Pattern formation in colloidal explosions

We study the non-equilibrium pattern formation that emerges when magnetically repelling colloids, trapped by optical tweezers, are abruptly released, forming colloidal explosions. For multiple colloids in a single trap we observe a pattern of expanding concentric rings. For colloids individually trapped in a line, we observe explosions with a zigzag pattern that persists even when magnetic interactions are much weaker than those that break the linear symmetry in equilibrium. Theory and computer simulations quantitatively describe these phenomena both in and out of equilibrium. An analysis of the mode spectrum allows us to accurately quantify the non-harmonic nature of the optical traps. Colloidal explosions provide a new way to generate well-characterized non-equilibrium behaviour in colloidal systems.Comment: New restructured version (supplementary material goes into main text, no change of content), added journal reference and DOI information; 6 pages, 6 figures, published in Europhysics Letters (EPL

Three- and four-body interactions in colloidal systems

Three-body and four-body interactions have been directly measured in a colloidal system comprised of three (or four) charged colloidal particles. Two of the particles have been confined by means of a scanned laser tweezers to a line-shaped optical trap where they diffused due to thermal fluctuations. By means of an additional focused optical trap a third particle has been approached and attractive three-body interactions have been observed. These observations are in qualitative agreement with additionally performed nonlinear Poissson-Boltzmann calculations. Two configurations of four particles have been studied experimentally as well and in both cases a repulsive four-body interaction term has been observed

Samenstelling van gescheiden ingezamelde kunststof-verpakkingen

The composition of Dutch separately collected post-consumer plastic packaging waste has been determined for 23 different municipalities during the time period of 2010-2013. In this report weighted averages are presented based on the previously analysed samples. The most important packaging types present are in order of relevance: PE film, PET rigid packages (mostly trays and thermoformed trays), PP rigid packages (mostly butter tubs, yoghurt pots), PE flasks and PET bottles. The variance in the presented data is, however, large due to regional variance and seasonal influences. The reported weight-average compositional values should therefore only be used as indicate values

