Elastic constants of two-dimensional (2D) colloidal crystals are determined by measuring strain fluctuations induced by Brownian motion of particles. Paramagnetic colloids confined to an air-water interface of a pending drop are crystallized under the action of a magnetic field, which is applied perpendicular to the 2D layer. Using video-microscopy and digital image-processing we measure fluctuations of the microscopic strain obtained from random displacements of the colloidal particles from their mean (reference) positions. From these we calculate system-size dependent elastic constants, which are extrapolated using finite-size scaling to obtain their values in the thermodynamic limit. The data are found to agree rather well with zero-temperature calculations.62.20. Dc, 82.70.Dd During the last two decades interest in colloidal systems has grown substantially, on one hand because of their widespread technological applications and on the other due to the availability of precisely calibrated particles for use as model systems for studying phenomena in classical condensed matter physics [1]. The crystallization of colloids, both in two and three dimensions has been a continuous matter of interest. The research mostly focused on the analysis of structure and dynamics of colloidal systems on different length and time scales through static or dynamic light scattering techniques. Measurements of elastic constants of colloidal crystals, however, have been limited to the determination of the shear modulus µ. This was based on the observation of shear induced resonance of a crystal using light scattering techniques (see [2] for a recent work). The value of µ is found to depend strongly upon the crystalline morphology and changes significantly between randomly oriented crystallites and shear-ordered samples [3]. In addition, using this method only a very reduced number of modes can be investigated. Very recently, the elastic moduli of colloidal solids have also been estimated [4] by observing relaxation behaviour after deformations using laser tweezers. FIG. 1.A snapshot of the triangular lattice of paramagnetic colloidal particles. A few thousand snapshots such as this, taken at regular time intervals of about one second were used to calculate elastic constants.

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A new method for the determination of elastic constants of colloidal systems is described. We study super-paramagnetic microspheres confined by gravity to a two-dimensional layer at a water-air interface. Under an external vertical magnetic field the particles arrange in a crystalline triangular phase because of the repulsive dipole-dipole interaction. By use of an optical tweezer, one triangle formed by three spheres is rotated from its equilibrium position and the relaxation time measured using video-microscopy. We demonstrate that this time is directly related to the shear modulus µ of the crystal and study µ as a function of the magnetic particle interaction strength.During the last decades the interest in colloidal systems has grown tremendously because of their widespread technological applications and due to the availability of precisely calibrated particles used as model systems in "classical" condensed-matter physics [1]. The crystallization of colloids, both in two and three dimensions (2D and 3D), has been a continuous matter of particular interest. The research mostly focused on the analysis of structure and dynamics of colloidal systems on different length and time scales through static or dynamic light scattering techniques.Elastic constants of colloidal crystals -essentially the shear modulus µ-were determined from the shear-induced resonance of the crystal through light scattering techniques (see [2] for recent work). As in real crystals, the value of µ is found to depend strongly upon the crystalline morphology and changes significantly between randomly oriented crystallites and shear-ordered samples [3]. In addition, using this method, only a very reduced number of modes can be investigated. A different approach to determine elastic constants is based on the analysis of the thermally induced vibrations of the particles in the crystal [4]. These fluctuations are inversely proportional to the elastic constants but depend also upon the system size studied. Therefore a finite-size scaling method is applied to extrapolate to the macroscopic elastic constants. We will show [5] that this method is well applicable to our system as described below and gives results in good agreement with theoretical predictions. However, so far the method can only be used for defect-free samples, a situation not always easy to realize in experiments.

Fraunhofer EMFT’s research and manufacturing portfolio includes piezoelectrically actuated silicon micro diaphragm pumps with passive flap valves. Research and development in the field of microfluidics have been dedicated for many years to the use of micropumps for generating positive and negative pressures, as well as delivering various media. However, for some applications, only small amounts of fluid need to be pumped, compressed, or evacuated, and until now, only macroscopic pumps with high power consumption have been able to achieve the necessary flow rate and pressure, especially for compressible media such as air. To address these requirements, one potential approach is to use a multistage of high-performing micropumps optimized to negative pressure. In this paper, we present several possible ways to cascade piezoelectric silicon micropumps with passive flap valves to achieve these stringent requirements. Initially, simulations are conducted to generate negative pressures with different cascading methods. The first multistage option assumes pressure equalization over the piezo-actuator by the upstream pump, while for the second case, the actuator diaphragm operates against atmospheric pressure. Subsequently, measurement results for the generation of negative gas pressures down to −82.1 kPa relative to atmospheric pressure (19.2 kPa absolute) with a multistage of three micropumps are presented. This research enables further miniaturization of many applications with high-performance requirements for micropumps, achievable with these multistage systems.