than that at the triple point), the value of S(k) at its first maximum is close to the value 2.85 given by the Hansen-Verlet freezing criterion. However, at lower colloid packing fractions freezing occurs when the maximum value is much lower than 2.85. Close to the critical point of the fluid-fluid transition we find Ornstein-Zernike behaviour and at very dilute colloid concentrations S(k) exhibits pronounced small-angle scattering which reflects the growth of clusters of the colloids. We compare the phase behaviour of this model with that found in studies of additive binary hard-sphere mixtures.

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Depletion potential in hard-sphere fluids

Cited by 91 publications

References 26 publications

Local Size Segregation in Polydisperse Hard Sphere Fluids

Local Size Segregation in Polydisperse Hard Sphere Fluids

Excluded-volume polymer-induced depletion interaction between parallel flat plates

Phase behaviour and structure of model colloid-polymer mixtures

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