Kolloide als Modellsysteme für kondensierte Materie

We use colloids as model systems for condensed matter in four independent studies employing charged-stabilized colloidal suspensions, optical tweezers and digital video microscopy. In charged colloidal suspensions, particles interact via a repulsive screened Coulomb potential with the screening length determined through the concentration of salt ions. Optical tweezers refer to strong laser-intensity fields which allow trapping of dielectric colloids in regions of maximum intensity. We use optical tweezers to induce extended two-dimensional (2D) substrates by means of overlapping expanded laser beams. In addition, we control the particle density with a scanned focused laser beam creating one-dimensional (1D) boundary potentials. Particle trajectories are measured with digital video microscopy and we determine physical quantities including pair correlation functions and mean-square displacements from the trajectories. We first both numerically and experimentally determine the phonon band structure of 2D triangular colloidal crystals in the presence of commensurate 1D and 2D periodic substrates. The numerical studies are based on the harmonic approximation where springs describe both the particle pair interaction and the particle-substrate interaction. Our results demonstrate that a substrate can both shift and deform phonon-band structures and, in addition, can even induce band gaps. As a consequence, a substrate can modify sound and thermal properties which both crucially depend on the phonon-band structure. In the experiments, we prepare a 2D triangular crystal and create 1D and 2D periodic substrates by means of two overlapping expanded laser beams. The phonon-band structure is determined from the measured particle trajectories and our experimental results confirm the theoretical findings. Moreover, we theoretically investigate phonon dynamics. As a result, we find that a Laplace transformation relates the mean-square displacement to the phonon spectrum. We then investigate the structural properties of a binary colloidal hard-sphere mixture using confocal microscopy. Our results confirm the existence of structural crossover, an effect predicted by theoretical studies. Structural crossover refers to a marked change in the wavelength of damped oscillatory pair correlation functions; depending on the packing fraction of the two particle species, the wavelength is slightly larger than the diameter of either the big or the small particles. Furthermore, we find that structural crossover is related to the size of networks consisting of only equally sized particles connected through nearest-neighbor bonds. This is supported by Monte-Carlo simulations which are performed at different ratios of the particle sizes and total packing fractions. Next, we experimentally study single-particle diffusion on a quasicrystalline substrate created by means of five overlapping laser beams. As a result, we observe subdiffusive behavior characterized through an increase of the mean-square displacement in time according to a power law with the power smaller than unity. We interprete the subdiffusive particle motion as a thermalization process; to thermalize, the particle must explore the entire distribution of potential well depth which is characteristic for non-periodic quasicrystalline substrates. In addition, we find normal diffusion at large times when the particle has thermalized. Our experiments are paralleled by theoretical studies employing Brownian dynamics simulations and rate equations. The numerical results agree qualitatively with the experimental findings. We finally focus on confinement-induced like-charge attraction, a mysterious phenomenon since an anomalous long-ranged attractive pair interaction is observed in confined charged colloidal suspensions. Two particles are subjected to a radially symmetric light-induced trap and the measured particle-distance distribution yields the pair interaction. As a result, we find that like-charge attraction is caused by an optical artifact arising from overlapping particle images and leading to erroneous distance measurements. The corrected pair potentials show excellent agreement with mean-field theories. This clearly manifests that the pair interaction in charged colloidal suspensions is indeed purely repulsive. Moreover, we demonstrate that the role of confinement is simply associated with a strong screening of the repulsive interaction which leads to overlapping images. We finally show that one can avoid optical artifacts e.g. through the use of core-shell particles.In vier voneinander unabhängigen Studien setzen wir Kolloide als Modellsysteme für kondensierte Materie ein und verwenden ladungsstabilisierte kolloidale Suspensionen, optische Pinzetten und digitale Videomikroskopie. In ladungsstabilisierten kolloidalen Suspensionen wechselwirken Teilchen über ein repulsives abgeschirmtes Coulomb-Potenzial, wobei die Abschirmlänge durch die Konzentration von Salzionen bestimmt ist. Optische Pinzetten bezeichnen starke, mit Lasern erzeugte Intensitätsfelder, mit denen sich dielektrische Kolloide in Bereichen maximaler Intensität fangen lassen. Wir verwenden optische Pinzetten, um ausgedehnte zweidimensionale (2D) Substrate mittels überlappender aufgeweiteter Laserstrahlen zu erzeugen. Wir kontrollieren zusätzlich die Teilchendichte mit einem gerasterten Laserstrahl, der eindimensionale (1D) Randpotenziale erzeugt. Teilchentrajektorien werden mit digitaler Videomikroskopie gemessen und anschließend die interressierenden physikalischen Größen wie Paarkorrelationsfunktionen oder mittlere Verschiebungsquadrate bestimmt. Wir bestimmen zuerst theoretisch und experimentell die phononische Bandstruktur von 2D kolloidalen Kristallen auf kommensurablen 1D und 2D periodischen Substraten. Unsere Rechnungen basieren auf der harmonischen Näherung, die sowohl die Paarwechselwirkung als auch die Partikel-Substrat-Wechselwirkung durch Federn modelliert. Unsere Ergebnisse zeigen, dass ein Substrat phononische Bandstrukturen verschieben und deformieren kann. Es ist sogar möglich, Bandlücken zu erzeugen. Ein Substrat kann daher Schall- und thermische Eigenschaften beeinflussen, die maßgeblich durch die phononische Bandstruktur bestimmt werden. In den Experimenten werden 2D kolloidale Kristalle präpariert und 1D und 2D periodische Substrate mit überlappenden Laserstrahlen erzeugt. Die phononische Bandstruktur wird aus den Teilchentrajektorien bestimmt, und unsere experimentellen Resultate bestätigen die numerischen. Wir untersuchen außerdem theoretisch die Dynamik von Phononen und finden, dass mittleres Verschiebungsquadrat und Phononenspektrum über eine Laplace-Transformation verknüpft sind. Wir untersuchen dann mit konfokaler Mikroskopie die strukturellen Eigenschaften einer binären kolloidalen Harte-Kugel-Mischung. Unsere Ergebnisse bestätigen die Existenz des theoretisch vorhergesagten strukturellen Übergangs. Dieser äußert sich in einem scharf ausgeprägten Wechsel der Wellenlänge, auf der Paarkorrelationsfunktionen gedämpft oszillieren; je nach Packungsdichte der beiden Teilchensorten ist die Wellenlänge etwas größer als der Durchmesser der großen oder der kleinen Teilchen. Darüber hinaus zeigen wir, dass sich der strukturelle Übergang in der Größe von Netzwerken widerspiegelt, die nur aus Nächste-Nachbar Teilchen derselben Sorte bestehen. Dies wird durch Monte-Carlo Simulationen unterstützt, die für verschiedene Verhältnisse der Teilchengrößen und verschiedene totale Packungsdichten durchgeführt werden. Als nächstes studieren wir experimentell die Diffusion von einzelnen Teilchen auf einem quasikristallinen Substrat, das mit fünf überlappenden Laserstrahlen erzeugt wird. Wir beobachten subdiffusives Verhalten, d.h., das mittlere Verschiebungsquadrat wächst mit der Zeit gemäß einem Potenzgesetz, wobei der Exponent echt kleiner als Eins ist. Subdiffusives Verhalten kann als Thermalisierungsprozess aufgefasst werden; ein Teilchen muss die für quasikristalline Substrate charakteristische Verteilung der Tiefen der Potenzialtöpfe durch Diffusion erkunden, um zu thermalisieren. Für große Zeiten, wenn der Thermalisierungs- prozess beendet ist, finden wir außerdem normales Diffusionsverhalten. Unsere Experimente werden von einer theoretischen Arbeit begleitet, die Brownsche-Dynamik Simulationen und Ratengleichungen einsetzt. Numerische und experimentelle Ergebnisse stimmen qualitativ überein. Wir beschäftigen uns schließlich mit der Anziehung gleichnamig geladener Kolloide, die in eingeschränkten Geometrien beobachtet wird und bisher nicht erklärt werden konnte. Zwei Teilchen werden in einer radialsymmetrischen optischen Pinzette gefangen, und die gemessene Abstandsverteilung liefert die Paarwechselwirkung. Unsere Ergebnisse zeigen, dass die Anziehung der Teilchen durch ein optisches Messartefakt verursacht wird, das von überlappenden Teilchenbildern und dadurch fehlerhaften Abstandsmessungen herrührt. Die korrigierten Paarpotenziale zeigen hervorragende Übereinstimmung mit Molekularfeld-näherungen. Damit ist die Paarwechselwirkung in ladungsstabilisierten kolloidalen Suspensionen in der Tat rein repulsiv. Darüber hinaus zeigen wir, dass der Einfluss der eingeschränkten Geometrie einfach durch eine starke Abschirmung der repulsiven Wechselwirkung und die dadurch überlappenden Teilchenbilder begründet ist. Wir erläutern abschließend, dass Messartefakte zum Beispiel durch Verwenden von Kern-Schalen Teilchen vermieden werden können

