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Correlations between the thermal vibrations of two cantilevers: Validation of deterministic analysis via the fluctuation-dissipation theorem
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10.1063/1.3681141
/content/aip/journal/apl/100/5/10.1063/1.3681141
http://aip.metastore.ingenta.com/content/aip/journal/apl/100/5/10.1063/1.3681141
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Figures

Image of FIG. 1.
FIG. 1.

(Color online) (a) Light microscope image of closely spaced AFM cantilevers seen from above and the side. The cantilevers are 200 μm long and 40 μm wide. (b) Schematic of the cantilevers separated by a distance s, and the shape of the free end of the simulated cantilever. The real cantilever has a flat 10 μm end and then slopes back at about 59°; this slope is simulated by two equal steps for computational simplicity. (c) Schematic of the detection system.

Image of FIG. 2.
FIG. 2.

(Color online) (a) Auto-correlation. (b) Cross-correlation. (c) Noise spectrum, G12. These results are for a pair of commercial AFM cantilevers (ORC8 B: length = 200 μm, width = 40 μm, and Nm−1) separated by 8 μm in liquid water at 23 °C. In (a) and (b), the experimental measurements are shown using data symbols and the theoretical prediction is given by the solid line. The left axis shows the correlation function normalized by k b T/k where kb is Boltzmann’s constant, T is the temperature, and the right axis shows the same data in units of nm2 using the measured value of the spring constant. In (b), the single error bar shows the range of data in three repeat experiments at this time lag. Each repeat experiment has a different pair of cantilevers. In (c), the noisy line is the experimental measurement and the smooth line is the theoretical prediction.

Image of FIG. 3.
FIG. 3.

(Color online) Autocorrelation of equilibrium fluctuations in cantilever displacement for an AFM cantilever in a series of Newtonian fluids. The left axis is normalized by k b T/k and the right axis is in units of nm2.

Image of FIG. 4.
FIG. 4.

(Color online) Cross-correlation of equilibrium fluctuations in cantilever displacement for a pair of AFM cantilevers in a series of Newtonian fluids. Experimental measurements are shown as data symbols and theoretical predictions are shown by the solid lines. The left axis is normalized by k b T/k and the right axis is in units of nm2.

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/content/aip/journal/apl/100/5/10.1063/1.3681141
2012-02-03
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Correlations between the thermal vibrations of two cantilevers: Validation of deterministic analysis via the fluctuation-dissipation theorem
http://aip.metastore.ingenta.com/content/aip/journal/apl/100/5/10.1063/1.3681141
10.1063/1.3681141
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