1,721,174 research outputs found
Barrier Crossing in a Viscoelastic Bath
No full textWe investigate the hopping dynamics of a colloidal particle across a potential barrier and within a viscoelastic, i.e., non-Markovian, bath and report two clearly separated timescales in the corresponding waiting time distributions. While the longer timescale exponentially depends on the barrier height, the shorter one is similar to the relaxation time of the fluid. This short timescale is a signature of the storage and release of elastic energy inside the bath that strongly increases the hopping rate. Our results are in excellent agreement with numerical simulations of a simple Maxwell model.publishe
Properties of a nonlinear bath : experiments, theory, and a stochastic Prandtl-Tomlinson model
No full textA colloidal particle is a prominent example of a stochastic system, and, if suspended in a simple viscous liquid, very closely resembles the case of an ideal random walker. A variety of new phenomena have been observed when such colloid is suspended in a viscoelastic fluid instead, for example pronounced nonlinear responses when the viscoelastic bath is driven out of equilibrium. Here, using a micron-sized particle in a micellar solution, we investigate in detail, how these nonlinear bath properties leave their fingerprints already in equilibrium measurements, for the cases where the particle is unconfined or trapped in a harmonic potential. We find that the coefficients in an effective linear (generalized) Langevin equation show intriguing inter-dependencies, which can be shown to arise only in nonlinear baths: for example, the friction memory can depend on the external potential that acts only on the colloidal particle (as recently noted in simulations of molecular tracers in water in (2017 Phys. Rev. X 7 041065)), it can depend on the mass of the colloid, or, in an overdamped setting, on its bare diffusivity. These inter-dependencies, caused by so-called fluctuation renormalizations, are seen in an exact small time expansion of the friction memory based on microscopic starting points. Using linear response theory, they can be interpreted in terms of microrheological modes of force-controlled or velocity-controlled driving. The mentioned nonlinear markers are observed in our experiments, which are astonishingly well reproduced by a stochastic Prandtl–Tomlinson model mimicking the nonlinear viscoelastic bath. The pronounced nonlinearities seen in our experiments together with the good understanding in a simple theoretical model make this system a promising candidate for exploration of colloidal motion in nonlinear stochastic environments.publishe
Recoil experiments determine the eigenmodes of viscoelastic fluids
No full textAbstractWe experimentally investigate the transient recoil dynamics of a colloidal probe particle in a viscoelastic fluid after the driving force acting on the probe is suddenly removed. The corresponding recoil displays two distinct timescales which are in excellent agreement with a microscopic model which considers the probe particle to be coupled to two bath particles via harmonic springs. Notably, this model exhibits two sets of eigenmodes which correspond to reciprocal and non-reciprocal force conditions and which can be experimentally confirmed in our experiments. We expect our findings to be relevant under conditions where particles are exposed to non-steady shear forces as this is encountered e.g. in microfluidic sorting devices or the intermittent motion of motile bacteria within their natural viscoelastic surrounding.Deutsche Forschungsgemeinschafthttp://dx.doi.org/10.13039/50110000165
Two step micro-rheological behavior in a viscoelastic fluid
No full textWe perform micro-rheological experiments with a colloidal bead driven through a viscoelastic worm-like micellar fluid and observe two distinctive shear thinning regimes, each of them displaying a Newtonian-like plateau. The shear thinning behavior at larger velocities is in qualitative agreement with macroscopic rheological experiments. The second process, observed at Weissenberg numbers as small as a few percent, appears to have no analog in macro rheological findings. A simple model introduced earlier captures the observed behavior, and implies that the two shear thinning processes correspond to two different length scales in the fluid. This model also reproduces oscillations which have been observed in this system previously. While the system under macro-shear seems to be near equilibrium for shear rates in the regime of the intermediate Newtonian-like plateau, the one under micro-shear is thus still far from it. The analysis suggests the existence of a length scale of a few micrometres, the nature of which remains elusive.publishe
Observation and control of nonmonotonic recoils in a viscoelastic fluid
No full textWe experimentally study the relaxation dynamics of a colloidal particle in a micellar viscoelastic fluid following different driving protocols. When the particle is driven at constant velocity for a finite duration, its recovery to equilibrium is always monotonic. In contrast, altering the driving velocity during the protocol induces nonmonotonic relaxation. Our results are in quantitative agreement with the analytical solution of a minimal micromechanical model exhibiting only two distinct eigenmodes independent of the specific protocol. Notably, the model enables selective suppression of one or both modes—an effect confirmed experimentally. Because the model is broadly applicable to diverse viscoelastic fluids, our findings offer a general framework for tailoring relaxation dynamics in complex environments.publishe
