Measuring Boltzmann’s constant with a low-cost atomic force microscope: An undergraduate experiment
A schematic that illustrates the operational principle of the ID sensor, with the detection laser shown incident from the top of the figure. When both finger sets are aligned (left box), the even-numbered diffraction orders are brightest and the odd ones are the darkest. When one of the finger sets displaces out of plane by a distance equal to one quarter of the laser wavelength, the situation reverses (right box). This repeats every in either direction. The inset shows the geometry of a pair of cantilevers used for the experiment described in Sec. III.
The nonlinear intensities of the zeroth- and first-order modes plotted as a function of out of plane finger displacement. See Refs. 5 and 6 for details.
(a) A typical force curve measured with the ID detector (more negative x-axis values correspond to a higher stage position). Approach and retraction are shown by different line types, and arrows indicate the direction of motion. Several non-idealities of a measured force curve, as compared to the theoretical ID output shown in Fig. 2, are apparent: the variation in amplitude of the curve is due to angle mismatch that arises as the cantilever bends; hysteresis between the approach and retraction portions of the curve is due to forces between the tip and the sample. The difference in location between the contact and release points is discussed in the text. (b) A sketch of the method used to bend one of the cantilevers against the edge of a sample.
PSD data (curves “a” and “c”) and corresponding fit functions (curves “b” and “d”) for 350 and long cantilevers, respectively. See the text for a discussion of fitting, and Sec. V for the theoretical background.
Schematic of the optical path.
(a) A scanning electron micrograph image of a cantilever probe used for imaging. This view is of the underside of the device, showing the integrated tip. The short side levers are used as fixed reference beams and do not contact the sample. (b) A sample image taken with the AFM of human red blood cells, imaged in air after they were dried on a glass substrate. The image is square, and consists of 32 lines of data with 250 data points acquired per line. The image was linearly interpolated and up sampled to .
Normalized data collected for an experiment to measure the elastic modulus. Force curve 1 was taken using a hard sample (silicon nitride), and curves 2 and 3 were taken using a compliant polymer (PDMS) of variable hardness. Each curve is an average of three data sets. For clarity, only the part of the curve corresponding to upward stage movement is shown (data points captured during downward stage motion are omitted). PDMS samples were prepared by mixing Dow Corning Sylgard 184 in ratios of 10:1 (2) and 25:1 (3), depositing a layer onto a silicon substrate, then curing at for . Modulus data can be extracted from analyzing the period of the detector output curve.
Approximate cost of major AFM system components.
Typical results of calculations and the associated parameters.
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