A planar view of the AFM chip used in the calibration experiments. The cantilevers are made of silicon nitride with backside gold coating. Their nominal stiffness values are (from left to right) 0.5, 0.1, 0.03, 0.01, and 0.02 N/m, respectively.
(a) Overview of the experimental component arrangement (not drawn to scale). The experimental chamber has one opening on the right (the two coverslips on the top and bottom are omitted for clarity). The AFM chip is attached in a notch carved on the vertical wall of the experimental chamber. The micropipette is shown as a cylinder. (b) The cantilever tip (only one cantilever is shown) is pressed against by the force-transducer bead of the MAT. The pressing force is controlled by the repulsive pressure inside the micropipette which is in turn controlled by the height of a water reservoir mounted on a nanoscale vertical moving stage (not shown). The inset shows the actual microscopic view of the force-transducer bead and the AFM tip.
(a) The cantilever response to periodic pressure loading and unloading. The pressure first linearly increased from 0 to 50 Pa in 1 s (corresponding to rising displacement), was kept at 50 Pa for and linearly returned to 0 in 1 s (corresponding to falling displacement). This pressure loading pattern was repeated five times. The black bars represent the average displacement levels at the maximal applied pressure. Note the displacement drift over time. (b) Linear regression of the displacement data, which yields , during the second pressure loading in (a).
AFM chip drift magnitude over one second measured by the drift of the maximal displacement magnitude during calibration.
Schematic of the transducer rotation inside the micropipette. Due to imperfect alignment and thermal fluctuation, the transducer can rotate around the cantilever tip during calibration. Because the deflection of the cantilever was measured by tracking the transducer horizontal movement, this rotation might result in undesired error in the cantilever-tip displacement and the calibrated cantilever stiffness. Here the rotational angle and the micropipette-transducer gap are exaggerated for the purpose of illustration. The transducer rotated from its original position (dashed circle) to a new position (solid circle). At the same time, the transducer center moved a distance of and in the horizontal and vertical direction, respectively, even though the cantilever tip actually did not move.
(a) The cumulative results (33 cantilevers in total) for the calibrated stiffness by the MAT method and the thermal noise method. The black line shows the expected values based on the nominal stiffness. (b) Direct comparison of the calibrated stiffness by the two methods for six individual cantilevers with a nominal stiffness of 0.01 N/m. (c) Calibration precision by the MAT method and the thermal noise method. Precision is shown against cantilever nominal stiffness. For each nominal stiffness group, there were at least six cantilevers calibrated. Each cantilever was calibrated multiple times and the percentage standard deviation (standard deviation divided by the mean) was calculated. The precision for each group was defined by the group mean of the percentage standard deviation.
Cantilever stiffness comparison among nominal and calibrated values. [The calibrated stiffness is expressed as “ (the number of calibrated cantilevers).” The measured means by MAT and TN for each group are significantly different, as shown by repeated measures ANOVA test . The relative difference was calculated as the group mean of the relative difference for every individual cantilever within the group. MAT and TN represent the MAT calibration method and the thermal noise calibration method, respectively.]
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