Memory-induced alignment of colloidal dumbbells
No full textWhen a colloidal probe is forced through a viscoelastic fluid which is characterized by a long stress-relaxation time, the fluid is excited out of equilibrium. This is leading to a number of interesting effects including a non-trivial recoil of the probe when the driving force is removed. Here, we experimentally and theoretically investigate the transient recoil dynamics of non-spherical particles, i.e., colloidal dumbbells. In addition to a translational recoil of the dumbbells, we also find a pronounced angular reorientation which results from the relaxation of the surrounding fluid. Our findings are in good agreement with a Langevin description based on the symmetries of a director (dumbbell) as well as a microscopic bath-rod model. Remarkably, we find an instability with amplified fluctuations when the dumbbell is oriented perpendicular to the direction of driving. Our results demonstrate the complex behavior of non-spherical objects within a relaxing environment which are of immediate interest for the motion of externally but also self-driven asymmetric objects in viscoelastic fluids.publishe
Memory-induced Magnus effect
No full textAbstract Spinning objects moving through air or a liquid experience a lift force—a phenomenon known as the Magnus effect. This effect is commonly exploited in ball sports but also is of considerable importance for applications in the aviation industry. Whereas Magnus forces are strong for large objects, they are weak at small scales and eventually vanish for overdamped micrometre-sized particles in simple liquids. Here we demonstrate a roughly one-million-fold enhanced Magnus force of spinning colloids in viscoelastic fluids. Such fluids are characterized by a time-delayed response to external perturbations, which causes a deformation of the fluidic network around the moving particle. When the particle also spins, the deformation field becomes misaligned relative to the particle’s moving direction, leading to a force perpendicular to the direction of travel and the spinning axis. Our uncovering of strongly enhanced memory-induced Magnus forces at microscales opens up applications for particle sorting and steering, and the creation and visualization of anomalous flows.publishe
Active matter in space
Full text linkIn the last 20 years, active matter has been a highly dynamic field of research, bridging fundamental aspects of non-equilibrium thermodynamics with applications to biology, robotics, and nano-medicine. Active matter systems are composed of units that can harvest and harness energy and information from their environment to generate complex collective behaviours and forms of self-organisation. On Earth, gravity-driven phenomena (such as sedimentation and convection) often dominate or conceal the emergence of these dynamics, especially for soft active matter systems where typical interactions are of the order of the thermal energy. In this review, we explore the ongoing and future efforts to study active matter in space, where low-gravity and microgravity conditions can lift some of these limitations. We envision that these studies will help unify our understanding of active matter systems and, more generally, of far-from-equilibrium physics both on Earth and in space. Furthermore, they will also provide guidance on how to use, process and manufacture active materials for space exploration and colonisation
Microscopic thermodynamics of colloidal particles
No full textEinhergehend mit der industriellen Revolution des 19. Jahrhunderts entwickelte sich ein neues eigenständiges Teilgebiet der Physik, die Thermodynamik. Im Mittelpunkt des Interesses standen damals Wärmekraftmaschinen und das Verständnis der Umwandlung von Wärme in mechanische Arbeit. Im Rahmen der Thermodynamik lassen sich auch chemische Reaktionen oder biologische Prozesse beschreiben. Dabei bleibt sie auf große Systeme beschränkt, wo eine Vielzahl von inneren Freiheitsgraden dazu führt, dass Fluktuationen vernachlässigt werden können.
Mit zunehmender Verfeinerung und Miniaturisierung der physikalischen Prozesse im allgemeinen und der damit verbundenen Ausdifferenzierung der Manipulations- und Messmethoden erlebte das Interesse an thermodynamischen Prozessen - diesmal auf mikroskopischer Ebene - eine Renaissance. Richtungsweisend für diese Verfeinerung sind vor allem Kraftmikroskopie und optische Pinzetten, die es erlauben, Systeme auf einer Nanometer-Skala zu untersuchen. Von Bedeutung sind hierbei biologische Maschinen, Makromoleküle, oder auch miniaturisierte mechanische Bauelemente. Typischerweise sind die charakteristischen Energieskalen dieser Systeme von der Größenordnung her vergleichbar mit der thermischen Energie, so dass Fluktuationen nicht vernachlässigt werden können. Als weitere Kategorie von mesoskopischen Systemen stehen kolloidale Partikel im Blickpunkt dieser Arbeit. Diese in einem Lösungsmittel suspendierte Teilchen erweisen sich dabei als ideale Objekte, um die statistischen Eigenschaften kleiner Systeme zu untersuchen. Hierbei kombinieren kolloidale Systeme zwei Vorteile. Erstens spielen sich die Fluktuationen auf einer Längenskala ab, auf der sie mittels optischer Mikroskopie beobachtet werden können. Zweitens können Wechselwirkungen in kolloidalen Systemen durch Zugabe von Ionen bzw. Polymeren maßgeschneidert werden. Die Wechselwirkung der Kolloidpartikel mit externen Feldern bietet eine weitere Möglichkeit der Manipulation. Dabei eröffnen Laserpinzetten die Möglichkeit, durch Einstellung externer Parameter wie Intensität, Position, Polarisation etc., das System auf einer mikroskopischen Skala schnell und reproduzierbar von außen zu manipulieren.
