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Dynamics of tapping mode atomic force microscopy in liquids: Theory and experiments
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Image of FIG. 1.
FIG. 1.

Tip motion observed in water on mica and LDPE samples for lever R1 (Table I) [(a) and (b)], and for lever T2 (Table I) [(c) and (d)]. For R1, and the amplitude at 100% set point is . For T2, and the amplitude at 100% set point is . The wave forms for both levers are acquired from 100% to 30% set point at 10% decrements. Each division on the ordinate axis corresponds to .

Image of FIG. 2.
FIG. 2.

(Color online) Comparison of experimentally measured and theoretically predicted tip dynamics as lever R1 (Table I) dynamically approaches mica in de-ionized water. The simulation results are obtained by solving Eqs. (4a) and (4b) with zero initial conditions and using interaction and cantilever parameters from Ref. 11. (a) Experimentally measured tip oscillation data, and predictions from (b) the point-mass model, and (c) the two-mode model on mica. Comparison of the point-mass model and the two-mode model with the experimental (d) amplitude-distance and (e) phase-distance plots on mica in water.

Image of FIG. 3.
FIG. 3.

Theoretically predicted tip displacement history of levers R1 and T2 (Table I) on mica in water as the set point ratio is decreased. (a) Lever R1, point-mass model, and (b) two-mode model; (c) lever T2, point-mass model, (d) two-mode model. The amplitude at 100% set point corresponds to . Tip displacement data from 100% to 30% set point ratio are presented at 10% decrements. The two-mode model predictions match closely with the observed tip displacement data shown in Figs. 1(a) and 1(c).


Generic image for table
Table I.

List of levers and substrate materials studied. All samples were investigated with each cantilever. R1, R2, and R3 are rectangular levers and T1 and T2 are triangular levers. , , spring constant, and ’s modulus.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dynamics of tapping mode atomic force microscopy in liquids: Theory and experiments