(a) A schematic of DACs simulation of an excited cantilever approaching the sample. (b) A schematic of the AMS simulation of a topographical scan over a sample.
Continuous, uniform, rectangular microcantilever with base excitation , linear mass density , elastic modulus , and area moment and the corresponding point-mass model with equivalent mass , stiffness , and base excitation .
Geometric approximation for imaging artifacts due to finite probe-tip sizes. For the actual sample height at a position , a convolved sample height is observed at position due to a contact with the sample at position .
A simplified comparison between the DDASKR routine and conventional integration routines. Both fixed and adaptive time step routines integrate from to without detecting the boundary between contact and noncontact regimes. The DDASKR routine solves for the intersection with the sample surface and creates an intermediate and appropriate subsequent intermediates until reaching point .
Screenshots from the GUIs of the DAC and AMS tools showing the input panels. The input panels of DAC are (a) operating conditions and cantilever properties, (b) tip-sample interaction properties, and (c) simulation parameters. The input panels of AMS include (e) operating conditions, cantilever, simulation, (f) tip and substrate properties, and (g) feature properties. Additional information about an individual input parameter can be found in the GUI itself or in the comprehensive online manual.
Section IV A: comparison between performed with DACs tool in VEDA and performed by García and San Paulo (Ref. 2). Data from (Ref. 2) was loosely interpreted graphically.
Section IV B: power dissipation, , and its derivative with respect to , . Curves predicted consistent with the signature viscoelastic curves demonstrated in Ref. 19 (see Table II).
Section IV C: approach and retraction curves simulation with DAC for a -controlled cantilever (Ref. 20). From the mean force, we see the that the probe remains in the attractive regime [defined by the mean force (Ref. 2)] for the entire approach/retaction. Input parameter values for the simulation are listed in Table III.
Section IV D: scanning simulation over a hypothetically flat but heterogeneous surface containing with a patch of contrasting material from . A larger phase contrast occurs in the case on contrasting elasticity than for the case of contrasting viscosity. Results in this figure may be recreated with the input parameter values in Table IV.
Section IV E: scanning simulations with strong controller settings (large proportional and integral gains) and weak controller settings (small proportional and integral gains). Weak controller settings allow transient oscillations which can damage the sample as well as produce phase contrast on homogeneous samples (see Table V).
Simulation parameter values for the attractive and repulsive regimes of oscillation example (Sec. IV A).
Simulation parameters for the viscoelastic dissipation identification (Sec. IV B)
Simulation parameter values for the -control example (see Sec. IV C)
Input parameters for the material properties in heterogeneous samples example (Sec IV D).
Input parameters for the strong and weak controller parameters example (Sec. IV E).
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