Brownian Motion: A Tool To Determine the Pair Potential between Colloid Particles

Vondermaßen, K.; Bongers, Joern; Mueller, Andreas; Versmold, H.

doi:10.1021/la00017a007

Cited by 82 publications

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“…This so-called like-charge attraction (LCA) was only observed in thin cells (typical sample height H < 10µm) while the pair-interaction in bulk suspensions has been experimentally confirmed to be entirely repulsive in agreement with Poisson-Boltzmann theories [2][3][4] . Therefore, it was speculated that the confining plates are responsible for the deviations from theory.…”

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confidence: 71%

“…The resulting potential can be successfully described with a screened Coulomb potential So far, we demonstrated that overlapping colloidal images lead to erroneous particle distances which -if not taken into account -can lead to long-ranged attractive components in U(r). If LCA is really the result of falsely interpreted video images, why the above discussed optical artefacts are only relevant in thin sample cells while pair potentials in unconfined systems were concordantly reported to agree with a screened Coulomb potential 3,23,25 ? This is easily understood by recalling that the Debye screening length in charged colloidal suspensions is given by where z s,c and c s,c are the valency and the concentrations of the salt ions and that of the counter ions, the latter released from any surfaces in the system.…”

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confidence: 99%

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Like-charge attraction in confinement: myth or truth?

Baumgartl¹,

Arauz‐Lara

Bechinger³

2006

Soft Matter

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It is general wisdom that likely charged colloidal particles repel each other when suspended in liquids. This is in perfect agreement with mean field theories being developed more than 60 years ago. Accordingly, it was a big surprise when several groups independently reported long-ranged attractive components in the pair potential U(r) of equally charged colloids. This so-called like-charge attraction (LCA) was only observed in thin sample cells while the pair-interaction in unconfined suspensions has been experimentally confirmed to be entirely repulsive. Despite considerable experimental and theoretical efforts, LCA remains one of the most challenging mysteries in colloidal science. We experimentally reinvestigate the pair-potential U(r) of charged colloidal particles with digital video microscopy and demonstrate that optical distortions in the particle's images lead to slightly erroneous particle positions. If not properly taken into account, this artefact pretends a minimum in U(r) which was in the past misleadingly interpreted as LCA. After correcting optical distortions we obtain entirely repulsive pair interactions which show good agreement with linearized mean field theories. 82,70.Dd, A controversial debate in colloidal science has been launched in 1994 when Kepler and Fraden reported an unusual long-ranged attractive component in the pair potential of charged colloidal particles 1 . This so-called like-charge attraction (LCA) was only observed in thin cells (typical sample height H < 10µm) while the pair-interaction in bulk suspensions has been experimentally confirmed to be entirely repulsive in agreement with Poisson-Boltzmann theories 2-4 . Therefore, it was speculated that the confining plates are responsible for the deviations from theory. Soon after its initial observation LCA was also observed by other authors 5-11 which then provoked considerable theoretical interest in this phenomenon. In the meantime it has been rigorously proven that the observed attraction can not be explained within the framework of mean field theories, irrespective of whether the particles are suspended in bulk or in confinement [12][13][14] . Several other approaches beyond PoissonBoltzmann have been proposed as the origin of confinement-induced attraction. While correlation effects of the electrolyte indeed can lead to a short-ranged attraction of negatively charged colloids, none of the existing theories can account for the long-ranged attraction as observed in experiments 15,16 . Accordingly, even after more than ten years of considerable research, LCA is still one of the most challenging unsolved mysteries in colloidal science. In this study we reinvestigate the pair potential U(r) of charged colloidal particles in thin sample cells. Contrary to previous experiments where U(r) was derived from the pair correlation function g(r) in semi-dilute suspensions, here we determine the pair potential directly by measuring the probability distribution of two silica spheres. This is of particular advantage because it avoids the...

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confidence: 71%

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Like-charge attraction in confinement: myth or truth?