Diese Arbeit wendet sich der experimentellen Überprüfung der stochastischen Thermodynamik zu. In einem ersten Experiment befindet sich das untersuchte Kolloidteilchen vor einer Glasoberfläche und wird von zwei koaxialen antiparallelen optischen Pinzetten festgehalten. Mit Hilfe dieser kann das Partikel aus dem Gleichgewicht heraus getrieben werden, gleichzeitig wird dessen Position durch evaneszente Lichtstreumikroskopie (TIRM, engl.: Total Internal Reflection Microscopy) mit hoher zeitlicher und räumlicher Auflösung verfolgt. Sowohl die geleistete Arbeit W als auch die ins Wärmebad übertragene Wärme Q können aus der gemessenen Partikeltrajektorie direkt berechnet werden. Somit bringt dieses Experiment den Nachweis, dass der erste Hauptsatz der Thermodynamik auch für fluktuierende Größen erfüllt ist.
Charakteristisch ist jetzt nicht mehr der Wert einer Einzelmessung W, sondern die Verteilung p(W), die man erhält, wenn über viele Messungen gemittelt wird. Den theoretischen Vorhersagen entsprechend ist diese Verteilung asymmetrisch und nicht Gauß'sch. Dennoch zeigen die Experimente, dass sowohl die Jarzynski-Relation als auch das das detaillierte Fluktuationstheorem erfüllt sind.
In einem zweiten Experiment wird ein Kolloidteilchen mit Hilfe einer rotierenden Laserpinzette so getrieben, dass es sich mit konstanter Geschwindigkeit auf einer Kreisbahn bewegt. Durch Modulation der Laserleistung wird ein zusätzliches schwaches sinusförmiges Potential V entlang der Kreisbahn erzeugt. Der so generierte stationäre Nichtgleichgewichtszustand wird zwar wie ein Gleichgewichtszustand durch eine zeitunabhängige Wahrscheinlichkeitsverteilung charakterisiert, besitzt im Gegensatz zu diesem jedoch einen nicht verschwindenden Strom, permanent wird Energie ins Wärmebad abgegeben. Dies führt zur Verletzung des Boltzmann-Faktors, der im Gleichgewicht das Potential mit der stationären Wahrscheinlichkeitsverteilung verknüpft. Unter Berücksichtigung des Stromes leiten wir eine Erweiterung des Boltzmann-Faktors her, so dass das Potential auch unter stationären Nichtgleichgewichtsbedingungen direkt aus der stationären Wahrscheinlichkeitsverteilung berechnet werden kann.
Die diffusive Bewegung des Kolloidpartikels in einem gekippten periodischen Potential unterscheidet sich fundamental von der Brown'schen Bewegung im thermischen Gleichgewicht, wo ein zusätzliches Potential V immer die Diffusionsbewegung eines freien Teilchens einschränkt. Im stationären Nichtgleichgewicht kann diese durch die Anwesenheit eines Potentials verstärkt werden. Wie die Experimente zeigen, durchläuft der Diffusionskoeffizient als Funktion der treibenden Kraft ein Maximum. In dem als Giant Diffusion bekannten Phänomen übersteigt, in guter Übereinstimmung mit theoretischen Vorhersagen, der gemessene Diffusionskoeffizient seinen Gleichgewichtswert um das Fünffache.
