Long-Time Self-Diffusion in Concentrated Colloidal Dispersions

Medina‐Noyola, Magdaleno

doi:10.1103/physrevlett.60.2705

Cited by 202 publications

(125 citation statements)

References 13 publications

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“…For both large and small separations analytical expressions for these functions exist [48] and are supplemented by tabulated numerical data for intermediate ranges [150]. At higher volume fractions approximations are required to obtain the hydrodynamic functions and a number of schemes have been developed which aim to incorporate the effects of many-body hydrodynamics [28,50,100,151,152]. In the absence of hydrodynamic interactions A = B = 0 and G = H = 1 leading to considerable simplification.…”

Section: Pair Smoluchowski Equationmentioning

confidence: 99%

Nonlinear rheology of colloidal dispersions

Brader¹

2010

J. Phys.: Condens. Matter

128

156

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Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states.

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Section: Pair Smoluchowski Equationmentioning

confidence: 99%

Nonlinear rheology of colloidal dispersions

Brader¹

2010

J. Phys.: Condens. Matter

128

156

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“…However, for short times (i.e. small Λ), it is generally accepted that an interacting diffusion process can be replaced by a free one [25], which here means that the (E…”

Section: A Derivation Of Eqs (28)-(210)mentioning

confidence: 99%

The level splitting distribution in chaos-assisted tunnelling

Leyvraz

Ullmo²

1996

J. Phys. A: Math. Gen.

109

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A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain two-dimensional systems. This mechanism is known as chaos-assisted tunneling. We study its consequences for the distribution of the level splittings and obtain a general analytical form for this distribution under the assumption that chaos assisted tunneling is the only operative mechanism. We have checked that the analytical form we obtain agrees with splitting distributions calculated numerically for a model system in which chaos-assisted tunneling is known to be the dominant mechanism. The distribution depends on two parameters: The first gives the scale of the splittings and is related to the magnitude of the classically forbidden processes, the second gives a measure of the efficiency of possible barriers to classical transport which may exist in the chaotic region. If these are weak, this latter parameter is irrelevant; otherwise it sets an energy scale at which the splitting distribution crosses over from one type of behavior to another. The detailed form of the crossover is also obtained and found to be in good agreement with numerical results for models for chaos-assisted tunneling.

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“…However, in line with ref. 13, we correct for this effect by multiplying our Monte Carlo results for f n c by a factor a f [ D s f =D 0 , where D s (f) is the short-time self-diffusion coef®cient at volume fraction f. Several, rather similar, functional forms for a(f) have been proposed in the literature. Here we use the phenomenological expression a f 1 2 f=0:64 1:17 (ref.…”

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confidence: 99%

Prediction of absolute crystal-nucleation rate in hard-sphere colloids

Auer

Frenkel

2001

Nature

914

997

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Crystal nucleation is a much-studied phenomenon, yet the rate at which it occurs remains dif®cult to predict. Small crystal nuclei form spontaneously in supersaturated solutions, but unless their size exceeds a critical valueÐthe so-called critical nucleusÐthey will re-dissolve rather than grow. It is this rate-limiting step that has proved dif®cult to probe experimentally. The crystal nucleation rate depends on P crit , the (very small) probability that a critical nucleus forms spontaneously, and on a kinetic factor (k) that measures the rate at which critical nuclei subsequently grow. Given the absence of a priori knowledge of either quantity, classical nucleation theory 1 is commonly used to analyse crystal nucleation experiments, with the unconstrained parameters adjusted to ®t the observations. This approach yields no`®rst principles' prediction of absolute nucleation rates. Here we approach the problem from a different angle, simulating the nucleation process in a suspension of hard colloidal spheres, to obtain quantitative numerical predictions of the crystal nucleation rate. We ®nd large discrepancies between the computed nucleation rates and those deduced from experiments 2±4 : the best experimental estimates of P crit seem to be too large by several orders of magnitude. The probability (per particle) that a spontaneous¯uctuation will result in the formation of a critical nucleus depends exponentially on the free energy DG crit that is required to form such a nucleus:where T is the absolute temperature and k B is Boltzmann's constant. According to classical nucleation theory (CNT), the total free energy of a crystallite that forms in a supersaturated solution contains two terms: the ®rst is a`bulk' term that expresses the fact that the solid is more stable than the supersaturated¯uidÐthis term is negative and proportional to the volume of the crystallite. The second is à surface' term that takes into account the free-energy cost of creating a solid±liquid interface. This term is positive and proportional to the surface area of the crystallite. According to CNT, the total (Gibbs) free-energy cost to form a spherical crystallite with radius R is DG 4 3 pR 3 r S Dm 4pR 2 g 2 where r S is the number-density of the solid, Dm (,0) is the difference in chemical potential of the solid and the liquid, and g is the solid±liquid interfacial free energy density. The function DG goes through a maximum at R 2g= r S jDmj and the height of the nucleation barrier is:The crystal-nucleation rate per unit volume, I, is the product of P crit and the kinetic prefactor k:The CNT expression for the nucleation rate then becomes: (6). A prerequisite for the calculation of the nucleation barrier is the choice of à reaction coordinate' that measures the progress from liquid to solid. As our reaction coordinate we use n, the number of particles that constitute the largest solid-like cluster in the system. A criterion based on that in ref. 8 was used to identify which particles are solid-like. If two solid-like particles are less t...

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Long-Time Self-Diffusion in Concentrated Colloidal Dispersions

Cited by 202 publications

References 13 publications

Nonlinear rheology of colloidal dispersions

Nonlinear rheology of colloidal dispersions

The level splitting distribution in chaos-assisted tunnelling

Prediction of absolute crystal-nucleation rate in hard-sphere colloids

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