We demonstrate how the ineluctable presence of thermal noise alters the measurement of forces acting on microscopic and nanoscopic objects. We quantify this effect exemplarily for a Brownian particle near a wall subjected to gravitational and electrostatic forces. Our results demonstrate that the force measurement process is prone to artifacts if the noise is not correctly taken into account.The concept of force plays a central role in our understanding of nature. Due to the ongoing trend towards miniaturization, the investigation of forces relevant at microscopic and nanoscopic length scales is attracting an increasing amount of attention. Examples range from the elastic properties of biomolecules [1] to Casimir forces [2]. Instrumental in such trend has been the invention of new methods to measure ultra-small forces in a range down to few femtonewtons [3,4]. Apart from the technological challenge intrinsic to measuring such minute forces, it is important to realize that the general concept of how forces are measured in macroscopic systems cannot be simply scaled down to nanoscopic objects, mainly due to the presence of thermal noise affecting the motion of small objects (Brownian motion). As will be demonstrated below, force measurements in the presence of thermal noise are prone to artifacts, unless the noise is properly taken into account. However, despite the great number of experiments measuring forces in microscopic systems, the role of noise has not been adequately addressed yet.In this Letter, we measure the forces acting on a Brownian particle in front of a wall: using two widely employed force-measurement methods, we obtain strongly contrasting forces, which deviate in their magnitude and even their sign. We track this disagreement down to a well-known mathematical controversy about the interpretation of stochastic differential equations in the presence of a diffusion gradient and we demonstrate how experimental data should be analyzed in order to obtain the correct underlying forces and to avoid artefacts.When a microscopic body is suspended in a liquid, viscous forces prevail by several orders of magnitude over inertial effects [5]. The presence of a constant external force F in such an overdamped system results in a constant particle drift velocity v d = F/γ, where γ is the particle's friction coefficient. Since v d = dz/dt can be retrieved from the measured particle displacement dz within time dt, the force can accordingly be measured as F = γv d . In the case of large forces this obviously leads to a univocal result. However, when the force exerted on the object is comparable or even smaller than the random forces due to the permanent collisions with the surrounding liquid molecules, a different value of the force is measured in each experiment. Typically one can average over many independent measurementswhere we definev d = 1 dt dz j and j denotes the j-th experimental value.Indeed Eq. (1) is key in non-equilibrium force measurements, e.g. studying the relaxation of biomolecules [6][7][8], collo...
The study of microsystems and the development of nanotechnologies require alternative techniques to measure piconewton and femtonewton forces at microscopic and nanoscopic scales. Among the challenges is the need to deal with the ineluctable thermal noise, which, in the typical experimental situation of a spatial diffusion gradient, causes a spurious drift. This leads to a correction term when forces are estimated from drift measurements [G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, Phys. Rev. Lett. 104, 170602 (2010)]. Here we provide a systematic study of such an effect by comparing the forces acting on various Brownian particles derived from equilibrium-distribution and drift measurements. We discuss the physical origin of the correction term, its dependence on wall distance and particle radius, and its relation to the convention used to solve the respective stochastic integrals. Such a correction term becomes more significant for smaller particles and is predicted to be on the order of several piconewtons for particles the size of a biomolecule.
Abstract:Total Internal Reflection Microscopy (TIRM) is a sensitive non-invasive technique to measure the interaction potentials between a colloidal particle and a wall with femtonewton resolution. The equilibrium distribution of the particle-wall separation distance z is sampled monitoring the intensity I scattered by the Brownian particle under evanescent illumination. Central to the data analysis is the knowledge of the relation between I and the corresponding z, which typically must be known a priori. This poses considerable constraints to the experimental conditions where TIRM can be applied (short penetration depth of the evanescent wave, transparent surfaces). Here, we introduce a method to experimentally determine I(z) by relying only on the distance-dependent particle-wall hydrodynamic interactions. We demonstrate that this method largely extends the range of conditions accessible with TIRM, and even allows measurements on highly reflecting gold surfaces where multiple reflections lead to a complex I(z).
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Liquids on-chip describes a reagent storage concept for disposable pressure driven Lab-on-Chip (LoC) devices, which enables liquid storage in reservoirs without additional packaging. On-chip storage of liquids can be considered as one of the major challenges for the commercial break through of polymer-based LoC devices. Especially the ability for long-term storage and reagent release on demand are the most important aspects for a fully developed technology. On-chip storage not only replaces manual pipetting, it creates numerous advantages: fully automated processing, ease of use, reduction of contamination and transportation risks. Previous concepts for on-chip storage are based on liquid packaging solutions (e.g. stick packs, blisters, glass ampoules), which implicate manufacturing complexity and additional pick and place processes. That is why we prefer on-chip storage of liquids directly in reservoirs. The liquids are collected in reservoirs, which are made of high barrier polymers or coated by selected barrier layers. Therefore, commonly used polymers for LoC applications as cyclic olefin polymer (COP) and polycarbonate (PC) were investigated in the context of novel polymer composites. To ensure long-term stability the reservoirs are sealed with a commercially available barrier film by hot embossing. The barrier film is structured by pulsed laser ablation, which installs rated break points without affecting the barrier properties. A flexible membrane is actuated through pneumatic pressure for reagent release on demand. The membrane deflection breaks the barrier film and leads to efficient cleaning of the reservoirs in order to provide the liquids for further processing.
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