Die beobachtete Kraftabhängigkeit des Diffusionskoeffizienten hat weitreichende Konsequenzen. Die für das Gleichgewicht so fundamentale Einstein-Relation ist im stationären Nichtgleichgewicht nicht mehr gültig. Die Experimente zeigen eine Abweichung von fast einer Größenordnung. Wir zeigen, dass durch Addition einer Geschwindigkeitskorrelationsfunktion die Einstein-Relation korrigiert werden kann. Deren Gültigkeit umfasst dann auch wieder stationäre Nichtgleichgewichtszustände.In coincidence with the industrial revolution of the 18th century, thermodynamics developed as an own field of physics. However, thermodynamics is only able to describe large systems where the variety of internal degrees of freedom allows to neglect fluctuations. In accordance with miniaturization trends in general and the development of micromanipulation techniques like atomic force microscopy or optical tweezers in the late 1980's in particular, scientists have become able to investigate thermal systems on length and energy scales where fluctuations are not negligible. Today the broad variety of such systems, e.g. molecular machines, proteins, polymer molecules, and micro-mechanical motors, inspire scientists with physical, chemical, and biological background to contribute to this rapidly developing field.
The present experimental work is devoted to investigate colloids, which belong to another category of systems where fluctuations cannot be neglected. Colloids are small particles immersed into a solvent, with sizes between 10 nm and 10 µm. Therefore, they are small enough to obey a random diffusive motion, the Brownian motion.
Colloids have the advantage that fluctuations take place on length and time scales that can be observed easily using ordinary light microscopy techniques. Furthermore by adding polymers or ions to the solvent, their interactions can be tailored according to the experimental needs. Their interaction with light delivers another powerful possibility of external manipulation.
The first experiment emphasizes on the laws of thermodynamics and their generalization to microscopic systems. In this experiment the colloidal particle is confined using two antiparallel coaxial laser tweezers. To drive the bead away from equilibrium the intensity and thus the light pressure of one of the laser tweezers is varied by means of an electrooptical modulator (EOM). From its trajectory we directly determine the work W, and the heat Q transferred from the system to the bath. Our experiment demonstrates that even in the case of strong fluctuations, these energies are constrained by the first law of thermodynamics.
When fluctuations cannot be neglected the characteristic quantity is the distribution of work values p(W) instead of a single value W measured for an individual realization of the protocol. The data fulfills both the Jarzynski relation and a detailed fluctuation theorem valid for symmetric protocols only. Finally, we compare the measured distribution with theoretical Fokker-Planck calculations. The excellent agreement confirms that the equilibrium fluctuations of the thermal environment determine the stochastic forces, even though the bead is driven deep into the nonequilibrium regime.
The second experiment investigates nonequilibrium stationary states (NESS). A NESS is undoubtedly the simplest nonequilibrium situation thinkable. Characterized by its stationary probability distribution a NESS is closely related to an equilibrium state, but unlike in equilibrium detailed balance is no longer fullfilled and a current leads to permanent energy dissipation. Based on scanning laser tweezers we experimentally create a NESS by forcing a colloidal particle to circle in a three dimensional toroidal laser trap. By modulating the laser intensity we additionally superimpose a stationary light potential along the torus. As a consequence the colloidal particle moves in a tilted periodic potential. By means of standard video microscopy in combination with a custom made microscope we record the trajectories with a spatial and temporal accuracy of 20 nm and 50 ms respectively.
Since we are able to generate a nonequilibrium stationary state we concentrate on a generalization of Jarzynski's relation. It was predicted theoretically that by taking the total entropy production instead of the work W, a Jarzynski relation like fluctuation theorem can be formulated for stationary states. Our data confirms the validity of this generalization independently of wether the particle, as in the case of strong driving, is moving smoothly along the torus, or, in the case of a small driving force, it obeys a hopping motion jumping from minimum to minimum.
Finally, we investigate two fundamental relations, the fluctuation dissipation theorem and the Boltzmann factor, both valid in thermal equilibrium but in general violated under nonequilibrium conditions. In equilibrium the Boltzmann factor allows to directly determine a potential V by taking the negative logarithm of the probability distribution. We show that if the currents are treated properly the Boltzmann factor can be generalized to stationary states, allowing, also away from thermal equilibrium, the reconstruction of the potential by additionally measuring the current j in the system.
As an integrated version of the famous fluctuation dissipation theorem the Einstein relation is only valid within the linear response regime. To analyze its breakdown we first concentrate on the diffusive motion of the particle. In equilibrium the diffusion of a free colloidal particle is always reduced when an additional potential is present. Away from equilibrium this situation is not so generical. We find an enhancement of the diffusion coefficient in the nonequilibrium regime. This behavior, known as giant diffusion is in very good agreement with the theoretical predictions.
To complete Einstein's relation we compare the diffusion coefficient with an independent measurement of the mobility. The observed discrepancy of almost one order of magnitude demonstrates the strong violation of Einstein's relation but it furthermore justifies that the particle is indeed driven far beyond the linear response regime. We show that the Einstein relation can be generalized for NESS by introducing an additional term which involves an integral over measurable velocity correlation functions
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