An upper limit on the Casimir force is found using the dielectric functions of perfect crystalline materials which depend only on well-defined material constants. The force measured with the atomic force microscope is larger than this limit at small separations between bodies and the discrepancy is significant. The simplest modification of the experiment is proposed allowing one to make its results more reliable and answer the question if the discrepancy has any relation with the existence of a new force.The Casimir force 1 between closely spaced macroscopic bodies is an effect of quantum electrodynamics (QED) and for that reason could be predicted very accurately. In the rigorous Lifshitz theory 2,3 the force is defined by the optical properties of used materials. Knowledge of these properties is the weakest element in the theory restricting the accuracy that can be achieved. Though the measurement of the Casimir force is not the best way to test QED, such experiments are of great importance because they are sensitive to the presence of new fundamental forces 4 predicted in many modern theories (see, for example, Ref. 5 and references therein). To distinguish a new force from the background, we should be able to calculate the Casimir force with a precision better than the experimental one. In the series of recent experiments this force has been measured with the torsion pendulum (TP) 6 in the range of distances 0.6-6 µm and with the atomic force microscope (AFM) 7,8 in the range 0.1-0.9 µm. The corresponding precisions were 5% and 1%, respectively.The force per unit area between parallel plates arising as a result of electromagnetic fluctuations at nonzero temperature T is generalized by the Lifshitz theory, 3 where the plate material is taken into account by its dielectric function at imaginary frequencies ε(iζ):
We discuss the temperature correction to the Casimir force between nonideal metallic bodies which caused disagreement in the literature. A general method to find the troubling term is proposed that does not require a direct reference to the Lifshitz formula. The linear in temperature correction is shown to survive for nonideal metals. It is important for small separations between bodies tested in the recent experiments.12.20.Ds,
The temperature correction to the Casimir force is considered for real metals at low temperatures. With the temperature decrease, the mean free path for electrons becomes larger than the field penetration depth. In this condition, description of metals with the impedance of anomalous skin effect is shown to be more appropriate than with the permittivity. The effect is crucial for the temperature correction. It is demonstrated that in the zero-frequency limit, the reflection coefficients should coincide with those of ideal metal if we demand the entropy to be zero at Tϭ0. All the other prescriptions discussed in the literature for the nϭ0 term in the Lifshitz formula give negative entropy. It is shown that the temperature correction in the region of anomalous skin effect is not suppressed as it happens in the plasma model. This correction will be important in the future cryogenic measurements of the Casimir force.
We analyse the result of precise measurement of the Casimir force between bodies covered with gold. The values of the parameters used to extrapolate the gold dielectric function to low frequencies are very important and discussed in detail. The finite temperature effect is shown to exceed considerably the experimental errors. The upper limit on the force is found which is smaller than the measured force. Many experimental and theoretical uncertainties were excluded with gold covering and we conclude that, possibly, a new force has been detected at small separations between bodies.12.20. Ds, 12.20.Fv, 03.70.+k, 14.80 c a 4 has been found as change in the zero point energy between two parallel perfectly conducting plates separated by the distance a. For sphere and plate the expression above has to be modified with the proximity force theorem (PFT) [7] to the followingwhere R is the sphere radius. Real metals are not ideal conductors and there is an important correction to (1) taking into account their real properties. In the Lifshitz theory [8], which generalizes the Casimir approach, the force is represented in terms of the metal dielectric function ε (iω) at imaginary frequencies. This theory was applied for description of the experiments in [6,9]. Different but equivalent method has been developed in [10], where detailed calculations were made for Al, Au, and Cu metallization of the bodies using the handbook optical data for these metals. The result for Au is in good agreement with the torsion pendulum experiment [4]. For the atomic force microscope (AFM) experiment [5,6] Al metallization has been used. This metal is oxidized easily and charges can be trapped in the oxide. To prevent influence of these charges on the force, Al was covered with a thin layer (20 or 8 nm thick) of Au/P d. The conclusion has been made [6] that the result of the AFM experiment was in agreement with the theory. However, in all calculations [5,6,11] the role of Au/P d layer was ignored. Importance of this layer was stressed in [12] (see also [13]), where the upper limit on the force has been found using parameters of single-crystalline materials. This limit was smaller than the measured force in both experiments [5,6] and the discrepancy far exceeded the experimental errors. To exclude uncertainties connected with aluminum oxidation, Au/P d layer and clarify the origin of the discrepancy, it was proposed [12] to use Au metallization instead of Al. Very recently the AFM experiment with Au metallization has been carried out [14]. In this experiment the residual potential was reduced to a negligible level so as the surface roughness. The force was measured for smaller separations up to 62 nm with uncertainty 3.5 pN . In the previous experiments the photodiods response on the cantilever deflection was calibrated assuming that the plate-sphere system on the contact behaves as a rigid body. As the new experiment showed this natural assumption was not quite correct and different calibration method was proposed [14]. To all appearance the exc...
Water electrolysis performed in microsystems with a fast change of voltage polarity produces optically invisible nanobubbles containing H2 and O2 gases. In this form the gases are able to the reverse reaction of water formation. Here we report extreme phenomena observed in a millimeter-sized open system. Under a frequency of driving pulses above 100 kHz the process is accompanied by clicking sounds repeated every 50 ms or so. Fast video reveals that synchronously with the click a bubble is growing between the electrodes which reaches a size of 300 μm in 50 μs. Detailed dynamics of the system is monitored by means of a vibrometer by observing a piece of silicon floating above the electrodes. The energy of a single event is estimated as 0.3 μJ and a significant part of this energy is transformed into mechanical work moving the piece. The observations are explained by the combustion of hydrogen and oxygen mixture in the initial bubble with a diameter of about 40 μm. Unusual combustion mechanism supporting spontaneous ignition at room temperature is responsible for the process. The observed effect demonstrates a principal possibility to build a microscopic internal combustion engine.
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