Dynamic analysis of AFM by applying Timoshenko beam theory in tapping mode and considering the impact of interaction forces in a liquid environment
Bibliographic record
Abstract
In an atomic force microscope (AFM), the cantilever vibrates by excitation at a frequency near the fundamental frequency, and the changes in vibration parameters, which result from the nonlinear forces of interaction between sample and cantilever tip, can be used as a tool to reveal the properties of the sample. To properly describe the images acquired by the AFM and to approximate the properties of the investigated sample, it is essential to use analytical and numerical models that can accurately simulate the dynamics of the cantilever and sample. For short beams, the Timoshenko model seems to be very accurate. Considering the fact that short beams (cantilevers) have many applications including the imaging of biological samples in liquid environments, the use of this theory seems to be necessary. In this paper, by employing the Timoshenko beam model, the effect of rotational inertia and shear deformation has been taken into consideration. The interaction forces between sample and cantilever in liquid, ambient air, and vacuum environments are quite different in terms of magnitude and formulation, and they play a significant role in the system’s dynamic response. These forces include hydrodynamic forces, electrostatic double layer force, etc. Using an accurate model for the interaction forces will improve the simulation results significantly. In this paper, the frequency response of the atomic force microscope has been investigated by applying the Timoshenko beam model and considering the forces of interaction between sample and tip in the air and liquid environments. The results indicate that the resonant frequency changes and cantilever vibration amplitude diminishes in a liquid environment compared to the air environment. The simulation results have good agreement with the experimental ones. The frequency responses for the attractive and repulsive regions in the two environments are compared and it is demonstrated that the dynamic response is highly dependent on the hydrodynamic and interaction forces in the liquid medium.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".