[Paper Review] Comparison between Atomic Force Microscopy and Force Feedback Microscopy static force curves

Luca Costa, Mário S. Rodrigues+4 more|arXiv (Cornell University)|Jun 12, 2013

Force Microscopy Techniques and Applications17 references3 citations

TL;DR

This paper demonstrates that Force Feedback Microscopy (FFM) enables direct, quantitative measurement of full static force curves—including strong short-range attractive forces like capillary condensation—by actively counteracting tip-sample interactions via a feedback loop, allowing stable use of soft cantilevers even when force gradients exceed cantilever stiffness by up to fivefold.

ABSTRACT

Atomic Force Microscopy (AFM) conventional static force curves and Force Feedback Microscopy (FFM) force curves acquired with the same cantilever at the solid/air and solid/liquid interfaces are here compared. The capability of the FFM to avoid the jump to contact leads to the complete and direct measurement of the interaction force curve, including the attractive short-range van der Waals and chemical contributions. Attractive force gradients five times higher than the lever stiffness do not affect the stability of the FFM static feedback loop. The feedback loop keeps the total force acting on the AFM tip equal to zero, allowing the use of soft cantilevers as force transducers to increase the instrumental sensitivity. The attractive interactions due to the nucleation of a capillary bridge at the native oxide silicon/air interface or due to a DLVO interaction at the mica/deionized water interface have been measured. This set up, suitable for measuring directly and quantitatively interfacial forces, can be exported to a SFA (Surface Force Apparatus).

Motivation & Objective

• To directly measure the complete interaction force curve between two surfaces at the nanoscale, including short-range attractive forces that are inaccessible in conventional AFM.
• To address the limitation of conventional static AFM, where the 'jump to contact' prevents accurate measurement of attractive forces due to high force gradients.
• To demonstrate that FFM enables stable operation with soft cantilevers by actively balancing tip-sample forces via feedback, enhancing instrumental sensitivity.
• To validate FFM's capability to measure time-dependent interactions such as capillary bridge nucleation, which are problematic in dynamic AFM techniques.
• To show that the FFM setup can be adapted for use in other force measurement instruments, such as the Surface Force Apparatus (SFA).

Proposed method

• A fiber optic interferometer measures the tip position in real time, enabling precise feedback control.
• A static feedback loop applies a counteracting force $ F_{\text{feedback}} = k \Delta z $, where $ k $ is the cantilever stiffness and $ \Delta z $ is the base displacement, to maintain zero net force on the tip.
• The feedback loop ensures tip position stability by dynamically adjusting the cantilever base using a piezoelectric actuator, preventing mechanical instability.
• The same cantilever is used in both conventional AFM and FFM modes, enabling direct comparison of force curves under identical conditions.
• Force gradients up to 5–10 times the cantilever stiffness are compensated by tuning PID gains, with proportional gain increasing stiffness and integral gain handling time-dependent forces.
• The system measures both conservative force gradients and damping coefficients via a secondary dynamic loop, though this study focuses on the static feedback mode.

Experimental results

Research questions

• RQ1 Can Force Feedback Microscopy (FFM) measure the full static force curve, including strong attractive forces, without mechanical instability?
• RQ2 How does FFM performance compare to conventional AFM in measuring attractive interactions at solid/air and solid/liquid interfaces?
• RQ3 To what extent can FFM handle time-dependent interactions such as capillary bridge nucleation?
• RQ4 What is the maximum force gradient that FFM can stabilize, and how does this affect instrumental sensitivity compared to conventional AFM?
• RQ5 Can the FFM approach be extended to other force measurement instruments like the Surface Force Apparatus (SFA)?

Key findings

• FFM successfully measures the complete interaction force curve, including the nucleation of a capillary bridge at the native oxide silicon/air interface, which is inaccessible in conventional AFM due to jump-to-contact.
• The force feedback loop stabilizes the tip even when attractive force gradients are five times higher than the cantilever stiffness, enabling use of soft cantilevers for enhanced sensitivity.
• At the solid/liquid interface (mica/deionized water), FFM measures DLVO interactions directly and quantitatively without mechanical contact.
• The FFM system maintains tip position stability with an error within the feedback loop's resolution, as confirmed by the inset in Figure 4.
• The system can compensate for time-dependent interactions such as capillary condensation, which occur on a millisecond timescale, demonstrating robustness in dynamic force regimes.
• The maximum measurable attractive force gradient is limited by the instrument’s feedback bandwidth and actuator range, with performance degrading at force gradients exceeding 10× the cantilever stiffness.