Baumgartl¹,

Arauz‐Lara

Bechinger³

2006

Soft Matter

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“…The classic Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [1,2,3,4,5,6] predicts that an isolated pair of charged colloidal spheres in an aqueous salt solution interacts via a repulsive Yukawa potential at large separations, a prediction that has recently been confirmed by direct experimental measurements [7,8,9]. However, in nature colloidal particles usually do not occur simply as pairs, but rather in form of suspensions.…”

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confidence: 99%

Many-body interactions and the melting of colloidal crystals

Dobnikar

Chen

Rzehak

et al. 2003

The Journal of Chemical Physics

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We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions between the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids.Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pairinteraction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions. If the salt concentration is high, we find configuration-independent pair-forces of perfect Yukawa form with effective charges and screening constants that are in good agreement with well-established theories. At low added salt, however, the pair-forces are Yukawa-like only at short distances with effective parameters that depend on the analyzed colloidal configuration. At larger distances, in contrast, the pair-forces decay to zero much faster than they would following a Yukawa force law. This is explained with a screening effect of the macroions. Based on these findings, we suggest a simple model potential for colloids in suspension which has the form of a Yukawa potential, truncated after the first coordination shell of a colloid in a crystal. Using this potential in a one-component simulation, we find a melting line that shows good agreement with the one derived from the full PoissonBoltzmann-Brownian-dynamics simulation.2

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“…To extract u r from r; t , we adopt the approach pioneered by Kepler and Fraden [2] and Vondermassen et al [14] by calculating the pair correlation function, g r 1 n 2 h r 0 ÿ r; t r; t i;…”

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Confinement-Induced Colloidal Attractions in Equilibrium

2003

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The Poisson-Boltzmann theory for colloidal electrostatic interactions predicts that charged colloidal spheres dispersed in water should repel each other, even when confined by charged surfaces. Direct measurements on highly charged polystyrene spheres, however, reveal strong, long-ranged confinementinduced attractions that have yet to be explained. We demonstrate that anomalous attractions also characterize the equilibrium pair potential for more weakly charged colloidal silica spheres sedimented into a monolayer above a glass surface. This observation substantially expands the range of conditions for which mean-field theory incorrectly predicts the sign of macroions' interactions, and provides new insights into how confinement induces long-ranged like-charge attractions. This problem's intractability reflects the complexity of the macroionic environment. Under equilibrium conditions, charge-stabilized colloidal particles' long-range interactions result from a combination of direct Coulomb repulsions and indirect interactions mediated by microscopic ions in solution. The spheres' effective pair potential, u r , is an average over the simple ions' degrees of freedom. The Poisson-Boltzmann formalism performs this average in the mean-field approximation and so cannot account for fluctuations or correlations in the simple ions' distributions. Thermodynamically selfconsistent liquid structure calculations demonstrate that particle-ion and ion-ion correlations indeed can mediate long-ranged attractions [6] consistent with metastable phase separation in bulk suspensions [7]. This mechanism's relevance to pairs of spheres confined by charged walls remains to be determined, however.The apparent subtlety of confinement-induced likecharge colloidal attractions has inspired a critical reassessment of the experimental evidence. For example, all previous observations of confinement-induced attractions [2,4,8,9] were performed on polystyrene (PS) microspheres with highly acidic surface groups [10]. The only related study on confined silica spheres found no deviations from mean-field theory's predictions [10]. Anomalous interactions therefore might be peculiar to highly charged spheres in general, or to PS in particular, in which case the effect would be far less generally important than originally supposed. Concern also has been raised that hydrodynamic coupling [11,12] or other experimental artifacts [10] might explain the observed attractions, particularly because error estimates were not available for some of the measurements [2,8].This Letter describes digital video microscopy measurements of the equilibrium pair potentials for charged colloidal spheres under varying degrees of confinement. These measurements reveal strong and long-ranged likecharge colloidal attractions not only between PS spheres confined to the midplane between parallel glass walls, but also between more weakly charged silica colloid sedimented into a monolayer above a glass wall. Even though the sedimented spheres' dynamics should be influenced princip...

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Brownian Motion: A Tool To Determine the Pair Potential between Colloid Particles

Cited by 82 publications

References 1 publication

Like-charge attraction in confinement: myth or truth?

Like-charge attraction in confinement: myth or truth?

Many-body interactions and the melting of colloidal crystals

Confinement-Induced Colloidal Attractions in Equilibrium

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