On the limits of digital video microscopy

We explore the limits of digital video microscopy which is established as a standard method in physics, chemistry and biology. At particle distances close to contact we observe small but systematic deviations between the optically measured and the real particle distances. This difference is caused by the overlap of the optical images between neighboring particles. Exemplarily we discuss the consequences of this effect on pair potential measurements of charge stabilized colloids in confined geometries.publishe

Locked-Floating-Solid to Locked-Smectic Transition in Colloidal Systems

We investigate two-dimensional melting of a colloidal system in the presence of a one-dimensional periodic substrate potential created by two interfering laser beams. We study the commensurability ratio p=sqrt[3]a/2d=2 with a the mean particle distance and d the period of the periodic potential. In contrast with the previously investigated case p=1, here we observe that melting of the locked-floating solid occurs via a novel locked-smectic phase, predicted by recent theoretical studies.We investigate two-dimensional melting of a colloidal system in the presence of a one-dimensional periodic substrate potential created by two interfering laser beams. We study the commensurability ratio p=√3a/2d=2 with a the mean particle distance and d the period of the periodic potential. In contrast with the previously investigated case p=1, here we observe that melting of the locked-floating solid occurs via a novel locked-smectic phase, predicted by recent theoretical studies.publishe

Like-charge attraction in confinement : myth or truth?

It is general wisdom that like-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.publishe

Phonon dispersion curves of two-dimensional colloidal crystals : the wavelength-dependence of friction

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Optically mediated particle clearing using Airy wavepackets

The Airy wavepacket solution for a free particle exhibits propagation invariance and, surprisingly, acceleration transverse to the propagation direction(1). Discovered as a solution of the free-particle Schrodinger equation, Airy wavepackets have been predicted(2), and in a recent major step forward, realized(3) in the optical domain, but have never been used in any application. In this Letter we demonstrate the first use of the Airy light beam in optical micromanipulation(4,5). Based on the characteristic intensity pattern, the beam drags particles into the main intensity maximum, which guides particles vertically along a parabolic trajectory. This unusual property of Airy beams leads to a new feature in optical micromanipulation-the removal of particles and cells from a section of a sample chamber. We term this highly robust and efficient process 'optically mediated particle clearing', which enables novel microfluidic applications within the colloidal and biological sciences.</p